Principles of Radio Communication PDF
Principles of Radio Communication PDF
Principles of Radio Communication PDF
OF
RADIO COMMUNICATION
BY
J. H. MORECROFT
Associate Professor of Electrical Engineering,
Columbia University
ASSISTED I1Y
A. PINTO
Assistant to Chief Electrical Engineer, Sew York Edison Co.
AND
W. A. CURRY
Instructor in Electrical Engineering, Columbia University
NEW YORK
JOHN WILEY & SONS, Inc.
London: CHAPMAN & HALL, Limited
1921
v
wit
HARVARD UNI rr;r,|TY
ENGINEERING SCHOOL
Copyright, 1921
Bt J. H. MORECROFT
BRAUNMORTH CO.
KOOK M*NUrACTURtHS
BROOKLYN. N. V.
PREFACE
The student desiring to familiarize himself with the theory and practice
of Radio Communication should be thoroughly grounded in the ordinary
laws of continuous and alternating-current circuits; he should also have
a clear physical conception of the transient conditions continally occurring
in such circuits. These elementary ideas are best obtained by consider
ing the electric current from the electron view point, i.e., as a compara
tively slow drift of innumerable minute negative electric charges, which,
at the same time they are drifting through the substance of the conductor,
are executing haphazard motions with very high velocities, continually
colliding with each other and with the molecules of which the conductor
is composed.
Due to the extremely high frequencies encountered in radio practice
it is necessary to expand somewhat one's ideas of resistance, inductance,
and capacity, the so-called constants of the electric circuit. As a result
of the non-uniformity of current distribution the resistance of a conductor
at high frequency is generally much higher in a radio circuit than it is at
ordinary engineering frequencies; due to non-penetration of magnetic
flux and hysteretic lag, the apparent permeability of an iron core is much
less at radio frequencies than at the customary sixty cycles; due to imper
fect polarization of dielectrics the apparent specific inductive capacity
of an insulator may be much decreased at radio frequencies and the heat
ing due to dielectric losses may be thousands of times as great as is the case
in ordinary engineering practice. Furthermore, due to the unavoidable
internal capacity, the apparent inductance of even an air core coil may
be expected to vary at high frequencies; in fact, a piece of apparatus
which is physically a coil, when used at radio frequencies, may, by electric
measurement, be found a condenser.
All of the effects indicated above are treated in the early chapters of
the text, not in as comprehensive manner as is possible, to be sure, but
with sufficient thoroughness to open the student's eyes to the possible
peculiar behavior of circuits when excited by the very high frequencies
of radio practice.
Because of its importance to the radio art a considerable part of the
text is given over to the theory and behavior of the thermionic thrce-
v
vi PREFACE
electrode tube; at the time this material was compiled there was no com
prehensive treatment of the subject anywhere, but there has recently
appeared an excellent volume on Vacuum Tubes (by H. J. Van der Bijl)
which every student of radio should carefully peruse. It is hoped that
the subject matter presented in this text may supplement, rather than
duplicate, that given in the above mentioned volume; the actual behavior
of tubes in typical circuits is covered in this text in a more thorough
manner than has been attempted in other texts, and practically all the
theoretical deductions are substantiated by experimental data, much
of which has been obtained in the author's laboratory.
A chapter has been devoted to each important phase of the radio art ;
there is also incorporated a short, course of elementary experiments which
may well be carried out by electrical engineering students especially inter
ested in Radio. For those desiring to specialize in Radio, the material
given in the body of the text will furnish ideas for unlimited further
experimentation.
On certain parts of the text very valuable assistance has been given
by the author's former colleague, Mr. A. Pinto, and by Mr. W. A. Curry,
who is at present associated with him in radio instruction; due credit
is given to them on the title page of the text.
J. H. M.
Columbia University,
April, 1921.
ERRATA
Page 20, 13th line from bottom. For 6.38 read 6.28.
37, 11th line from bottom. Insert " of current " after " equation ".
41, 14th line from bottom should read: sine wave of current is the square root of
one-half the (maximum value)5.
46, 6th line from top. Insert R after Im.
48. For eq. 22 read: p = E I cos <*>(1 — cos 2wt).
— g—
73. At bottom of page add line: We might keep B fixed and vary the value of
the capacity of condenser Ci,
80, next to last line. For L read L\.
80, last line. For (L'c-L'd) -M' read (L'e+L'a) - A/'.
86, 9th line. For circuit 2 read circuit 1.
93. In legend of Fig. 91 for eqs. 64 and 65 read eqs. 84 and 85.
99, Fig. 97. For frequencies lower than 68 cycles reverse the dashed and full line
curves.
171, 4th line from bottom. For 1000w/i read lOOO^A.
208, last equation on page. Insert sin before (2tt 110.5/).
379, Fig. 13. Negative end of heating battery connects to thimble
434, 21st line. Insert n before E„.
456, second equation. Multiply right-hand side by R.
492, Eq. 46. For 2irLi read 4tL,.
.505, Eq. 77. For u>(L, - M) —^ read W(L3 - M) —^ .
506, last equation. For b1 read b.
591, 17th line from bottom. For smaller read larger.
733. The right-hand side of eq. 16 is twice as large as it should be (because of
incorrect reference to eq. 9). Divide it by the factor 2 as well
as the subsequent formulx- and problems depending on it,
.including eqs. 17, 18, 19, 20, 21, and 22.
733, Fig. 46. For sin 9 read cos 6.
774, 3d line from bottom. For 80 read 79.
821, 4th line. For L,T2Af +Lj read L,±2A/+LJ.
822, Fig. 34. Insert ammeter A in a condenser lead instead of where shown.
889, 4th and 5th lines. Delete: adjusting the secondary turns so as to give maxi
mum secondary current and.
CHAPTER I
Fundamental Ideas and Laws
Electrons—Electric fields—Induced charges—Electric current—Conductors
and insulators—Continuous and alternating current—Wave shape—
Magnetic fields—Units— Induced e.m.f. —Self-induction—Coupling—
Capacity—Oscillograph—Current flow in inductive and condensivc
circuits—Time constant—Alternating-current flow in various circuits—
Effect of frequency—Transients in inductive circuits—Resonance—
Decrement—Decrement from resonance curve—Parallel circuits—Various
types of coupling—Effect of neighboring circuits on resistance and re
actance—Resonance in coupled circuits—Resonance in electrically long
. circuits 1-110
CHAPTER II
Resistance—Inductance—Capacity
General concept of resistance—Various factors affecting resistance—Skin
effect and its elimination—Skin effect in coils—Eddy currents in iron
cores—Characterisitics of iron core coils—Resistance of arc and spark-
Resistance of an antenna.
Coefficient of self-induction—Self-induction of single vertical wire—Single
horizontal wire—Single circular turn—Single layer solenoid—Flat spiral—•
Toroid—Single layer square coil—Flat square coil—Multilayer coil—
Mutual induction of two single turns—Coaxial solenoids—Two-wire
antenna—-Two concentric coils—Two coaxial spirals.
Capacity in general—Capacity of an isolated sphere—Parallel circular plates—■
Single vertical wire—Mutual capacity of two horizontal wires— Multi-
plate condenser—Forms of condensers—Specific inductive capacity—
Losses on condensers—Phase difference of a condenser—Internal capacity
coils—Natural period of coils. 111-178
CHAPTER III
General View of Radio Communication
Wave motion in water—Electro-magnetic waves—Velocity of propagation—
Different types of waves—Spark telegraphy—Continuous-wave teleg
raphy—Radio telephony—Receiving station—Selectivity—Interference-
Simultaneous sending and receiving—Atmospheric disturbance—Elimi-
vii
viii CONTENTS
CHAPTER IV
Laws op Oscillating Cikcttits
Condenser discharge through inductance—Effect of condenser leakage—
Frequency—Wave-length—Voltage and current relations—Damping and
decrement—Decay of current, voltage and energy—Effect of spark gap—
Number of waves in a train—Effective value of damped sine wave cur
rent—Effect of neighboring circuits upon oscillatory discharge—Coupled
pendulums—Oscillations in coupled circuits—Phases and amplitudes of
currents—Vector diagram of currents in coupled circuits—Frequency of
beats—Quenching gap—Oscillatory circuit excited by continuous vol
tage—Oscillatory circuit excited by application of alternating voltage—
Periodic disturbances in oscillatory circuit—Oscillatory circuit excited by
pulse—Impulse excitation of parallel resonant circuit—Oscillatory circuit
excited by damped sine wave and resonance curve for such a case 202-274
CHAPTER V
Spark Telegraphy
Normal transmission equipment—Battery and coil—Alternators for radio
transmitters—Transformers—Condensers—Resonance conditions in audio
frequency circuit—Different types of spark gaps—Oscillation trans
former—Energy distribution curves of a transmitter and effect of
coupling—Adjustment of a spark transmitter—Elements of a receiving
set—Need of a rectifier—Types of coupling—The telephone receiver—
Crystal rectifiers—Vacuum tube detector—Adjustment of receiving set—
Wave-lengths and ranges of transmission in spark telegraphy—Arrange
ment of apparatus in typical transmitting stations . . . 275-363
CHAPTER VI
Vacuum Tubes and Their Operation in Typical Circuits
Possibility of electron emission—Theoretical prediction of electron evapora
tion—Electron atmosphere—Power required to produce emission—Two-
electrode vacuum tube—Fleming valve—Space charge and its effects—•
Three-electrode tube—Deforest audion—Potential distribution in three-
electrode tube—Uses of three-electrode tube—Operating limits of a
tube—Effect of gas—Ionization—Evacuation of a tube—Detection of
gas in a tube—Characteristic curves of typical three-electrode tubes—■
Free grid potential—Equation of plate current—Resistance of tube
circuits—Capacity of input circuit—Three-electrode tube as detector—
Action of grid condenser—Triode as generator of alternating current
power—Output and efficiency—Heating of plates—Phase relations in a
triode—Possibility of self-excitation—Triode as detector of continuous
CONTENTS ix
CHAPTER VII
Continuous-wave Telegraphy
Advantages of continuous-wave telegraphy—High-frequency generators—
Poulsen arc—Elementary theory of oscillating arc—Types of oscillation
of arc—Commercial form of arc—High-frequency alternators—Alexan-
derson alternator—Goldschmidt alternator—Frequency transformers
using iron cores—Marconi multiple-gap generator—Methods of signalin"
used with different generators—Reception of continuous-wave signals—
Tone wheel—Heterodyne—Effect of upper harmonics on beat reception—
Arrangement of apparatus in continuous-wave tube transmitters 578-645
CHAPTER VIII
Radio Telephony
Field of use—The transmitter—The receiver—Modulation —The microphone
transmitter—Analysis of modulation—Percentage modulation—Schemes
for modulation—The vacuum tube in radio telephony—Heising scheme of
modulation and its analysis—Alexanderson scheme of modulation—
Analysis of modulated wave—Oscillating tube as receiver—Effect of
decrements upon quality of speech—Multiplex radio telephony—Amounts
of power used and distances covered—Arrangement of apparatus in a
commercial set—Simultaneous transmission and reception 646-693
CHAPTER IX
Antenna and Radiation
Radiation from simple antenna—Effects of moving electric and magnetic
fields—Open and closed electric systems—Fields involved in radiation—
Radiated field at a distance from the antenna—Radiation from a coil—
Excitation of the transmitting antenna—Various types of antenna; and
their characteristics—Relation between simple antenna and coil antenna—
Antennae for air ships—Underwater antenna;—Ground antennae—Law
of radiation from an antenna—Radiation resistance—Current in receiving
antenna—Merits of different types of antennas—Limitation of transmission
formulae—Counterpoises—Antenna resistance—Natural wave-length of
an antenna—Current and voltage distribution along an antenna and
effect of loading—Direction finders—Reliability of direction finders—
Transient effects in an antenna 694—780
X CONTENTS
CHAPTER X
Wavemeters and Their Use
PAGES
Frequency and wave-length—Principle of wavemeter—Extending range of a
wavemeter^Schemes for indicating resonance—Classification of resonance
indicators—Condenser for even scale—Autodyne wavemeter—Measuring
the wave-length of a transmitter—Energy distribution—Decrement
determination with spark transmitter—Determination of decrement of
wavemeter—Decremcter—Measurement of constants of an antenna—
Mutual induction and coefficient of coupling determination—An im
provised wave-meter 781-823
CHAPTER XI
Amplifiers
Amplifiers in general—Characteristics of triodes—Effect of plate circuit
resistance and reactance—Classification of amplifiers—Transformer-re
peating amplifiers—Construction of transformers for audio-frequency—
Impedance of telephone receivers—Connections of transformer-repeating
amplifier — Transformer-repeating amplifiers for high frequencies—
Resistance amplifier—Proper resistances for repeating—Grid condenser
and leak—Inductance-repeating amplifier—Filters and their charac
teristics—Stability of amplifiers—Tube noises—Arrangement of appa
ratus in amplifiers 824-879
CHAPTER XII
Radio Experiments
Resonance curves—Buzzer-generator and crystal detector characteristics—
Study and use of wavemeter—Setting up and adjusting a spark trans
mitter—Measurement of antenna constants—Continuous current charac
teristics of three-electrode tube—Tlvree-electrode tube as detector of
damped waves—Determination of tube constants—Triode as power
converter—Triode as source of power in self-exciting circuit—Resistance
measurements at high frequency—Oscillating triode as receiver of
continuous-wave signals—Study of the audio-frequency amplifier-
Study of radio-telephone set 880-919
PRINCIPLES
OF
RADIO COMMUNICATION
CHAPTER I
to the atom the balance of charge is restored and the atom is again un
charged, or neutral.
A positively charged body, therefore, is one which has been deprived
of some of its normal number of electrons; a negatively charged body is
one which has acquired more than its normal number of electrons. Thus
when a piece of sealing wax is rubbed with dry flannel the wax becomes
negatively charged and the flannel becomes positively charged. The
friction between the wax and the flannel must have rubbed some of the
electrons off the flannel molecules and left them on the surface of the wax.
The extra electrons on the wax are attracted by the deficient mole
cules of the flannel (positive and negative charges attract each other) and
if the flannel and wax are left together after being rubbed they soon lose
their charges; the molecules of the flannel regain their proper number of
electrons.
Number of Electrons Removable from an Atom.—Although there may
be a great number of electrons associated with an atom or molecule it
is generally not possible to remove more than one; in a body which is
positively charged most of the atoms are
neutral, having their proper complement
of electrons; others have had one electron
removed. If but few of the atoms of a
body have had an electron removed the
body has a small charge; the more highly
the body is charged the more deficient
atoms there are on it.
From this viewpoint it seems that the Fl0 2.—Conventional model of a
amount of charge on a body should be simple atom charged positively,
counted; the charge consists of discrete one of its electrons being free,
things. Instead of saying that a body has
a certain amount of negative electricity on it, we might more reason
ably say that a certain number of electrons have been deposited on it.
Electric Fields.—If a light substance, such as a pith ball, is touched
to a charged body, it becomes charged with electricity of the same polarity
as that on the body itself ; as like charges repel one another the pith ball
will be repelled from the charged body. By experimenting it may be
found that the repulsive force between the pith ball and the original charge
exists even when there is considerable distance between the two. The
Bpace surrounding a charged body is evidently under some kind of strain
which enables it to act upon a charged body with a force, attractive or
repulsive, according to the relative polarities of the two charges. This
space surrounding a charged body, in which another charged body is
acted upon by a force tending to move it, constitutes an electric field,
sometimes called an electrostatic field.
4 FUNDAMENTAL IDEAS AND LAWS [Chap. I
shown as very intense between the two plates, weaker towards the edges,
and very weak in the space not directly included between the two plates.
Closed and Open Electric Systems.—In Fig. 5 most of the electric
field is shown directly between the plates on which the charges are situated;
Fig. 4. Fia. 5.
Flo. 4.—Charged body near the earth has its electric field radial near the body, all
lines of force, however, bending over so that they end on the earth.
Fig. 5.—Two metallic plates, close to one another, one charged positively and the
other negatively, have an intense electric field between the plates, and weak field
elsewhere.
most of the electric field is evidently included directly between the earth's
surface and the antenna wire, so the field is a closed one as contrasted
with that of Fig. 6, which is regarded as an open field. The operating
characteristics of the two antenna shown are quite different, the difference
being due to the different distribution of the field in the two cases.
| > ++
by the attractive force of the positive charge on the ball. The negative
charge on the rod is called a bound charge and the positive charge which
runs away if given the opportunity is called a free charge.
An illustration of the way in which this method of producing charges
is useful in radio circuits is shown in Fig. 9. The charge on ball A is
to produce a charge of the opposite kind on the conductor F through
the two condensers BC and DE. When A comes in contact with B, this
becomes positively charged. A nega- A bc de
tive charge appears at C due to the 1
inducing action of B. An equal \_y
positive charge must appear at D + ~ + ~
and this must induce a negative 9._A charged oody inducing charges
charge on E. But if a negative 0n conductor F, acting through two
charge appears at E there must be condensers,
an equal positive charge induced
on F. If now the conductor F is connected to the ground this positive
will run off to earth and there will be left on the conductor EF a
negative charge. This charge will, however, be bound by the positive
charge on D; if B is now grounded (connected to earth) its charge will
run off and so the negative charge on C becomes free. This free charge
on C will combine with the positive charge on D and neutralize it, thus
leaving on the conductor EF a free negative charge.
Induced Charges from the Electron Viewpoint.—As will be explained
later, the electrons in a metallic conductor are more or less free to pass
from one atom of the substance to another; they are continually moving
around the complex molecular structure of atoms comprising the metal.
When the rod of Fig. 8 is brought into the neighborhood of the charged
ball the electric field due to the charge on the ball acts on the free elec
trons of the rod, attracting them. Hence the free electrons of the rod
tend to congregate at that end of the rod which is nearest to the ball;
they constitute the negative charge at this end of the rod.
But if the rod was uncharged before coming into the influence of thf
charged ball there must be just enough electrons on it to neutralize the
positive charges of the atoms. If more than a proper portion of the elec
trons gather at one end of the rod there must necessarily be a shortage
of them at the other end. This shortage of electrons at the end C of the
rod constitutes the positive charge at this end.
When the end C is grounded, the positive atoms of the rod cannot
leave the rod and go into the earth, but electrons from the earth can run
up into the rod and they do so, being attracted by the deficient atoms at
C. These electrons from the earth appear in sufficient quantity to make
the atoms at C neutral. When the wire connecting the rod to the earth
is removed and the charged ball is also removed the rod has on it a free
8 FUNDAMENTAL IDEAS AND LAWS [Chap. I
many moving more slowly. Contrary to what one would naturally think
the progressive movement of the electrons is very slow. To produce
a current of one ampere in a copper wire one millimeter in diameter re
quires that the average velocity of the electrons be only .01 cm. per
second.
Although the progressive motion of the electrons is very slow, as
indicated above, it must not be thought that the actual velocity of the
electrons is small. If we assume the " equi-partition of energy " idea
of thermc-dynamics and thus calculate the average velocity of the electrons
in a copper wire, at ordinary temperature, we obtain a result of about
6X106 cm. per second. That is, even when no current is flowing in the
wire the electrons have a haphazard motion, due to the thermal agita
tion of the atoms (or molecules), which give them, on the average, a velocity
of about 35 miles per second.
Now when current flows the required progressive velocity of the
electrons is only a fraction of a centimeter per second; with a current
so large that the copper wire is heated to the melting-point the velocity
of drift of the electrons is less than 1 cm. per second. Thus an accurate
concept of the electric current in a conductor shows it to be an inappreciable
" drift " of the electrons which have, due to temperature effects, hetero
geneous velocities millions of times as great as the velocity of drift.
The reason for the slow progressive motion of the electrons is to be seen
in the tremendous number of collisions they have with the molecules of
the substance. A given electron, acted upon by the potential gradient
in the wire carrying current, accelerates very rapidly and would acquire
tremendous velocities if it did not continually collide with the more massive
molecules; the mean free path of the free electrons in a copper wire is
so small that, between successive collisions, the electron falls through a
very small potential difference and hence gains a velocity (along the con
ductor) due to the current, which is extremely small.
Suppose that we wanted to measure the rate of flow of people past a
given point in a large city; the unit of flow might be 100,000 persons per
hour. At any time there will be people going in all directions, some
uptown, some downtown, and some crosstown. In the morning a million
people pass a certain point where the flow is to be ascertained. If 200,000
move in the uptown direction and 800,000 move downtown, the net flow
is 600,000 people. If this number of people pass in one hour the flow is
6 units downtown. At noon time again a million people pass the same
place let us suppose; 400,000 move uptown 400,000 move downtown and
150,000 move crosstown west and 50,000 move crosstown east. The net
flow is now 100,000 people west and if this number pass in one hour the
flow is one unit west. Some of the people would be moving rapidly and
others going more slowly and some might, at times, be standing still.
10 FUNDAMENTAL IDEAS AND LAWS [Chap. I
A Conducting Rod E
© © © © © ©
© © © © ©
Direction of Electron. Drift
v ^ y
Battery
Fig. 10.—Electric current caused by flow of free electrons.
wire, through the battery, through the other connecting wire, and so
back to the rod. As long as the circuit remains closed as shown the elec
trons will continue to move around the circuit, bounding backward,
forward, and across the conductor, but on the whole progressing grad
ually around the circuit; this progression of the electrons constitutes the
electric current. The cause of the flow is the battery; it holds one end
of the rod positive with respect to the other and so maintains the flow
of electrons. The maintenance of this difference of electric pressure (or
difference of potential) across the rod is due to chemical changes going
on inside the battery.
A piece of apparatus which has the ability to maintain one of its ter
minals at a higher potential than the other, even though current is allowed
to flow through it, is said to develop an electromotive force. As sources
of electromotive force for the production of currents on a commercial
scale we have only the ordinary battery and the electric generator. The
battery depends upon chemical action for maintaining its difference of
potential and the generator depends upon the conductors of its armature
being driven through the magnetic field produced by its field poles.
ELECTROMOTIVE FORCE AND POTENTIAL DIFFERENCE 11
i—vwwwww1——1
< Current
AlterDAting >
Fig. 12.—A battery in
combination with a
rotating commuta
tor may produce an Fig. 13.—The lamp will burn even though there is a perfect
alternating current. insulator in series with the circuit.
Plrton B
d .7>
t » ^
from its normal central- position to position B', and then the flow would
cease because the pump would not be able to further displace the dia
phragm. '
The water system corresponds very closely to the electrical circuit
having a condenser in series with it and excited by a continuous e.m.f.;
in luch a circuit the current flows long enough to charge the condenser
to such an extent that its back pressure (pressure tending to discharge
the condenser) is just equal to the impressed e.m.f. and then the current
ceases. It is to be remembered, however, that if the pressure is alternat
ing there will be a flow in the system all the time, the current being an
alternating one.
In electric circuits, therefore, it is possible to send an alternating
current through a circuit in which continuous current cannot flow. Such
A
of voltage has a maximum value of 141 volts its effective value (or equiva
lent continuous voltage as far as producing heating is concerned) is 100
volts.
Magnetic Field.—The action of the magnet is familiar to everyone.
If a piece of iron is placed in the vicinity of the magnet a force of attrac
tion is set up between the two and the piece of iron will, if free to move,
be drawn to the magnet.
All the region surrounding a magnet, in which the magnet is able to
exert a force on pieces of magnetic material, is said to be filled with the
field of the magnet. Thus the magnetic field is exactly analogous to the
electric field surrounding an electrically charged body.
The magnetic field is represented by lines in just the same way as
the electric field; the direction of the lines indicates the way in which
the north pole of a compass would be urged if placed at that point of
the field, and the proximity of the lines to each other serves to show the
relative intensity of the magnetic force at various points of the field.
Magnetic Field Set Up by an Electric Current.—The field of the per
manent steel magnet is interesting historically, but it plays very little
part in the electrical engineering of to-day. When an electric current
flows through a conductor a magnetic field is set up around that con
ductor; such a field is frequently called an electro-magnetic field. The
magnetic fields used in modern apparatus are practically all of this type.
The strength of a magnetic field set up by an electric current depends
upon the strength of the current, in general being directly proportional
to the current strength. The direct proportionality holds good for mag
netic fields without iron; use of iron in the magnetic circuit makes the
relation between current and strength of field a complex one.
Ampere-Turns.—When the magnetic field is produced by a coil of
several turns its intensity is much greater than if only one turn were
used. The magnetizing effect of a current depends not only on the strength
of current, but also on the number of turns through which the current
flows. In fact the magnetizing effect of a coil is proportional to the prod
uct of the current strength and the number of turns in the coil; this
product is called the ampere-turns of the coil. If a coil consists of one
turn and is carrying a current of one ampere it has one ampere-turn; a
coil of twenty turns carrying 2.7 amperes has fifty-four ampere-turns.
Direction of the Magnetic Field Produced by a Current.—The direc
tion of magnetic field around a conductor carrying a current may be
easily determined by the application of the following rule. Imagine the
conductor grasped in the right hand, fingers around the conductor, with
the extended thumb pointing along the conductor in the direction in which
the current is flowing; the fingers then point in the direction of the mag
netic field. This is illustrated in Fig. 17; it is to be remembered that
MAGNETIC FIELD PRODUCED BY ELECTRIC CURRENT 19
— (4)
»*%
in which
e = the voltage induced at any instant of time;
N = the number of turns in the coil;
<i> = the flux through the coil.
The minus sign is necessary because of the relation between the direction
of the induced e.m.f. and the change in magnetic field, i.e., increase or
decrease.
Direction of Induced E.M.F.—The change of flux is of course produced
by a change of current; if the flux is decreasing it must be that the cur
rent in the coil is decreasing. The direction of the induced e.m.f. is always
such as to prevent the change of current which is producing the induced
voltage. Hence when the current (or
flux) is decreasing, the direction of /
the induced e.m.f. is such as to pre
vent the decrease of current. +
Suppose a circuit arranged as shown
in Fig. 18; A is the battery, B is a
coil, C is a switch, across which is
connected a resistance D. With the
switch closed current will flow in the Fio. 18.—Opening the switch will re
direction of the arrow and will be fixed duce the current in the circuit.
in magnitude by the voltage of the
battery and the resistance of the coil. The resistance D will play no
part in fixing the value of the current, because with the switch closed
this resistance is cut out of the circuit, or short-circuited.
A certain flux <f>, will be set up in the coil, the value of this flux being
fixed by the current. If now the switch is opened the current must change
24 FUNDAMENTAL IDEAS AND LAWS [Chap. I
to some lower value because of the added resistance D. This lower cur
rent will produce a lower flux fa. While the flux is changing from fa
to fa an e.m.f. will be set up in the coil B and the direction of the e.m.f.
will be the same as the battery e.m.f., i.e., it will assist the battery e.m.f.
in tending to maintain the current at its original value.
In Fig. 19 the switch is supposed to be closed until time A and here
it is opened. The flux will decrease from the value AE to BF, the time
taken for the change being that shown on the diagram between A and B.
The decreasing flux generates a voltage in the coil shown by the curved
line AIB, and this is in the same direction as the battery voltage, hence
the total voltage acting in the circuit during the time A-B is shown by
the curved line GJH.
increasing flax
Fig. 19.—Curves showing direction of induced e.m.f. 's when current is increasing and
when decreasing.
When the switch is closed again at time C the flux increases from fa
to <f>i; the induced voltage is now in the opposite direction and is shown
by the curved line CKD; it results in a total circuit voltage less than
the battery voltage, as shown by the curved line MNO. (The shape
of the induced voltage will not be exactly that shown by the lines of
Fig. 19; these curves are only approximate indications of the actual form
of the induced voltage. The exact form will depend upon the sparking
taking place at the switch, etc.)
Summarizing the facts brought out by Fig. 19 and its explanation we
have the proposition that when the current in an inductive circuit is
decreasing the induced voltage acts to increase the total voltage of the
circuit, when the current is increasing the induced voltage is in such a
direction that the total voltage acting in the circuit is decreased.
Illustrating the above ideas there is a certain circuit used in radio
in which a continuous voltage of 1200 volts is applied through a coil to
the plate of a vacuum tube; as the current in this circuit pulsates, alter
nately increasing and decreasing from its normal value, the induced volt
SELF INDUCTION OF A CIRCUIT 25
age in the coil has a maximum value of 1100 volts. When the current
is increasing this induced voltage acts in the opposite direction to that
of the generator furnishing the 1200 volts, so that the total voltage effect
ive in maintaining current through the resistance of the circuit is only
100 volts. When the current is decreasing the induced voltage assists
the generator voltage and the total effective voltage in the circuit is 2300
volts. The effect of induced voltage in this special circuit is to produce
a pulsating voltage, between 100 volts and 2300 volts, although there is
in the circuit a generator to supply the current which furnishes a contin
uous voltage of 1200 volts.
This voltage set up in a coil by the changing flux in the coil (the flux
being caused by current in the coil itself) is called the e.m.f. of self-dnduc-
lion.
Coefficient of Self-induction.—Instead of expressing the magnitude
of the induced voltage in a coil in the form given by Eq. (4) we may write
—4 • (5)
in which
?'=the current in the coil;
e = the instantaneous value of the induced voltage, due to
the changing current, i,
L = the coefficient of self-induction.
when possible) in coils which perform their function owing to the value
of their self-induction.
The unit of self-induction is defined by Eq. (5); if a rate of current
change of one ampere per second gives an induced voltage of one volt, the
coil has a self-induction of one unit. This unit is called the henry; the
henry is, however, too large a unit for most of the coils used in radio
work, so that subdivisions of the henry are used. The milli-henry is one
thousandth of a henry and the micro-henry is the millionth part of a
henry. Sometimes a still smaller unit is used, the centimeter, which is
the billionth part of the henry. It may seem strange that the unit of
I length is also the unit of self-induction, but such is the fact; the deriva
tion of the dimensions of the various units is outside the scope of this
text. The coils used in " tuning " radio circuits vary from a few micro
henries to several millihenries, according to the frequency of the current
being used.
Energy Stored in a Magnetic Field.—It requires work to set up a
magnetic field just the same as it requires work to set into motion a heavy
body. The greater the self-induction of a coil the greater is the work
required to start current flowing in the coil ; similarly the greater the mass
of a body the greater is the work required to start it in motion.
The amount of work required to give a mass m, a velocity v, is measured
by \mv2, as shown in all texts on mechanics.
The amount of work required to set up, in a coil of self-induction L,
the magnetic field caused by a current / is,
Energy, or work = |L/: (6)
where L is measured in henries and / is measured in amperes and the
energy is measured in joules.
The field coil of a large generator may have many joules of energy
stored in its magnetic field; in radio circuits the amount of energy in
the coils of a transmitting set is variable because the current is variable.
The maximum value of the energy in the coils of the ordinary transmitter
is about one joule per kilowatt capacity of the set.
Mutual Induction.—When the flux through a coil varies an e.m.f.
is set up in it; if the flux is produced by current in the coil itself the e.m.f.
is spoken of as the e.m.f. of self-induction, but if the flux is due to some
other coil, in proximity to the one in which the voltage is being induced,
the e.m.f. is spoken of as the e.m.f. of mutual induction. The voltage
induced in the second coil is proportional to the rate of current change
in the first coil (the one producing the flux) and the mutual induction
of the two coils. The relation is expressed in the form of an equation
(6)
MUTUAL INDUCTION AND MAGNETIC COUPLING 27
shown in o and will have a smaller value for either position b or position c.
The scheme of rotating one of the two coils to diminish M has the advan
tage over the other method that it is compact and so permits the design
of a set to be kept to smaller dimensions, a very important point if the
sets are to be portable.
Coefficient of Coupling.—If all the flux produced by one coil threads
with all the turns of the other, the coils are said to have 100 per cent
coupling; if but a small fraction of the flux produced by the first coil
threads the turns of the second, the coupling is weak. Also if all the
flux of the first coil links with but a few turns of the second, the coupling
is again weak.
The coefficient of coupling1 between the two circuits is given by the
relation
*-T#r>
vLiL2 (7)
of the power transformer where the coupling is about 90 per cent; in the
high-frequency oscillation transformer the coupling is about 20 per cent;
in the coupler of the receiving set the antenna is coupled to the local tuned
circuit with a coupling of perhaps 2 to 10 per cent.
Effect of a Short-circuited Coil on the Self-induction of a Neighbor
ing Coil.—Suppose a coil A has a certain self-induction by itself; it will
be found that if another coil B is brought close to A , and in such a position
that M is not zero, the effective L of coil A is decreased, if the second
coil is connected to form a closed circuit so that current can flow in it.
The amount of decrease in L depends upom the coupling between the
two coils, upon the frequency, and upon the resistance in the circuit of
the second coil.
This effect is likely to occur in certain variable coils used in radio
circuits; in the type of coil referred to the change in the self-induction
of the coil is accomplished by using more or less turns of the coil by means
of a sliding contact as indicated in Fig. 22. If the sliding contact B
happens to make contact with two adjacent turns at once (quite a nor
mal occurrence), there is one turn of the coil short-circuited, and this short
CHARGING A CONDENSER 29
circuited turn is quite closely coupled with that part of the coil which
is being used. The effect of this turn is to decrease very much the effect
ive self-induction of the part of the coil A-B, which is being used. Now
as the slider is being adjusted it will, with very little movement, make
contact with two turns or with only one turn; a signal may come in very
strong at a certain setting of the slider and the slightest movement of
the slider one way or the other will make the signal disappear. This is
Sliding Contact
B "
Fig. 22.—Variable Inductance with sliding contact.
due to the large change in the self-induction of the coil as the slider makes
the short-circuited turn or does not make the double contact.
A short-circuited turn in a coil not only produces a decrease in the
L of the coil, but it also increases very materially the resistance of the
coil, and this is detrimental to the proper operation of the set; these two
points will be taken up more in detail on pp. 85, et seq.
Capacity—Charging a Condenser.—Suppose a battery is connected
through a switch to a condenser as indicated in Fig. 23. The condenser
, <J 1
nected, is called charging the condenser. A current flows during the short
interval of time required for the redistribution of the electrons; this cur
rent is called the charging current of the condenser.
It is more or less evident that the condenser will take sufficient charge
to bring its potential difference equal to that of the battery; as long as
the condenser is at a lower potential difference than the terminals of the
battery, the e.m.f. of the battery causes more electrons to flow; if, by
any chance, so many electrons accumulate on the b plate of the condenser
that potential difference of the condenser is greater than that of the battery,
the excess of potential difference would so act as to make the condenser
discharge itself until it was at the same potential difference as the ter
minals of the battery.
Capacity of a Condenser.—Suppose the amount of electron flow neces
sary to charge two different condensers to a certain potential difference
is measured by a ballistic galvanometer or similar device. It will be
found in general that the different condensers require a different amount
of charge to bring them to the same difference of potential. For example,
if two condensers are made of the same-sized met al plates, but in one the
plates are only half as far apart as in the other, it will be found that the
one with closer plates requires twice as much charge as the other; if two
condensers have the same spacing for the plates, but one has larger plates
than the other, again it will be found that one requires more charge than
the other, in this case the one with the larger plates.
That characteristic of a condenser which determines how many elec
trons it takes to bring the condenser plates to a certain potential dif
ference is called its capacity. A condenser which requires one coulomb
of electricity to bring its plates to a potential difference of one volt, has
a capacity of one farad. Such a condenser would require immense plates
very close together; the unit is altogether too large to represent the ca
pacity of ordinary condensers. In ordinary engineering practice, such as
telephone circuits, the microfarad is used as the unit of capacity. A con
denser of one microfarad requires a charge of one millionth of a coulomb
to charge it to one volt. Stated in another way, a current of one ampere
would have to flow only one millionth of a second to charge the condenser
to one volt potential difference, or one microampere, flowing for one second
would charge it to the same extent.
In radio circuits the microfarad is too large a unit to be conveniently
used; a more suitable unit is the milli-microfarad, which is the thousandth
part of a microfarad. Another unit is the micro-microfarad, which is one
millionth of a microfarad. Still another unit is the centimeter; which
is one nine hundred thousandth of a microfarad. The micro-microfarad
and the centimeter are nearly the same-sized units, the centimeter being
about 1.1 of a micro-microfarad.
ENERGY IN CHARGED CONDENPER 31
(10)
has to disappear when the current dies to zero because there can be no
magnetic field without current.1 The greater the self-induction of the
circuit the greater is the amount of energy (for a given current) and the
larger will be the arc when opening the circuit. The decay of current
in an inductive circuit cannot be well examined therefore by opening
the circuit, but it can be shown by short-circuiting the coil in which die
current is flowing. In such a case the current dies away on a logarithmic
curve quite similar to the curve of current rise. The equation of current
decay is quite similar to that of the current rise and is
; = |(<_i), (ID
current than for the rising current; the rising current had for its resistance
that of the coil, that of the battery, and that designated by E, while the
decaying current took place through the resistance of the coil only.
Effect of Rising and Decaying Currents on Neighboring Circuits.—As
the current in the coil increases and decreases it must induce electro
motive forces in any neighboring circuits which are so placed that they
link with its magnetic field. If the neighboring circuit is closed current
will flow, in one direction when the current in the first circuit is rising
and in the opposite direction when the current in the first circuit is falling.
Hence when a circuit is closed and current starts to flow all neighboring
i=|(«"^), (12)
»=-|(«'^), (13)
where the letters have the same meaning as they have in Eq. (12). This
current is evidently of the same shape as that taken by the charging
operation with the exception that there is a minus sign before it; this
38 FUNDAMENTAL IDEAS AND LAWS [Chap. I
signifies that the discharge current is of the same form as the charging
current, but it flows in the opposite direction.
Time Constant of a Condenser Circuit.—The quantity RC is called
the time constant of the condenser circuit; it is evidently the time taken
for the current to fall from its maximum value to 37 per cent of this value;
another way of defining the time constant of a condenser circuit is in
terms of the charge on the condenser; the time constant is the time required
for the condenser to accquire 63 per cent of its final charge or, in the case
of the discharging condenser, it is the tune required for the condenser
to lose 63 per cent of its charge.
Fig. 29 shows an oscillogram of charge and discharge which was
taken from the circuit shown in Fig. 28. Some extra resistance must
be necessarily added to the inherent resistance of the battery and con
denser because the time constant of such a circuit is excessively small,
too short for the oscillograph to function. Thus a one microfarad
condenser in series with two ohms (a probable value for the battery)
would have a time constant of .000 002 second, that is, the current
would rise instantaneously upon closing the switch, to some value (de
pending upon the voltage used in charging) and in .000 002 second
would have fallen to 37 per cent of this value, and in a correspondingly
short time would have dropped to practically zero. Such an instanta
neous occurrence is too rapid even for the oscillograph, hence to increase
the time constant to a value suitable for the use of the oscillograph an
extra resistance had to be introduced in the circuit.
The effect of adding resistance in series with a condenser to be charged
is shown by the curves of Fig. 30; these were calculated from Eq. (12).
They show that the initial current is cut down as the resistance is increased,
in fact being equal to E/ R, and that the duration of the current increases
with the increase of resistance. The area between the X axis and any
of the curves is the same; this area represents the quantity of electricity
on the condenser and so must be the same for all conditions, because the
quantity of electricity on the condenser after the charging process is com
plete is the same no matter what the resistance of the circuit may be.
Power Expended in a Continuous-current Circuit.—If a current of /
amperes is caused to flow through a circuit by an e.m.f. of E volts the
rate of doing work in the circuit is
Watts = EI, (14)
If the circuit has a resistance R we know that E=IR and so
Watts = IRXl = PR (15)
from which we get
Watts
R= (16)
P ;
TIME CONSTANT OF CONDENSER CIRCUIT 39
40 FUNDAMENTAL IDEAS AND LAWS [Chap. I
\
\
\\
\J Coml< as* r <■ •n ad to 1 00 *'ol s
C;i p.n Ity .if ■on len scr -2 [10 '(, r.ul
Ci rv( l- R- 10 Jlu l.s
Ci rv< 2- R = 20 Jhi IS
c Ci rv( 8- R = ■10 Jlu IS
Ea
v_>
.6. .8
TlmeJn.1000 Ihs Seconds
Fig. 30.—Condenser charging currents for different values of series resistance.
nating current work, where Eq. (16) affords the only feasible means of
determining the resistance of the circuit.
Power Consumed in a Circuit Excited by Pulsating Current.—In case
the voltage or current of a circuit, or both of them, are pulsating the power
consumed in the circuit cannot be obtained by using the product of the
average voltage by the average current, as might at first seem correct;
an error would be introduced making the power consumed too low, the
amount of this error depending upon the amount of fluctuation. The
greater the amount of fluctuation or pulsation of the current or voltage,
the greater is the error introduced.
POWER USED BY PULSATING CURRENT 41
sine wave of current is one-half the square root of its maximum value.
Hence the effective value of the pulsating current is ^I^+^h2- The
power used when such a current flows through a circuit of resistance R is
If the average value of the current were used in calculating the power
used, the power represented by the second term would be completely
neglected, and so an error would be incurred equal to \Iz2R. The amount
of this error depends upon the amount of pulsation of the current. In
such a circuit as the primary circuit of spark-coil transmitting set excited
by storage battery the error would be very largo, and the power used in
the circuit cannot be obtained at all accurately without knowing the form
of the current flowing in the primary winding of the coil.
The above statement is made with the idea in mind that in such a
circuit as this, excited by storage battery, a direct-current ammeter would
42 FUNDAMENTAL IDEAS AND LAWS [Chap. I
same instant they are in phase. In case the current passes through its
zero value after the voltage has passed through its zero value it is said
to be a lugging current; if it goes through the zero value before the voltage
it is said to be a leading current.
In Fig. 32 are shown curves of current and voltage with (a) current
and voltage in phase, (b) with current lagging behind the voltage by the
angle <j>, and (c) with the current leading the voltage by the angle <£.
The magnitude of the angle of lag or lead may be easily approximated
when it is remembered that the time from one zero point to the next zero
point of the same curve is 180°; in curve 6 the current lags by about 30°
and in curve c the angle of lead is about 70°.
In case the circuit has lesistance only the relation between voltage and
current is expressed by Ohm's law, whether instantaneous, maximum, or
effective values are considered. Thus the equation for current flow in
this circuit is
7=I <17>
Fig. 33.—Power curve for an alternating current circuit containing resistance only.
current instrument knows that if the connection of the meter to the cir
cuit is reversed the reading will reverse. Such an instrument, if actuated
by an alternating current, would tend to oscillate between a certain direct
reading and the equal reversed reading, but, as the alternating current
reverses too rapidly for the needle of a meter to follow, it is evident that
the meter would read zero no matter how much current was flowing
through it.
Various types of meters are suitable for use on an alternating-current
circuit, the dynamometer type, the soft-iron vane type, the induction
type, the thermo-couple type and the hot wire type. The last two types
named are used almost exclusively for making measurements in radio
circuits, as it is practically impossible to make the other types function
properly at the very high frequencies used in radio work.
Transient Current on Switching a Resistance Circuit to an A.C. Line.—
If a resistance circuit is switched to an a.c. line the current rises instanta-
neously to the value it should have, depending upon the value of the volt
age at the instant the switch is closed, as shown in Fig. 34. This condition
of affairs is expressed by stating that there is "no transient current " or
no transient condition, after closing the switch; the current rises at once
to the value it would have had (at the time of closing the switch) in case
the switch had been closed at some previous time.
Current Flow in an A.C. Circuit Having Inductance and Resistance.—
Suppose that an inductance (without resistance) and a resistance, con
nected in series, are connected to an a.c. line so that an alternating e.m.f.
is impressed, as indicated in Fig. 35. Although the inductance must
really have resistance, it is shown as resistanceless, all the resistance of
the circuit being supposed concentrated in R. The current flowing in
such a circuit depends upon four things, L, E, R, and the frequency of
the impressed e.m.f. Provided that L and R are constant throughout
the cycle (do not vary with the value of the current) it is a fundamental
law of electrical circuits that the current will have the same form as the
46 FUNDAMENTAL IDEAS AND LAWS [Chap. 1
Drop= o) LI
f • To Supply of
alternating Emf
Drop =i R
drop and the inductance drop, and is so shown by the curve marked e in
Fig. 36.
CIRCUITS CONTAINING RESISTANCE AND INDUCTANCE 47
Fig. 37.—Vector diagram for an a.c. circuit containing inductance and resistance.
The quantity uL is called the reactance of the circuit and the quantity
Z is called the impedance of the circuit. The current lags behind the volt
age by the angle <f>, which is determined by the relation
Fig. 38.—Power curve for an a.c. circuit containing inductance and resistance.
So average power
P=EI cos <t> (23)
The power in the circuit is equal to the product of the volts and amperes
in the circuit and the quantity cos 4>. For this reason cos </> is called the
power factor of the circuit; it may have any value between unity and
zero. In ordinary power circuits it has a value between about 0.7 and
0.95, very seldom being unity. In some parts of efficient radio circuits
the power factor may be as small as .005.
The power may be expressed in terms of current and resistance by
changing the form of Eq. (23).
P=EI cos <t> = EI R
V£2+(«L)2
= IXlVR*+(a,L)2 / R ~==PR. . (24)
This equation for the power used in an a.c. circuit is really a definition
of the effective resistance of the circuit; the resistance of the circuit, for
alternating current, may be entirely different from the continuous-current
resistance of the circuit. There are many effects which combine to make
the a.c. resistance sometimes several times as great as the c.c. resistance
(or the a.c. resistance may be negative even, while the c.c. resistance is
positive) and the only way1 of measuring this resistance is by use of Eq.
(24). The power used in the circuit is measured by a wattmeter, the
current by an ammeter, and the resistance found by the relation
Effective resistance = W<L (25)
/X'=2^ <*>
I
T J
e y
1 lR
-- E = 100 L=0.1 R = 10
§e
10 frequency
Fia. 39.—Current variation with frequency in an a.c. circuit containing inductance and
resistance in series.
Fig. 40.—Curves of e and i in a circuit containing inductance and resistance, for steady
state.
in Fig. 40, when e has a maximum value AC, the current has the value
AB, and whenever the voltage has the value AC the current will have
TRANSIENT CURRENT IN INDUCTIVE CIRCUIT 51
the value AB. Now suppose the switch to be closed when the voltage
has the value AC ; the current should have the value AB, but in an induc
tive circuit the current cannot rise instantaneously; this was shown by
the oscillograms in Figs. 24 and 25. The complete equation for the cur
rent in an inductive circuit must therefore include a transient term as
well as the term for the steady state; it is properly written
_Rt
The second part of the current, Ke h , is determined in magnitude
by the value of the current, in the steady state, at the time in the cycle
f Sm doled
4
1 1t
1/
/ // 3 SI mi y ci rre n "/ //
/
)1 /
I/
// /
1
// -—
Trn ns-i< Qt ( urrL-nt
tua1 I'UrrciIt
A
y
Fig. 41.—Curves of e and i in a circuit containing inductance and resistance for transient
state.
corresponding to the time in the cycle that the switch is closed. Thus
in Fig. 41, at the time of closing the switch the current should have the
value AB; this fixes the value of K in Eq. 27. In Fig. 41 is plotted
Rt
the steady value of the current i, the transient current Ke L , and the
actual current for the first cycle after closing the switch; this actual cur
rent is the sum of the other two.
In Figs. 42 and 43 are shown oscillograms of the current flowing in
an inductive circuit for the first few cycles after the switch had been closed;
in one the switch was closed at the peak of the voltage and in the other
it was closed when the voltage was very nearly zero. In Fig. 42 the effect
of the transient term is plain ; the current (steady value) has been plotted
in dotted lines, as has also the transient term, the latter having been
52 FUNDAMENTAL IDEAS AND LAWS [Chap. I
1
CIRCUITS HAVING IRON CORE INDUCTANCE 53
calculated from the value of the steady current at the time the switch
was closed and the L and R of the circuit. It may be seen that the actual
current is correctly given by Eq. (27). In Fig. 43 the switch was closed
at that part of the e.m.f. cycle which, in the steady state, is the proper
time for the current to be zero; it is seen that for this case the transient
term reduces to zero, and the actual current is represented completely
by only the first term of Eq. (27).
Circuits Having Resistance and Iron-core Inductance.— In case the
L of the circuit, Fig. 35, consists of an inductance having a closed iron
path for its magnetic circuit, the conclusions deduced will not be correct.
The value of L in this case is not constant, but varies throughout the
v. \ \ /7 \ ' \7 7 \
hi,-!' \X/" W v
r • 1 *■
cycle, and for this reason the relation between the current and voltage
is a complex one; the current in this case requires an equation with an
infinite number of terms to express it accurately. The current, instead
of being sinusoidal, has a decided hump, as shown by Fig. 44, which shows
the magnetizing current of a closed-core transformer. |
Not only is. the steady value of current in such a circuit irregular,
but the transient current may show even greater irregularities. This
irregularity may last for many cycles, depending upon the kind of iron
used in the core and upon its condition of magnetization at the time the
switch is closed, as well as upon the part of the cycle selected for the clos
ing of the switch. Thus in Fig. 45 is shown the current in the primary
circuit of a transformer for a few cycles after closing the switch; the tran
sient current may be so large in this case that during the first cycle the
current never reverses its direction.
54 FUNDAMENTAL IDEAS AND LAWS (Chap.
TRANSIENT CURRENT WITH IRON CORE INDUCTANCE 65
Fio. 45.—Oscillogram showing the transient current when switching an iron core
inductance to an a.c. line.
current. The actual form of rising current in such a circuit, when con
nected to- a c.c. line, is shown in Fig. 46; it is quite evidently different
from that shown in Fig. 24, which was for an air-core inductance.
Fig. 46. Peculiar growth of current when an iron core inductance is switched to a
source of continuous e.m.f.
Current Flow in a Condenser.—By the definition of a condenser no
electrons can actually pass from one plate to the other; they are insulated
from one another. If, however, a condenser is connected to a source of
66 FUNDAMENTAL IDEAS AND LAWS [Chap. I
*
alternating e.m.f., current will flow in this circuit, as may be seen by the
reading of an a.c. ammeter placed in series with the condenser.
Suppose a condenser of capacity C farads is connected to a line the
e.m.f. of which is given by the equation e = E sin tot. The condenser will,
of course, take enough charge to bring the potential difference of its plates
continually equal to that of the line to which it is connected. As this
impressed e.m.f. continually varies in magnitude and direction, electrons
must be continually running in and out of the condenser to maintain its
plates at the proper potential difference. This continual charging and
discharging of the condenser constitutes the current read by the ammeter.
The electrons, the motion of which constitutes the current, do not actually
pass from one plate of the condenser to the other through the dielectric;
Fiq. 47.—Current and voltage for a perfect condenser connected to an a.c. line.
they merely flow in and out of the condenser. With this idea in mind
it is easy to see why the changing current of a condenser increases with
the capacity of the condenser, also with the frequency of the impressed
e.m.f.
The magnitude of the charging current is obtained as follows:
The charge q = Ce and the current i = dq/dt.
Now q = CEm sin tit,
so
i=«C Em cos tit (28)
This current is then of the same form as the impressed e.m.f. (a cosine
curve is similar to a sine curve in form) but leads it by 90° as shown in
Fig. 47; its maximum value, in amperes, is equal to uCEm.
In effective values the relation between the impressed voltage and
the charging current is,
I = tiCE = 2*fCE
CIRCUITS CONTAINING RESISTANCE AND CAPACITY 57
It is evident that, other things being equal, the charging current of a con
denser is directly porportional to the frequency of the impressed e.m.f.
This should be contrasted to the inductive circuit in which the current
varies inversely as the frequency, if the resistance is small compared to
the reactance.
The relation between the current and voltage may be written
M+5k (30)
The impressed voltage must be the sum of the drop over the resistance
and that over the condenser and is so shown in Fig. 48. The current leads
the impressed voltage by the angle <j>, the magnitude of which is fixed by
the relative magnitudes of the reactance and resistance drops.
The three curves of Fig. 48 are shown vectorially in Fig. 49, effective
values being used instead of maximum values. From this vector diagram
we have
*2=<7*>2+(i)2'
or
'•' | (3D
and
^♦-T-OT (32)
58 FUNDAMENTAL IDEAS AND LAWS [Chap. I
The current in the circuit, as shown in Eq. 31, evidently depends upon
the frequency; its variation as the frequency is changed, is shown in Fig.
50. At very high frequency the current approaches the value E/R, the
Fig. 48.—Voltages and current curves for circuit containing R and C, in series.
capacity reactance being negligible, while at zero frequency, the current
is zero, the condenser being equivalent to an open circuit.
Transient Current in a Circuit Consisting of Resistance and Condenser
in Series.—In general there will be a transient current when switching
0 ri such a circuit to an a.c. line;
' ^ " the duration of the transient
term is so short, however, on
all commercial circuits that an
oscillogram shows the current
hC
rising immediately to its proper
value, this being fixed by the
time on the e.m.f. cycle that the
switch is closed.
Current Flow in a Circuit
Having Resistance, Inductance,
Fig. 49.-Vector diagram of voltages and 811(1 CaPacity m Series.—The
current for circuit containing R and C current flowing in the circuit
shown in Fig. 51 will require
three components of e.m.f., the resistance drop IR, the inductance
drop 2irfLI, and the capacity drop The resistance drop is in
phase with the current, the inductance drop is 90° ahead of the current
EFFECT OF FREQUENCY IN CONDENSIVE CIRCUIT 59
>o,LI
and the capacity drop is 90° behind the current. These three compo
nents of the impressed e.m.f. are shown vectorially in Fig. 52. The two
reactance drops evidently tend to neutralize one another.
The total reactance drop
-2"'"-2^ (33)
E=I^R*+(2«fL-J^)2 (34)
/- , = . i -I (35)
\2 &
/i\
1 ' 1 —*I
' I I
1 ' * i
I
Is
4
E = 100 L = 0.10
R = 18 C = 25.3 x 10
3
>r
20 40 60 80100 120 140 160 180 200 220
Frequency
Fro. 53.—Variation of current with frequency in circuit containing R, L, and C in
(37)
2wfCR
2t/L = ; 1
2*fC
/= \= (38)
>
In this equation L must be in henries, C in farads, and / will be in cycles
per second. As the microfarad is the usual unit of capacity a more con
venient form is
(39)
2WLC
i
C being in microfarads. In determining this frequency the separate values
of L and C do not matter; the product LC is the quantity which fixes
the critical frequency. This is a circuit having L=.24 henry and C =
10 microfarads will be resonant at. the same frequency as one which has
L=.06 henry and C = 40 microfarads.
The sharpness of the resonance curve is determined by the resistance
of the circuit, the less the resistance the more sharply denned is the resonant
frequency and the larger is the current at the resonant frequency. In
Fig. 54 are shown the resonance curves obtained for a circuit having L =
.15 henry and C = 28.5 microfarads. The one curve shows the variation
of current with a circuit resistance of 5.8 ohms and the other shows the .
same thing after the resistance had been increased to 17.2 ohms.
In a low resistance circuit the resonance is said to be sharp and in
a high resistance eircuit it is said to be flat or dull.
Series Resonance with Varying Capacity — Decrement.—If the fre
quency impressed on the circuit of Fig. 51 is held constant and the capac
ity or inductance varied, resonance curves similar to those in Fig. 53
will be obtained except the variables will be different. Suppose such a
curve has been obtained, as shown in Fig. 55. We shall now show how
the shape of the curve depends upon the resistance and how to actually
calculate the value of this resistance from the shape of the curve, provided
that the value of L is known.
The quantity which is actually determined from the resonance curve
is . the ratio R/2/L, f being the resonance frequency of the circuit. This
FORM OF RESONANCE CURVE 63
ratio is called the decrement of the circuit, for reasons which will be
apparent when the subject of oscillations is discussed.
Referring to Fig. 55, let C, be the capacity which gives resonance, the
current for this value of capacity being I,. Let C\ and C2 be the two
values of capacity, one greater than Cr and the other less than Cr, which
serve to reduce the current to 7r-r- V2 or .707 7r. When the capacity has
the value CT there is no effective reactance in the circuit, so we have,
E
For C = C„ Jr=£.
E
For C=C2, /= = .707 7,
1 •
I
/ \
1 ?_ EXPERIMENTAL
@J rc \ RESONANCE OURVES
IB / \
E = M volt* / \
/ \
L = M ha m
C = H. 1 1 1 r far.
50 70 80 90 100
Frequency
Fig. 54.—Effect of resistance on resonance curve,
which can be true only on condition that X2 = R, or
(40)
For C = Ci,
E
= .707 IT
VW+X2
which can be true only if
X,-* or -(2JL+^=R (41)
64 FUNDAMENTAL IDEAS AND LAWS [Chap. I
Oi Cf ct
Capacity
Fiq. 55.—Variation of current with capacity in a resonant circuit.
Now if C2 and C\ do not differ from C, very much (say 10 per cent) we
may put without appreciable error
C2Ci = Cr2 (44)
This is, of course, an approximation, and is more nearly true the sharper
the resonance curve. We may now put,
1 (CrzCxj 2R_
/■1
2rVLC,'
C, being the "value of the capacity which gives resonance.
DECREMENT FROM FORM OF RESONANCE CURVE 65
So (45) becomes,
C2 — Ci 2R
Cr 2xJL
R r C2—C1 (46)
2fL~2 Cr "
As an illustration of the application of this formula suppose that the
resonant capacity for a certain circuit is 32 microfarads and that the values
of C2 and Ci are 34 microfarads and 30.2 microfarads respectively. Then
for this circuit the decrement, generally designated by the Greek letter
t, is
, R =T 34-30.2
= 0.187
2/L 2 32
The decrement may also be calculated from a resonance curve plotted
with frequencies as abcissse as given in Fig. 56; we have derived the
formula when capaci
ty is used for abscissa?
because such is gen
erally the case in ra
dio measurements. If
however, frequency,
is used as abscissae,
the frequency having
been varied in getting
the resonance curve,
L and C having been
maintained constant,
the derivation of 8
from the half energy /, /, /,
points of the resonance Frequency
curve is as follows: Fig 56_—Variation of current with frequency in a refeonant
circuit.
1
2tt/iL- = -R
2a/iC
2wf2L- =R
2irf2C
To eliminate C from these two equations, multiply them by 2tt/iC and
2t/2C respectively and get the two equations
(2wfi)2LC-l = -R2TrfiC
(2wf2)2LC-l = R2wf2C
66 FUNDAMENTAL IDEAS AND LAWS [Chap. I
1 C2-Ci
For a given circuit ^2 . — is approximately equal to - <"2„ — . This
/r * Lr
follows from the relation between frequency and capacity; to pro
duce a certain small percentage change in the natural frequency of a cir
cuit it is necessary to change the capacity of the circuit by twice this
amount, the frequency varying not with the capacity, but with the square
root of the capacity.
Flow of Current in Parallel Circuits and Relation of Line Current to
Branch Currents.—When a circuit consists of two or more branches in
parallel the line current cannot be obtained by calculating the branch
currents and adding them arithmetically as is done in continuous current
circuits, because of the difference in phase of the various branch currents.
The line current, instead of being equal to the arithmetical sum of the
branch currents, may be even smaller than either of the branch currents
and, in fact, is so in
I. many radio circuits. It
is necessary to calculate
>3.67 ohms not only the magnitude
of the different branch
e~Emsln at * 11 ohms currents, but also their
phase; these branch
0 ii microfarads currents are then added
veciorially to give the
line current.
Suppose a circuit
Fig. 57.—Parallel circuits. made up as shown in
Fig. 57, the current Ii
being 10 amperes, in phase with the line voltage and the current I2 being 15
amperes, leading the line voltage by 60°; the line current will be the
CURRENT WITH PARALLEL CIRCUITS 67
Pro. 58.—Vector diagram of currents in the parallel circuit shown in Fig. 57.
In case the branched circuit is more complex than that given in Fig.
57, such as that given in Fig. 60, the branched part must first be replaced
by its equivalent single circuit, calculated as shown for Fig. 57 ; the resist
ance and reactance of this equivalent
~) circuit must then be added to the
<R= „~. ..
3.02 ohra» resistance and reactance .....
of Ri and
In- By vectonally combining this
total resistance and reactance the im
pedance of the simple equivalent cir-
Bkrotodi curt is obtained.
Fig. 59.-Simple series circuit equivalent t Impedance of a Circuit Made Up
to parallel circuit of Fig. 57. of L« R> 811(1 C» m Series.—The
reactance of this circuit is calculated
by finding the sum of the inductance
and capacity reactances at all the frequencies necessary; the equivalent
resistance of this circuit is independent of frequency and equal at all
frequencies to the actual resistance, R. The several quantities are shown
in the form of curves in Fig. 61. The reactance, , is shown negative;
the total reactance, X, is negative at frequencies lower than the resonant
value and positive above this value. The impedance is positive for all
values of frequency, having its
minimum value when the total
reactance X, is zero, then being |
equal to R.
The current leads the volt
e = Emsio cot.
age for frequencies lower than
the resonant value and lags J ^Ri
behind the voltage for higher
frequencies.
Impedance of a Branched
Circuit, Having L and R in L '
One Branch and C and R in F10- 60.—Series-Multiple circuit,
the Other.—The simplest way
of comprehending the impedance of this complex path, Fig. 62, is to calcu
late for each value of frequency, the magnitude and phase of the current
in each branch. The active and reactive components of the two branch
currents are then calculated. The active component of line current is
found by adding the two active branch currents and the reactive com
ponent of the line current is found by adding the reactive branch
currents. These additions are to be algebraic; in the case of the active
current the algebraic sum is the arithmetic sum but the reactive current
in the line is the difference of the reactive currents of the branches.
REACTANCE AND IMPEDANCE FOR SERIES CIRCUIT 69
In Fig. 63 is shown the vector diagram for frequency above the reso
nant frequency of the circuit; the line current in this case leads the voltage
by the capacity branch ; the equivalent simple circuit for this case would
consist of a resistance in series with an inductance.
The above simple analysis shows that the branched circuit of Fig. 62
may be represented by a single circuit, but the constants of this simple
circuit must be made to vary as the frequency is varied.
The equivalent R may be obtained by calculating the PR loss in each
branch and adding to give the total loss in the circuit; this total loss,
In case the line current is leading sin <t> is negative and the equivalent
inductance would be negative. In this case the reactive component of
the impressed voltage, E sin <j>, is put equal to > where C is the
equivalent series capacity of the circuit.
The circuit is analyzed exactly most easily by the use of complex alge
bra, a method of treatment explained in all standard texts on alternating
currents.
Hence
Z=
,J__L
RcRl{Rc+Rl) + Rv(uL) 2 + Rlt^,,2 +j \ Rc2uL - RL2
wC C
So
RcRl(Rc+Rl) + Rc(uL)2+Rl-, 1
*— ,— (48)
m
(RL+Rc)a+LL-±)
R2j+{m2-\)2
L'=-L ~ -, (51)
m2R2j+(m2-\)2
The resistance will not be the same when measured between points
C-D as it is for the points A-B. It may be proved that the resistance
between any two points in the circuit is nearly proportional to the square
of the reactance included between the two points, in either branch. The
reactance in each branch of the parallel circuit will be the same, no matter
where the two points are taken, but the reactance will be inductive in one
branch and capacitive in the other.
Fig. 67 illustrates another combination of inductance and condensers;
such a circuit is used in one of the common forms of radio telephone appa
ratus. The frequency of current in the closed circuit is fixed by the reso-
1 , C1C2
nant period of this circuit, that is /= where C = The
2WLC " C1+C2
alternating current supply for the circuit is furnished across the condenser
C,
A
Ci
B
Fig. 66. Fiu. 67.
Fig. 66.—Resonant multiple circuit.
Fig. 67.—Resonant multiple circuit used in a radio-telephone set.
Ci, and the power factor of this circuit (i.e., between points A and B)
is unity; the impedance offered to the supply circuit is resistance only. If
the point B is moved around the circuit so as to include part of the induct
ance L in either path, as shown at B', the impedance between the two
points A and B' would still be resistance only.
It is often desired in radio circuits to alter the impedance of the cir
cuit to which the power is supplied. Thus in certain vacuum-tube cir
cuits a resonant circuit (as shown in Fig. 67) is used as load for the tube
output and, to get the maximum output from the tube, the circuit must
offer resistance only (no reactance), and this resistance must have a proper
value. Evidently such a circuit as that shown in Fig. 67 offers such pos
sibility; by properly adjusting the position of B' the desired resistance will
be obtained.
74 FUNDAMENTAL IDEAS AND LAWS (Chap I
S
o
a>
I
o
76 FUNDAMENTAL IDEAS AND LAWS [Chap. I
pacity were connected in parallel and the impressed frequency was varied
until the line current showed a minimum value. The form and phase of
the currents in the two branches of the circuit are shown well on the film,
and it is at once evident that the great difference in form of the two cur
rents would prevent the resonance phenomena being very marked. Prob
ably 50 per cent of the current flowing in the condenser circuit is of some
frequency much higher than that for which the circuit was resonant and
at least this much current would persist in the supply line no matter how
carefully the circuit was adjusted for resonance.
56 80 66 70 75
Frequency
Fig. 70.—Reactance and resistance curves for a parallel resonant circuit having low
resistance.
65 70
Frequency
Fig. 71.—Effect of increasing the resistance in a parallel resonant circuit; compare
with curves of Fig. 70.
A rather extraordinary effect is seen in these curves; the equivalent
series resistance at resonance is higher the lower the actual resistance of
the circuit. Thus in the first case where the actual resistance was 6 ohms
the equivalent resistance has a maximum value of 320 ohms; in the second
case where the actual resistance has been increased to 16 ohms the maxi
mum value of ft is only 240 ohms. In neither case is the equivalent
resistance nearly as great as calculation by Eqs. (48) and (49) would indi
cate; the reason for this discrepancy lies in the method of measurement
which involves an error depending upon the non-sinusoidal form of the
voltage impressed on the circuit as outlined above.
78 FUNDAMENTAL IDEAS AND LAWS [Chap. I
It will be noticed from the curves given in Figs. 70 and 71 that the
effective inductance of a coil may be increased by putting a condenser
in parallel with the coil; the equivalent resistance of the coil also increases
and this increase rapidly grows larger as the amount of capacity shunting
the coil is increased.
For the frequencies far removed from the resonant frequency of the
circuit ^so that (m2— 1) is large compared to m2R2-^j we get rather simple
formulae for the equivalent inductance and resistance of the coil. Formulae
(50) and (51) in this case reduce to the forms
, *'=(^IF ■ • • <52)
L'=^i <w
IC
that is,
(L
By inserting this condition in Eqs. (48) and (49) it will be found that the
reactance of the circuit is zero for all frequencies and that the resistance is
constant for all frequencies and equal to the resistance of each path.
Resonant Frequency of Parallel Circuits.—If we define the resonant
frequency of a parallel circuit as that frequency which makes the reactance
of the circuit zero, thus making the power factor of the circuit unity, we
find the resonant frequency by using Eq. (49), putting the numerator
equal to zero. This gives the equation
or
1/L R,\_V
«Li/i-^+toilf(/1-/2) = 0, . . . . . (59
and
0L2I2 —^r+oiM(I2-h = 0 (60)
C0C2
For the circuit shown in Fig. 73 we may put L„+ L&= L3 and Lc+La=
the reactive voltages for these circuits then become,
co(Li+M)7i—^—cojl/72 = 0, (63)
coCi
and
w{L2+M)I2 —%— <iMh = 0 (64)
COL 2
By collecting terms these may be changed into the forms,
coLi71-^+coM(71-72) = 0, (65)
and
wUh-^-+<*M(h-h)=<) (66)
But these equations, which are for an inductively coupled circuit, are
identical with Eqs. (59) and (60), which are for the directly ocupled
circuit.
The author does not believe that this method is as satisfactory a one
as that using transformed L and C in the secondary because of certain
ambiguities which may arise. As an illustration of the cases in which
the method works out all right we take Fig. 78. For the Li of Fig. 72
we must put 0.2 — 0.1=0.1 henry and for L2 of Fig. 72 we put 0.4 — 0.1 =
0.3 henry. M, Ci and C2 remain as in Fig. 78. The equivalent directly
coupled circuit is given in Fig. 79; it is electrically equivalent to Fig. 78.
1 See Bulletin 74 of the Bureau of Standards, p. 50.
CAPACITIVE COUPLING 83
5?f
Fig. 78. Fig. 79.
Fig. 78.—Inductively coupled circuit.
Fig. 79.—Direct-coupled circuit equivalent to circuit of Fig. 78.
For the circuit shown in Fig. 74, we get the coupling coefficient from
Eq. (56) in the following manner.1
1
Capacity reactance of circuit 1 =
in which
Cl Cm
(68)
V(C1+C3)(C2+C3)'
in which
C'C"
C3 ='C'+C'r
-
Mi.
h-3 =
A/3-4
fc3-2 =
VL4(L2+L3)'
Then
M1-2XM3-
fci -2 = fci -3 X ka -2 = . . (69)
(L2+L3WUU
1 In case it is not evident just what the mutual reactance of the two circuits is it
may be obtained by calculating the voltage generated in circuit 2 when a current of
one ampere is flowing in circuit 1, or vice versa. This voltage is equal to the mutual
reactance, in ohms.
EFFECT OF NEIGHBORING CIRCUIT ON RESONANCE CURVE 85
fa cos Q = —-Y.—.
£12 62
The voltage induced in circuit 1 by this current is
As this voltage lags 90° behind the inducing current fa cos 8 and as fa cos 8
lags 90° behind fa this voltage (^^j ^2 is 180°.behind fa and so is an IR
R'i = Ri +
Now the reactive current in circuit 2 is fa sin 8, and this current lags
90° behind E2, which itself lags 90° behind fa. The voltage induced in
circuit 1 by this current fa sin 8 will be equal to uMfa sin 8, and this
will lag 90° behind the inducing current fa sin 8, and hence will lag 270°
behind fa, that is it leads fa by 90°.
Now the reactive voltage in circuit 1 due to L\ is 90° behind the cur
rent fa- This may seem incorrect at first glance, because it makes the
current fa lead the reactive voltage by 90°, whereas we know that an
inductive circuit draws a lagging current. It must be remembered that
the component of the impressed voltage which overcomes the reacting
voltage of the circuit must be 180° ahead of the reacting voltage itself;
this makes the current in an inductive circuit lag behind the impressed
voltage, as it should.
It appears then that the voltage induced in circuit 1 by the current
fa sin 8 is 180° out of phase with the reactive voltage in circuit 1 due to
Li of circuit 1, hence the total reactive voltage of circuit 1 will be less
when circuit 2 is present than when it is not present.
The amount of voltage induced in circuit 1 by fa sin 8 is aiMfa sin 8
and this is equal to (^~*J
So the total reactive voltage in circuit 1 when a current of one ampere
is flowing is
a,Li ~ (~Jr) »u = w(Li ~ (W) 2lz) -
RESISTANCE AND REACTANCE OF COUPLED CIRCUITS 87
L\-I*-(*j£)%U (74)
<=i M
||C
Fig. 84.—Inductively coupled cir- £/j = ]J1— (<^M\
cuits with a condenser in the 1 1 \Z2J '
primary.
EuM (78)
J (u>M)2+ R1R2 - <*U L,Li—~j j 2 + + R2 (uLi - -^j j '
h= (83)
RiV2(Z22+R2Z2)'
is seen that the adjustments for maximum power of this circuit are not
very critical.
The resonance curve for such a circuit as that shown in Fig. 84 differs
from the curve of the primary alone in that the critical frequency is higher
and the resonance curve is not so sharp. The resistance of circuit 1 is in
creased by the amount given in Eq. (73) and the inductance is decreased by
the amount shown in Eq. (74). Fig. 87 shows the resonance curve of a cir
cuit arranged like that of Fig. 84; in dotted lines is shown the resonance
curve of the primary without the presence of the secondary. The same
1 1 1 1 1 1 1 1 1
II > J
M
/■ ■ Ri f T
/ \
11
to 1
\ A = Circ lit 2 open
I B -c ire Lit 2 ,-lr i R,- 8.0
1 C " " R»- 20.
1 \\
/ ^ «
3.0 \ / \ L , =14 L =• 11
/ \ / \
\ C, =28.6 X 1( *
f ) R .- 1 5 M =. 066
/1 h \
1 / \ s
/ V \ s
/ 1 // s\ \
// \ \^ s
/ // s
/ //
-- -
68 70 72 74 76 78
82 84 86 88 90 92 94 96 80
Frequency
Fig. 88.—Current vs. frequency in circuit of Fig. 84 with added secondary resistance.
voltage was applied to the primary circuit in getting the two sets of curves,
hence the magnitudes of current for the two curves give an exact measure
of the effect of the secondary circuit upon the first. The calculated R'
and U of the primary, using first the experimental data on the curve sheet
of Fig. 87 and then Eqs. (73) and (74) agree within the precision of the
experimental work.
The resistance of the secondary circuit was then increased by 12 ohms
and another resonance curve taken; the results are shown in Fig. 88;
the curves of Fig. 87 are shown in dotted lines for comparison. It is seen
that the addition of resistance to the secondary circuit makes the sharp
REACTANCE AND RESISTANCE OF COUPLED CIRCUITS 91
ness of resonance less and the effect of the secondary in determining the
resonant frequency of the primary is somewhat less than for the lower
resistance secondary circuit.
We will next consider the circuit shown in Fig. 89; the condenser is now
in the secondary circuit instead of the primary.
In this circuit the resistance of the primary is always increased by
the presence of the secondary, but the effect upon the inductance depends
upon the frequency impressed on the primary circuit. If the fre
quency is such as to satisfy the condition for resonance in the secondary
(f= ^y/L c ) ' *ne aPParen* inductance of circuit 1 will be the same as
the actual inductance, that is, the presence of circuit 2 does not affect the
inductance of circuit 1. With higher
than resonant frequency the appar I—WW vww—1
ent inductance of circuit 1 is decreased
by circuit 2 and with lower fre
quency the inductance of circuit 1 is
increased . In other words, if I2 lags 1
behind E2, the effect on circuit 1 is Fig. 89.—Inductively coupled circuit
to reduce the apparent inductance, with condenser in secondary.
whereas if the current in circuit 2
leads the generated voltage in this circuit, the effect on circuit 1 is to
cause an increase in the apparent inductance.
Applying Eqs. (73) and (74) to the circuit of Fig. 89 we get,
R'x = Ri + ) (84)
(85)
in which
<oZ/2 —4r)
C0C2/
It is seen that if is greater than L2, Li is greater than L\\ if
co2C2
1
L'i = L\\ if L2 is greater than then L'i is less than L\.
«2C2
Using the constants given in Eqs. (84) and (85) we can write at once
h . (86)
E01M
(87)
»]*^h(f)Vi)]i
92 FUNDAMENTAL IDEAS AND LAWS [Chap. I
%noqi3 A"q aq^ uoi%ve jo aq^ ^uaijno ui ^mojp !g A"aqi aaaM pauiuuaqap tq
8urpBJ}qns uiojj aq^ lua-reddB aou^sisaj pire aouB^OBaj jo ^truwp x aq^
sarqsA jo asaqi satipuBnb naqM aq^ jtrepuooas imajp sbai •nado
a •a
MAAM
y jasop Apn%s jo asaq} saAjno jjiav aq q;aoA\ ajiqM oaqM SuizAprat? aqq.
corps jo ure^iaa Sui^fpso aqm 'siirmp uy ^uptqjpso aqn^ Avw asnjaj
uoipunj ji aqi aoui^sisai jo aq^ ^inojp qoiqAV 11 si pa^oauuoa si oo^
qSJiq pus ^i jjia\ aq punoj ^Bqi b aqn^ Avw aq opuui do^s Sui^tqipso Xq
Suiting o} sji ijnojp jaq^ouB ^mojio pajdnoo -ji aqj^ uosBaa si aq
94 FUNDAMENTAL IDEAS AND LAWS [Chap. I
found in the extra value of the resistance added to the oscillating circuit
by the second circuit when
this second circuit is brought
into resonance with the tube
circuit.
We next consider the more
general case of two coupled
circuits, each of which has
, , ,, , . . , . , inductance, capacity, and
iio. 92.—General case of inductively coupled . , 7 ,. ' .
circuits resistance, as indicated in
Fig. 92. The resistance and
inductance of circuit 1 are obtained from Eqs. (73) and (74), as before.
R\=Ri+(^)2R2 (90)
(91)
Then we have,
E
(92)
f. (93)
'hich
in which •
Z2 = ^+(«L2-^)2
Li- (94)
co2Ci V z2
RESONANT FREQUENCIES OF COUPLED CIRCUITS 95
The two solutions for to, which we call to' and to", are
,_ L2+to22-V(lo72-to22)2-|-4A;2to,W
(97)
« -\ - 2(ra2) '
and
«1 2 + "22 + V(tO, 2 - t022) 2 +4A2«1 21022
(98)
2(1 — A;2) * * '
When k is large (approximately unity) the values of to' and to" are nearly
toi2to22
/t0!2 + t022'
and
^->/!w (100)
96 FUNDAMENTAL IDEAS AND LAWS [Chap. I
When k is small the values of co' and co" approach the limits
, C02
CO = (101)
Vl-k2'
and
(102)
vr^p'
In Fig. 93 are shown the relations between co' and co" and k; for small
values of k Eqs. (101) and (102) determine the values and for the large
values of k Eqs. (99) and (100) are used.
In radio operation it is the practice to tune the primary and secondary
circuits, that is, adjustments are made to make coi equal to C02. In this
case Eqs. (97) and (98) reduce to the very simple forms
co = (103)
and
(104)
in which co = coi = C02.
The curves of variation in co' and co" as the coupling is varied for this
case of tuned circuits are shown in Fig. 94. It is seen that for weak cou
pling both co' and co" approach co, the natural frequency of each circuit ; how
ever, it has been pointed out that the neglect of R2 in obtaining the solu
tions of the resonant frequencies that the values of co' and co" do not hold
good when they have values in the vicinity of the natural frequency of
RESONANCE IN COUPLED CIRCUITS 97
the secondary circuit. Hence we can now see that for weak couplings the
solutions for a>' and w" do not hold good.
Referring to Eq. (93) it is seen that h = h"^, and hence in so far as
the factor -=- is independent of the frequency changes, I2 will have maxi-
Z2
mum values at the same frequencies as give maxima for h. However, the
factor is not independent of the frequency, and this is especially so
111 the region of frequency fixed by the relation (a>I/2 \r \ = 0; f°r f1^"
quencies less than this the value of %r~ increases with the frequency and
Z2
COAT
for values of frequency higher, the value of -=- - decreases with an increase
Z2
of frequency.
We can then conclude that, for frequencies in the region of
VL2C2
Eqs. (103) and (104), while incorrect for primary current maxima, are
still more incorrect for the maxima of secondary current. In consequence
of the changes in the value of noted above, we may predict that when
to' and to" are not in the region of u>2 the calculated values of J and o>"
will be more accurate for the primary than for the secondary circuit, and
that the actual value of o' of the secondary circuit will be somewhat
98 FUNDAMENTAL IDEAS AND LAWS [Chap. I
higher than that for the primary and that the actual value of co" for the
secondary will be somewhat lower than to" for the primary current.
The general form of the resonance curve of the circuit shown in Fig.
92 is indicated in Fig. 95; the dotted curve shows the resonance for one
circuit by itself.
The value of the coefficient of coupling can be calculated from the
spacing of the resonance peaks of the current curves; thus from Eqs.
(103) and (104) we get the relation
1+k'
from which there is obtained
o"2-co'2
(105)
co"2 + co'/2"
Frequency
Fig. 96.—Experimental resonance curve for single circuit.
In case the resonance frequency of one circuit by itself is known, and
assuming tuned circuits, the equation for coupling value becomes more
simple in form, giving the closely approximate value
(106)
to being the frequency of one circuit by itself.
In the foregoing discussion of resonant frequencies formula? have been
derived using co for frequency; it is of course to be remembered that co is
RESONANCE CURVES OF COUPLED CIRCUITS 99
not frequency, but 2ir times the frequency. The value of to has been used
rather than frequency itself to save the repeated writing of the quantity
2t throughout all the derivations.
In Figs. 96 to 103 are shown some experimental curves of resonance
in coupled circuits for different conditions as regards coupling, resistances,
tuning, etc. ; Fig. 96 shows the resonance curve for a single circuit having
L = 0.140 henry, C = 28.9 microfarads, and 72 = 4.50 ohms.
Fig. 97 shows the resonance curves for two coupled circuits, each cir
cuit had the same constants as those given for Fig. 96; the coefficient of
coupling was 0.36. The curve of primary current is shown by the full
line and that for the secondary circuit by the dotted line. The two reso-
Fig. 97.—Resonance curve for coupled circuits; each circuit having constants as in
Fig. 96.
nant frequencies check with those calculated from Eqs. (103) and (104)
within the precision of the test.
In Figs. 98 and 99 are shown curves of current for the same two cir
cuits as those used in Fig. 97 but with different values of coupling, this
being 0.18 for Fig. 98 and 0.07 for Fig. 99. It may be seen that with
small values of coupling the two frequencies merge into one another and
Eqs. (103) and (104) do not predict accurately the resonant frequencies
of the primary circuit and for reasons noted in the derivation of the formulae ;
the predicted values of to' and to" for the secondary circuit differ from the
actual values more than do those of the primary circuit.
A peculiarity of all these resonance curves is seen in the relative values
of the primary and secondary currents; between the two resonant fre
100 FUNDAMENTAL IDEAS AND LAWS [Chap. I
quencies the secondary circuit carries a greater current than the primary
but for all other frequencies the primary carries a greater current. If
a weaker coupling than that used in the adjustments for Fig. 99 had been
i 1 1 1 1 M 1 1 1 1 1 I 1 M 1
L.= L.= .140 C.= C = 28.9x 10"" R,= R.,= 4.50 E = 20 volts K = .18
1
L
17 c, "'3 ■
Li—1{ 1
\\
<y i
i/' i, i
n < '
I \V I 1/ / /
> V
-ii i, >v A\
ii \
i \
i1
>i *
■r -- m>
■Frequency
Fig. 98.—Resonance curves for circuit as shown in Fig. 97, fc=0.18.
used it would have been found that the primary current was greater than
the secondary current for all values of frequency.
In Fig. 100 is shown the result of increasing the resistance of the
secondary circuit from 4.5 to 9.7 ohms; with this exception the circuits
RESONANCE CURVES OF COUPLED CIRCUITS 101
were exactly the same as those used for Fig. 97. By comparison of the
two sets of curves it will be seen that the two resonant frequencies are,
within the precision of measurements, the same for the two conditions;
the value of the current at resonance is, however, decreased in nearly the
proportion predicted from the value of resistance, calculated from Eq.
(90). The decrease in current, it will be noted, takes place in both cir
cuits although the resistance of the secondary circuit only was increased.
The resonance is much less marked than for the lower resistance used
in Fig. 97.
Form of Resonance Curve.—The form of the resonance peaks is deter
mined by the combined decrements of both circuits. For the simplest
Fig. 100.—Resonance curves for circuit shown in Fig.97 with added secondary resistance.
case, that of tuned circuits, it will be found that the decrements will be
nearly given by the approximate formulae:
For the frequency to'
(107)
2V1+A;'
and for the frequency u"
= h + 52
(108)
in which 5i and 82 are the decrements of circuits 1 and 2 when not affected
by other circuits.
The decrements 5' and 5", calculated from the shape of the curves of
Figs. 97 and 98 by use of Eq. (47) check with the values given by Eqs.
201 ivxNaivvaNiLJ svaai qnv smvi
(ZOl) Pub (80T) Xjjiraj Ijpjtt %\ si oiqraaopou ys\\\ ui flra aq; saAjno uo.uS
aqi qipiM jo aqi aourauosaj aAjno si ja^raajS joj aqi jaq9iq Xonanbajj treqi
1 1 1 1 1 1 1 II II 1 1 1 1 II 1 1 M TI 1 1
0 ='a ii = 0Tt 0 01 _l- 3 = 0B sjto.v
—1—l—VW l_iVW\— /
'a / \
OX TL i '"I ' Is-.
n—"v1 i
*/ I11
3 /
0S!» t
/t
\
// \\
1;
01 / \
t' T— — .~ -I
1 1 1 II 1 1 1 1 1 1 1 II 1 1 1 II 1 1 1 1 1 1 1 L!
Of otr=*n='n a='a c o = „01*6-8? ="0 lit Z * 01 „ sjio.\(b=3 X = 96'
I \
/
r im 5 /
08 ya /
£ ) I
IU-, , , /
— / / \
roe // \\
\ :i
/
^\
01 \ N '1*
/ \l >
/ ~> s
—
jJlM »8098 9 111 i 1 9 i 08 8 t o i 06 1 j g !0OT> f o Oils ?. » o s »OSI 1
Circuits not Tuned.—In Figs. 101 and 102 are shown the resonance
curves for two circuits which are not tuned, that is, u\ is not equal
to a)2. For this condition the curves are not as symmetrical as for
the tuned condition, and the currents in the two circuits are no longer
nearly equal to each other at the two resonant frequencies. At one
resonant frequency the primary circuit carries more current than the
secondary and at the other frequency the reverse is true. The dif
ference in the two currents is greater the greater the difference in the
1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1
1 J Fi L. R
■
k :
—
II u■ : c
i
11,1.
L, = U=.140 R, = R,=7.20
C ,=C,=38.6x NT4
/
/r
J
/
J/
.04 .06 .08 .10 At .14 .16 .18 .20 22 .24 .26 . 28 .30 .32 .34 .36
Coefficient of Coupling
Fiq. 103.—Secondary current vs. coefficient of coupling in tuned coupled circuits.
natural peroids of the two circuits. For Fig. 101 the natural fre
quency of circuit 2 is 15 per cent lower than that of circuit 1, and for
Fig. 102 circuit 2 has a natural frequency 29 per cent lower than that
of circuit 1.
Variation of Coupling with Tuned Circuits.—In Fig. 103 is shown
the effect of varying the coupling between circuits 1 and 2, they being
tuned alike. A constant e.m.f. was impressed on circuit 1 and the
coupling of the two circuits was gradually increased from zero to the
maximum obtainable. It might seem at first sight that the secondary
current would be greater the greater the coupling, as would occur in
ordinary transformer tests, but with tuned circuits as used in radio
this is not the case. For a given resistance of circuits there will be
104 FUNDAMENTAL IDEAS AND LAWS [Chap. I
a certain coupling which gives the greatest secondary current and the
lower the resistance of the circuits the less this critical value of coupling
will be.
This might be predicted from Eq. (93) by differentiating I2 with
respect to M; it will be found that with tuned circuits having impressed
on the primary a voltage of the same frequency as that for which the cir
cuits are tuned, a certain value of M will produce a maximum secondary
current and this value of M will depend upon the resistances in the two
circuits. This condition for maximum secondary current proves to be
fixed by the relation,
w2M2 = RiR2 (109)
The curves of Fig. 104 were taken with the idea of proving this relation
and also to show the effect of the secondary resistance on the sensitive
ness of the adjustment for maximum secondary current. If the two cir
cuits are tuned alike and the frequency of the e.m.f. impressed on the pri
mary is the same as the natural frequency of either circuit the values of
the primary and secondary current may be obtained by simplifying Ecfs.
(92) and (93) and are found to be
ER2
Zi = (110)
RiR2+o>2M2
CIRCUITS WITH CAPACITIVE COUPLING 105
and
j _ EwM
The experimental curves given in Fig. 104 follow the values predicted
from Eqs. (110) and (111) within the precision of measurement, that is,
within less than 1 per cent.
Resonance in Circuits with Capacitive Coupling.—The equations for
h and I? are obtained for this case in a fashion exactly the same as that
used for the magnetic coupling, and the conclusions reached are nearly
the same. Using &>i, 02 and k in the same sense as for the magnetically
coupled circuits we get for the two resonant frequencies of the combi
nation
4 2 .... (ii*)
■4
In applying these formuhe the values of coi and &>2 must be calculated in
a somewhat different manner than was used for the magnetically coupled
circuits. It will be remembered that for magnetic coupling these two
frequencies were fixed by the L and C of the circuit in question and were
independent of the constants of the other circuit and of the coupling used.
Such is not the case for
capacitive coupling, how
ever. The frequencies
ui and o>2 depend upon
the capacity used in the
other circuit and upon
the coupling in the fol
lowing manner.
In Fig. 105 the fre
quency on is fixed by Li Fig. 105.—Capacitively coupled circuits.
and by the capacity C\
in parallel with C3 and C2 in series. Thus wi may be varied by changing
either the coupling condenser C3, or the capacity of the second circuit C2.
Hence we have the formulae
■ (H4)
C2+C3/
901 ivxMawvaNiii svaai qnv smvt JVHO] I
PUB
(SIT)
. (w+'3)f
.v = / — — -_ • (9IT)
uj Sij qq\ airs UAvoqs aq^ aoireuosai saAina joj rs uoiretnquioo jo -aro
s^ino AjJijau a>jq req^ nAvoqs hi '^ij 'goi aq} Suqdnoa jasuapuoo si3A\ m
oml% s^juđ sb uAvoqs ui aq} qo^s uo aqj aAjno "jaaqs
« T » 8 09 8 » 9 8 09 8 I » I 01 ! ) I I 08 i I I 1 16 I I I 1 DOl i M l Oil
From the curve sheet/" = 82.5 and /' = 67.0, so we find k from the curve
sheet to be 0.208, by Eq. (106). By using the known values of L and Ci,
C2, and C3, and Eq. (116), we find A; to be 0.207.
The value of k could have been calculated without knowing the con
stants of the circuits, by using Eq. (105).
We have
82.52-67.0*_
K 82.52 +67.02
When L\C\ = li2C2, Eqs. (114) and (115) reduce to the simple forms
goes from very small to very large values, while the reactance changes
from a large inductive reactance to an equally large capacitive reactance.
Moreover, these changes occur periodically as the impressed frequency is
continually changed.
To demonstrate experimentally the peculiar characteristics of a cir
cuit having distributed constants, the author built an artificial line having
inductance, capacity, and resistance, as shown in Fig. 107; this line
resembles somewhat a long antenna, having inductances and capacities,
however, several times as large as those of an actual antenna.1
A variable frequency was impressed on this artificial line and, by means
of a wattmeter, ammeter, and voltmeter its resonance characteristics were
determined. The impressed voltage was kept constant at 20 volts and
the frequency varied in small steps, from 12 to 152 cycles per second.
Fig. 108 shows the current which flowed from the generator into the line
at the various frequencies, the line being open at its distant end. The
line showed six frequencies in the range used, at which we can say the line
1 See "Some Experiments with Long Electrical Conductors," by John H. Morecroft,
Proc. I.R.E., Vol. 5, No. 6, Dec., 1917.
DISTRIBUTED INDUCTANCE AND CAPACITY 109
10 20 30 40 50 6070 80 SO 100 110 120 130 140 150 160 170 180
Impressed Frequency
Fid. 108.—Current vs. frequency for circuit shown in Fig. 107.
10 20 30 40 50 60
70 80 90 100 110 120 130 140 150 160
Impressed Frequency
Fig. 109.—Resistance and reactance vs. frequency for circuit shown in Fig. 107.
110 FUNDAMENTAL IDEAS AND LAWS [Chap. I
i
CHAPTER II
RESISTANCE—INDUCTANCE—CAPACITY
D Eimp— Ee
K= —j ,
where
Eimp = the impressed voltage;
Ec = the counter voltage of motor, batteries, etc.
This restated definition must be still more generalized when the ordi
nary alternating current circuit is considered, in fact, a new concept of
resistance must be obtained. It might seem that Joule's law would serve
sufficiently to define resistance; this law states that the electrical power
liberated as heat in a circuit is given by the equation
This " power transferred " between a and b may be leaving the electrical
circuit between these two points or it may be entering the circuit
between these points. If power is leaving the circuit between these points,
as heat or otherwise, the resistance is positive; if power is entering the cir
cuit between these two points the resistance is negative, and if power is en
tering the circuit at the same rate as it is leaving then the resistance is zero.
From this standpoint any electrical
circuit carrying current, after reach
ing the steady state (no change in
Direction of the amplitude of the current) has
energy flow
Part of R is positive on the whole, zero resistance. Of
circuit under course we know that the circuit
consideration does actually have resistance, but
Direction of
energy flow we may consider the source of power
R is negative supply as having as much negative
resistance as the rest of the circuit
has positive resistance. At the
Fio. 1.—If power is leaving the circuit the generator (or other source of power
resistance is positive so that if power is supply) energy is entering the
entering the circuit its resistance must circuit as fast as it is dissipated
be considered negative. in other parts of the circuit. If
the circuit, as a whole, has positive
resistance the current must be decreasing in amplitude; this state of
affairs occurs in the ordinary damped oscillatory discharge of a con
denser, whereas a circuit which takes an appreciable time to build up
to its steady state has, during the time required to reach the steady state,
on the whole a negative resistance because, considering the circuit as a
whole, energy is entering at a rate faster than that at which energy is
leaving.
Various Factors Affecting the Resistance of a Circuit.—Among the
factors contributing to the resistance of a radio circuit are to be con
sidered (1) resistance of the conductor itself; (2) resistance of neighbor
ing closed ciruits and their proximity; (3) magnetic material close enough
to the circuit to be magnetized by it; (4) losses in the dielectric of any
condenser in the circuit; (5) corona losses from parts of the circuit; (6)
VARIOUS FACTORS AFFECTING RESISTANCE 113
R=* (2)
a
in which p is the specific resistance of the material composing the con
ductor.
I is the length of the conductor;
a is the cross-sectional area of the conductor.
This formula assumes that all parts of the cross-section of the con
ductor carry the same proportion of the total current; in other words
that the current density is uniform throughout the section of the con
ductor. This assumption is true for continuous current or for alternating
current of very low frequency. If the conductor is large in cross-section
or the frequency is high, the inner sections of the conductor carry a rela
tively small part of the total current, the density of current being greatest
at the surface of the conductor; in fact for very high frequencies a com
paratively thin skin on the surface of the conductor carries practically
all the current, so much so that if the center part of the conductor were
removed, leaving nothing but a thin walled tube of the same diameter
as the original wire, the resistance would be practically the same. This
tendency of the current to concentrate on the outer surface of the wire at
high frequencies is called the skin effect, the reason for the name being
obvious. If there are no other conductors carrying current in the vicinity
of the one in question this distribution of current will be symmetrical
about the axis of the wire, but if there are other current-carrying con
ductors in the neighborhood the distribution of current through the cross-
section of the wire may be irregular, perhaps only the surface part of
the conductor on one side carrying an appreciable current.
Axry distribution of current other than the regular distribution of
equal current density throughout the section of the conductor will result
in an increase in the resistance of the conductor; this increase may be
so great that the resistance for a high frequency alternating current may
be many times as much as the resistance of the same wire for continuous
current.
A simple illustration of this effect is given in Fig. 2, showing three
10-ohm resistances in parallel. Suppose the resistance of this combi
nation is determined by the power loss instead of by the ordinary law for
114 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
An exact analysis shows that the ratio of a.c. resistance to c.c. resist
ance may be expressed in terms of diameter, permeability, frequency, and
resistivity; a correct expression involves an infinite series of terms, but
these series have been summed so that accurate data are available for
calculating the resistance of any round wire, the permeability and resis
tivity of which are known. For copper wire, in which the permeability
is unity, tables have been compiled which present the data in convenient
form. In the curves of Figs. 3 and 4 is shown the factor, m, by which
the c.c. resistance must be multiplied to give the resistance for alternating
current. Plotted as abcissae are values of rv/, where r is the radius of
the wire in cm. and / is the frequency of the current being used.
It is sometimes useful to know how a large wire can be used without
having its a.c. resistance exceed its c.c. resistance by more than a specified
amount. The data given in the accompanying table, compiled by L. W.
Austen, may be useful for this purpose:
TABLE I
Wire Diameters
Largest wire (straight) which can be used without the high frequency resistance exceeding the c.c.
resistance by more than 1 per cent
i=l0r^W)^n(.t-{^)x), . . . (3)
116 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
SIMPLE ANALYSIS OF SKIN EFFECT 117
in which
Jo= current density at surface;
i= current density a distance x cm. below the surface;
u=2irf, where/ is the frequency of current;
v = permeability of the substance;
p= specific resistance of the substance, abohms per cm3.
Not only does the density of current decrease as the distance below
the surface is increased but, as indicated by Eq. (3), it reaches its corre
sponding values at later time than at the surface, this amount of time lag
increasing as the depth below the surface is increased. This really means
that the current penetrates into the substance with a wave motion; the
attenuation is, however, very high, so that probably only a fraction of
a wave length is actually set up in the conductor with an appreciable
amplitude.
A Simple Analysis of Skin Effect.—Although an exact analysis of skin
effect in a conductor requires the theory of wave propagation, and special
mathematical series for a solution, a very good idea of its cause (and,
what is much more important, its remedy) may be had from the ordinary
laws of current flow in inductive circuits. The first thing to notice about
the problem is the effect of frequency upon the division of current between
two paths in parallel, as shown in Fig. 5, the two paths having equal
i
I. R» - -L*
At low frequency ■— =-!r^
It Kx
At high frequency I. = **'.
LS
Fig. 5.—For branched circuits the resistance controls the division of current at low fre
quency whereas the reactance controls the division at high frequency.
resistance but unequal inductance. The formula for the current flow in
each path is
7= E .
Vff»+(«L)5
At very low frequency the uL term is negligible, and so we have the
currents dividing between the two paths inversely as the two resistances,
that is, the two currents will be alike. At very high frequency, however,
the resistance term becomes relatively negligible and the current divides
inversely proportional to the inductance in the two branches. The same
118 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
From Eqs. (4) and (6), the flux density throughout th ecross-section of
the wire and in the region surrounding the wire may be calculated; Fig.
7 shows the result of such a calculation. In the upper part of the figure
the flux is shown in the form of circles concentric with the axis of the wire,
the closeness of the circles representing the flux density, and in the lower
part of the figure is shown a plot of the flux densities, ordinates being
values of flux density and abscissae being distance from center of wire.
The total flux surrounding any point is obtained by adding the flux
from a point infinitely distant from the wire, up to the point in question;
a curve showing the value of this flux for different points inside and out
side the wire is shown in Fig. 8. The ordinates of the curve are obtained
by integrating the density curves of Fig. 7. The flux <fo , is the total flux
produced by the current in the wire, outside of the wire itself, whereas
SIMPLE ANALYSIS OF SKIN EFFECT 119
surrounding any point outside the wire as, e.g., C of Fig. 6, there is a
flux equal to <fo. There is a certain amount of flux inside the wire
itself and the flux surrounding the innermost filament is obtained by
adding to <t>i this internal flux ; it is shown by fa in Fig. 8.
Now let us consider the wire made up of a bundle of separate parallel
filaments, such a wire as would be obtained by using a cylindrical
bundle of very fine wires, each insulated from its neighbor, except at the
Fio. 7.—Closeness of circular lines show the density of magnetic field around a non
magnetic wire; in lower part of figure magnetic field density is shown by distance
from reference line to curve marked B.
ends of the wire in question, where they are all electrically connected
together. Let the resistance of each of these filaments be R. If an
e.m.f., E sin ait, is impressed across the ends of this composite wire,
all filaments will have the same impressed e.m.f., and it is therefore
evident that the sum of the reactions in each filament must add up
(vectorially) to equal this impressed force.
filament in question. Hence for two filaments, one at 0 and the other at
A (Fig. 6) we must have
*»-(Ii2D*+(«*i)»
and
Fia. 8.—Curve showing total flux outside any point considered in Fig. 7.
there is no internal flux the flux density everywhere inside the wire must
be zero, and as the flux density at any point in the wire distant r from the
axis is equal to .21/ r, where I now signifies the current flouring in the wire
inside of a circle through the point in question, we must conclude that there
is no current anywhere inside the wire.
At ordinary frequencies the resistance drop is not negligible in com
parison with the reactance drop, so that the sweeping conclusion of the
previous paragraph (no current anywhere inside the conductor) isnot true,
but it is evident that, as the frequency increases more and more the dif
ference between fa and <j>\ of Fig. 8 must continually decrease.
If instead of a copper wire an iron wire had been assumed, the internal
flux density would have been very much increased so that Figs. 7 and 8
would have more nearly the appearance of Figs. 9 and 10. The value
of the internal flux (<fc — <£i) would be very much increased, so that the
EFFECT OF PERMEABILITY ON SKIN EFFECT 121
Fig. 11, the three curves showing how, as the frequency is increased,
the current shifts more and more to the outer skin of the conductor. The
current density at the surface of the conductors has been assumed the
same for the three frequencies.
It is evident from the foregoing discussion that a substance having
high specific resistance and low permeability will have the least skin effect;
this is shown in Table I on p. 115. The wires used for resistance in making
tests and measurements in high-frequency circuits should be made of
small wires of the high-resistance alloys, practically all of which have unity
permeability.
122 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
from the connectors of the ammeter to two circular disks, and these disks
are connected by a set of very thin high-resistance strips, the whole arrange
ment having the appearance of a barrel, the thin strips taking the place
of the barrel staves. Such a construction is shown in Fig. 12, this showing
the construction of a 40-ampere, so-called " hot-wire " meter. As the
METHODS OF ELIMINATING SKIN EFFECT 123
radial thickness of these strips is only about .004 cm., there is practically
no internal cross-section to the conductor; it is all " skin."
In the scheme ordinarily employed for reducing skin effect the required
cross-section of conductor (which depends upon the amount of current to
be carried), is made up of a great many small wires, each completely
insulated from all the rest; a common form of this cable used for winding
radio coils consists of 48 No. 38 enameled wires properly woven together.
In eliminating skin effect by this construction it is not sufficient to merely
Fig. 12.—A hot wire ammeter showing how the skin effect is minimized by special
arrangement of very thin strips of high-resistance metal.
in making a coil than if it is used in the form of a straight wire. The dis
tribution of magnetic flux inside a single layer solenoid is somewhat as
shown on Fig. 13; the flux density is high just inside the solenoid and
practically zero at the outer surface of the coil. Assuming that this density
decreases to zero from the inner surface of the winding to the outer (nearly
.Flux density -B
Fig 13.—Approximate flux distribution inside a short solenoid.
the case for ordinary coils) it is evident that the outer filaments of
the wire are linked with much more flux, than are the inner filaments.
Thus an imaginary filament on the outside of the wire as at 6, Fig. 13,
will be linked with a flux in excess of that linked with filament a by an
amount equal to B/2Xd (where B is the flux density at the inner surface
of the winding and d is the
radial depth of the wind
ing) per unit length of the
wire. It is apparent that
the current will tend to
crowd into that part of the
wire which is on the inside
of the coil, the inductance
reaction being less for the
filaments on the inner side
of the winding than for
those on the outer ^ ide. ^ —Distribution of current in the conductors of
But besides this ten- & ghor(. soIenoid; density of shading corresponds to
dency of the current to current density,
redistribute itself, there
is also the tendency to redistribution about the axis of the wire, and also
each conductor exerts a certain effect on its neighbor—these all combine
to produce a current distribution about as indicated in Fig. 14, the density
of current being indicated by the proximity of the dots.
In constructing variable resistances for use in making radio measure
126 RESISTANCE—INDUCTANCE-CAPACITY [Chap. II
ments, skin effect must be carefully considered. The most convenient form
of variable rheostat is a cylindrical one with a sliding contact, the almost
universal form of laboratory rheostat for ordinary c.c. and a.c. measure
ments. But this type of winding is not satisfactory for high-frequency
currents because of the extra skin effect caused by solenoidal winding and
also because the amount of self-induction in such a rheostat is too great to
be neglected in radio circuits. Radio cable cannot be used with sliding
contact rheostats for evident reasons: solid wire must therefore be used
and still the skin effect and self-induction be reduced to a minimum. This
is done by winding on a porcelain tube a bifilar high-resistance solid wire ;
the two wires making the bifilar construction are wound around the cylinder
in opposite directions, the two wires crossing each other twice per turn.
Such a winding has a self-induction practically zero, and hence has a
minimum skin effect.
The increase in resistance of coils, due to skin effect, is a very difficult
problem to analyze mathematically; only the simplest cases have been
considered, and even then assumptions have been made which make the
validity of the equations obtained doubtful.
An experimental investigation of the skin effect in coils was carried
out by the author, measurements being made on a Wheatstone bridge, and
the results are given herewith; they serve to indicate how much increase
in resistance from skin effect may be expected with coils similar in form.
The single layer coils were wound on dry wood reels with double cotton-
covered wire, the wires being laid as closely together as possible. The
length of the winding was 10 cm. and the approximate diameter (the cross-
section was actually octagonal) was 10.5 cm. The datum is given in the
accompanying table, both self-induction and resistance being given, the
results being probably accurate to within 1 per cent unless otherwise stated.
There are two effects which must be kept in mind when interpreting
these results; there is an actual increase in resistance due to redistribution
of current in the conductor of which the coil is made, and there is an
increase in the measured value of resistance due to the effect of internal
capacity, explained in the previous chapter when analyzing resonance in
parallel circuits.
Every coil has internal capacity due to one part of the winding being
equivalent to one plate of the condenser, acting with every other part to
form a condenser. It was shown that the apparent resistance of an induc
tance, shunted with a condenser, increases as the frequency is increased,
in accordance with Eq. (48). Although this equation is not directly
applicable to these coils (the capacity of which changes with frequency
changes) it indicates that the measured value of resistance may be expected
to increase entirely aside from any skin effect which may be present. But
this effect of capacity which gives an apparent increase in resistance pro
SKIN EFFECT IN SINGLE-LAYER COILS 127
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128 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
duces at the same time an increase in the apparent inductance of the coil,
so that in the results of the table any increase resistance which occurs
without a corresponding increase in inductance, is due to redistribution
of current in the conductor of the coil (i.e., real skin effect) ; for frequencies
high enough to produce an increase in the apparent inductance the skin
effect is not alone in producing the increase in resistance, the inter
nal capacity contributing its effect also in increasing the apparent
resistance.
It will be noticed that for the larger wires the inductance actually
decreases as the frequency increases, for the lower values of frequency.
Illustrating this effect we take the data for coil No. 1 made of No.
11 wire. In the range of frequencies used the indvictance decreased with
increase of frequency, whereas the resistance increased from .050 ohm
to .803 ohm. The radius of this wire is .114 cm. and so the factor, rV7
for 2X105 cycles, is 51. Referring to Fig. 3 the factor m is found to be
4.2. If, therefore, the wire had been used in the form of a straight con
ductor, we might have expected an increase in resistance from .050 ohm,
the c.c. resistance to 4.2 X.05 = .21 ohm. Actually it changes from .05
ohm to .80 ohm, thus showing how the skin effect is augmented when the
wire is used in the form of a coil. The superiority of the radio cable,
either 42/36s or 48/38s is at once evident from the results given in the
table.
If the coil used has more than one layer, the magnetic field density is
much greater than it is for a single layer coil, hence we should expect a
much greater skin effect for multi-layer coils than for single-layer coils and
the experimental results of Table III which were obtained with ten layer
coils, prove the point. Thus the single layer coil of No. 18 wire showed an
2 18
increase in resistance of ~ =3.6 times as the frequency varied from zero
to 100,000 cycles. This same wire wound in a 10-layer coil showed an
84
increase through the same range of frequency of Yf4=^ times so that the
resistance increase is 13 times greater when used in a 10-layer coil than
when used in a single-layer coil.
It must be noticed also that this great increase in resistance is not
due to the internal capacity of the coil. These multilayer coils were
built on wooden reels in a special way first described by the author; the
construction was such that a considerable air space (in this case .16 cm.)
was used between consecutive layers, this construction giving such a low
internal capacity that, up to the highest frequency used the inductance
of the coil showed but slight increase. These multilayer coils were octag
onal in form and had 10 layers each, wound back and forth. Each layer
was 2.6 cm., long separated from the next layer by .16 cm. air. The
SKIN EFFECT IN MULTILAYER COILS 129
inner diameter was approximately 10.5 cm. and the outside diameter
varied with the size of wire used, being greater for the larger wires.
TABLE III
CoU 16 17 18 19 20 21 22 23 24 25 26
12 18 20 22 24 26 28 30 32 34 48,/38s
Number Turns. . . . 100 197 239 300 343 410 586 719 859 898 250
Frequency in *
Kilocycles
0 R 12 1.74 3.30 6.7 11.5 21.3 49 96 172 300 5.1
R .48 2.48 3.40 6.8 11.7 21.6 50 96.5 173 300 5.2
1.2 L 1.46 5.21 8.10 12.6 16.7 23.7 48 72 102 117 9.2
R L .33 .48 .42 .54 .70 .91 1.0 1.3 1.7 2.6 .56
R 3.85 6.27 7.80 11 4 10.2 27 64 122 210 345 6.7
10.5 L 1.42 5.18 8.10 12.6 16.8 24.0 48 73 104 120 9.3
R/L 2.7 1.2 .96 .91 .90 1.1 1.3 1.7 2.0 2.9 .72
R 5.50 10 2 113 15 4 20 2 32.0 71 126 225 370 7.2
15 4 L 1.39 5.20 8.12 12.7 16.9 24.0 49 74 105 124 9.3
R L 4.0 1.9 1.4 1.2 1.2 1.3 1.5 1.7 2.1 3.0 .77
R 7.40 21 0 22.3 25.7 28.5 42 97 104 360 600 8.5
25 L 1 37 5.20 8.14 12.8 17 1 24.5 51 78 116. 138 9.3
R L 5.4 4.0 2.7 2 0 1.7 17 1.9 2.5 3.1 4.3 .91
R 10.9 48.0 63.5 78 82 100 200 465 1080 1450 15
50 L 1.37. 5.22 8.17 13.2 17.7 25.3 55 87 131 150 9.5
R/L 7 9 9 1 7.8 5 9 4 6 4.0 3.6 5.3 8.2 9.7 1.6
R 14. 1 73.0 94 155 133 W2 19
75 L 1.37 5.23 8.22 13.6 18.6 27.5 9.7
R/L 10.3 14.0 11.1 11.4 7.2 6.2 2.0
B 16.6 84 142 267 268 415 37
100 L 1 38 5.27 8.55 14.3 20.3 30.6 10.4
R L 12.0 15.9 16.6 18 7 13 2 13.6 36
R 18.8 104 190 362 462 61
125 L 1.37 5.32 9.07 15 1 21 0 10.8
R L 13.7 19.5 21 24 22 5.6
R 20 5 124 260 550 840 115
150 L 1.38 5.56 9 30 15.7 22.0 11.4
R L 14.9 32.3 28 35 38 10
sized wire. Thus the 10-layer coil wound with No. 26 wire increased its
resistance from 21.3 ohms to 415 ohms, but at the same time the induc
tance increased from 23.7 X10-3 henries to 30.6 X10~3 henries. Hence
for this coil the internal capacity was making itself felt so that the actual
increase in apparent resistance must be regarded as due to the combined
effect of redistributed current and internal capacity.
Three of the coils were wound with radio cable; in two of them there
were used 48 No. 38 enameled strands in the cable—three twisted cables,
each having 16 strands, were twisted together to make the cable. The
solid wire most nearly approaching this cable in cross-section was No.
22. In the single-layer coils the solid wire increased its resistance by
220 per cent, and this radio cable coil increased by 72 per cent, only one-
third as much increase as for the solid wire over the same range of fre
quency. In the multilayer coil the solid wire increased its resistance from
6.7 ohms to 267 ohms, an increase of 40 times as the frequency was varied
from zero to 100,000 cycles whereas the multilayer coil wound with the
radio cable increased (in the same range of frequency) from 5.1 ohms
to 37 ohms, an increase of only 7.2 times, that is, the stranded wire coil
showed a resistance increase due to skin effect only one-sixth as great as
the nearest size solid wire. In this resistance increase there is some effect
due to the internal capacity of the coil, and if this effect (which is approxi
mately the same in amount for both coils) were taken into consideration
the superiority of the radio cable over the solid wire would be even more
striking.
From the results presented in Tables II and III there was calculated
for each coil the " ohms resistance per millihenry " and the results are
presented in the form of curves in Figs. 15 and 16. The most interesting
conclusion to be drawn from these curves is the idea that the higher the
frequency the smaller the wire should be to keep the ratio of resistance
to reactance low. Thus in the single-layer coil it is evident that below
40 kilocycles No. 16 wire is better than No. 20 (such factors as cost, bulk,
current-carrying capacity, etc., not considered) but above this frequency
No. 20 wire is better than No. 16.
For the multilayer coils this feature is shown to a much greater degree
and at lower frequencies; thus at 1200 cycles No. 34 wire has about 8
times as many ohms per millihenry as No. 12, but at 15 kilocycles the
No. 12 wire has more resistance per millihenry than has the No. 34 wire.
The multilayer coil of radio cable is indicative of what a good coil
should be; its reactance at 75 kilocycles is 220 times as much as its resist
ance and this ratio holds over a wide range of frequency. Other coils
have been built by the author, using better stranded wire, more of it,
keeping the radial depth of conductor low, which showed a reactance
450 times as great as the resistance at 50 kilocycles. The ideas to be kept
SKIN EFFECT IN MULTILAYER (jOILS 131
in mind in building good radio coils are to use carefully stranded and
insulated cable, keep the radial depth of conductor small, keep the coil
as compact as possible and at the same time to keep the internal capacity
low, and avoid dielectric losses.
In Fig. 17 is shown the construction of a coil which has about 10 milli
henries inductance and 7 ohms resistance at 50,000 cycles; sufficient air
space was used between layers to keep the internal capacity to about
120 micro-microfarads. This coil operated satisfactorily when carrying
0 1 2 3 4 5 6 7 8 9 10 11 12 13 It 15 IS 17 18 19 20
Frequency in 10 cycles per second
Fig. 15.—Variation of resistance with frequency in single layer solenoids of various wires.
4 amperes with 12,000 volts across its terminals. If it were used in a good
insulating oil it would probably be satisfactory when carrying 200-300
kilovolt amperes, although in this case its internal capacity would be more
than doubled.
To illustrate in as striking a manner as possible the skin effect which
may be present in poorly designed coils tests were made on two coils
made of copper strip, wound edgewise. The first coil had 29j turns of
strip 1| in. wide and in. thick; the spacing between successive turns
was nearly ys in- ; its inside diameter was 14j in. and outside diameter was
171 hi- Its resistance for continuous current was .013 ohm and at 150
132 RESISTANCE—INDUCTANCE—CAPACITY [Chap, n
32
30
28
26
24
22
».
£20
,S6
= lb
B
£M
in
o
12
10
«
(i
I
0 1 2 3 4 5
6 1 8 9 10 11 12 13 14 15
Frequency in 10 'cycles per second
Fig. 16.—Variation of resistance with frequency of multilayer coils; short coils of ten
layers each, air space between layers.
Effect of Neighboring Circuits on the Resistance of a Coil—Tuning
These Circuits.—It has been shown in the previous chapter that the
resistance of a circuit is always increased by the presence of neighboring
circuits in which induced currents flow. The power for supplying the
losses in these circuits must be furnished by the coil inducing the current
and so this effects an apparent increase in the resistance of this coil; the
amount of this increase is given by Eq. (73), page 86. This increase in
resistance evidently depends upon the tuning of this second circuit. If in
RESISTANCE AFFECTED BY NEIGHBORING CIRCUITS 133
Eq. (73) the reactance of the second circuit is put equal to zero the apparent
increase in the resistance of the first circuit may be very great; the curves
illustrating this effect were shown in Fig. 91, Chapter I.
As an instance of the losses occurring in neighboring circuits it is inter
esting to note that one of the terminal posts of the coil pictured in Fig.
17 was fastened on a piece of hard rubber, and this rubber block was
fastened to the wood-end piece of the coil with small iron screws. When
operating this coil with four amperes at 50 kilocycles flowing in the wind
ing the. heat generated in those screws was such that they burned them
selves free from the wood after the coil had been in the circuit but a
short time.
134 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
the plates, caused by imperfect fit of the punch and die used in making
the plates, is especially bad in causing eddy currents.
The flux density in the steel plates has about the distribution shown
by Fig. 19, the penetration of magnetic flux into an iron sheet decreases
as frequency increases, increases with the specific resistance of the iron,
etc., in fact follows the same distribution law as the penetration of cur
rent itself into a conducting medium given in Eq. (3). Because of this
lack of penetration the apparent permeability of the iron decreases as
the frequency increases, resulting in a decrease in the self-induction as
the frequency increases. The curves given in Fig. 20 show how the
resistance and inductance of a laminated iron-core coil change as fre
quency changes. It will be noted that the increase in resistance is practi
cally all due to eddy-current losses; the hysteresis loss is nearly negligible.
Flux density at
<surface of1 lamina5>
I FTtax density
~>
Fiq. 19.—Flux density variation throughout the section of a lamination of an iron core;
the higher the frequency the greater is the variation in flux density.
It is evident that iron of the quality used in this coil must be used in
laminations less than .0075 cm. (the thickness of those in the test coil)
to maintain a low resistance at high frequency. The decrease in induct
ance of this coil is comparatively small in the range of frequencies used.
In Fig. 21 are shown the variations in L and R of another toroidal
coil, using thicker laminations. Even for the comparatively low frequen
cies used in this test the decrease in inductance is very pronounced.
Iron dust, suitably prepared, makes very excellent material for the
cores of coils intended for high-frequency use, having very low eddy-
current loss. It has, in common with all iron cores, the disadvantage
of a permeability varying with magnetic density. A dust-core coil (toroid)
was tested to show this effect and gave the results shown in Fig. 22; the
measurements were carried out at a frequency of 2000 cycles. In Fig.
23 are shown the characteristics of this same coil measured at various
frequencies. The ratio of reactance to resistance brings out very well
the fact that a coil is always most efficient at some certain frequency.
It is to be noticed for all these iron-core coils that, at radio frequency,
136 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
10 1 20 25 30 35 40 45 50 55 60 65 70
Frequency in Kilocycles
Kig. 20.—Characteristics of a toroidal shaped coil having laminated iron core.
of the set and must be considered when getting decrement, losses, etc. The
resistance of a spark gap varies with many factors, principally the length
of gap and magnitude of current through the gap. Within the ordinary
range of currents used in radio circuits the resistance of an arc or spark,
for constant length of gap, varies inversely with the current to some
0 2 * 6 8 10 12 14 16 18 20 22 24
Frequency in Kilocycles
Fig. 21.—Characteristics of a toroidal shaped coil having laminated iron core, lamina
tions being much thicker than those of Fig. 20.
power higher than the first, in such a way that the IR drop actually
decreases with an increase of current. Other factors affecting the resist
ance of the gap are the nature of the gas through which the arc or spark
is passing and the material of which the gap terminals are made. Silver
and copper electrodes give a higher resistance gap than such metals as
138 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
RESISTANCE OF SPARK AND ARC 139
zinc, magnesium, etc.; hydrogen and illuminating gas give a higher resist
ance than air.
Experiments indicate that for such currents and gaps as are used in
radio sets the resistance (effective) of a spark gap is not more than 1 ohm,
and is generally only a few hundredths of 1 ohm. This value of resistance
is obtained from the heating effect, and so gives a kind of average value
of the resistance during the cycle. For low frequencies the resistance
of an arc or spark varies a great deal throughout a cycle of current, and
it probably does (even if to a less extent) at radio frequencies.
In Fig. 24 is shown the oscillogram giving the form of voltage across
an arc and the current through the arc; if the resistance is denned as the
ratio of volts to amperes it is evident that the resistance varies through
widely differing values during the cycle.
#' Y //me
■ f
Fig. 24.—A sine wave of e.m.f. impressed across an arc in series with an rton core induct
ance gave voltage and current forms as shown.
characteristic of nearly all circuits in which gas of some kind takes part
in the conduction of the current; in some special cases even a pure electron
stream may have a negative resistance for an alternating current, as will
be explained when discussing vacuum tubes.
The magnitude of this alternating current arc resistance varies some
what with frequency, it becoming less as the frequency increases.
Mr—r
0123456789 10
Amperes
Fig. 25.—Resistance of small arc, in air.
in the network of wires and in the earth due to actual heat loss produced
by the conduction currents; losses occur due to induced currents in guy
wires, etc.; losses occur in the earth's surface and any other dielectrics in
the field of the condenser such as trees, etc., and power is radiated. That
resistance caused by radiation is the only useful resistance; the other fac
tors increase the resistance of the antenna but perform no useful function.
The resistance of an antenna varies with the frequency about as indi
cated in Fig. 28. With very high frequencies the resistance is high; it
decreases to a minimum at a frequency about twice that of the natural
142 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
oscillation of the antenna (without any added inductance) and then rises
gradually, the amount of this rise being determined principally by dielec
tric losses in objects located in the electrostatic field of the antenna.
Antenna wires -
Inductance
Earth
Fig. 27.—Antenna with loading inductance.
For small land antennae the minimum on the curve may be 20-30
ohms, for aeroplane antennae perhaps 5-10 ohms; for ships' antennae
3-6 ohms, and for the large antennae used for long distance communica-
Frequency of quarter
wave length oscillation.
High Low
Frequency
Fiq. 28.—Typical resistance curve for an antenna, showing variation with frequency.
tion the minimum value may be 1-2 ohms. The more complete discus
sion of antennae and their characteristics will be given in Chapter IX.
Resistance due to dielectric loss and corona loss will be treated in the
section dealing with capacity.
COEFFICIENT OF SELF-INDUCTION 143
INDUCTANCE
Self-induction
(9)
TABLE IV
Diameter Diameter
Length A' Length K
ing. Multilayer coil are, however, preferable, but they must be built in
such a way as to keep the internal capacity low, as described on p. 133.
TABLE V
Resistance and Inductance op Edgewise-wound Ribbon Coils
Coil No. 1
Frequency in 10»
.043 .088 .128 .248 .338 .450 .730 1.250 3.50
L in 10—• henry. . . . 489 485 482 476 472 470 466 464 460
R in 10-' ohm . 13 15 19 26 31 36 46 72 176
Frequency in 10'
7.00 16.4 25.2 50.0 75.0 100 125 150
L in 10 henry 458 455 452 451 454 457 456 460
R in 10- » ohm 295 725 945 1345 1775 2205 2745 3440
Coil No. 2
Frequency in 10'
cycles .043 .100 .150 .200 .300 400 .600 1. 000 IM)2.44
L in 10_f henry. . . . 613 608 604 602 598 595 592 585 585 583
R'm 10-sohm 23 25 26 30 40 45 49 70 100 145
Frequency in 10»
cycles 3.50 6.46 15.3 21.5 50 75 100 125 150
L in 10_s henry.. . . 581 578 574 572 570 568 568 570 572
R in 10~» ohm 245 495 1095 1345 2640 2940 3730 5280 7860
Ci and C2 are constants depending on the shape of the spiral for their
values. They are given in Table VI.
TABLE VI
Ratio ~d c. Ci
Eq. (12) gives incorrect values if the turns are not close together; the
values obtained from the equation must be increased as much as 5 per
cent for the spacing used in ordinary transmitting coils in spiral form.
Fig. 32 shows how the value of L for a given spiral varies with the number
of turns used.
It is interesting to note that the same length of wire will give about
the same inductance whether wound into a flat spiral or a single-layer sole
noid, provided that the mean radius of the spiral has the same value as
the radius of the solenoid.
COEFFICIENT OF SELF-INDUCTION 149
Inductance of spiral
Inner diam.— i'i
On cr diam. - 3!i'f
Strip >, a x %
cE
U
4 6 6 7 8 9 10 11 12
Number of turns counted from inside
Fig. 32—Inductance of a spiral similar to that shown in Fig. 31.
Toroid
Fig. 33.—Toroidal coil of rectangular cross-section.
where n = total number of turns;
1 = axial length of coil;
Z?2 = outer radius;
Ri = inner radius.
150 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
L=47rn2(ft-V#2-r2) cm (14)
c
Torus
Fia. 34.—Toroidal coil of circular cross-section.
d A d A Number of B
D D Turns, n
1.00 + 557 .18 1.16 1 .000
.90 .452 .16 1.28 2 .114
.80 .334 3 .166
.70 .2C0 .14 1.41 4 .197
.60 + .046 .12 1.56 6 .233
.50 -.136 .10 1.75 8 .253
.40 .356 .08 1.97 10 .266
.35 .443 .06 2.26 20 .297
.30 .647 .04 2.66 40 .315
.25 .830 .02 3.36 60 .322
.20 1.05 100 .328
Fig. 35.—Single layer square coil, such as is used for a coil antenna.
r (2wRn)2
F'F" cm.. (16)
b+l.5t+R
where R = mean radius of coil in cm.;
n= total number of turns in coil;
6 = axial length of coil;
< = radial depth of winding.
ll
F"=1.151og10 (l00+1fg-).
For accurate results with this iormula the distance between wires
must be small compared to the diameter of the wire.
A multilayer coil of very ingenious construction is being made at pres-.
ent, using a so-called honeycomb construction. A picture of such a coil
1 An excellent article on the design of multilayer coils was published in Univ. of
California Publications in Engineering Vol. 147, by F. E. Pernot.
VARIABLE INDUCTANCE 153
~~~~
its proper value for the position of the contact, and, due to the current
in the shortr-circuited turn, increasing the effective resistance of the coil.
Also there is not much useful variation of inductance obtainable by this
method; for long solenoids the value of L increases with the first power
of the length only and the coil cannot be used effectively with the con
tact set to connect in only a small portion of the coil because of the losses
occurring in the long unused portion. This part of the coil (generally
called a " dead end ") is excited like the secondary of a step-up auto trans
former; the charging current circulating in the dead end produces losses
and so increases the effective resistance of that part of the coil which is
OOOOOOOOOOOOOOOQ.
o0ooooo0o _
>
L /
1K j /"
/
1
O /Form of Coils
c
is _j»»
s oooooooooooooocr — t__
-j
is j
1 [ |
L 2N
i .—.—
0 10 20 30 40
Setting of rotating coil, in degrees
Fia. 39.—Calibration curve of a variable inductance commonly known as a variometer.
disk on a shaft inside the solenoid, so that the axis of the disk may be
made parallel or not to that of the coil. The eddy currents in the disk,
with parallel axes, will very materially reduce the inductance of the sole
noid.
The effect of such a solid disk placed inside a short solenoid is given
in Table X. The coil was a single layer solenoid 12 cm. in diameter and
of 2 cm. axial length; the various disks were 11 cm. diameter and were
placed inside the coil, centrally, with the plane of the disk perpendicular
to the axis of the coil. It is evident that a copper disk very materially
TABLE X
Effect of Metal Disk Inside Solenoid
Coil alone fa-'m. Copper ft-in. Brass A-'n. Brass A-in. Tinned
Disk Iron
Frequency in
Kilocycles
L R
io- » ohms L R L R L R L R
henry
i 1.060 3.03 .807 3.49 .895 3.77 1.025 3.53 1.055 3.25
5.35 1.052 3.20 .762 4.18 .785 5.13 .870 6.40 .970 6.40
50 1.058 3.35 .751 .5.79 .756 8.13 .783 12.6 .865 18.6
149 1.092 5.08 .760 9.17 .765 13.5 .792 17.8 .861 44.3
35
M 1282'
,...]
247
|/+16a 2048" cm. . (17)
6(128) HI
When the circles have nearly the same radii and the distance between
coils is small compared to the radius, the simpler form may be used,
cm. (18)
where M0 is the mutual induction between the central turns of the two
coils (by Eq. ( 17)) . The curves of Figs. 43 and 44 show the experimentally
determined values of M for two typical cases.
1 1 1
E K' h ^ »i! ll: sSO t urns of :opper i it) >OI •
.o;-5c m * 1 .27cm . 1 1SI la :ion fc veen tn rn
of «■ IX ■il X'
■g.01
Separation
3
s
.01
10 20 30
Separation in cm.
Fig. 43.—Variation of mutual inductance of two multilayer circular, coaxial, coils;
separation measured between nearest sides.
The exact expression for M has not been calculated, but an experimentally
determined value of M for a certain combination is shown in Fig. 46.
In case the two coils are connected in series the self-induction of the com-
1
.030 1 1
L ti • coil ■■
0?8 i -.0400
L lit nt' r c »l = . J2'.
026 u% 1 <"
II < u
.024
MM .1
i
.020
si m
.018
012346678
Separation in inches
Fig. 45.—Variation in mutual induction of various single layer solenoids placed coaxially.
160 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
fitted into one another. When both coils are wound in straight cylin
drical form (short solenoids) the range in L will not be as great as when
both coils are wound on spherical surfaces, making a closer fit possible.
A typical calibration of such an inductance is given in Fig. 39, the form
of the coils being shown on the curve sheet.
Mutual Induction between Two Coaxial Spirals.—A tedious calcu
lation is necessary to calculate the value of M for two flat spirals arranged
coaxially but an idea of what may be expected is indicated in the experi
mentally determined curves of Fig. 47.
22 MINI
L ol 12 t< ri s = n m cr 'ii ic 1
$ 18l
x t
§ 16| Li 4.6" K
u .5"
a r
JB 12 —
*3
g /
B 10
"T Separation
\
"s
-> , S< pa ra 10 » - en v, l 25"
3 -* 2 1 00!'
/ > r' 3 -2 00f
I > i ■3.001'
5 -3.761'
1 1
0 1 3
5 G 7 8 9 4 10 11 12
Number of turns
Fig. 47.—Mutual induction of the two flat spiral coils of an oscillation transformer.
CAPACITY
c=MV+^{hg—d^+dha—+1)\cm-> • • (23)
C=^cm <*)
1= length in cm.;
r= radius in cm.
In several experiments with the lower end of the wire close to the
earth, the measured capacity exceeded that calculated from the formula
by about 10 per cent.
C=—~cm (26)
2log2^
This formula assumes the charge in the wire distributes itself uniformly
over the periphery. Actually the lower side of the wire has a slightly
CAPACITY OF OVERHEAD WIRES 163
When h/r =5 Formula (27) gives a result 15 per cent greater than does
(26). For greater values of h/r the discrepancy between the two is less.
In general whenever two wires are so close together that the separation
is not more than 5 times their diameter, hyperbolic functions are required
for precise results, rather than the ordinary logarithmic formulae, for either
the inductance or capacity. In practice the ratio of h/r is much greater
than 5 except for one or two cases, such as the wires of a telephone cable, etc.
Mutual Capacity of Two Horizontal Wires, Such as Two Wires of
an Antenna.—
log
epi 4 d2
cm., . . (28)
The mutual capacity is not the same as the capacity of the two wires
regarded as the two plates of a condenser, one charged positively while
the other is charged nega
tively. It really represents
a decrease in the capacity
of one of the wires with re
spect to earth caused by the
presence of the field of the
other. In Fig. 48 this point 11 1; i i i > i i
is illustrated; the normal
field of wire a to earth is
shown by the full lines and Fia. 48.—Diagram illustrating the "overlapping"
that of wire b is shown by of the electric fields of two antenna wires.
dotted lines, and it is evi
dent that the two fields overlap. The total capacity of these two wires,
to earth, is diminished to some extent by this overlapping of the two
individual fields, and a measure of the decrease in capacity is given by
the value of M from Eq. (28).
164 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
C = —^cm, (29)
4 log -
where / = length of one wire in cm.;
d = separati an of the two wires;
r = radius of the wire in same unit as d.
This formula supposes the distance between the wires is small compared to
the height above the earth ; for wires close to the earth, compared to their
separation, this formula gives values of C too low.
Capacity of Two-wire Antenna.—This is the case of the two wires of
Fig. 48 being connected together and their capacity with respect to earth
being determined. It is equal to twice the capacity of one wire with
respect to ground (Eq. (26)) diminished by the mutual capacity of the two
wires (Eq. (28)).
In case the two wires are far apart the value of capacity is twice that
of one wire, and as the wires approach each other the capacity decreases,
until when the two wires touch, their combined capacity is not greatly
in excess of that of a single wire.
It is interesting to note that the self-induction of a pair of wires (the
two wires of an antenna, for example) increases as the wires approach,
whereas the capacity of the pair diminishes. In fact the variation is
nearly reciprocal, so that the product of L and C of the pair is independent
of the spacing of the two wires.
The foregoing formulae for capacity of wires with respect to earth are
not very accurate, not being corrected for end effects, etc. It docs not
seem worth while to use more elaborate formula?, however, because the
presence of foreign bodies in the electrostatic fields of antennaj, such as
trees, masts, stays, etc., influences the value of capacity to a large extent.
Also the height of a wire is ambiguous; this height is really to be measured
to conducting earth (wet) and the height of the wires above wet earth
may not be easy to determine.
Recently Austin1 has given an empirical formula for the capacity
of an antenna, the formula apparently being fairly accurate (say within
10 per cent) for any ordinary form of antenna. It is
C=(36VJ+7.97'£)cm (29a)
In case the length of the antenna is more than eight times the
breadth a slight additional correction is necessary, this increase being
, , length „ „
^ualt0b7e^dThxl-5-percent-
In calculating A, the length of the antenna is multiplied by its
breadth, the area thus obtained being of course much greater than the
actual surface of the antenna wires. With the ordinary antenna a spac
ing of one meter between wires will give a capacity about 90 per cent of
that which would be obtained if sufficient wires were used to completely
fill the space occupied by the antenna, so that neighboring wires touched
each other.
Two typical calibration curves are shown in Fig. 49, for semicircular
plates with central shaft, and for specially formed plates, with displaced
shaft. In the first the capacity varies directly as the angle of the movable
plates and in the second the scale reading is proportional to the logarithm
of the capacity.
Losses Occurring in Condensers.—When a condenser is used in a high-
frequency circuit there are various losses which occur, all of which are
detrimental and to be avoided if possible. The losses may be due to
actual leakage from one plate to the other through or around the dielec-
Condensers using glass, paper, rubber, or mica for the dielectric have
some dielectric losses, although this loss in a well-constructed mica con
denser (air and moisture excluded) seems to be very small; the dielectric
losses in paper and some grades of glass are high. Dry oil is in general a
very good dielectric with very low losses; the oil has an added advantage
over a solid dielectric, in that a disruptive breakdown does not spoil the
condenser, the oil repairing itself with no deleterious effects unless sufficient
arcing occurs in the oil to produce considerable carbonization. A good
grade of mineral oil is generally used, but the author has found castor
oil to be excellent, having a high dielectric strength, low losses, and having
such a high specific inductive capacity as to give about twice as much
capacity as the same amount of mineral oil. The value of K for various
dielectrics is shown in Table XI.
TABLE XI
Specific Inductive Capacity op Materials Used More Generally in Radio
Condensers (Measurements at Low Frequency)
Equivalent
dielectric . ■hunt
resistance
PiQ. 50.—A condenser with imperfect dielectric may be represented by one having per
fect dielectric in series with, or shunted by, a suitable resistance.
These simple calculations hold only for condenser of low power factor,
say 0.02 or less, but as all good radio condensers have a lower power factor
than this the method outlined above is accurate enough. The relation
between the equivalent series resistance and equivalent shunt resistance
is obtained from the relations (which, it must be remembered, hold good
for low power factor condensers only)
PR=u2C2E2R = —,
r
or
r=o^#' (31)
The mica used was built up from small mica sheets and some binding
cement; it seems likely that the losses in the cement and possible small
air cavities caused more loss than did the mica itself; the small temperature
rise in a good mica condenser built especially for radio work would indicate
that a comparatively small part of the loss found by Alexanderson was
due to losses in the mica itself, unless a poor grade had been used. He
found some samples of built-up mica with a power factor as high as .07 ;
it would seen likely that a lot of air was trapped in this sample. Some
recent tests have indicated a power factor in mica as low as .0003.
It will be noticed that there is a considerable difference between Austin's
results and those of Alexanderson; e.g., glass gave power factors of .005
and .014, in the different measurements. The difference is probably
attributable to the different quality of glass used and also to the fact that
different methods of experimentation were used; in one case the material
was subjected to the loss continuously and in the other for only a small
fraction of the time. Alexanderson used continuous wave excitation and
Austen a 120-cycle spark; the resulting temperature rise was undoubtedly
different in the two tests.
Most of the solid dielectrics using bakelite for base have a power factor
(at radio frequencies) of about 4 per cent. Some show a power factor,
increasing with age of the material, the power factor of some of them
increases with increase in frequency and in others a decrease of power
factor occurs.
PHASE DIFFERENCE IN CONDENSERS 171
layer solenoid, as it should, but when tested at 500,000 cycles it acted like
a condenser, not like an inductance; in fact it ceased to act like an induc
tance for frequencies above 200,000 cycles. This peculiar behavior was
caused by the internal capacity of the coil; this internal capacity may
be represented to a certain degree of approximation, as a condenser
connected in parallel with the terminals of the coil. It is then evident
that above a certain frequency the current taken to charge the condenser
01234 6 6 7 8 9 lu
Position of rotating plates
Fia. 51.—Variation of equivalent series resistance of a radio condenser having ebonite
dielectric.
will be greater than the current through the coil itself, making the com
bination circuit act like a condenser, of capacity varying with the frequency.
The calculation of the internal capacity of a coil is most conveniently
carried out by calculating the electrostatic energy stored in the coil for
a given voltage; the value of C is then at once obtained. The capacity
of the two-layer solenoid referred to above will first be calculated. Fig.
52 depicts the arrangement of the electrostatic and magnetic fields of the
coil when current is flowing through it; when the impressed e.m.f. is
continuous, the difference in potential between the two layers varies
directly as the distance from the end where the two layers connect together,
INTERNAL CAPACITY OF COILS 173
being zero at this point. When the impressed e.m.f. is alternating, this
potential difference between the two layers is no longer a straight line
variation but varies more rapidly in the center of the coil; the exact form
of this potential difference curve varies with the frequency and with the
shape of the coil.
End where layers are
connected together
O O O Q.connec
6 6 6 dyy
Magnetic field-*^.
Klrrtro static field
Cotton insulation
then we can calculate the capacity by replacing the actual coil by two
conducting cylinders having the same diameter and length as the coil,
and separated by a distance equal to four times the thickness of insula
tions of the wire. As the separation of the cylinders is so small compared
to the diameter, the capacity may be calculated by using the formula for
flat plates. Hence we get
r 2rrlK rlK ....
174 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
Electric fleldt
Fia. 54.—Variation in potential difference between the layers of a two layer solenoid,
at low frequency.
the other. The diagram in Fig. 54 gives the elements of the problem;
rK
two plates, capacity per unit length =-777 with potential difference as
01
represented by the e curve in the upper part of Fig. 54. The energy
stored in an element of length of the condenser is,
rK e2 _rKE2/ x\
dx.
m \ I)
The total work stored in the electrostatic field,
rKE2 2 _rKE2 I
dX~ Wt 3'
m TH)
Now we define capacity in a problem like this by putting the total
C'E2
energy stored in the field equal to ^ where C is the capacity we desire
to calculate.
_ C'E2 rKEH „, rKl
^^ = -48T°rC=24r (35)
end to the other, is equal to one-third of the static capacity of the two
surfaces.
The actual distribution of potential differences between the two layers
is more nearly as shown in the curve of Fig. 55; such a distribution will
result in C" being somewhat smaller than the value obtained in Eq. (35).
Internal Capacity of a Multiple-layer Coil.—A multilayer coil con
structed with an air space between each layer may have a comparatively
small internal capacity in spite of the fact that it has 10 or 20 layers of
winding; a short analysis shows that the internal capacity, as a matter
of fact, decreases with an increase in the number of layers. If the capacity
Fig. 55.—Potential difference between the two layers of a two layer solenoid at high
frequencies.
between two adjacent layers of the coil is C then the internal capacity
of a coil having N layers is nearly C/N, as will be shown.
The electrostatic field in such a coil has a distribution about as shown
in Fig. 56, which represents a cross-section through the winding of an air-
spaced coil, having 8 layers. The cross-section is shown through one. side
of the coil only, the other side of the coil would be similar.
If a voltage of E volts is impressed across the terminals of the coil,
the voltage between adjacent layers (at the ends where the two layers
are not connected) is E+N/2.
Let the normal geometrical capacity between two adjacent layers be
C, this is the capacity between two cylinders, insulated from one another,
of same dimensions as the layers of wire, and spaced by the space between
the two layers of wire. If the potential gradient between two adjacent
layers is assumed to vary uniformly from a maximum at one end to zero
at the other (where the two layers connect together) as illustrated in Fig.
54 the energy between two adjacent layers is found by integration to be
2E2
C~™. As there are N— 1 spaces between layers where this much energy
oiV
2 Z?2C
is stored the total energy stored is (N— 1) «
176 RESISTANCE—INDUCTANCE—CAPACITY [Chap. II
I C \E2
\N-l) 2 '
But from the previous paragraph the stored energy in the coil is actu
ally
2ff2C_ /N-1\22E2( C \
( }3N2 \ N ) 3 \N-lJ'
INTERNAL CAPACITY OF COILS 177
(36)
the value calculated from Eq. (36). As examples of how well the pre
diction may be made the data for two coils are given herewith.
The natural period of a multilayer coil docs not increase rapidly with
increase in inductance. Thus if the number of layers in such a coil is
doubled, the inductance is increased nearly four times, but, as the capacity
has been decreased to only half its previous value, the natural period has
been increased only about 40 per cent.
CHAPTER III
Fig. 1.—Cross-section through surface of water, immediately after pebble has been
dropped at A.
tions) towards B and C, and will produce the bulges at B and C known
as " crests." These bulges are due to the fact that the water displaced from
A tends to raise the level all around A, but, on account of inertia, this
cannot be done quickly enough, with the result that the level is raised
most at B and C, and hence the " crests."
Considering the disturbances to the right of A alone, the particles of
water in the space EBD will, because of gravitational forces, seek the
average level of the water, and, in so doing, the bulge EBD will be made to
1 If a wave is so high as to " break," i.e., an impure wave, this statement is not
quite true.
179
180 GENERAL VIEW OF RADIO COMMUNICATION [Chap. Ill
disappear, and a depression will be created thereat due to the fact that,
on account of inertia, the particles move beyond the average " level posi
tion." Not only is this the case, but the particles to the right of D will,
one after the other, be urged, as if elastically tied together, to perform
motions similar to those of the particles within EBD, so that a crest will
presently appear to the right of D at the same time that a depression or
" trough " is created in the region EBD. The result is that a " trough "
and a " crest " of a wave will appear to move in all directions, away from
the center of disturbance at A, and with a definite velocity.
It must be understood that the motion of the particles is limited to
a small region around their positions of equikbrium, and that the wave
is propagated by imparting this motion to one particle after the other,
while each particle, after the disturbance has passed, remains in practically
the same position as it originally occupied.
An exact analysis of the motions of the particles is extremely complex
and will not be attempted here, but we will give certain well-known ele
mentary facts regarding it because of the analogy between certain points
regarding water waves and electromagnetic waves.
Theory indicates and experiment corroborates that the water particles
within the path of a wave execute motions which are in the simplest cases
circular. Taking this case of circular motion of the particles and con
sidering Fig. 2, at C a particle of water will just be passing through the
->. Direction of wavejtravel
tinguish it from the " radiation field," wherein we are more vitally inter
ested.
In the case of the " radiation field " at any point such as P, Fig. 3,
the magnetic field would act along PD and the electric field along the
line PC at right angles to PD, while the disturbance would travel in the
direction of the arrow at right angles to both PC and PD. Both fields
change in value and in direction in accordance with the variations of the
current in the conductor producing the disturbance; if this is harmonic
the two fields will change harmonically. At some other point such as
Pi the disturbance will arrive a little later than at P with the result that
the fields at P and Pi are out of phase, the phase difference depending
upon the frequency and the velocity of propagation.
Considering one of the two fields, say the magnetic, and plotting the
instantaneous value of the field against distance from the conductor of
Fig. 3 we would obtain a curve such as A in Fig. 4, which applies to any
v= (2)
TV Surface of ocean
that is, the wave would stop completely; 1 the energy of the wave would
1 This conclusion is not strictly accurate; the velocity in such a case would be much
less than the velocity of light, but would not be zero. The discrepancy arises from
the very elementary viewpoint from which wave motion is here considered.
TYPES OF WAVES USED IN RADIO 185
system, depending upon the kind of current used to produce the waves.
Thus, two systems of radio transmission are at present in use, which are
distinguished by two different kinds of waves. These are known as
" Undamped wave " and " Damped wave " systems. In the former the
current which is made to flow through the antenna when the operator
presses his key is an alternating current of constant amplitude (undamped),
so that the waves produced are such that at any point in space the maxi
mum value of the intensity of the electric field and of the magnetic field
is constant as long as the wave is passing.
In the " Damped wave " system, on the other hand, the current sent
into the antenna at the pressing of the key may be represented by the
graph of Fig. 6, from which it may be seen that the waves are sent out in
" trains," each train consisting of a number of waves of diminishing ampli
tude; so that at any point in space the maximum value of the intensity
of the electric and magnetic fields will not be constant but will be damped.
nf 1 flAAfin — A
ill
Frequency of antenna current
Time *■ A B fixed by time from A to B
v=\f
. v
or /"
X = ^ = 30,000 meters
Antenna
Oscillation transformer,
transfers nigh frequency
energy from closed
circuit to antenna
high power, long range, and utilizing the lower radio frequencies. Chief
among the advantages obtained are:
1. A given amount of power in the form of a continuous wave signal
will in general give a louder response in the telephone receivers
than would the same amount of power in the form of spark
signal (due to the characteristics of the receiving circuits).
2. Due to the scheme of reception the interference between stations
is much less for continuous waves than for spark waves.
8. To radiate a given amount of power requires less voltage on
the antennae (hence cheaper antennae construction) for con
tinuous waves than for spark waves, due to the fact that in
one case energy is being continuously radiated, and in the
other case for a small fraction of the time only.
Undamped oscillations may be generated by the high-frequency alter
nator (Alexanderson and Goldschmidt types), the Poulsen arc, a scheme
utilizing saturated iron cores, or the oscillating vacuum tube; all act to
send through the antenna circuit an undamped high-frequency current.
This current may be varied by means of a key, which may interrupt the
supply to the antenna?, or change the frequency of the oscillations
CONTINUOUS WAVES 189
Second. The relative strength of the desired signal and signals received
from interfering stations. When the interfering station is relatively
close to the receiving station, thus producing heavy interference, the
reception of the desired signal may be extremely difficult, even though
the frequency of the interfering station may differ to a considerable extent
from that for which the circuit is tuned.
Third. The pitch of the signal note heard in the phones, as deter
mined by the group frequency of the several transmitters in operation.
If the pitch note of the desired signal is distinctive, as compared to the
notes of the interfering stations, then the signals may be read " through
the interference " and the message obtained. This would be the only
feature whereby the signal could be distinguished if the radio frequencies
of the several stations agreed closely and the interfering stations were
relatively close to the receiving station.
Simultaneous Sending and Receiving.—In the development of radio-
telephony one of the problems to be met was the elimination of the necessity
of any action on the part of the subscriber, required to change over from
sending to receiving and vice versa. A simple method of duplex oper
ation, as described by E. F. W. Alexanderson,1 is included at this point
to show the possibility of using radio communication in exactly the same
way ordinary telephone communication is carried on.
The arrangement utilizes separate sending and receiving antennae,
located sufficiently far apart, and having natural frequencies differing
from one another a sufficient amount, to make the operation stable. The
general arrangement is indicated in Fig. 10, wherein it will be noted that
the radio system has the same relation to the subscriber as the toll line
in wire telephoney.
A radio telephone current set up in the receiving antenna, due to
excitation from the distant transmitter, is transformed into a current flow
ing in the closed circuit between the subscriber's instrument and the trans
mitting station. The same path is followed by a telephone current origi
nating in the local subscriber's station. Therefore the current set up in
the local receiving station, due to a signal from the distant transmitting
station, will be retransmitted by the local sending station in the same
way as the current set up by the local subscriber station^and consequently,
both sides of the conversation are transmitted by each station and could
be overheard by a third party tuned to either of the two wave lengths used.
If the amplification of the received signal were made too great, so
that the telephone current set up by the speaker came back to him in
intensified form, a cumulative reflective action would be created, which
would result in self-exciting inarticulate oscillations being set up. Any
1 E. F. W. Alexanderson, "Simultaneous Sending and Receiving," Proceedings of
the Institute of Radio Engineers, August, 1919.
ATMOSPHERIC DISTURBANCES 193
High
frequency
generator
static, strays, or X's have been variously applied. These strays have beer,
arbitrarily placed by De Groot 1 in the following classes:
Their intensity and character is a function of the time of day, the sea
son of the year and the location of the station; thus, in the tropics, De
Groot found the most unfavorable time was that of the trade wind. In
general, the worst trouble is experienced when the sun's altitude is highest .
Their intensity is probably dependent somewhat on the dryness of the
air and wind conditions, increasing dryness and high-wind velocities
increasing interference due to this cause.
Elimination of Strays.—It has been described how interference, due
to simultaneous operation of other transmitting stations within range,
may be minimized or eliminated by selective tuning, provided the wave
lengths are not too closely in agreement, and the signals received from
the interfering station are not too strong. This means also fails if their de
crements are high. It may be noted that very powerful or strongly damped
waves act like an impact excitation of the receiving circuits, which are
set into oscillation at their own natural frequency. This response is
secured regardless of the wave length of the incoming highly damped
oscillation; for this reason the circuit is not selective to these waves.
Stray waves are always highly damped, and may be very much stronger
than the incoming signal waves. Therefore, their elimination cannot be
satisfactorily accomplished by selective tuning, but some other arrange
ment must be used which results in their neutralization.
A neutralization scheme, suggested by De Groot, is shown in Fig. 11;
many similar arrangements have been recommended.
Antennae No 1 and No. 2 are similar, but the former is tuned to the
radio frequency of the incoming signal, while No. 2 is practically untuned
because the detector Z>2 is inserted directly in the circuit; the circuit is
made nearly aperiodic and signals from distant stations are impossible
of reception by this antenna. The reception of static signals is just as
strong, however, as are obtained with the tuned antenna.
The receiving circuits of both antennae are coupled together and to
a third circuit containing the phones and condenser (this condenser is
used for tuning the phone circuit to the audio-frequency), this coupling
ELIMINATION OF DISTURBANCES 195
being arranged so that the static currents tend to neutralize one another,
leaving only the received signal current to act on the third circuit.
A later arrangement, as developed by R. A. Weygant,1 is based on
the inventor's belief that static disturbances of the third type specified
above are propagated in a direction perpendicular to the earth's surface,
whereas the signal waves are transmitted parallel to the earth's surface
(horizontally). Two loop aerials were used in the experimental work,
located about 5000 feet apart, the plane of the loops being vertical. The
waves due to static cut both loops in phase, whereas the signal waves,
traveling horizontally, induced e.m.f.'s in the two loops, which were out
of phase by an amount depending on the separation between the two
Similar Antenna)
Antenna No. 2
receiver; if this response is not more than two or three times as loud as
the signal a good operator can read the signal right through the interfer
ing noises.
Attenuation of Propagated Waves.—The electromagnetic waves set
up by the transmitter are propagated in all directions through the ether
at a velocity corresponding to that of light, as discussed in the earlier
portions of this chapter. As the distance from the transmitter increases
their amplitude or intensity decreases, due to the wave spreading out in
ever-widening circles and energy absorption by the different media through
or over which the wave may be propagated. This decrease in intensity,
expressed in terms of the initial intensity at the source, is called the attenu
ation of the wave.
Many investigations have been made to determine the attenuation
of these waves, among the more important of which may be mentioned
those carried out by L. W. Austin 1 in 1909-1910, using the station at
Brant Rock, Mass., as the receiver and the transmitting sets on U. S.
cruisers for sending. His results cover one special case only, namely,
transmission during daylight over sea water. The variation of currents
flowing in the receiving antennae is indicated in Fig. 12. The dotted
curve is plotted to show what the results would be if no absorption of
energy had occurred, in which case the received current would have been
nearly inversely proportional to the distance from the source.2
Through the points, obtained from the experiments, the full-line curve
was drawn, as shown by Fig. 12, the equation of which as deduced by
Austin, is as follows j t ;. _ 0.0015-==
. T n,hr d
r *"wx~"e x
where A is a constant;
I, is the effective current in the transmitter antenna;
I, is the effective current in the receiver antenna;
h, is the height of the transmitting antenna;
hr is the height of the receiving antennae;
d is the distance between the two stations;
X is the wave length of transmission.
All lengths are expressed in kilometers.
For the ranges covered by Austin's investigation, namely:
7, =7.0 to 30.0 amperes
h, and h,= 12 to 40 meters
X = 300 to 3750 meters
d=up to 1500 kilometers
the constant A was found to be equal to 4.25.
1 L.W. Austin: Bull. Bureau of Standards, vol. 7, p. 315, 1911 and vol. 11, p. 69, 1914.
2 More recent tests by Vallauri on the strength of signals received at Leghorn from
Annapolis indicate that the attenuation is much less than Austin's formula predicts.
Vallauri's measurements gave a field strength at his receiving station about ten times as
great as the value calculated from Austin's formula.
VARIATIONS IN ATTENUATION OF WAVES 197
100 200 300 400 500 600 700 800 900 1000
Distance in Miles
Fig. 12.—Calculated and experimental values of current in receiving antenna, as dis
tance from transmitter is increased.
time, the range of transmission being sometimes increased two and one-
half times or more. The transmission, however, is very much more
uncertain, the range sometimes being only slightly greater than in the
daytime.
The electromagnetic waves are generally belived to be propagated
through the layer of atmosphere immediately adjacent to the earth's sur
face, this layer being considered about 30 to 40 miles thick. Above this,
198 GENERAL VIEW OF RADIO COMMUNICATION [Chap. Ill
the atmosphere, due to this low density, and the ionizing action of the
sun's rays, rapidly increases in conductivity, and forms a bounding plane,
of high conductivity, for the layer of atmosphere adjacent to the earth,
whose resistance is comparatively high.
During the day, however, this layer adjacent to the earth is also ionized
to a small extent, increasing its conductivity and decreasing the efficiency
of transmission of the electromagnetic waves, which is a maximum for
a dielectric possessing zero conductivity. With the removal of the sun
and its ionizing effects on this transmitting layer of atmosphere, this
efficiency is increased and thus also the range of transmission. During
daylight the refracting effects of the upper ionized portion of the trans
mitting layer cause the waves to bend over, so that when they reach the
receiving antennse they may be bent at such an angle as to have very
little effect on the aerial. This effect is diminished at night, when the
ionization of this transmitting belt is largely reduced, as already described.
Another interesting fact concerned with the diurnal variation in trans
mission is the fact first recorded by Marconi in his early transatlantic
experiments. When the line of sunrise or sunset is between the two
stations transmission is almost impossible, according to Marconi's results.
It seems as though the twilight line acts as either a reflector or absorber
of the radio waves.
Seasonal Variation in Signal Strength.—The strength of received
signals varies also with the seasons, and in 1912, an investigation cf this
effect was made by L. W. Austin,1 signals being received at Washington,
D. C, from the radio stations in the Philadelphia and Norfolk Navy Yards.
The results obtained are shown in Fig. 13.
The reason for this seasonal variation of signal strength is ordinarily
considered as being due to the absorption of the waves by vegetation,
thus causing a marked decrease in intensity during the summer months.
This seems to be a reasonable conclusion, in view of the fact that trees
have been successfully used as antennas, thus demonstrating their energy-
absorbing qualities. It was found that rainfall had no appreciable effect
of the signal intensity.
Amount of Power Sent Out and Received.—Hertz showed that the
electric and magnetic forces in the radiated wave varied inversely as the
distance from a small Hertzian oscillator. The same relation is true for
an ordinary grounded antennae if the distance assumed does not exceed a
few hundred miles.2 The energy thus decreases inversely as the square
of the distance, while the amplitude varies inversely as the distance.
(See dotted curve shown in Fig. 12.)
'L. W. Austin "Seasonal Variation in the Strength of Radiotelegraphic Signals."
Proc. Institute of Radio Engineers, June, 1915.
!See Chapter IX, page 707.
AMOUNT OF POWER USED IN RADIO 199
Duddell and Taylor 1 were the first to investigate the decrease of field
as the distance from the transmitter increases, and a few of their results
are given in the following table; the transmission was over land, but
it is likely that for such short distances as were used in their tests, the
values indicate accurately what might be expected over water also.
From these figures it is readily seen how small the received power is
compared to the power input to the transmitting antenna circuit.
The experiments of Austin, previously described, resulted in the
empiric formula given on page 196, which holds approximately for dis
tances up to 1000 miles. For the smallest distance considered, viz., 22
miles between the stations, using a 1000-meter wave, the following values
were noted:
Antenn-e Corbent.
Miles Receiving Wave
between Sending Station. Station. Length Sending Receiving
Stations. Meters. Station Station
Amperes. Micro-
Amperes.
22 U. S. S. Birmingham Brant Rock 1000 33 10,500
22 U. S. S. Salem Brant Rock 1000 27 11,000
22 U. S. S. Birmingham Brant Rock 3750 27 3,200
22 U. S. S. Salem Brant Rock 3750 24 4,100
XB
Fig 14.—A peculiar effect often observed in radio communication, giving rise to the idea
of radio "shadows."
L^+Ri+v = 0,
v being the voltage across the condenser at any instant. Then
202
FORM OF CONDENSER DISCHARGE CURRENT 203
and
At"'(m2+~m+^j=0 (la)
m2+zm+zc=0-
There are two roots to this equation either of which will satisfy it. As
Eq. (1) involves the second derivative of i we know there must be two
independent solutions for t and these two values of m which we call mi
and m.2, permit the two required solutions being written. The complete
solution of Eq. (1) is the sum of the two particular solutions, so we write
as the complete solution
i=Aiemii+A2tm*, (2)
where
So we have
i = t-<*(Alf*+A2t-iu) (3)
-2=(fi-a)Ai-Q+a)A2 (5)
in which
The quantity a is always real, which means that the amplitude of the
current continually decreases with increase of time. The quantity
— which determines the form of the current, while it is decaying,
depends for its value on the quantity /3; this may be either real or imag
inary, according as a2 is greater or less than The form of the current
will be analyzed for the three conditions—
Case 1. °?>j£-
E
-(^-2—) = -^-<*Sinh#. ... (7)
PL'
The negative sign indicates that the effect of the current is to decrease
E, i.e., to release the charge on the condenser—as to whether or not cur
rent is actually positive or negative depends upon the polarity of charge
on the condenser assumed positive.
The form of current in this case is shown in Fig. 2; the lines properly
marked give the two terms t~at and sinh fit. The figure is drawn to scale
for £=100 volts, C = HV/, L = .20 henry, and ft = 500 ohms. By cal
culation we find a =1250 and /3 = 1030.
The maximum current is reached at a time calculated from putting
the first derivative of Eq. 7 equal to zero.
NON-OSCILLATORY CONDENSER DISCHARGE 205
or
<. = 20log«c^
1 , *+P
(8)
!
!
i Ci rrt nt
i
I
Ea: t = o-fJi1 lo ci±
Io
SI 111] It
-a
/
/
Time in 10" seconds
Fig. 2.—Calculated discharge current when the R of Fig. 1 is too high for oscillatory dis
charge.
Case 2. a2 =
LC
1 2L€ V 0 )'
the value of the expression in the parenthesis being indeterminate. We
evaluate it by differentiation and get,
d_
dp
0=0
206 LAWS OF OSCILLATING CIRCUITS (Chap. IV
Hence in this case the equation for the discharge current is,
For the conditions given this time is .001416 second after closing the switch.
Case 3. a2 <j£
/i/oer/vJtc discharge \
o>*<!? condense \
77
F
e - °' sin uit (ID
1.0 1
.8
hi I' r V <
/ p // IE - Q it t t
// > f \ 1 I1
A / ( , \ 1 1
1
l)1 1 • |
OS"J .2 ■J Vu f ?* i;
i III e "a — _ |UJ" |
&o n sir r ftT
E A t • i « 1
3J 4 Ci rr •nt /
1 > 1
.1 i 1•
I\- 11 i • \\
— {1 \\ A/
.« y I
( 'V,
.8
1.0
Fig. 6.—Value of R of Fig. 1 reduced sufficiently to permit the ordinary oscillatory dis
charge, giving a "damped sine wave,"
In Fig. 6 are plotted, in dotted lines, each of the terms of Eq. (11) for
a circuit of #=100 volts, C=10 m/, L=.20 henry, and R = 50 ohms.
R _ 50
We have = 125
~~2L 2X20
-^/L^2=^/^1xl-o-1252=695•
a = 2T+2%' (13)
and
EFFECT OF CONDENSER LEAKAGE 211
The three cases considered in the previous section occur also for this
circuit; the conclusions reached are the same, except where previously
2£ determined the damping, we now have the quantity
The conditions for oscillations or no oscillations is affected by the con
denser leakage in a manner not to be expected; with no leakage the non-
oscillatory condition is reached when
R 1
2L<VLC
and for the leaky condenser the criterion is
\2L 2C)cyTLC t
that is, greater than before, but we now have an oscillatory circuit because
less than ^jjq ^nus we nave *ne unexpected phenomenon
of increased damping changing a non-oscillatory circuit to an oscillatory
one. Fig. 9 shows the three currents for the circuit with leaky condenser,
as in Fig. 8.
The frequency of the free oscillation is lowered by the series resistance
of the circuit, but it is raised by the effect of shunt resistance until this
Bhunt resistance reaches the value such that jj = jj- If the shunt, or leak
resistance, is made still less the frequency will again decrease; from this
it is seen that the effect of a leak resistance (with no series resistance)
is to increase the damping and increase the period, just as is the case for
a series resistance above, but that when both are present the damping
is increased by an amount depending on the sum of the series resistance
and leak resistance, but that the effect of these two on the period is sub-
tractive, and that a certain relation between them suffices for complete
neutralization, so that the natural period is the same as it would be if
the circuit had no dissipative reactions at all.
212 LAWS OF OSCILLATING CIRCUITS [Chap. IV
where V is the velocity of travel of the waves. We therefore find for the
value of wave length of these electromagnetic radiations
^rjjoo^.^ (18)
equal to
VLC
Equation (11) therefore becomes,
as we had before.
In an oscillatory circuit there is a certain amount of energy oscillating
back and forth from coil to condenser, and being wasted during the trans
214 LAWS OF OSCILLATING CIRCUITS [Chap. IV
fer. The frequency of transfer will be the same no matter what the
relative value of L and C, so long as their product is constant. It is
sometimes* desired to establish resonance in a circuit and keep the voltage
low; in such a case a low value of L and correspondingly high value of
C should be chosen. In radio-receiving circuits, however, it is generally
desired to obtain as high a voltage as possible; this is done by using as
low a value of C as possible (sometimes as low as 100 micro-microfarads)
and a correspondingly high value of L.
Damping and Decrement.—In Eq. (19) the factor t 2L represents a
• 5=m • •. (20)
An ordinary radio set has a decrement about 0.1; the large stations may
have a decrement as low as .02, while the upper limit for a transmitting
station is 0.2, this being fixed legally as the maximum decrement a spark
station is allowed. As is evident from Eq. (20), the decrement of a cir
cuit depends directly upon the resistance of the circuit, this resistance
being interpreted in the broadest sense as suggested on page 112. In
transmitting stations the ground resistance of the antenna is likely to
be very important in its effect on the decrement. The decrement meas
DAMPING AND DECREMENT 215
ured from the upper curve of the film of Fig. 7 was .150, while that cal
culated from the constants of the circuit was .152.
In a continuous wave transmitting station the source of high-frequency
power maintains a constant amplitude to the successive cycles and the
station is said to have a zero decrement; in certain receiving circuits
using a vacuum tube for receiver, the effective resistance of the circuit
made to approach zero as nearly as desired, thus making the decrement
of the receiving set approach zero. As explained in Chapter I, pp. 62-65,
the decrement is the important factor in determining the selectivity of
a receiving circuit, as it determines the sharpness of resonance.
Decrement Determined by Energy Waste per Cycle.—The decrement
may be defined as the ratio of the energy dissipation per cycle to the energy
transferred during the same interval of time. Neglecting the small change
in value of maximum current during one cycle we have:
RI2
Energy dissipated per cycle =-st"i
If we substitute for Jo its rvalue determined above (^-\^) and then add
we get
wc+wL=w=^-€-^: : . . . . . (2i)
r
_l_
Tc>t: 1 t lie » V >v -n U (
\ Ki IT .ir IT at •nt ti ■ 1 el rl
\\ , K 10 rt.'J M l c !c Dtl ic lit Id
Ni y
V !
"v"
E /A \
// \\\ 1 V
r
;/ / \\\ \ A1
/ \ / \ -/ V r ^>
// - \\ nj A / \
</ s -
i k
\ T in
\ -
1 )r
C urrent Ru«rrSfa \\ In re I
/*» (_ f I'C s
Ml r< m condeii e
From the equation we see that the original energy stored in the con-
CE2 undergoes a logarithmic decay, with damping coefficient
denser, —5—,
Z , , . , . . . ... ... ,
twice that of the current.
The curves of current, voltage, and energy are plotted in Fig. 10; the
total energy is obtained by adding the corresponding instantaneous values
of the magnetic and electric energy. In reality the current and voltage
are not exactly 90° out of phase, due to the effect of the resistance of the
circuit so that the addition of the two components of energy does not give
ENERGY DECAY IN AN OSCILLATORY CIRCUIT 217
the smooth exponential curve shown in Fig. 10, but a wavy exponential
curve as indicated in Fig. 11. Here a decrement of 0.3 has been assumed,
3
giving a power factor of — = .0955; the phase difference of E and I is there-
7T
fore 84.5°. The energy for the electric and magnetic fields no longer adds
to give the smooth energy curve of Fig. 10, but indicates that the dissipa
tion of energy from the system is more rapid at certain parts of the cycle
than at others. When all the dissipated energy appears in the form
of heat in the series resistance (as supposed for Fig. 11), the maximum
rate of dissipation corresponds with the time of maximum current as it
should; when the current is zero there is no energy being dissipated.
ot Ei iei n
\^\ 1
re n i Kill ■1. IK a.
t' tin ■no i » cor dens Bl
/
/ ■
/ >
/ / i
/ t \ <■
7 / >\
f s // J S A -> > / M ST
/ *
j / N ■—
Curr et t
Vn 1 iir
r
The relation may also be expressed
IL
rC
or we may also put it in the form,
L C
Such a proportionality 1 in the series and shunt resistances of the cir
cuit will result in a power consumption in the oscillating circuit which
does not fluctuate throughout the cycle as it does when the relation is
not maintained. Hence the energy decay in the circuit is not a wavy
line as given in Fig. 11, but a smooth logarithmic curve as given in Fig. 10.
It is interesting to note that this proportionality of series and shunt
resistances is the same as is required to make the natural period of oscil
lation the same as if no dissipative reactions were present in the circuit.
The natural period of such a circuit was given in Eq. (14); it is seen that if
R=g
L C
then
*
/-_
2*\rLC'
--^('-f^-vfe' <23)
where i?o= initial resistance of spark gap. Although not so stated in
Stone's paper, this value Ro must be approximately this resistance at the
LAWS OF OSCILLATING CIRCUITS [Chap. IV
first current maximum. The other symbols have their ordinary meanings.
The solution is really of little importance in radio work, because in no
case is the spark gap the controlling factor in a radiating circuit. Such
a circuit would use up practically all of its stored energy in heating
the spark gap, so it is practice to remove the high-frequency power from
the spark-gap circuit as quickly as possible and let it radiate from a. cir
cuit which has no gap. Even when the energy is in the spark-gap circuit
the resistance of the gap is small compared to the resistance introduced
into this circuit by the coupled antenna circuit as indicated by Eq. 84, p. 91.
The current of Eq. (23) is different from that of Eq. (11) in that the
successive maxima have a constant difference, whereas those of Eq. (11)
have a constant ratio. Thus the linear damping gives a wave train (group
of oscillations) which has. a definite end, whereas the logarithmic decre
ment never actually reduces the current to zero.
Number of Waves in a Train.—When an oscillatory current is expressi
ble by Eq. (11) it is evident that there must be an infinite number of cycles
per discharge of the condenser (or per wave train) ; the damping factor
_ Rt.
e 2ij makes the current approach zero value, but theoretically it never
reaches the zero value. It is customary in radio practice to say that a
wave train has ended when the current amplitude has fallen to 1 per cent
of its initial amplitude; this means of course that the energy remaining
in the circuit is only (1 per cent)2 = .0001 of its initial value.
The successive maxima of current are related by the equation
/„=/i€7("-1)a. .., . . ,
and if ...
4i=ioo,
In ' ■ ■• • i .
we have - log, 100= (n -1)5, 1 "
or
n=> —T—». . . ... ... . . . (24)
4 6+ 05
Thus if the decrement of an antenna is .05 there will be —'-—^— =93
.Uo
complete cycles before the energy has been sufficiently dissipated to reduce
the current to 1 per cent of its initial value.'
In the case of a linearly damped wave train the number of waves is
very few, principally because if the gap resistance is so large that the rest
of the circuit resistance is negligible (a necessary assumption for linear
decrement) the decrement is of such a high value that the wave train
cannot have more than perhaps five to ten cycles before it is completely
finished. .i ■ i.., • ,. .
EFFECTIVE VALUE OF A DAMPED SINE CURRENT 221
Evidently the value of this integral will vary with the length of time over
which the integration is extended, and is to this extent indeterminate in
value. • As in practice one wave train follows another in rapid succession
we are really interested in an integral of the form,
so
a*2 =" ■ (2*Q2 ■
«2+<o2 (/«)*+ (2*/)2
1+
So
72=
4/5 .
1 1\* .
Now, 1^1 is, for the most radio circuits, negligible compared to
unity. If we write in place of the theoretical value of current Jo2, its
C ■ 1
equal, E2 T, and put . ., ,= 1, we get the expression,
T2 NE*C NE2C
4/5L- 2R '
222 LAWS OF OSCILLATING CIRCUITS [Chap. IV
or
(25)
We could have obtained the same result by noticing that all the energy-
stored in the condenser is transformed in heat or radiation by the oscil
latory current. So we can put
■PR,
2
or
as before.
The value of I is what a hot-wire meter in the circuit would indicate;
the maximum instantaneous value of the current directly after the dis
charge starts may be a hundred times as great as the value given by
Eq. (25).
Effect of Neighboring Circuits on Frequency and Damping.—If another
closed circuit of inductance and resistance is so situated that currents
are induced in it by the oscillatory current of the first circuit, the damping
•of the first circuit is increased and the frequency is increased because of
the decrease in inductance. The changes in L and R due to the extra
circuit are calculable from Eqs. (73) and (74) of Chap. I; the effect on the
, decrement is increased not only by the increase
in R, but also by the decrease in L.
In spite of these effects it is sometimes the
practice to intentionally short circuit part of the
coils in a transmitting set. Thus in Fig. 13 is
shown a diagram of such a scheme; the induct
ance is made in three sections, connected elec
trically, and also magnetically. When being
Li used for short wave lengths (high frequency)
only one section of the inductance, L\ is con
nected in series with the condenser, the others
Fig. 13.—In many radio being used when longer wave lengths are desired.
sets part of the multi- Now with the connection as shown, the inductance
sectional transmitting acts like an autotransformer, generating very
inductance Li-Lj-Ls is high voltages at the open end of the coil. This
short circuited when
but one part (e.g., La) is high voltage may cause excessive losses due to
being actually used for both corona and dielectric losses in the insulating
transmitting. supports. Also the voltage generated at the free
end may be high enough to break down the
coil insulation. To obviate these difficulties the parts Lz and L3 are
short circuited, as shown by the dotted line, thus increasing the decre
ment of the LiC circuit, as noted above. The decrement may in certain
OSCILLATIONS OF COUPLED PENDULUMS 223
where f and f" are lower and higher respectively than the natural period
of each pendulum and V\ and V2 are maximum velocities of these two
component velocities, and a\ and <*2 are the damping factors of the coupled
system for the two frequencies /' and /". In Fig. 15 are shown the graphs
of Eqs. (26) and (27), when applied to pendulums of equal length; the
resultant vi and t>2 will be recognized at once as the form of the velocity
226 LAWS OF OSCILLATING CIRCUITS [Chap. IV
Fig. 15.—Full line curves show actual motion of the two bobs of Fig. 14 for tight coup
ling; the dashed lines represent the two sinusoidal components of the actual complex
motion.
Analysis of Oscillations in Coupled Circuits.—When the switch S,
(Fig. 16), is closed currents flow in each circuit and the equation of reactions
for each circuit is given by
Li D*qi +MD2q2+Ri DQl +ff = 0, .... (28)
where the letters have the meaning shown in Fig. 16, M being the mutual
induction between L\ and L2 and gi and q2 being the charges on con-
d d2
densers C\ and C2 respectively. D stands for^ and D2 for jp, etc.
CURRENTS IN COUPLED CIRCUITS 227
1—vww AMAH
Fig. 16.—When the switch is closed C, will discharge through Li and Ri ; current will also
be set up in circuit 2, the actual current in the two circuits being similar to the
motion of the pendulum bobs of Fig. 14.
i.e., the resistance of the circuit has a negligible effect on the frequency
of oscillation. We may therefore neglect the resistance terms in Eq. (36)
in solving for the periods of oscillation; by doing this we get the compara
tively simple equation,
By substituting
M M2 2 1 2 1
L1L2' L\Ci L2C2
this becomes
' (l-F)D*9i + (a>l2-|-«22)i)23i+a)iWgi = 0. . . . (38)
A similar analysis for 52 would yield
(l-A:2)Z)4g2+(coi2+a)22)Z)2?2+u)i2co2292 = 0 . . . (39)
The solutions of (38) and (39) are, by inspection, of trigonometric
form, so we put
qi = Ai cos (ut+4>), (40)
q2= A2 cos (<jit+4>') (41)
By differentiating these equations and inserting the values of the
proper derivatives in Eqs. (38) and (39) we obtain the two values of to.
,\ (44)
Vl-fc
and ... .
(45)
Vi + fc'
And it is to be noticed at this point of the analysis that these two
frequencies are exactly the same as those given in Eqs. (103) and (104)
of Chapter I for coupled circuits excited by an alternating e.m.f. of vari
able frequency. Indeed from the similarity of procedure we may conclude
CURRENTS IN COUPLED CIRCUITS 229
The constants of Eqs. (48) and (49) must be chosen correctly to satisfy
the initial conditions of the problem.
It will be noticed that these solutions give alternating currents of
constant amplitude, evidently an impossible condition for the circuit of
Fig. 16. The currents must rapidly die away as the energy originally
stored in the condenser C\ is used up in the resistances of the two circuits.
The reason no damping term appears in the expressions for t'i and t2 is
the neglect of the resistance terms of Eq. (36) in passing to Eq. (37). Of
course, a circuit having no resistance has no damping.
Before proceeding to further analysis of the currents in the two cir
cuits it is well to summarize the results so far obtained. When the svriteh
in circuit 1 is closed complex shaped alternating currents begin to flow in
both circuits 1 and 2; these complex currents are exactly represented by two
currents of frequencies fixed by a>" and to', in each circuit. We have there
fore to determine the relative amplitude and phases of four currents I\
and I'2 of frequency fixed by »' (J'i in circuit 1 and I'2 in circuit 2),
and I"i and r'2 of frequency fixed by w" in circuit 1 and V'2 in
circuit 2).
Relative Amplitude and Phases of Currents in the Two Circuits.—An
analysis of the phase and magnitude relations of the four currents
I"2 was carried out by Chaffee and the deductions verified by
an ingenious experiment; the results given below are taken from his
paper.1
By using Eqs. (46) and (47) in combination with Eq. (28) (neglect
ing the resistance term in the latter) we get,
from which
fcco"2 \La'
B2 (ji2-b),z [LI
Bi fcu'2 "S/Lz'
(51)
/'1
Eq. (50) gives the ratio of amplitudes of the short waves in the two
circuits and (51) that of the long waves. As o>" is greater than «i (see
Eq. (42)), it is evident that and l"\ are in opposite phase; when one
is positive the other is negative. The long waves J'2 and 1\ are in the
same phase, however, as their ratio is positive, coi being greater than a/
for all conditions of coupling.
In the oscillation transformer of a transmitting set, therefore, the
effective flux for the short waves is much less than it is for the long waves;
of course, this might be surmised, because the short wave in each circuit
could only occur if the effective L\ and L2 were each diminished by the
action of the other, which means currents in the two coils nearly 180°
out of phase. The long waves, by a similar argument, must occur because
the mutual action of Li and L2 increases the effective inductance of each;
this could only occur if the long wave currents in the two coils h\ and L2
are in phase, i.e., they magnetize their mutual field in the same direction.
To express the amplitude relation of the two currents in each circuit
it is more convenient to express the relations of Eqs. (42) and (43) in terms
2 V
of wave lengths. Using the relation X = for each frequency involved
G)
(V* being velocity of propagation of the electromagnetic waves), we get,
(52)
(53)
As Eqs. (42) and (43) were simplified by supposing the two circuits
tuned alike, i.e., Xi = X2= X we may write, for this condition, Eqs. (52) and
(53) in the abbreviated forms
(54)
(55)
232 LAWS OF OSCILLATING CIRCUITS [Chap. IV
Eqs. (50) and (51) may also be written in terms of wave length and
they become,
»\ 2
I"2_ rr.
[Ll
(56)
/"i k \L2
i
r* (xi)
(57)
J'i k
To determine the ratio -stt- and yjr- we set down the initial conditions
1 i 1 2
of the circuit. When t = 0 (time of closing switch) qx=Qo, 92 = 0, i'i=0,
and i2 = 0. Using these values in Eqs. (46), (47), (48) and (49), we get,
Qo = A i cos <f>" + Bi cos <f>' (58)
0= A2 cos <t>"+B2 cos <j>' (59)
0=Aiw" sin 4>"+Biw' sin <j>' = I"i sin 4>"+I'i sin <&'. . (60)
0= A2to" sin 0"+B2</ sin 4>'= 1"2 sin c>"+/'2 sin <*>'. . (61)
To satisfy these conditions we must have <f>'=<6" = 0. Then we find
as A2= —B2, and I"2 = A2w" and I'2 = B2oi', that
(£) (62)
/"2 «'
t)'
Dividing (50) by (51)
/'Vi, co^-a.!2 a/2 _ u"2-m2o>'2
V'xl'i co"2 wi2-co'2 a>i2-co'2 to"2
Multiplying by (62) and get,
For convenience in using the relations of Eqs. (62) and (63), the values
X" X'
of — and t- have been calculated by Chaffee and are reproduced in Fig.
Xi Xi
X" X' \o
18. In this figure are shown the variations in — and — as r-, is varied.
Xi Xi X!
this ratio being varied by varying X2 by a variation in condenser C2.
. X2 .
This keeps k constant as the ratio — is varied.
CURRENTS IN COUPLED CIRCUITS 233
To get the magnitudes of the four currents, we solve for Ai, B\, and
A2, B2. From (58)
Qo = Ai+Bi
From (60) J'l = JW and I'\ = AW,
Bio' I\
from which
Aiw" I'\
.5 1.0 16 2.0
Value of X*/x,
Fia. 18.—Variation in ratios of X"/X, and T/7, as the ratio of Xi /Xi is varied, for
different values of coupling.
(64)
And as B\ = Qo —A\, we have
(65)
From (61)
234 LAWS OF OSCILLATING CIRCUITS [Chap. IV
and by using (50) then substituting for h" its equal u"A\, we get
a a /""2-"i2\ fin
F",=
#(B2(6
WW
Wot
The values of these F factors are plotted in Figs. 19-22, which serve to
show how the four different currents vary as C2, the condenser in circuit
2, is varied, other things remaining constant. An examination of these
curves shows that with weak coupling and tuned circuits the variation
in amplitude (due to beats) is from maximum to zero as the values of F"i
and F'i are equal in magnitude as are those of F"* and F'2. For tighter
couplings the ratio of r- must be different than unity to make F'\=F'\
CURRENTS IN COUPLED CIRCUITS 235
or F"i ~ F'2. Furthermore with other couphng than very loose no ratio of
r- can be found which will make both F"i = F'i and F"2 = F'2 so that,
^10
F,"
0.1
.6
0 1 L5 2
Uutto % \
A
-.5
1.0 1
.5 \
—— —
17
0 .1 ■I
10 1
i>.
Ill tio -X*
.5
for any value of coupling by the proper amount of de-tuning, but the values
of Fn2 and F'2 are such as to preclude the possibility of zero amplitude beats
F,'
fe- 0.5
.5
f'
>
0 1 1s 2
s.
&
,k-- = 1.0
0 i 1. 1 i
Pi tio
current occurs in the second circuit when the ratio of — is slightly greater
Al
than unity. This might have an important bearing on the use of a wave
meter; this instrument is a coil and variable condenser which has an
ammeter (or other device) for indicating resonance with the circuit, being
tested. A precise analysis shows that maximum current will occur in
this wave meter when its natural period is somewhat longer than that
of the circuit being tested; as maximum current in the wave meter is
ordinarily taken to signify resonance with the circuit tested it is evident
that an appreciable error might be incurred.
It appears, however, that with a coupling between wave meter and
the circuit tested as high as 10 per cent the error in wave meter reading
is less than 1 per cent and as the wave meter coupling is, in practice,
seldom more than 1 per cent or 2 per cent, the error is probably well within
the precision of measurement.
The previous analysis of amplitudes, resulting in Eqs. (68) and (69)
for the currents in the two circuits, was carried out without considering
the resistance terms in the original equations, (28) and (29). The consid
eration of damping would have greatly complicated the derivations, and
the damping factors can be introduced now without invalidating the pre
vious work.
The damping factor of the high-frequency wave is the same for the
high-frequency current in both circuits and similarly for the low-frequency
wave. If we call the damping factors a" and a', it is possible to derive
the relations 1
(70)
al' being for the high-frequency currents and a' for the low-frequency
currents.
It is to be noticed that if Eqs. (70) and (71) are changed to give decre
ments (the two circuits being tuned), they assume the forms
and
where Si and 52 are the decrements of the primary and secondary circuits,
respectively. These solutions are approximate and good only when the
decrements are low.
The complete solutions then become,
ii = coiQo(F"i(-a"' sin w"<+F'ie-«''sina/tV (72)
cuits being practically identical. For each L = .0395 henry and C = 39.5
microfarads. The coefficients of coupling were .424, .282, .114, and
.0707, respectively, for the several curves. The films do not quite bear
out the preceding theory on amplitudes, as the values of Fx' and F\"
are evidently not near enough in amplitude to neutralize each other for
even the minimum coupling, 7.07 per cent. It is quite likely that the
rather high decrement of the circuit had an appreciable effect on the
various amplitude factors, not accounted for in the previous analysis.
Frequency of the Actual Complex Current.—By inspection of the films
shown in Figs. 23-26 it is seen that the time between successive zero points
in the current wave is practically constant (indicating constant frequency);
in fact, careful measurement shows the frequency constant (for Fig. 26),
within about 1 per cent, except at the points of minimum amplitude, where
CURRENTS IN COUPLED CIRCUITS 239
the time between successive zero points changes very much. Just what
changes take place in the magnitude and phase of the current at this
time depends altogether upon the relative amplitudes of the two component
currents.
In Figs. 27, 28, and 29 are shown three possible conditions at this
tune of minimum amplitude of the actual current. In Fig. 27 we have
shown the condition for Fi" = .5 F'i, in Fig. 28 for F"i = .9 F'i and in
LAWS OF OSCILLATING CIRCUITS [Chap. IV
Fig. 29 for F"i = 1.25 F\. For all three figures we have «"= 1.20a/,
which means a value of coupling of the two circuits of about 20 per cent.
It might seem that as the frequency (time between successive zero
points) of this " beating " current is constant, that a third circuit, coupled
to the circuit carrying this complex current, would respond most strongly
if tuned to this frequency. As a matter of fact but little response will
be had in this third circuit if tuned to this actual frequency; if tuned to
either of the component currents of this actual complex current, however,
a strong response will be obtained.
Thus suppose the two circuits of Fig. 16 are each adjusted for a natural
period of 100 cycles, and they are coupled 20 per cent. Then the two
3**,* 03SS A
1 » ' . ; If " f
the actual current t"i. As the two vectors OA and OB rotate their mag
nitudes must continually diminish to keep them equal to F'\e ' and
The loci of the terminals of the vector are logarithmic spirals
about the point 0. The logarithm of the ratio of the values of a vector,
in two successive passages through the same phase gives the decrement
90 100 110
Natural frequency of third circuit
Pig. 30.- -Amplitude of current in a third circuit coupled very loosely to either of the
two coupled oscillating circuits.
OM
of the current represented by that vector; thus we have log. 8" the
ON"
logarithmic decrement of the current
The unusual motion of this resultant vector as the two component vec
tors pass through phase opposition is indicated in Fig. 33. Vector OA, the
Fig. 31.—At minimum amplitude points the actual current in either of the two oscil
lating circuits reverses its phase.
one with less angular velocity, is shown stationary and the vector OB
is shown in several successive positions around its phase opposition posi
tion; OB is slightly greater in magnitude than OA. With OB in the
position indicated by OB\, the resultant of OA and OB\ is shown by OR\,
etc. It may be seen that this resultant vector moves through the angle
R1OR5, which is more than 180°, while the vector OB has moved about
45°.
The case of OB being smaller than OA is given in Fig. 34; in this
case when OB goes through its opposition phase the resultant vector,
244 LAWS OF OSCILLATING CIRCUITS [Chap. IV
CURRENTS IN COUPLED CIRCUITS ' 245
instead of speeding up as it did in Fig. 33, slows down and goes through
the successive values ORi, OR2, OR3, etc., for the correspondingly marked
Fia. 34.—Resultant vector when low-frequency current has the greater amplitude.
Fia. 35.—Resultant vector when both currents have the same amplitude.
dition when the two vectors are 180° out of phase the resultant vector
is zero.
It is quite possible so to adjust the tuning of the two circuits that
the vector OB is greater than OA at the start of the oscillations; then
as the oscillations continue, OB, having greater damping than OA, will
become equal to OA and then smaller. Hence in three successive beats
it is possible to have the resultant vector OR go through phase changes as
depicted in Figs. 33, 34 and 35, respectively, as the amplitudes of the actual
current goes through its minimum values. The effects of these peculiar
angular velocities of the resultant vector, in combination with its changes
in magnitude, account for the peculiar form of the actual current during
the one or two cycles of minimum amplitude. It is seen in Figs. 27 and
29 that the 180° phase shift which occurs at the point of minimum ampli
tude may be produced by either a gain of 180° or a loss of 180° at this
time. Fig. 27 shows a loss and Fig. 29 a gain of nearly 180° during the
time shown in those curves.
Frequency of Beats.—The beats are not well pronounced unless the
two circuits are tuned to the same natural frequency; in this case all of
the energy surges back and forth from one circuit to the other. With
untuned circuits only a part of the energy is exchanged between the two,
most of it remaining in the primary circuit; in this case the beats are not
so pronounced as for the tuned circuits, because it is really the to-and-fro
flow of the energy which gives the beats
In the case of tuned circuits the two frequencies are given by Eqs.
(44) and (45),
to" = <>> ( ,—— ) and w' = wl —. ^ |.
Vl-jfc/ Wl + k/
Hence
«" - a/ = o> ( .L_ —7^=\ ^ «fc (74)
Wl-k Vi + k/-
This holds, of course, for low values of k only.
As the number of beats per second is equal to the difference in frequency
per second of the two component frequencies, we must have the number
of beats per second which are given by the relation N=fk.
We have shown previously that the frequency of the complex current
for tuned circuits (except at the minimum amplitude point) is /. The
number of cycles of current per beat is therefore obtained from Eq. (74)
by writing,
M • <75>
ACTION OF QUENCHING SPARK GAP 247
Flo. 36.—Forms of primary and secondary currents if primary circuit is opened at the
first minimum.
Fig. 37.—Forms of currents in coupled tuned circuits when the coupling is weak and
damping is high.
ment, having a large condenser and only one or two turns in its induct
ance. This gives a high value to especially when the resistance of the
spark gap is taken into account. In addition to the high primary decre
ment, the gaps used in this method of generating oscillations are of the
quenching type so that when they are functioning properly but one pulse
exists in the primary and the secondary is left free to oscillate at its own
period and its own decrement.
Oscillatory Circuit Excited by Continuous Voltage.—In case a circuit
of L, C, and R, in series is connected to a source of continuous voltage
E, Fig. 38, the equation of reactions is
B-L%+Ri+% (76)
By differentiating once this equation becomes tne same as Eq. (1), and
so its solution must be the same. The same three cases are to be con
250 LAWS OF OSCILLATING CIRCUITS [Chap. IV
sidered here as they were for Eq. (1) ; the more important one of the solu
tions being that of Eq. (11). The initial and final conditions of the problems
are different than those considered previously. Evidently at < = 0, ve = 0
and at <=oo, vc= E; these conditions affect the equation of voltage across
the condenser terminals, which becomes approximately,
•b-Js(l-«-2Zcos~^ (77)
This equation brings out the interesting fact that the maximum volt
age across the condenser in such a circuit as that given in Fig. 38 is nearly
double that of the source of e.m.f. to
-N-v—WWV—I which the circuit is connected. This
R | is illustrated by the film shown in
Fig. 39; the voltage of the c.c. line to
] which the circuit was connected
1 was 105 volts, whereas the maximum
Fig. 38.—Oscillatory circuit con- potential difference across the eonden-
nected to a source of continuous- ger was 190 volts. It is evident from
current power. oscjii0gram tflat if the dielectric
strength of a condenser is to be tested
by connecting it to a source of continuous e.m.f., a resistance should be
used in series with the condenser of sufficient magnitude to make the
circuit aperiodic. If this is not done the maximum voltage across the
condenser is not E, the voltage of the line used for testing, but is equal
_^
to E(l-j-t 2), where 5 is the decrement of the circuit.
Oscillatory Circuit Excited by Energy Stored in Inductance.—In
certain radio-testing circuits oscillations are produced not by the energy
stored in a condenser but by the energy in the magnetic field of the induct
ance. The circuit is indicated in Fig. 40; in the actual testing set the
battery circuit is made and broken many times a second, perhaps 1000,
the function of the switch being performed by the contact points of a
small buzzer. When the switch & is closed the condenser C charges at
once to battery voltage and the current through L and R rises on a log
arithmic curve—Eq. (10), p. 32, to a value E/R, the magnetic energy in the
LE2 . . . .
coil being When the switch is opened this magnetic energy is
emptied into the condenser C, and then the energy surges back into I
as described in the first paragraph of this chapter.
At the end of the first quarter of a cycle of the oscillation all the energy
from the coil is in the condenser; it is then charged to such a potential
CIRCUIT EXCITED BY CONTINUOUS VOLTAGE 251
252 LAWS OF OSCILLATING CIRCUITS [Chap. IV
difference E' that we have (if the decrement of the circuit is so low that
the damping for one-quarter of a cycle may be neglected),
CE^^E* LE2_p2/C . L
2 ~ 2 + 2R* ,2+2«2)'
V
or
E' = Ey[l (78)
CR2'
The cycle of events in such a circuit as shown in Fig. 40 is shown in
the film of Fig. 41 ; of course, all the constants of the circuit used in getting
this film are much greater than those used in the so-called " buzzer wave-
generator " used in radio, but the form of voltages and currents are nearly
the same as those occurring in the radio circuit.
Oscillating Circuits Excited by being Connected to a Line of Alter
nating e.m.f.—If a circuit of L, R, and C, in series, Fig. 42, is suddenly
switched to an alternating current
line, the current must be zero, no
matter at what point the e.m.f. wave
the switch is closed; in general,
the condenser of the circuit will not
be charged. Now in the steady
state the current must have a certain
Fia. 40.—Oscillatory circuit to be ex value for any given value of e.m.f.
cited by stored magnetic energy. as fixed by Eqs. (35) and (36) of
This circuit is the same as used for Chapter I. Also the condenser must
" buzzer excitation " of radio circuits. have a definite charge for this value
of impressed e.m.f. It is evident,
therefore, that in general the initial conditions, when the switch is closed,
will not satisfy the conditions required by the steady state.
For this reason the current for the first few cycles after switching the
circuit to the line will be of irregular form; the circuit requires time to
" settle down " to the steady state. Mathematically this is accomplished
by adding to the equation for the steady current a suitable damped
oscillation, the magnitude of which depends upon the time the switch is
closed and the frequency of which is fixed by the L and C of the circuit.
The actual current after closing the switch is therefore the sum of
the steady value of current and a damped oscillation at the natural period
of the circuit, the two sufficing to satisfy the required initial conditions
on closing the switch.
If the impressed voltage is e = E sin pt, the circuit having constants,
L, C and R and / U r '
<-£~„ the solution is,
2L
At-*' sin (wt') + sin (pt -<t>), (79)
yjR2+(pL
254 LAWS OF OSCILLATING CIRCUITS [Chap. IV
R i H~ ■ 4. i
a = 2L an a,= \LC" aPProxunately>
and t' is the time counted from the start of the supposititious transient
oscillatory current; it is sometimes written (£+Af) where At is the time
between the start of the supposititious transient term and the closing of
the switch—this increment of time is indicated in Fig. 44.
A and t' are to be suitably determined to satisfy the initial condition
that i = 0 and vc=0. This condition, vc = 0, supposes the condenser to be
uncharged at the time of switching the
-^WSAAAA/—| circuit to the line; if it is charged to a
R certain potential difference V, then the
initial conditions are i = 0, vc=V.
L I Let us suppose the steady state of the
-^TJO^JO^r^"^ circuit is as represented in Fig. 43, and
„ ,. . .„ , . further let us suppose that the switch is
Fia. 42.—Oscillatory circuit to , . . , . ,. . . . T ,,
be connected to source of closcd at the Phase '"Seated by 6. In the
alternating-current power. steady state the current should be /' and
the voltage across the condenser should be
V. Actually the current at the time of closing the switch is zero, and
we also suppose an uncharged condenser, so that vc = 0. We must then
determine t' and A of Eq. (79) that these initial conditions are satisfied.
The equation for voltage across the condenser, due to the transient
term only, we write,
ve= Eof-"1' cos wt', (80)
and hence, the current due to the transient term is,
i = C^= -wCE0t~at' sin a>;' -aCE0t-a'' cos ut'.
at
We here make the same assumption we have previously made for
similar circuits, that a is negligible compared to to, and so we get,
t= -uCEot-**' sin W (81)
Using the condition that the voltage across the condenser must be
zero at the time of closing the switch, we have
vc+ V = 0 or - V = t-°"'E0 cos wt'o,
in which i'o is the value of I' when the switch is closed.
Then
V
CIRCUIT CONNECTED TO ALTERNATING VOLTAGE 255
Also,
i+l' = 0, so from (81) using also (82)
j, a>CV e-'"'' sin ut'o
Fig. 43.—Proper "steady state" values of voltages and current of circuit of Fig. 42,
at time of closing switch.
In case the damping of the circuit is small this equation may be written
From this equation we get tan ut'o and so may find the value of cos oit'o.
Knowing ut'o and w we get t'o and so can calculate t_a''° and then substi
tuting in (82), we get Eo; evidently A = -o>CE0, which can now be
substituted in Eq. (79).
256 LAWS OF OSCILLATING CIRCUITS [Chap. IV
the steady value of current and the transient current gives the full line
curve which is the actual current in the circuit after closing the switch.
In Fig. 45 is shown an oscillogram of the transient current after switch
ing such a circuit as the one used in plotting the curves of Fig. 44. From
PERIODIC DISTURBANCES IN OSCILLATORY CIRCUIT 257
/..-/-..>4\
. J i ■ w / m \'
j \ :
FlG. 47.—Voltage and current in such a circuit as that shown in Fig. 46, the switch S
being closed synchronously. Natural frequency of secondary circuit greater than
alternative frequency.
of this ratio. In Fig. 47 the natural period was less than that of the
alternator, in Fig. 48, the two were equal, and in Fig. 49, the natural
period was greater than that of the alternator. As the films were taken
at high speed they are not very distinct, so two cycles have been dotted
in with ink.
It will be seen at once that any mathematical expression to represent
these curves must be a complex one. With the switch adjusted to make
one closure per cycle the circuit is a rectifying one; if the voltage across
the condenser at the time of short circuit is E it is evident that each cycle
1 Fulton Cutting, "The theory and design of Radio Telegraphic Transformers,"
Proc. I. R. E., Vol. 4, No. 2, April, 1916. This article serves to show how complicated
an exact treatment may become; in Chapter V, p. 307-8, are shown some curves which
are calculated from simpler formula?, which curves represent quite accurately the form of
disturbance in the ordinary spark transmitting set.
PERIODIC DISTURBANCES IN OSCILLATORY CIRCUITS 259
Fia 49.—Similar to Fig. 47 but with secondary circuit having a natural frequency less
than that of the alternator.
shape or other; thus it is quite likely that atmospheric disturbances in
radio receiving circuits are due to some sort of highly damped oscillation
or a series of short pulses. The effect of a pulse on a resonant circuit
200 LAWS OF OSCILLATING CIRCUITS [Chap. IV
will depend upon two factors, the ratio of the duration of , the pulse to
the natural period of the circuit, and the intensity or amplitude of the
pulse. Also to a minor extent the exact form of the pulse will determine
the amount of disturbance produced.
The simplest kind of a pulse to consider mathematically is a "square "
pulse, one in which the voltage rises suddenly from zero to a certain value,
holds this value for a short time and then again drops suddenly to zero.
If such a pulse of voltage is introduced into a circuit consistent of L, C,
and R, in series the shape of the current can be obtained by properly com
bining the solutions of Eqs. (76) and (1). Eq. (76) gives the conditions
when the voltage is applied to the circuit and Eq. (77) gives the voltage
on the condenser at any time to after the voltage has been applied. When
the pulse of voltage ends, Eq. (1) applies, the voltage on the discharging
condenser being that determined from Eq. (77).
Thus in Fig. 50 is shown at a the pulse of e.m.f. introduced into the
oscillating circuit, in b is shown in full lines the condenser voltage curve,
determined from Eq. (77) and in the dotted line the current produced
in the circuit by the introduction of voltage E.
Counting <=0 at the beginning of the pulse, we have
i. = —j
E t~al. sin
. ut,,
(84)
and
VC=E(1 -€'"' cos wt), (85)
Now at the end of the pulse the solution of Eq. (1) is available if we
substitute the proper initial conditions. The circuit solved in Eq. (1)
was one in which the initial conditions were a charged condenser and the
zero current. By inspection of Eqs. (86) and (84) it is evident that if
we make T = — the current at the end of the pulse is zero (sin wT=0)
w
and the voltage in the condenser is vc= E(l + c~aT), as cos wT= —1.
The equation for current from the end of the pulse (for length of pulse
=7r/a>) is therefore,
where t' is reckoned after the end of the pulse. This current is shown in
curve c, Fig. 50. At time t' = 5—, sin wt' = 1 and the value of current is
I
t
Lenjrth of pulse \¥*here
(a)
1 >[ oe >
-
/ |y
)
S
-1 0
f V i „ N
\ UJ\ \
\ - /
> / / K s >
\ n F. u Ml !V 1
/ y
/
s / ^ //
(c
0 > t
i J
\ / i T
\ / j
L / E •I /
\ 1 ui ft .1 /
\
\V 1
ZL
TT 1
Fig. 50.—Effect of introducing a rectangular pulse of e.m.f. into an oscillatory circuit.
This is the maximum current obtainable from a rectangular pulse, of
amplitude E, no matter what its duration may be. Any duration either
more or less than t/u will give less value to 7max.
A more fundamental way of looking at the problem is to consider a
voltage of + E impressed on the circuit at the beginning of the pulse, and
that this voltage is maintained; at the end of the pulse a voltage of -E
is impressed on the circuit and maintained. Each of the impressed volt
ages will produce a current, and the actual current at any time is the sum
of the two.
262 LAWS OF OSCILLATING CIRCUITS [Chap. IV
in which t is the time after the (+E) voltage is impressed and t' is the
time after the second voltage ( —E) is impressed. If the interval between
the application of these two voltages is To, then the current after time
To has passed is
(T being the natural period of the circuit), the equation for current becomes
and if we now suppose wt'=ir/2 and write the damping in terms of decre
ment, we get
results are given in Fig. 54 and it is seen that the results are in accord
with the prediction of Eq. (87).
*jr
00
30 >r on (1 . .It rn lti< 11
25
O F, Alt to at
20 \S
15 V
//
/
10
I'll
.1 .2
.4 .3
.5 .6 .7 .8 .9 1.0 1.1 1.2 l.S 1.4
Ratio of pulse length to natural period of circuit
Fio. 54.—Variation in amplitude of oscillatory current with length of pulse.
It is evident (Fig. 55) that pulses properly timed may practically neu
tralize one another as in this case the circuit was nearly dead after the
last pulse.
EFFECT OF PULSE OF E.M.F. ON OSCILLATORY CIRCUIT
Impulse Excitation of a
Antenna Parallel Resonant Circuit.—A
condenser and coil in parallel
act like a circuit of very high
resistance for an e.m.f. of the
same frequency as that nat
5 Infinite
?L circuit ural to the circuit. The value
of the resistance is predicted
by Eq. (48), Chapter I, and
curves are shown in Chapter
"To detecting I, Figs. 70 and 71; because
circuit
of this characteristic the cir
cuit is often called an " infinite
Ground
impedance " circuit. The Eq.
Fig. 57.—Showing the use of a parallel resonant (48) was derived from the
circuit for weeding out undesired signals from an
antenna. Such a parallel circuit is often called steady state of the circuit.
an "infinite impedance."
If the pulse is a square one, such as used in Figs. 50-53, the current
flowing in the supply line (the impedance of the circuit other than that
of the " infinite impedance " being neglected) will be about as shown in
Fig. 58. The e.m.f. pulse form
is shown in curve a; the full
line curve of b shows the
current flowing through the
condenser and the dotted line
that through the coil; in c is
shown the actual current in
the line, that is, the current
which the " infinite imped
ance " circuit lets through.
These curves, as mentioned
before, are drawn on the as
sumption that the impedance
of the rest of the circuit is
negligible.
It would seem likely that
if the circuit does have such
a very high impedance for a
certain frequency then it will
offer a high impedance to a
pulse, if this pulse is in the
form of one alternation of a
sine wave of the same fre
quency as that natural to the
circuit. Fig. 59 shows the
analysis of this case; a shows
the form of pulse e — E sin coi Fio 59.—Effect of impressing a sinusoidal pulse
(holding only between u>t = 0 of e.m.f. across a parallel circuit.
and wt = ir); the curves of 6
indicate the currents through each branch, and curve c shows the current
passed by the combined circuit. As the resistance in the parallel path
is made to approach zero this line current approaches a true rectangular
form, i.e., current of constant magnitude and equal to 2wfCE, where / is
the frequency of the c.m.f. of wliich the pulse is the alternation.
Analyzed mathematically, we have
lL = E{/ t—prg
R SUl 0)< 1T COS 0>H 1Tt L I .
Adding to this the condenser current we get for the current passed by
this parallel combination,
/ R I 1 \ 1 _5T\
i=E\ -,—^-5 sin wt+ ( uC r ) cos n>t-\—j-e l ).
If now the constants of the circuit are such that coC = -V, then
COLi
i = —f —r sm cot+t L J (88)
o)L\<i)L I
Oscillatory Circuit Excited by a Damped Sine Wave.—Let us con
sider a circuit made of L, R, and C in series as e.g., the ordinary antenna,
to be excited by a damped sine wave of voltage such as is induced many
Fia. 60.—Form of voltage induced in a receiving antenna by the passage of one wave
train as emitted from the ordinary spark transmitter.
i = CTt>a = £t>
MMp2+k2)+2k(w2+c^)^t+[(p2+k2)(^+a2)]v = 0. . (91)
and
-**+(«-*>'.
2p(c* -fc)
Now by substituting in Eq. (92) the initial conditions that when (=0
v=0, then differentiating (92) and in this equation putting ^=0 when
t = 0 we get the value of V2 in terms of Vi. Substituting the value of
Vi from (94), we get,
From the values of Fj. and V2 we find at once h and 72 by using the
relations h = pC Vi and h = UCV2:
f,-g , . . , (97)
LV[a,2 -p2 + (a -fc)2]2+4p2(a -fc)2
The values of 0' and <f>'—Eq. (93)—are determined from the values
of 6 and <j> given above, by increasing each of them by jt/2.
The exact form of current in the circuit is now fixed by the values of
h, h, k, a, p and w. It will be evident that if both damping factors are
low and nearly equal, and the two frequencies, fixed by p and w, are nearly
equal, the conditions are the same as those for the secondary current in
coupled circuits as illustrated in Fig. 26 of this Chapter. If p = a> there
can be no beats; for all values of damping, the current, with frequency^-
increases in value from zero to a certain maximum and then decreases
again.
An analysis due to Bjerknes 1 shows that this current can be repre
sented by the equation
t = mCM cos (mt+i), (98)
T, . . p —w k+a , k —a ,
If we let n= 2—' a= 2 ' ~2~'
Equation 100
Equation 102
Fio. 61.—Two possible forms of current in the antenna excited by the wave trains from
a spark transmitter.
In case neither the damping factors nor frequencies are the same the
general form given in Eq. (99) must be used.
In Fig. 61 are shown the forms of current in the oscillatory circuit
for the cases given in Eqs. (100) and (102)
272 LAWS OF OSCILLATING CIRCUITS [Chap. IV
J&k+a 1
16L2 ka (p-o.)2-(Jfc+a)2 * ' U }
J "i u
/. %
Jr
Frequency
Fio. 62.—Resonance curve of a circuit excited by damped sine wave.
If we then read the two values of / (call them fa and fi, fz being greater
than n and fi being less than n), so chosen that the current is reduced to
-4= of its resonance value we shall have
V2
and also
f2 —n
Si + S2 = 2tt
n
Si+S2=l^ir (107)
This is the equation generally used when using a wave meter for getting
the decrement of a transmitting set; although approximations have been
made in deducing it, the errors incurred are small if the sum of the two
decrements is small (say less than 0.25), which is always the case in prac
tical radio sets.
CHAPTER V
SPARK TELEGRAPHY
Li, L'i, Ci, and the gap, in series is called the closed oscillating circuil;
(3) a third circuit, known as the open {radiating) oscillatory circuit, of
high frequency only, containing the following equipment : Inductance L2,
coupled inductively with Li, and forming with L\ the oscillation trans
former; a tuning inductance L3, the antenna or aerial (represented in
the diagram by a fictitious lumped capacity C2) the hot-wire ammeter
Ai, and the short wave condenser C3 equipped with short-circuiting switeh.
The detailed action and function of the above equipment, represent
ing all the essential elements of a spark transmitter, will now be discussed.
The Alternator.—The function of the alternator is to supply electrical
energy to the set, it itself usually being driven by a direct-current motor.
Where a supply of electrical energy is not available it may be driven
by a gas, steam, or oil engine. When motor driven, a storage battery
is sometimes connected across the supply mains, to steady the voltage
impressed on the motor and to act as a reserve in case of interruption
to the source of supply.
The construction and characteristics of the alternator are discussed
below (page 287).
The Switch K, called the key, is used to control manually the energy
supply to the step-up transformer. If this energy is interrupted in accord
ance with a prearranged or conventional plan (i.e., the International Morse
Code), then the radiated energy will vary in the same manner, and thus
signals may be transmitted. (See Chapter III.) The diagram indicates
the key as making and breaking the main circuit current. On the higher
powered sets it becomes impracticable manually to open the main circuit
directly, due to the large currents involved requiring a long break and
heavy set of contacts. The key, therefore, is usually arranged to operate
in an auxiliary circuit, connected to actuate one or more relays, whose
contacts, in turn, make and break the main circuit.
The Step-up Transformer.—Consisting of high and low-tension wind
ings <S and P, raises the potential of the energy supply from perhaps
120 to 10,000-20,000 volts. This increase in the voltage is required for the
proper operation of the spark gap.
For the lower powered sets, i.e., sets having less than 1 kw. rating,
the alternator and step-up transformer may be replaced by a storage
battery and high-tension induction coil. The limitation and operation
of the induction coil is considered in detail below (see page 282).
The capacity Ci forms the reservoir for energy storage as the voltage
impressed across the inductance (Li-f-L'i) and Ci approaches its maximum
value. That the impressed voltage is practically all consumed across the
condenser, and the condenser thus charged to this voltage, can be seen at
once if the reactance of (Li+L'i) and Ci are considered at the frequency
ESSENTIAL PARTS OF A SPARK TRANSMITTER 277
Since the same current flows through both (Li+L'i) and C\ on charge,
it is apparent that the drop across the inductance is negligible, and that
the charging voltage is practically impressed directly across C\. Forms
of high potential condensers and their construction are described below
(page 297).
The inductance Li is essential to the closed circuit, since high fre
quency oscillations are to be produced when the condenser C\ discharges.
In addition to its function of energy storage, L\ forms the means of coup
ling the closed and open (radiative) circuits; in conjunction with La it
is known as an oscillation or Tesla high-frequency transformer. The
variable inductance L'i is not essential to the operation of the set, and
is seldom used in practice.
The function of the spark gap G has already been briefly considered
(Chapter III). Essentially, its action is that of a trigger which permits
the stored-up energy of the charged condenser Ci to be discharged in
the form of high-frequency oscillations, when the potential between its
electrodes has reached a certain critical value. The several forms of
spark gaps used on modern transmitters, and their action, are considered
later.
The secondary winding L2 of the oscillation transformer forms the
seat of induced high-frequency electromotive force and is the means
of energy transfer from the closed oscillating circuit. To control this
energy transfer and to secure proper operating conditions the position
of this coil is varied with respect to L\, i.e., the coupling between the
two circuits is adjusted to give the best results.
When adjusting for' the transmission of long wave lengths, it becomes
undesirable to tune the open oscillating (radiating) circuit by increasing
L2, as this may increase the coupling to greater than the desired value;
excessive coupling possesses several disadvantages as outlined below.
Function of the Tuning Inductance L3.—To tune the circuit, without
increasing the coupling the tuning inductance L3 is inserted; note that
coefficient of coupling between the two circuits is decreased if L3 is increased
and L2 is unchanged. This inductance has no inductive relationship
with either Li, or L2, and is cut into the circuit only when adjusting the
set to transmit at the longer wave lengths. The insertion of a capacity
in multiple with Cz, or across L2, would produce a similar effect.
278 SPARK TELEGRAPHY [Chap. V
circuit coil). Direct coupling has the advantages of reduced space require
ments, simplicity and increased efficiency; it avoids also the necessity
of insulating the two windings from each other. This latter point is
important only when very tight coupling is desired, as under normal
coupling conditions the space between the two coils is such that the
insulation is ample, unless very high voltages are involved.
This arrangement may be used particularly for very small power sets,
using a storage battery and induction coil as the source of high potential
energy. It will be noted that the capacity of the aerial is charged by
the induction coil, and when the gap breaks down, a high-frequency dis
charge is produced exactly as in the case of the closed circuit. A portion
of the high-frequency energy will be radiated, and by its proper control
signals may be transmitted as with the indirectly excited transmitters.
The circuit possesses the fundamental disadvantage that the gap
resistance is in the radiating circuit. The radiated energy will thus have
a high decrement and cause interference to any station which may be
within its sending radius, ^ ■—
unless the station be tuned
to a wave length, remote
from that of the transmitter
considered. The efficiency
of such a radiator is low,
most of the energy being
dissipated as heat in the
spark resistance and as
other circuit losses. Also •=- ■=■
the capacity of the antenna FlG 4._The earliest type of radio transmitter, using
is small compared to the direct excitation, the spark gap being in the
capacity which may be antenna circuit,
placed in the closed cir
cuit when indirect excitation is used thus the current through the spark
gap is much smaller than it would be if the gap were in a high capacity
circuit. The resistance of the gap is higher the smaller the current through
it, hence the high damping effect of the gap when placed in the antenna
circuit. The decrement of the radiated energy is still further increased
by the increased length of gap required as well as by excessive leakage
losses, corona, etc., which may occur at these increased voltages. The
decrement may be reduced by inserting a low resistance inductance L
in the aerial circuit as shown in Fig. 4, and as shown by the formula for
decrement given on page 214. The oscillations will thus decay more
slowly, giving a more sustained effect to the radiated energy; but the
amount of energy radiated is less.
It may not be possible, however, to insert this inductance, if it is
desired to transmit at certain short wave lengths. For these reasons the
direct excitation method is not used on medium- or high-powered trans
mitters, and is found only on very small or emergency sets, when low
first cost or space restriction may be the primary consideration.
Means of Energy Supply.—Modern spark transmitters may be equipped
with one of two forms of energy supply to the closed circuit:
282 SPARK TELEGRAPHY [Chap. V
very rapidly, and (6) the time constant of the secondary or high-tension
circuit must be sufficiently low. In considering the above requirements,
it is desirable to analyze somewhat carefully the actions which occur in
the induction coil at " make " and " break."
Action of Shunting Condenser.—If we assume the operating key
closed, we have the condition of a constant e.m.f. impressed on an inductive
circuit. Therefore the current in the primary increases, as already
described (page 32), and as indicated in curve a, Fig. 5. The flux through
I i
! !
1 1 i
1
Make^j Make^l _
Y a
j Break, x
1 Break,,
1I
1
b
i
I* tfl sec; H
I
V \ e
i i
Fio. 5.—Currents and voltages in the circuits of a spark coil having a vibrating contact.
the core and linking both windings follows a nearly similar variation, as
shown in curve b. We therefore have voltages induced in both windings
of the coil; in the case of the primary this voltage represents the c.e.m.f.
of self-induction; in the case of the secondary, it is simply an induced
ejn.f. and is equal to ^«^» N* being the number of secondary turns.
The secondary induced e.m.f. is indicated by curve c.
At the instant the contact closes the primary circuit the changing flux
in the core must be just sufficient to balance the impressed, or battery,
voltage. We may therefore write for this instant, ^ = ~^~» E being
the impressed voltage and Np being the number of turns in the primary
284 SPARK TELEGRAPHY [Chap. V
1 The condenser should be only just large enough to suppress arcing at the contacts;
if the value of the capacity is greater than this required amount the secondary induced
voltage will be lower than if a proper condenser is used.
ACTION OF INDUCTION COIL 285
resistance then inserted in the circuit is very high and the time constant
is therefore very small. The collapse of the flux is then correspond
ingly rapid if we neglect the effect on this flux of whatever current may be
present in the secondary circuit during this time.
If a condenser shunts the contacts, the time is fixed by the natural
period of this circuit; thus if we assume Cv = lpf, Lv — .01 henry, the time
of the first alternation of secondary voltage is given by the equation
2^>/LC_2^Xl0-3XV^0Txi = 27rXl0-3X.l
= 3.14X10-* sec.1
2 2 2
If a spark does not take place, other alternations of voltage will follow
this one, but will be successively smaller in amplitude and hence would
evidently not produce a spark if the first alternation did not.
Action in the Secondary Circuit.—In the secondary circuit, the e.m.f.
induced must overcome the reactions of the winding resistance and the
condenser, or
N,^I,R,+ve. (1)
1 This elementary analysis is based on the assumption that the secondary circuit
has no effect on the time constant of the primary circuit; if a condenser is connected
across the secondary terminals (or the internal capacity of the secondary winding has
an appreciable effect) this assumption is hardly warranted.
286 SPARK TELEGRAPHY [Chap. V
primary " break " is indicated to a larger time scale in Fig. 6 1 where (a)
indicates the conditions with the spark gap disconnected from the second
ary circuit while (b) shows the operation when both the condenser and
gap are across the high-tension winding as in normal operation.
The duration of the train of high-frequency oscillations, assuming a
decrement of 0.2 (which is not excessive for this type of circuit), and a
frequency of 1,000,000, is calculated as follows:
4.6+5 4.6+0.2
= 24 waves,
0.2
and the duration is,
r=24X
1,000,000
24X10-6 seconds.
.00001
Conditions when gap does Conditions when |
not break down breaks down
Fig. 6.—Action of a spark coil connected to an oscillatory circuit.
This time would be indicated by practically a straight vertical line
on the scale of Fig. 5. Conditions as indicated in Fig. 6 (a) would also
apply to the primary circuit if a suitable condenser is used across the
contacts.
Types of Interrupters.—As has been mentioned, the induction coil is
used chiefly on sets of low power, usually representing emergency equip
ment. On these the principal type of interrupter used is the " hammer
1 In calculating the time scale for diagram 6 (a), it has been assumed that the
secondary winding has an inductance of 25 henries, and that the condenser used in
the secondary circuit has a capacity of .002 microfarad.
ALTERNATING CURRENT GENERATOR 287
Position of conductor
Fig. 7.—Induction of e.m.f. in the conductor of a revolving armature alternator.
Frequency of Generated E.M.F. —In the case of the first two types the
flux of adjacent poles is always in the opposite directions: Thus a con
ductor passing through the flux emanating from the N pole will have
induced in it an e.m.f. of one direction or polarity, and in passing through
the S pole flux, will have the direction of e.m.f. reversed, i.e., a complete
cycle of alternating e.m.f. is induced in the conductor as it passes a pair
of poles.
Armature Winding Field Winding
S ll |2 |a 14 Is
Fia. 8.—Action of an inductor alternator.
In the case of the inductor type, the direction of the flux relative to
the armature winding is always the same, but this flux varies periodically
with time as the reluctance of its path increases and decreases. When
the flux is increasing the induced e.m.f. (e = N will have a certain
polarity. When the rate of change of flux reverses, that is, becomes a
decrease, the induced e.m.f. reverses and an alternating e.m.f. is thus
developed.
ALTERNATING-CURRENT GENERATOR 289
For classes (a) and (6) the frequency, i.e., the number of complete
cycles per second, is equal to the number of pairs of poles (in passing one
pair of poles the induced e.m.f. passes from 0 to + maximum to 0 to
—maximum and back to 0) times the revolutions per second, or
Thus a 4-pole machine, when driven at 1800 r.p.m., will give a fre
quency of 60 cycles per second.
In the inductor type, a complete cycle is obtained when the rotor
moves through the angle of the pole pitch (pole pitch = distance from a
point on one field projection on rotor to the corresponding point on the
adjacent projection).
Thus, if the rotor makes one complete revolution, the cycles generated
are equal to the number of teeth or projections on the rotor. The cycles
per second are thus equal to
/=nX(r.p.s.), (2a)
Fig. 11.—Various directions of the armature magneto motive force, for loads of different
characteristics.
1 It must be noted that the short-circuit condition, i.e., broken down spark gap.
on the radio alternator exists for such a small fraction of the cycle, that conclusions
reached from the short-circuit diagram in Fig. 13 are not directly applicable. An
exact treatment would require the analysis of successive short-circuit transients.
REGULATION DIAGRAMS OF ALTERNATORS 293
mmf.
Fia. 13.—Regulation diagram for radio alternator showing greater effect of armature
leakage and magnetomotive force.
294 SPARK TELEGRAPHY [Chap. V
Whence:
2X670
= 10,500 volts.
0.012X10-6X1000
The above simply means that the transformer must be able to charge
the condenser to 10,500 volts once for every half cycle, and that at this
voltage the gap shall break down.
The transformer must be very well insulated, for the first few turns
at any rate, not only because it itself must develop a high voltage, as
shown above, but also because, after the gap has quenched,1 radio-fre
quency e.m.f.'s are induced by the antenna circuit into the primary of
the oscillation transformer and are therefore inpressed upon the secondary
winding of the power transformer. These high-frequency e.m.f.'s pro
duce high-frequency currents, which flow, by condenser action, from turn
to turn and layer to layer through the high-tension side of the power
transformer and even through the low-tension side; unless the insulation
has low dielectric loss and unless it is especially heavy near the end turns
of the high-tension side, where the dielectric currents are largest, it is likely
eventually to break down.
The second requisite of the power transformer is of importance because
if, when the gap breaks down, the current through the power transformer
and the gap should be large, not only would there be a large unnecessary
waste of power but, in addition, the large current would maintain an " arc "
through the gap and thus keep this " closed," a condition which, as is
pointed out on page 310, should be decidedly avoided. In order to meet
the above the circuit consisting of the alternator, the reactance V.R. (see
Fig. 14), the power transformer, the inductances H-H, the condenser C\,
and the inductances L\ and L\ are arranged so that, when the gap is
open, the impedance of this circuit at the alternator frequency will be low,
and, when the gap breaks down, the impedance of the circuit of the alter
nator V.R., the power transformer H-H, and the closed gap will be very
much higher. Thus, when the gap is open the flow of current will not
be impeded, while when the gap breaks ddwn the current from the alter
nator will be very much reduced. A simple way of obtaining this result
is by adjusting the circuit of A, V.R., PS, H-H, C\, L\, L\ to have a
natural frequency equal2 to that of the alternator; so that, when the con
denser Ci and the inductances Li and L\ are, by the breaking down of
the gap, separated from the power transformer, the current in this will be
only a small fraction of that flowing when the gap is open. In other words,
the entire circuit from the alternator to and including L\ must resonate
1 See p. 314 for discussion of quenching.
1 In practice, this circuit is adjusted to a natural frequency somewhat lower than
that of the alternator, as is pointed out on p. 303.
296 SPARK TELEGRAPHY [Chat. V
at the alternator frequency. This requires that the capacity Ci and the
various inductances, including the inductance of the alternator and of the
transformer, be properly chosen.
The values of C\, L\, and L'i have to be adjusted to give the correct
wave length, and this makes them comparatively small; hence in order
that the entire circuit, from the alternator to L\, may resonate at the
alternator frequency the inductances to the left of the gap (see Fig. 14)
must be high.
To illustrate, assume:
Ci = 0.012 = microfarad ;
X = wave length = 600 meters;
/= alternator frequency = 500 cycles per second;
L = total inductance from the alternator to and including Li,
expressed in terms of high-tension side of transformer, in
henries;
Li+L\ = inductance of L\ and L\ in microhenries.
From formula (15) page 212,
2tt VLC
Therefore, for resonance at 500 cycles per second,
1 8.5 henries.
4tt2X5002X0.012X10-6
Again, from formula (18), page 213,
X = 1885Vo.012(Li+L'i)
or
Ll+Ll,= 1885^X0.012 = 8-5 microhenries-
Thus, while the inductance of Li and L'i must be 8.5 microhenries, the
inductance of the entire circuit may be 8.5 henries or one million times
as large; hence, practically all of the inductance necessary to bring about
resonance at the alternator frequency must be in the alternator, V.R.,
the power transformer and the choke coils H-H.
Up to a few years ago it was common practice to design the trans
former with the highest possible inductance or, in other words, with a very
large amount of magnetic leakage, so that the most of the required induct
ance was in the transformer and comparatively little in the alternator
and the choke coils; such a transformer was called a "resonance trans
former," in so far as its inductance alone was nearly capable of bringing
about resonance at the alternator frequency. A transformer of this type
was generally made with an open magnetic circuit, a so-called " open-
core transformer." The tendency of late is to design the transformer
with little leakage (closed magnetic circuit) and hence little inductance,
TRANSMITTER CONDENSERS 297
2d. That the losses shall be small (see page 166, Chapter II). The
dielectrics generally used in power condensers are: air, glass, oil and
mica. Of these air has the minimum specific inductive capacity, and
it causes practically no losses, while the other dielectrics have a much
higher specific inductive capacity but suffer more or less energy loss. As
regards breakdown voltage air is at a disadvantage as compared with the
other dielectrics, but at pressures higher than atmospheric the break
down voltage for air is very high and it increases in nearly direct propor
tion to the absolute pressure. A comparison of the characteristics of
these dielectrics is given in Chapter II, page 169.
It will be seen from the characteristics of the various dielectrics that
if a condenser of a certain capacity is to be designed, the air condenser
would have the largest dimensions and the mica condenser the smallest.
However, the losses in the air condenser would be very small, while those
in a poorly constructed mica condenser might be so high as to make its
use prohibitive. Glass condensers in the form of Leyden jars have met
with much favor in the radio field and they are being extensively used.
Each jar has a capacity of about 0.002 nf, and is capable of withstanding
a voltage of about 15,000; for any particular desired voltage and capacity
the jars are grouped in series multiple, so that the combination will have
the required capacity and breakdown voltage. Condensers with glass as
the dielectric are also made with flat pieces of glass covered with tin foil,
the spate requirements of such condensers being much smaller than for
the Leyden jars. They do not stand continued use, however, as well
as the Leyden jars, because of the greater amount of heating due to smaller
cooling surface.
Oil condensers are not very much used in general practice, but their
use is very commendable in places where there is no possibility of spilling
the oil. It must be borne in mind, that although the dielectric properties
of oil are unfavorably affected by a flash through it, so that oil condensers
cannot be expected to give as good service after the oil has once
been flashed, they are still serviceable after a breakdown, whereas
a solid dielectric condenser, such as mica or glass, is completely
spoiled.
The mica condenser is a very desirable one, and is apparently going
to largely supplant the Leyden jar for ship sets and similar installations.
It is compact, and, if properly constructed, has a loss so small as to be
hardly measurable. The impregnation of the condenser with suitable wax
mu3t be done sufficiently well to drive out all air completely, as the trapped
air bubbles, suffering corona loss, are the source of local heating and
thus weaken the dielectric strength of the mica. It must be noted that
these condensers are made to be used at the rated voltage and frequency
for inlermitterd service only and that even a good mica condenser if used
TRANSMITTER CONDENSERS 299
continuously at the rated voltage and frequency will have its wax melted
after an hour or so.
Compressed-air condensers are very suitable where very high voltages
and low losses are required; the structure of the condenser, i.e., the metal
plates and their insulating supports, is placed in a steel container capable
of safely withstanding a pressure up to a dozen atmospheres or more and
dry compressed air is pumped in until the required pressure is obtained.
It may be easily seen that an air compressor and gauge are necessary
auxiliaries of such condensers, and that their use cannot be considered,
except for very large land installations, or for laboratories.
On the whole the Leyden jar with its simplicity of construction and
large heat-radiating surface affording cool operation is a favorite type
of transmitting condenser and would be even more widely used were it
not for its large space requirements and liability of breakage.
Transmitting condensers are very seldom constructed so that their
capacity may be continuously varied in view of the insulation difficulties
resulting from the high voltages dealt with.
The value of the capacity of the condenser used in the closed circuit
of a spark transmitter is fixed by the voltage, the spark frequency, and
the power set. This point has already been discussed on page 295, from
the point of view of the high-tension transformer, and it will be more
fully emphasized here from the point of view of the condenser. Rewriting
formula (3):
nv2
~-N = W, . . : (3)
where
C = capacity of condenser in farads;
V= voltage to which condenser is charged;
N = number of sparks per second ;
W= electrical power, in watts, given to condenser.
We immediately note that the power varies directly with N, C and V2.
The value of N is more or less fixed, because it represents the " tone " of
the set and the best tone is supposed to be that due to N = 1000 per second.
Therefore, if a certain amount of power must be imparted to the con
denser a suitable choice must be made of C and V. With a very high
voltage the dielectric and leakage losses are likely to be high, and the dif
ficulties of insulating the various parts of the set are such as to make it
impractical, and a limit in this direction is soon reached after which, if
more power is required, the condenser capacity must be increased.
Voltages of 100,000 might be used in large land installations, but in small
land and in ship installations the range is 10,000 to 20,000 volts.
It may be easily seen that in large power installations the condenser
300 SPARK TELEGRAPHY [Chap. V
must have a very large capacity, even though a high voltage is used.
For instance, assume:
W= 50,000 watts;
V= 100,000;
2V = 1000 per second.
rpu n 2 X 50,000 .„ ,
^ c=ioooxioo,ooo2=0-01^
Since this capacity affects the wave length it is plain that even though
a small inductance be used in the closed circuit, the wave length will be
large; and this is one reason why the wave length of high-power instal
lations is large; there are other reasons which are taken up on page 196.
In the example given, even if the inductance in the closed circuit were
200 txh (which is comparatively small) the wave length would be:
1885V200 X 0.01 = 2660 meters.
Again, from the formula:
/
■ ' I i i i i i i i i i_ i
01 23456789 10 H12
Number of jars
Fio. 16.—Variation of the high-frequency oscillatory current with the amount of
capacity used.
coils, and the condenser. This circuit may be simplified by noting that a
transformer may be treated approximately as a simple circuit consisting of
an inductance and a resistance entirely transferred to the high- or to the
low-tension side; furthermore, any impedance in the secondary circuit may
be transferred to the primary by multiplying by a suitable factor. On
this basis the audio circuit may be simplified to that of Fig. 17,
where
A = alternator armature, having both resistance and inductance:
302 SPARK TELEGRAPHY [Chap. V
/=
2wVLC
and this inductance may then be apportioned between the alternator, the
variable reactance, the transformer, and the choke coils. An example of
this calculation has already been given on page 296, where the compu
DESIGN OF LOW-FREQUENCY CIRCUIT
tations have been based on the high-tension side of the transformer. The
same computations will be repeated on the basis of the low-tension side.
Assume that the transformer ratio is 1 : 80; then, any inductance or
resistance in the high-tension side may be transferred to the low-tension
side by dividing by 802, or 6400, while a
capacity in the high-tension side may be
VWWWH
transferred to the low-tension side by mul
tiplying by 6400.
In our case:
Capacity of condenser in high-tension
side =0.012 nf. Hence, equivalent low-
tension capacity = 0.012 X 6400 = 77.0 nf.
If the audio-circuit must resonate at 500 L
cycles per second, Fia. 18.—Simplest possible rep
Total equivalent low tension inductance resentation of the low frequen
cy circuit, not quite equivalent
1 to the actual circuit.
3g = .00133 henry.
"5002 X4x2 X 77.0X10
Of this inductance probably the largest part is, in a modern set, found in
the alternator, while the transformer has comparatively little inductance,
and the balance is made up by the choke coils in the high-tension side and
the variable reactance V.R. in the low-tension side.
In order to show the manner in which the whole audio circuit may be
made to resonate the curves of Fig. 19 are here given as being representa
tive of an actual set. In obtaining these curves the field current and
speed of the alternator were kept constant, while the capacity in the high-
tension side of the transformer was changed with the circuit connections
as shown in Fig. 20. Under these conditions, as the capacity, and, there
fore, the natural frequency of the circuit, was varied, the current in the
primary of the power transformer as well as the voltage across it varied
and reached a maximum at the point corresponding to resonance condi
tions. A capacity of about 5.5 Leyden jars is seen to have produced
resonance. In an actual set the adjustment of the capacity, or of the
inductance, is made about 20 per cent to 30 per cent larger than neces
sary to give resonance at audio frequency, thus making the natural fre
quency of the circuit somewhat lower than the alternator frequency.
This point will be more fully emphasized further on. In the case
304 SPARK TELEGRAPHY [Chap V.
represented by the curves of Fig. 19 the set was actually operated with
8 Leyden jars across the secondary.
It now remains to investigate, as far as the conditions will allow, the
transient phenomena taking place in the audio circuit as the condenser
Number of Leyden jaifl connected in multiple across the secondary of tne transformer
Fia. 19.—Variation of alternator voltage and primary current of a 2 k. w. spark trans
mitter as the capacity in the secondary of the transformer was varied; field cur
rent of alternator and speed held constant. Gap set too long to permit sparking
at voltage of test.
is charged and discharged; we especially mean to refer to the variation
of the condenser current and voltage as the alternator e.m.f. is impressed
upon the audio circuit and, thereafter, as the gap breaks down. As shown
in Fig. 18, we are dealing with an oscillatory circuit, having the resistance,
inductance, and capacity R, L, and C, respectively, upon which there is
TRANSIENT CURRENT IN AUDIO CIRCUIT 305
pC)
in which p = angular velocity of impressed force;
03 = angular velocity of natural oscillations of the circuit;
4> = phase difference of E and J in the steady state;
A =a constant to be determined;
t' = time of duration of the transient term.
In deriving this equation (page 254) it was shown how to solve for A and t',
these depending for their value on the time the voltage is introduced into
the circuit. In a radio set there is no switch actually used, but the equiv
alent effect is caused by the operation of the spark gap; when the gap is
sparking its resistance is so low that the secondary of the power trans-
(8)
This equation shows that the condenser voltage rapidly changes its
phase during the first few alternations, the sin pi term predominating
at first, the cos pt term being zero.; as soon as t 2L departs appreciably
from unity the cos pt begins to predominate and this continually increases
with increasing time due to the increasing value of (1 — « 2t). Thus in
state the current should be —23.5 amperes and the voltage across the
condenser should be —92 volts. To satisfy the condition that the actual
current must be zero as well as the drop across the condenser a transient
term must be added to the steady state solution; by the process outlined
in Chapter IV this transient is found to be satisfied by charging the con
denser to -385 volts and starting this transient term .000756 second
before the alternator voltage goes through its zero value—this transient
term has the natural frequency of the circuit (given practically correct
J M
1 *! l" f 21 )
Rl-L I
b H - H ItL)
% r /dI*- f s i l I't Og 7-' 1
I 600 V
I 500
< \
40 400
\ Cc mlen .er
30 300 \\ \ ol K e
20 200 A, 1
--. 1 Ci rr nt v
10 100 / * s
f // 1/ \ \ \
/ 77 1// 1 n\ ST Iff
0 '.71
\ / \ \ /
10 100 si \ > /, /
>- \ -'■
1
M tei nator \
20 200 \ ol age
1
30 300 )
/
40 400 \ /
M IX Mil in 111 t'r Ml T en f= 150 1 .It
500 P = 3000
Rt = 2
too c = 20 in rr< ifa rail i
L = .0066 lie in !■ \
Similarly the equation for voltage drop across the condenser is found
to be represented by the equation
150 X106
sin 300O<-70°.7
-I)
3000X30>j22+(3000X.0056-3^35)2
2(1 +.000756)
-385 e 2 X 0056 cos {2440(i+ .000756)}
5 1 J
X- (Pi- '>) •I a sil in
> < K-'■ "(I L- -1pc )■1 In at
300 30 h 1 li: u t- <p\ _ r ) + E„ I L'L CO 0 V
1 c ;r'- ,11. pC >
250 25
200 20
150 15 \
/ \ c< nd •n or 1I /
100 10 { \\ ol 0 / \/
/ T // \ f/ A
s . > / \
50 5 // /
/y \s
\ // /
0 > < 1 o\ ' 2 1 1 1 A 1 b 20/ 2 J. J 2 1 26 2; / ■i 0
50 5 i imc n 1 10"* on (Is \ /
V-3\ /
Ci rr. nt
100 10 Al tel oa or
0 tas e - w i/
150 15 y
lat or c If 1 .0 1 ol ■
M XL in m al
pi 3000
300 30 R±2 ol IIS
C = 3 j n of t:\ U
L .( 06 henr ies
1 I
Fig. 22.—Transient current in audio circuit of a spark transmitter, circuit frequency
being about 40 per cent lower than alternator frequency.
It may be seen from Fig. 22 that the voltage across the condenser
is rising more rapidly, at times t=it, than was the case for the resonant
condition depicted in Fig. 21; it is quite likely this more rapid rise in
condenser voltage, by causing the spark to take place at a more definite
time, accounts for the more regular behavior of the spark when the cir
cuit is detuned as supposed in Fig. 22, than when the circuit is resonant.
In Figs. 21 and 22 the forms of current and condenser voltage have
been shown for nearly two cycles; actually if a spark occurs at the time
indicated by the letter A on the condenser voltage curve (which is the
time the spark should actually occur) the condenser voltage drops to zero
THE COMMON SPARK GAP 309
and it, as well as the current, goes through the same changes from it to 2jr
as it did from 0° to ir. The actual forms of the condenser voltage for the
circuits analyzed in Figs. 21 and 22 are shown in Figs. 48 and 49 of Chap
ter IV, page 259). It will be seen that the above analysis does give fairly
accurate results.
Types of Spark Gaps.—The construction of the several commercial
types of spark gaps in use at the present time may be conveniently sub
divided into the following classes:
(a) Open gap.
synchronous
(6) Rotating gap
nonsynchronous
self-cooled
(c) Quenched gap
fan-cooled.
The Open Gap and Operating Conditions.—Fig. 23 below illustrates
one form of the open gap. This type is also know as a plain spark dis
charger.
In considering the requirements which such a gap must fulfill, it is
desirable to review briefly that part which it plays in the production of
high-frequency oscillations. It will be
recalled that a high voltage is impressed
on the gap and condenser-inductance
circuit connected in parallel, and at a
certain critical voltage, the insulation of
the dielectric, usually air, between the FjG. 23.—Small open spark gap
terminals, breaks down, and permits a having cooling vanes on the spark
high-frequency oscillatory discharge knobs,
to take place. The gap must there
fore possess high dielectric strength or resistance to puncture, pre
vious to breakdown so that the condenser may be charged to a high poten
tial difference, as otherwise the high-frequency energy is reduced, and the
efficiency of the transmitter is lowered, due to the breakdown occurring
at too low a voltage.
After the gap has broken down it must possess a very low resistance,
otherwise the damping of the oscillations will be excessive, and the trans
mitter inefficient, most of the energy being dissipated as PR loss in the
gap. The gap must be conducting only during the interval of the passage
of a wave-train. If we assume a 300-meter wave and a decrement of .2,
the duration of the train is .000024 second. The time during which the
gap is conducting is thus very small. If we consider 1000 wave-trains
per second, the period between trains is .001 -.000024 = .000976 second,
and in this period the gap must recover its insulating properties. These
figures indicate the short time intervals involved in the functioning of
310 SPAEK TELEGRAPHY [Chap. V
more rapidly at this point. It is desirable that the wear on the gap faces
be uniform, as in this way the most effective use of the electrodes will be
secured. In addition to alignment, it is essential that the faces be clean
and polished. If they are neglected, oxide, dust, and dirt, etc., will collect,
and form an uneven surface. The spark will jump wherever the surfaces
may be closest together, and thus for this condition also the sparks occur
at a particular spot on the electrode. Since the oxide or dirt is not metal,
it will not conduct the heat away as rapidly as required. A hot spot will
thus be formed, causing arcing to take place, and operation to be inefficient
and unsatisfactory.
The following table indicates approximate minimum discharge volt
ages required for sphere gaps of 2.5 cm. and 1.0 cm. radius in air at
atmospheric pressure:
TABLE I
Minimum Discharge, Volts. Minimum Discharge, Volts.
Gap Length Gap Length
in Cm. in Cm.
R =2.5 Cm. R - 1 Cm. R = 2.5 Cm. R -1 Cm.
.1 5,000 5,000 .1.0 33,000 31,000
.2 8,500 8,000 1.1 35,500 33,500
.3 12,000 11,000 1.2 38,400 35,200
.4 15,000 14,000 1.3 41,000 37,000
.5 19,000 17,500 1.4 43,600 38,500
.6 21,500 20,000 1.5 46,000 40,000
.7 25,000 23,000 2.0 56,000 44,000
.8 27,500 27,000 3.0 74,000 50,000
.9 30,000 29,000
(positive and negative) of the voltage wave, and the gap separation
adjusted so, that the breakdown voltage is slightly below the maximum
voltage. Under these conditions the gap breaks down once during each
half cycle, and assuming a 500-cycle supply, the group frequency is evi
dently 1000. The number of teeth on the disk is determined by the number
of alternator field poles. For instance, if the alternator be equipped
with 24 poles, the disk would have 24 teeth, and 24 breakdowns would
occur per revolution. This would correspond to an alternator speed of
2500 r.p.m. if a group frequency of 1000 were desired.
Clearly, the number of breakdowns per revolution may be controlled
by substituting disks with different tooth spacing. Thus, we could omit
HotutaBTOtatafele thro twioe the
the alternator
Fiq. 24.—Arrangement of parts of a synchronous rotating gap; instead of using a metal
disk for the rotating member this is, sometimes made of a disk of bakelite or similar
material, the rotating studs being then all connected together by a metal strip.
alternate teeth, and cut the group frequency in half, etc. The tone of
a signal may thus be altered easily and quickly, in case this is found
desirable due to interference effects present. The quality of the note
may be made quite distinctive by introducing regular irregularities in
the arrangement of teeth as, e.g., omitting every third tooth.
The action of the gap, assuming one breakdown to occur every half
cycle is indicated conventionally in Fig. 25. Actually the condenser voltage
is not a sine wave, but has the peculiar form shown in Figs. 21 and 22.
Synchronous Gap Application.—The synchronous gap possesses a low
operating resistance, due to the electrodes being close together at the time
of discharge, and automatically recovers its insulating properties between
NON-SYNCHRONOUS GAP
discharges due to the electrodes being widely separated during this interval.
Arcing is prevented by the separation of the electrodes increasing as the
wave train passes, and also by the fanning and cooling action of the rapidly
moving electrodes. Partial discharges cannot occur, as the gap separation
may be adjusted for breakdown near the voltage maximum. This form
of gap will successfully handle large amounts of power and high spark
frequencies, and is at present widely used on commercial spark trans
mitters of large capacity.
Non-synchronous Gap—Operation and Application.—The non-syn
chronous gap is essentially similar to the synchronous rotary gap described
above, with the exception that the moving electrode disk is not attached
to the alternator shaft, but is driven by an independent motor. If the
La
— i
motor runs at exactly synchronous speed, and the phase relation is correct,
the operation will be equivalent -to the synchronous type.
This, however, is an unusual condition, and one which would be dif
ficult to maintain for any length of time. Normally the disk is run at
speeds greater than synchronous, the gap separation being adjusted for
some voltage somewhat less than the peak value. The action under these
conditions is shown conventionally in Fig. 26.
It will be noted that several breakdowns may occur during each half
cycle and that the voltage at which breakdown occurs is not of a definite
nor constant value. Thus the wave-trains do not occur at regular intervals,
nor is the energy of the several discharges the same. The received signal
is therefore of a higher pitch, and of a different musical quality than that
produced by the synchronous type. It finds its greatest application for
those installations where commercial frequencies only are available as a
supply. A 60-cycle service may thus be used to supply a transmitter
314 SPARK TELEGRAPHY (Chap. V
Condenser
Voltage
3. No part of the gas which forms the gap dielectric must be far from
a cool metal surface, that is, a very short gap only may be used.
Quenched Gap—Construction.—The above requirements are satisfied
in the commercial form of gap as follows:
1. The spark takes place in an air-tight chamber. The several elements
or sections of the gap are separated from one another by the insulating
gaskets as shown (Fig. 28A) and the whole clamped tightly together. When
the gap is first operated, the air, which is initially between the gap faces,
becomes separated into its elements, mainly oxygen and nitrogen, the
oxygen combining with the copper electrodes to form copper oxide, thus
leaving an atmosphere of essentially pure nitrogen between the gap faces.
The black oxide of copper disappears after the gap has been in operation
a short while, the gap faces being found bright and clean if the gap is
disassembled for inspection. (The exact reason for the disappearance
of this oxide is not apparent—it is probably absorbed into the material
of the separating gasket, under conditions present when the gap is in
operation.)
2. In addition to using good heat-conducting materials, such as silver
and copper, for the electrodes, the efficient cooling of the gap is assisted
by means of cooling vanes or fins, which radiate the heat produced during
the operation of the gap. These fins are clearly indicated in the diagram
316 SPARK TELEGRAPHY [Chap. V
(Fig. 27). There has been recently developed a staggered form of gap
construction, which permits air circulation on both sides of each element.
This construction, whereby cooling is accomplished by increased radi
ating surface, represents what is known as the self-cooled type. It is
sometimes necessary, with the higher-powered sets, to supply a small
motor driven fan to cool the gap satisfactorily.1 This form may be of
the type illustrated in Fig. 28, where the gap is supported in a trough of
insulating material, the cooling air blast provided by the motor-driven
Fia. 28.—Another type of quenched gap in which each copper disk is assembled sep
arately; the small blower forces cool air around the cooling vanes to prevent over-
heating.
fan, coming up through the trough, and thus effectually cooling the gap.
The cross-sectional detail of this gap is indicated in Fig. 28A.
3. The requirement that no particle of gas in the gap shall be remote
from a metal surface is satisfied by subdividing the gap into sections,
the number of sections increasing as the " break-down " voltage value
is increased. Each gap provides somewhat less than .01 inch separation,
with a breakdown voltage of approximately 1200 volts. Thus no particle
of gas in the gap is more than .005 inch away from the metal, and the gap
is rapidly de-ionized. This rapid de-ionization is due principally to the
loss of electrons by diffusion, although recombination of electrons and
positive ions is also a factor. By loss of electrons by diffusion is meant
1 Most modern gaps receive their supply of cooling air from a fan mounted on the
llternator shaft, thus dispensing with the extra motor required for blower.
CHAFFEE GAP 317
the removal of electrons from the gas to the face of the gap, due to the
attraction of the induced positive charges on the gap faces. As the most
distant electron has only a short distance (.005 inch) to go before arriving
at the gap face and the attracting charge, the Insulating Gasket
time required is extremely small.
Quenched Gap—Application.—The quenched
gap is used on spark transmitters of all powers, •Copper or silver
from the very small sets used in military field ■parking surface
work and aeroplanes, up to the 500-600 h.p.
(Input) equipment at the Nauen Station (Tele- > a'V"C0PPer Element
funken System). Quietness in operation, small U U If— Cooling Flange
space requirements, simplicity, and desirable
Fio. 28A.—Cross-sectional
operating characteristics (see page 324) are sketch of part of the gap
the particular advantages of this type of shown in Fig. 28.
gap.
The Chaffee Gap1—Construction.—The construction of this gap is
quite similar to that of the quenched gap described above. The electrodes
consist of a copper anode and an aluminum cathode, the spark occurring
between them in an air-tight chamber containing an atmosphere of moist
hydrogen. One electrode is mounted on a flexible diaphragm to permit
adjustment of the gap length, while the other is held fixed in a bakelite
mounting as indicated. As with the quench gap, it is highly important
that the electrodes and gap faces be kept cool, hence the large radiating
fins with which each electrode is equipped.
Operation of the Chaffee Gap.—This gap is supplied from a d.c. source
through resistances and high-frequency choke coils as shown in Fig. 29,
and is connected in
shunt with the oscillat
ing circuit C\L\. Nor
mally the gap separa
tion is 2 or 3 mm. and
under these conditions
the gap acts as a recti
fier, permitting current
Fig. 29.—Circuit used with Chaffee type of quenchec pulses to flow in one
by which the high-frequency current is maintained by direction only, e.g.,
impulse excitation.
from the copper to the
aluminum electrode.
One of these impulses sets the secondary circuit into oscillation, the
retro-action of which sets off successive primary impulses at the proper
time for maintaining the oscillations in the secondary. These secondary
oscillations are not constant in amplitude, but grow to a maximum
1 This is only one of several gaps of this general type which have been developed in
recent years. Tungsten is quite a favorite metal for making the terminals
318 SPARK TELEGRAPHY [Chap. V
w
era
o
Fig. 30.—For small portable sets the oscillation transformer is sometimes made with
only one coil as shown here.
closed circuit to the open or antenna circuit ; it is, in other words, a trans
former of high-frequency currents or oscillations. Because of these it is
important that it be constructed without iron core or other masses of
any metal whatever, for the hysteresis and eddy current losses would be
so large as to make the transformer efficiency very low.
Two general types of oscillation transformer are available, i.e., (a)
the two-coil type, (b) the single-coil type. As the names imply, the two-
coil type is made up of two separate and distinct coils more or less sepa
rated from each other, while the single-coil type consists of a single coil
connected as shown at YQWT in Fig. 30.
In the figure above, WT represents the part of the oscillation trans
former in the closed circuit, while QT is the part used in the open circuit.
It will be seen that here we have what is known in general electrical
engineering as an " auto-transformer," which, in turn, is a modification
of the simple transformer. The practical construction of the oscillation
transformer varies widely with different makes. In every case means
must be provided for changing the number of turns in the closed circuit
OSCILLATION TRANSFORMER 319
and in the open circuit and also (in the case of the two-coil transformer)
for changing the position of one coil relative to the other. As regards
the former of these two requirements two y Copper Strip of
* Oscillation Transformer
general methods are used: one consists of
using a clip as shown in Fig. 31, and shift
ing this by hand until the required number Spring Clip
of turns is obtained; and the other consists
of a roller contact which is rotated by means
of a suitable handle so as to make contact
with different turns as shown in Fig. 32. Fig. 31.—For making connec
tion at any desired point on
The changing of the position of one coil the coils of an oscillation
relative to the other may be accomplished by transformer a spring clip of
any one of several methods, two of which are this form h useful.
represented by Figs. 33 and 34, which are
self-explanatory. These figures also show the general construction of the
various types of transformers; in all cases either ribbon or braided copper
is used, and is supported in various ways as shown by the illustrations.
Fig. 32.—An adjustable transmitting coil is sometimes made with a rolling contact ; on
the opposite end of the arm is placed a roller of some insulation material to avoid
having a short circuited half-turn which would occur if both rollers were conductors.
The variation of the coefficient of coupling between the closed and
open circuits is accomplished, in the case of the two-coil transformer, by
changing the position of the two coils relative to each other and also
changing the inductances outside of the transformer coils; in the case of
320 SPARK TELEGRAPHY [Chap. V
Pig. 33.—A type of oscillation transformer in which one coil telescopes with the other
to vary coupling.
where
k — coefficient of coupling;
M= mutual inductance between the two coils of the oscillation
transformer;
L\ = total inductance in the closed circuit;
La= total inductance in the open circuit,
and in the case of the single coil type,
fc = ^=
VL1L2'
where
L= inductance common to both circuits.
k, Li, L2 have the same significance as above.
The Radio-frequency Circuits.—This consists of the closed and open
oscillatory circuits, coupled together through the oscillation transformer.
The whole of the radio-frequency cir
cuit for a two-coil oscillation trans
former is shown in Fig. 35. The
closed and open circuits are tuned to
the same frequency.
The theory applying to the above
is that which has been discussed
in connection with two inductively
couple oscillatory circuits (see Chapter _ „„ _ , ,
... . . , Fio. 35.—The two coupled radio fre-
IV, pages 226-246) . The main point quency circujts of a gpark tranamitter.
to be considered is that when the two
circuits are closely coupled there are produced in each two currents of
frequencies differing from the natural frequency of the two circuits; when
the natural frequencies of the circuits are the same, then the frequency
and wave-length of the component currents are given by (see Chapter
IV, pages 229-231)
where
/ and X= natural frequency and wave-length of either circuit;
f and X' = frequency and wave-length of one of the component cur
rents;
322 SPARK TELEGRAPHY [Chap. V
/" and X" = frequency and wave-length of the other component cur
rents;
k = coefficient of coupling.
The relative amplitudes of the two currents have been discussed in
Chapter IV, pages 230-237; generally the higher-frequency current has the
greater amplitude. Futhermore the higher-frequency currents of the
primary and secondary are about 180° apart, while the lower-frequency
currents of the primary and secondary are about in phase. The effect
of all this is to produce current " beats " in the primary and secondary
with a frequency equal to the difference of the frequencies of the com
ponent currents; again, while the resultant current in the primary is pass-
ing through the small amplitude values of the " beat cycle," the secondary
current is passing through the high amplitude values of the " beat cycle,"
and vice versa. This is illustrated by the curves of Fig. 36, where the
dotted line curves represent the resultant primary and secondary currents;
it will be noted that the primary resultant current starts with a high
amplitude at Q and decreases to a low amplitude at R, while the secondary
resultant current does just the opposite. In plotting the curves it has
been assumed that neither circuit suffers any losses, and the result is that
the decrement of the component currents is zero, while the resultant cur
rents would also periodically repeat themselves through the " beat cycle "
without any decay. This of course is not true of an actual case, where,
on account of the losses in both circuits, the decrement would have a
definite value, and the resultant currents would " decay " somewhat as
RADIO FREQUENCY CURRENTS 323
shown in Fig. 37, which represents the component and the resultant pri
mary and secondary currents for circuits with decrements. Another
assumption made is that the gap used is such (open-spark gap) that it
remains closed for considerable time after its breaking down, so that the
currents may flow through the closed circuit.
The phenomenon of the " beats " takes place most pronouncedly when
the coupling between the primary and secondary of the oscillation trans
former is closest. For loose coupling the two circuits oscillate at very
nearly a single frequency equal to their natural frequency, but when this
CURVES OF CURRENT IN COILS OF AN OSCILLATION
TRANSFORMER FOR A NON-QUENCHING GAP
Fig. 37.—Currents in the two circuits of Fig. 35, high damping assumed.
is the case the secondary current is generally low. On the other hand,
when the coupling is very close, although the current in the antenna is
large, yet since it is made up of two component currents of two widely
different frequencies the antenna will radiate energy at these two different
frequencies; this is very objectionable because the total available energy
is subdivided, and hence the range of transmission diminished, and also
because it would interfere with other stations. As a matter of fact, the
law in the United States requires that the energy of no other frequency
shall exceed 10 per cent of that of the frequency on which the station is
transmitting.
324 SPARK TELEGRAPHY [Chap. V
As outlined above, we find that when an open spark gap is used, which
remains closed for some time after its breaking down and thus permits
a current to be maintained in the closed circuit, we are confronted by
either one of two evils, i. e., low current in antenna at a single frequency
for loose coupling, and large antenna current of two frequencies for close
coupling; besides, for both loose and close coupling, energy is wasted in
the primary, since the latter has a current flowing in it for a longer time
than necessary, which produces unnecessary losses, and subtracts from
the energy which might otherwise be given to the antenna.
In order to overcome these difficulties advantage is taken of the fact
that, as has already been pointed out, and as shown in Fig. 37, the pri
mary and secondary currents (for close coupling and an open spark
CURVES OF RESULTANT CURRENT IN COILS OF AN
OSCILLATION TRANSFORMER FOR A QUENCHED GAP
gap) pass through beat cycles, and that the amplitude of the primary
current has minimum values at the same time that the amplitude of
the secondary current has maximum values. It is plain that if the
primary current were automatically interrupted when passing through
its minimum amplitude values, the secondary circuit would then go on
oscillating at its own frequency and damping. This, of course, would
be made possible by the fact that the primary current would be inter
rupted when the secondary current amplitude values are a maximum
and hence when almost the entire energy is in the secondary. Accord
ing to this plan the current would be interrupted in the primary at
the completion of the first one-quarter of a " beat-cycle " as shown at
A in Fig. 38. To interrupt the primary current several methods may
be used, the simplest of which is by replacing the ordinary open gap
RADIO FREQUENCY CURRENTS 325
by the so-called " quenched gap." The construction of this already has
been described on page 316. Its characteristic is that it " opens " when
the current in the primary of the oscillation transformer passes through
its low values, probably because the comparatively few ions, which are
formed between the sparking surfaces during the time of low current
amplitude, recombine very quickly, thus making it impossible to maintain
low currents through the gas between the sparking surfaces. Such a gap
is said to " quench " the spark formed upon the discharge of the condenser.
A quench gap may be and is generally operated with a close coupling of
the oscillation transformer, because the closer the coupling the greater
the amount of energy transferred to the antenna circuit; but if the coupling
should be made extremely close then it is possible that the gap may refuse
to quench, because of the very short time during which the closed circuit
has its low amplitude current; this may not be sufficient to permit the
gap to quench. A critical coupling, therefore, exists at which the gap
quenches best; this coupling is quite close and far closer than could be
used with an ordinary open gap; the secondary current as indicated by an
ammeter, is a maximum for the critical coupling. Of course if the gap
is quenching properly the secondary current should have a frequency
equal to its natural frequency, and, since no current flows in the
primary, the efficiency is higher and the decrement lower than for the
" open gap."
The adjustment of a transmitting set as regards the coupling of the
closed and open circuits, the gap, and the tuning of the two circuits is
best determined by obtaining the "energy
distribution curve." Such a curve is
obtained in the following manner: a
search coil of one or two turns is intro
duced in the antenna circuit as shown
at S, Fig. 39, and a wave-meter circuit,
consisting of Li, Ci and a hot-wire meter
A is loosely coupled to <S. With the
transmitter in operation the capacity C4 1
is set at different values, and the reading —
t a • ui • j it. ,1 , 1 Fig. 39.—Use of wave-meter for
of A is obtamed; thus, as the natural . .
, ' . . getting wave-length of antenna
wave-length of the circuit of d — Li — A circuit.
is varied, the ammeter reading varies.
A curve plotted with values of the natural wave-lengths of circuit
C* — Li— A against squares of ammeter readings is known as "energy-
distribution curve," and shows the relative amounts of energy radiated
by the antenna at each wave-length. Another way to look at it is that,
since the circuit C4-L4-A is nothing but a receiving circuit loosely
coupled to the transmitting antenna, it follows that the energy distribution
326 SPARK TELEGRAPHY [Chap. V
curve also represents the energy reaching the receiving circuit when it
is adjusted to different natural wave-lengths. Whichever way one chooses
to look upon the " energy distribution curve," it is plain that it is of great
importance in the study and adjustment of a transmitting set. Two
typical sets of such curves are given in Figs. 40 and 41 and a study of these
will bear out some of the points brought out in the previous discussion.
In these curves the ordinates represent squares of currents, and they were
in one case read on a so-called " Wattmeter " 1 and in the other on a
thermo-galvanometer.
Wave-length in meters
Fig. 40.—A set of resonance curves for a spark transmitter having a non-quenching gap;
even when the coupling is as low as 5 per cent two distinct waves are emitted from
the antenna.
Fig. 40 shows curves for an open gap and for different amounts of
coupling, curve (1) being for the closest and curve (8) for the loosest
coupling. It will be seen that for any but the loosest coupling there are
two maxima in the radiation of the antenna at two different wave-lengths
more or less separated from each other; thus, for curve 1, the two wave
lengths are 732 and 415 meters, while for curve 7 they are 616 and 588
meters. On the other hand, for curve 8 maximum energy is radiated at
1 Wattmeter is the name often given, in radio measurements, to a hot-wire ammeter
the scale of which is calibrated to indicate the power expended in the resistance of the
instrument itself.
ENERGY DISTRIBUTION CURVES 327
the one wave-length of 602 meters, i.e., the natural wave-length of the closed
and open circuits. Again, by referring to the table inserted in Fig. 40 we
note that the antenna current was a minimum for curve (8) (1.25 amperes)
and a maximum for curve (1) (1.57 amperes). Or, as already pointed out.
the loose coupling produces an antenna current which, though smaller
than for close coupling, radiates maximum energy at a single frequency
or wave-length.
mum and then decreases sharply for a further small increase in coupling.
The value of coupling just less than that at which the antenna current
decreases is the proper one to use; it is the maximum value which can
be used and still maintain the quenching action of the set.
Adjusting the Spark Transmitter.—In adjusting the transmitter
shown in Fig. 1, to radiate at a certain wave-length and energy output,
the following schedule of procedure should be followed. (Fig. 1 is repro
duced here as Fig. 42 for convenience in following the directions given.)
1. With the antenna circuit open, the closed oscillating circuit is
adjusted to the wave-length desired, by varying the value of inductance
la.1 The primary capacity is usually fixed in value and is not readily
changed, whereas the inductance la, forming also the primary of the
oscillation transformer, is always of the variable type, its construction
being as previously described (page 320). The wave-length at which
the circuit will oscillate may be marked on the inductance la, different
values of Li corresponding to different wave lengths, since Ci is fixed and
X meters = lSSSV'iiiCl,
Li and Ci being given in micro-units.
This calibration is usually made by the manufacturer before the set
is delivered. In certain emergency or special conditions, however, this
may not have been done, in which case a wave-meter is loosely coupled
to Li, and Li adjusted, until the wave-meter indicates a maximum deflec
tion for the wave-length, at which the set is to transmit.
The student is referred to Chapter X for a detailed treatment of the
wave-meter. For the present discussion it will suffice to say that it is
simply a calibrated oscillating circuit, the wave-length of which is known
for any and every position of a variable condenser element, the other
element consisting of a fixed inductance. An indicating device, e.g., hot-
1 In the discussion Lt stands for the total inductance in the closed oscillating circuit,
i.e., the sum of the inductances of Li and L\ of the diagram; as previously noted, the
extra inductance in the closed oscillating circuit, L\, is very seldom used.
ADJUSTMENT OF A SPARK TRANSMITTER 329
exist to some extent even with loose coupling and both circuits correctly
tuned. However, a wave-meter coupled to the loading coil or search coil
would give true indications under any condition. When the antenna is
carrying much current, no search coil at all is required ; if the coil of the
wave-meter is placed near the earth lead sufficient coupling will be obtained.
It is interesting to note the variation of antenna current when L2
or Lz is varied. Fig 45.A indicates the characteristics obtained when L3
2 4 6 4 6 8
Turns In L, Turns in L,
Fig. 45.—Tuning the antenna to the closed circuit by coil In will give a different form of
resonance curve than that obtained by varying Lj.
alone is varied, while Fig. 45B indicates the results obtained when L2
only is varied.
The difference is due to the fact that in Fig. 45.A, the e.m.f. induced
in the antenna circuit is not varied, but remains constant. Thus, as the
resonant condition is reached, the current becomes a maximum, and
ADJUSTMENT OF SPARK TRANSMITTER 331
Under certain conditions, as, for instance, the sending out of distress
signals, etc., a broad distribution of the energy radiated is of prime impor
tance and close coupling would be used. A large number of stations, all
of which may be tuned to different wave-lengths, would thus be reached.
This condition is shown by curve C-C, Fig. 46.
Under normal operating conditions, however, the distribution of the
radiated energy is of greater importance, and the coupling is adjusted so
as to cause a minimum of interference with other stations, within range,
for whom the message is not intended. Under this condition'the maximum
energy is radiated at the wave-length for which the receiving set is tuned
them most sensitive to a group frequency of about 1000 cycles per second,
and it is therefore undesirable to deviate from this value to any consider
able extent.
In practical installations, the closed-circuit capacity (Ci) is usually
fixed in value, and could not be varied to secure a change in the power
input.
The voltage to which C\ is charged, E, is readily controlled, however,
by adjusting the separation of the spark gap in the proper manner. This,
therefore, forms the means whereby the power input may be controlled,
and although limited in range, as discussed below, is widely used in
practice.
In case a quenched gap is used the power input is controlled by using
the proper number of gaps in series, many for high power and perhaps
only one or two for short-range sending. It must be remembered that
as the gap length is changed, or the number of sections of a quenched gap
varied, the voltage of the alternator must be correspondingly altered to
prevent arcing and irregular discharges.
Care of a Spark Gap.1—As previously mentioned, the power
input to the closed circuit condenser is immediately decreased if arcing
occurs across the spark gap. To prevent this condition it is essential
that the gap faces be clean and smooth. The electrode faces should there
fore be periodically cleaned and polished with sandpaper or emery cloth,
the necessity and frequency of this cleaning being determined by the
time which the gap is in service. The alignment and separation of the
electrodes must also be very carefully adjusted, if the maximum efficiency
of the set is to be obtained and a pure note radiated.
If this is neglected one or more partial discharges may occur per alter
nation, and a constant group frequency will not be obtained, nor will
successive trains possess equal energy. The action is similar to that of
the non-synchronous rotary gap, but the group frequency may be more
erratic, since it depends on the complex arc conditions existing in the gap,
whereas in the former, the group frequency is partially controlled and
fixed by the rotating element. These partial discharges, which may occur
considerably below the peak value of the charging potential and at indefi
nite intervals, produce a non-musical note in the phones at the receiving
station, which varies in intensity and pitch, and is disagreeable and fatigu
ing to the operator. It is also more difficult to hear the signal through
interference than if the transmitter gap were properly adjusted and energy
radiated at a single-group frequency. The above refers also to the syn
chronous rotary gap and quench gap if the separation of the electrodes
is too small.
1 The following remarks apply only to open gaps—A quenched gap should never be
opened for inspection until it actually fails (by short-circuiting) as can be detected by
feeing how long a spark will jump across the gap section outside.
334 SPARK TELEGRAPHY [Chap. V
60 X/
r.p.m. = -
V
Thus, assuming a 500-cycle alternator with 20 pairs of poles, we have,
60 X 500
r.p.m. = —20— = l^OO r.p.m.
as the motor speed.
The speed of the driving motor must be strictly constant if a musical
note of constant pitch is to be heard in the phones at the receiving station,
and as previously mentioned, the modern shunt-wound or differentially
wound motor satisfactorily fulfills this requirement. It is evident that
by suitably adjusting the driving motor speed (by means of the motor
field rheostat) a limited control of the group frequency of the set is possible.
Thus by driving the above alternator at 1200 r.p.m., the group frequency
may be made 800 instead of 1000. Similarly 1800 r.p.m. will give a group
frequency of 1200. There is no particular advantage in this, however,
as the telephones usually have maximum sensitivity for a group frequency
of about 1000 cycles per second, and the operation of the spark gap wili
be erratic at other than rated frequency, as explained on page 308.
Capacity and Inductance of the Closed and Open Circuits.—The proper
capacity to be connected into the closed circuit will depend on the amount
OPEN AND CLOSED HIGH-FREQUENCY CIRCUITS 335
'Represents approximately an " L" antenna, length of top = 200 feet, height = 98
feet, number of wires =6.
I
336 SPARK TELEGRAPHY [Chap. V
Time
Fia. 48.—Conventional diagram of current in antenna of receiving station; even if
such high-frequency currents could flow through the telephone the diaphragm could
not move so rapidly.
Antenna
Current
Diaphragm
Movement
Time
Fig. 49.—When a rectifier is used the antenna current is assymetrical; more flowing in
one direction than in the other; such a current will give the telephone diaphragm
one impulse per wave-train.
is reaching the antenna. Also the magnitude of the current flowing even
under the best conditions is very small. For these reasons it is desirable
and advantageous to connect the detecting apparatus in a separate cir
cuit coupled inductively to the antenna by means of coils
Li, Lv, Fig. 51, the two forming what is known as the
receiving coupler.
Inductively Coupled Receiver.—With this connection,
the primary or antenna circuit may be tuned accurately to
the frequency of the incoming energy, and since all high
resistances have been removed, the antenna current will
attain a maximum value very much greater than possi
ble with the preceding arrangements. Therefore the •<4r
e.m.f. induced in the secondary and the resulting current
Fig. 50.—A pos
flow will be maximum and the signal strongest, although sible scheme for
it will still be relatively weak due to the high resistances using telephone
in the second circuit, which diminishes the resultant and rectifying
current. This circuit possesses some selectivity due crystal.
to the adjustment of natural frequency possible in the low
resistance antenna circuit. To enable the circuit to be tuned over
wide ranges of wave-length, and additional inductance L', known
as a " loading " inductance, is inserted as shown for very long wave-
340 SPARK TELEGRAPHY [Chap. V
P = K<t>t2 = K{<t>,+K'iy
= K<t>2+2KK'<t>,i+KK,2i2 (12)
The total pull thus consists of three components, one of which is con
stant (K<f>„2) and thus has no effect on the diaphragm vibrational ampli
tude, while another is proportional to the current variation squared
{KK'2?). This term represents a distortional component of double fre
342 SPARK TELEGRAPHY [Chap. V
(1) The magnetic circuit is of low reluctances and thus small signal
currents will produce relatively greater fluxes and greater forces.
(2) The armature is similar in its mounting to a lever, with a force
acting at each end. The diaphragm, being rigidly attached to one end,
thus has an increased deflection for a given magnetizing force, and thus
the signal strength is intensified.
It is to be noted that this device is not truly balanced (when no signal
is being received) in the case of detectors where the initial current is not
zero, as in the vacuum tube and crystal equipped with polarizing battery.
The pull due to this current, however, is extremely light, compared to
the heavy pull exerted by the permanent magnet in the usual type cf
construction, and the diaphragm may be considered as essentially
unstressed.
Characteristics of Crystal Rectifiers.—From the previously mentioned
function of the rectifier as utilized in the reception of radio signals, it
will be seen that the essential characteristic which it must possess is that
of unilateral conductivity. This means that the rectifier possesses a
high conductivity for current of a given polarity, and relatively low con
ductivity for current of opposite polarity. Due to this property, a train
of high-frequency e.m.f. waves impressed on the circuit containing the
phones and detector (in series) will result in a net force being exerted on
the diaphragm, the resultant deflection producing a click in the phones.
With the detector omitted, the net effect is not obtained and no click
results, the diaphragm being unable to follow the high-frequency current
alternations due to its mechanical inertia. These effects have been previ -
ously indicated by the curves shown in Fig. 48 and 49.
The unilateral conductivity possessed by various crystals is shown
by the following curves (Figs. 55 to 58, inclusive). These curves indi
cate the relatively large currents obtained when e.m.f. of various values
and of a given polarity are impressed across the rectifier circuit and the
comparatively small (practically negligible) currents obtained when the
e.m.f. 's are reversed. These curves represent the " d.c. characteristic "
of the crystals in contradistinction to the " a.c. characteristic " dis
cussed below, and are obtained by means of the experimental circuit indi
cated in Fig. 60 (Insert A).
Fig. 55 illustrates the characteristics obtained for a carborundum
(silicon carbide) crystal. The curve is interesting as it illustrates the
function of the local battery, sometimes used in series with the detector
and phones, and known as a " polarizing " battery. The connection of
this battery in the detector circuit is illustrated below (Fig. 59).
It is evident that with any detector the greatest asymmetrical effect
(and thus maximum signal strength) will be obtained, if we adjust the
crystal to operate at the point of maximum change of curvature. In the
344 SPARK TELEGRAPHY [Chap. V
voltage values are also indicated. It should be noticed that the negative
alternations of the current are practically negligible in amplitude, while
the positive afternations are not
of sine wave form but consider
ably more peaked, due to the
variation in detector resistance,
which decreases as the current
increases.
This current may be graphi
cally resolved into its d.c. and
a.c. components as shown in the
figure. The -latter component
will not affect the d.c. ammeter
the deflection of which is pro
portional to the magnitude of
the d.c. component only, the
value of which it indicates. Thus,
for an effective a.c. voltage of
1.41 volts Fig. 60 (maximum
value equal to 2 volts as shown
in Fig. 61) the reading of the
Fio. 58.—Characteristic curves of a "Perikon" ammeter is 2 milliamperes, which
rectifier, utilizing the contact between zincite is the magnitude of the d.c.
and chalcopyrite. component as indicated in Fig.
61. Thus the curve obtained
from the a.c. test indicates the d.c. component plotted to various
corresponding a.c. voltages as indicated by the curve in Fig. 60.
The insert curve in Fig. 60 illus
trates the a.c. and d.c. characteristics
to a magnified scale in the region of the
zero voltage point. It is interesting
and important to observe that this d.c. Carborundum
characteristic indicates satisfactory detector
rectification, for very small voltage
values, such as would exist across the
Fio. 59.—Scheme of using such a crystal
detector-phone circuit under normal as carborundum in a receiving circuit.
conditions, although the more extended The best rectifying action is obtained
curve (main curve of Fig. 60) would by suitable adjustment of the poten
seem to indicate that for small voltage tiometer on the polarizing battery.
variations, a polarizing e.m.f. of about
+ .25 volt' would be desirable. These data demonstrate the fact that if the
characteristic curves are to be considered reliable, and truly indicative of
what the rectifier will do in its application to radio signal reception,
CHARACTERISTICS OF CRYSTAL RECTIFIERS 347
10 u
Fig. 60—Comparison of d.c. and a.c. characteristics of a Perikon detector. The a.c.
characteristic was obtained by measuring the current through the rectifier with
d.c. ammeter when an alternating e.m.f. was impressed. The insert shows the really
important action, as it is seldom that more than a small fraction of a volt is set up
across the rectifier when it is used in a receiving circuit.
a magnitude practically never encountered in normal radio reception.
348 SPARK TELEGRAPHY TChap. V
| Time
Fia. 61.—Analysis of the current through rectifying crystal.
Detector
Current
Phone
Current
Shunting
Capacity
Current
1
Tim»
Fig. 63.—Currents in the branched circuit shown in Fig. 62.
capacity, which has a relatively low impedance to high-frequency current,
while the audio frequency component flows through the phone windings.
Normally, however, the distributed capacity of the phone cords, etc.,
is only a few micro-microfarads in value and is not large enough to supply
>W. H. Eccles, Proc. Phys. Soc, London, Vol. 25, p. 273, June, 1913.
lR. H. Goddard, Physical Review, Vol. 34, 1912.
1 It is to be noted that any explanation must be able to take care of the fact that
certain crystals rectify in one direction for low voltages, and in the opposite direction
for higher voltages, not rectifying at all for some intermediate voltage.
350 SPARK TELEGRAPHY [Chap. V
" Audibility " may be defined as the ratio of the audio current flow
ing through the telephone receivers to that which is necessary to make
the signals just audible. To speak of a receiving circuit having an audi
bility of, say, 20, means that the current in the receiving circuit is twenty
times that which is just necessary to produce a just audible signal.
The audibility thus defined is directly proportional to the current in
the receiving antenna and, for weak couplings, say less than 5 per cent,
inversely to the coupling coefficient between the receiving antenna cir
cuit and the receiving closed circuit. Again for short distances the receiv
ing antenna current may be shown to vary as follows:
where
Jr= receiving antenna current;
7, = transmitting antenna current;
h, and h, = height of receiving and transmitting antenna, respectively;
R= effective resistance of the receiving antenna, including the
resistance due to the closed circuit being coupled to it;
d = distance between the two antennae.
From the above it follows that, if the coupling between antenna and
closed tuned circuit is very loose (generally the case in practice)
Ir I,h,hr . .
^k^RXdk' (14)
where
a = audibility;1
k = coupling coefficient between receiving antenna circuit and the
receiving closed circuit.
" Selectivity " of a receiving system may be defined as the ratio of the
natural wave-length of the transmitting and receiving antenna circuits
to the difference between this wave-length and the length of some other
wave which (of same field intensity as signal wave) will give a response
just audible. Thus, if:
X„= natural wave-length of the two antenna circuits;
Xa = length of wave (of same field intensity as signal wave) which
will give a just audible response in the telephone receivers.
S= selectivity,
Then: s=V^V (15)
s=«xdjA <16>
where, q=a constant;
dt and 8, = decrements of transmitting and receiving circuits, respectively;
a = audibility.
Practically no selectivity can be obtained with the transmitting and
receiving systems out of tune.
When making the adjustments of a receiving set the aim should be
to obtain the maximum selectivity compatible with a reasonable audi
bility; but it must be borne in mind that these two quantities are inversely
proportional to each other and that a high audibility means a low selectivity
and vice versa, as shown by the formula above.
We may now discuss the characteristics of the various types of
receivers, of which there are, in general, three:
1st. Those in which the detecting circuit is conductively coupled to
the receiving antenna circuit as shown in Fig. 64.
2d. Those in which the detecting circuit is inductively coupled to the
receiving antenna circuit, as shown in Fig. 65.
3d. Those in which the detecting circuit is statically connected to the
receiving antenna circuit, as shown in Fig. 66.
In all receiving systems the receiving antenna circuit is supposed
to be tuned to the wave-length of the incoming oscillations, so that the
e.m.f. impressed upon the receiving antenna due to the electro-magnetic
waves produce the maximum current.
First Type of Receiver.—In this type, since the energy of the signals
received in the antenna is applied directly to the detector circuit without
loss on any intermediary circuit, it is plain that comparatively loud signals
will be obtained, provided, of course, that the inductance to which the
detector circuit is connected is of any reasonable value, so as to produce
1 See Chapter IV, pp. 272-274.
RECEIVING CIRCUITS 353
a reasonable drop across the detector circuit; it has been shown (Fig. 60)
that the rectification given by the crystal is porportional to the square
of the impressed voltage, hence if the inductance used in the antenna for
tuning is low, the drop across this inductance will probably be low, so
that a poor signal will be obtained. The signal given by the connection
will probably be loud and be-
cause of the very loudness of
the signals, the system must, as
already pointed out, be lacking !
in selectivity. Of course, the
selectivity may be improved by
making the decrements of the
transmitting and receiving an
tenna circuits low; see Eq. (16).
Second Type of Receiver.—
Fig. 64.—Single-circuit receiving system.
This may be used either with
or without a tuning condenser
in the detector circuit. We will consider the two cases separately,
(a) Without a tuning condenser in the detector circuit. In this case the audi
bility of the signals may be changed by changing the coupling between
H and K (Fig. 65); it is superior to the first type because the selec
tivity may be greatly increased without decreasing the audibility. This
is done by using a weak coupling between H and K, thus increasing selec
tivity; the signal is main
tained at a loud intensity
by winding K with many
turns of wire compared to
the winding of H, thus
obtaining perhaps much
greater voltage across the
terminals of K than exists
across H. By thus using
Fia. 65.—Two circuit inductively coupled receiving high inductance for K,
systems. getting larger voltage, the
efficiency of rectification of
the crystal is increased sufficiently to permit the weak coupling required
for selectivity. (6) With a tuning condenser in the detector circuit. An
increase in selectivity results from this when, as is always the case, the
detector circuit is tuned to the receiving antenna circuit, which is, in turn,
tuned to the transmitting antenna. For this case it has been found that
the selectivity is affected most by the decrements of the detector circuit
and of the transmitting antenna, and very little by the decrement of the
receiving antenna. This result makes it possible to obtain great selec-
354 SPARK TELEGRAPHY [Chap. V
tivity even when the decrement of the receiving antenna is high, by using
a low decrement detector circuit. On the other hand, if the receiving an
tenna has a low decrement, then the use of a tuned detector circuit has
but little advantage, and it would show practically no increase in selec
tivity over the case where no condenser is used in the detector circuit.
, Third Type of Re-
ceiver.—This is similar
-H-
r
o oo to the case of the induc
1L« tively coupled type, ex
oo
cept, of course, that the
% When wring the static coupling is changed by
1 coupling. colU Liand Lj
-3k are adjusted to give no changing the two con
mutual inunction
densers C\ and C2, Fig.
66. Increasing the ca
pacity of these two con-
_ densers increases the
Fig. 66.—Electrically, or capacitively, coupled receiving coupling and hence the
system. audibility, while the se
lectivity is at the same
timer educed. Since the coupling condensers form, together with closed
circuit, L2 -C, a circuit which is in multiple with the antenna tuning
inductance, it is plain that the total equivalent inductance or capacity of
this multiple circuit must be changed somewhat by any change in the
coupling condensers, thus affecting the tuning of the antenna circuit.1
Of the three types of receivers described above the second (inductively
coupled type) is most
widely used, while the
statically coupled receiv
ers were largely used in
the U. S. Navy. The
first type is never used
except when first picking
up signals, when the
operator may, if the
apparatus will allow it,
place his detecting cir
cuit directly across the Fig. 67.—Ordinary type of receiving circuit.
antenna tuning induct
ance; and later he will change over to the inductively coupled or to the
statically coupled type, whichever the case may be.
We will now give the various steps through which an operator should
1 For a theoretical treatment of the selectivity of the electrically coupled receiver
see article by Louis Cohen, " Electrostatically coupled circuits," Proc. I. R. E., Oct., 1920.
ADJUSTMENT OF RECEIVING CIRCUIT 355
Formula (13) shows that the less the value of R (resistance of receiving
1 In case no switch, S, is provided, condenser C2 may be set at its minimum value;
this is practically equivalent to opening switch S.
1 The curves given on pp. 103-104 were obtained while an e.m.f. of constant ampli
tude was impressed on the primary circuit. In the circuit of Fig. 67 a damjxd e.m.f.
is impressed as the primary: if the damping is high these curves are not quite applicable
to the case.
356 SPARK TELEGRAPHY [Chap. V
system) the greater the audibility, and in this respect the effective resist
ance of the entire receiving system should be kept as low as possible.1
Again from Formula (16), i.e.:
(16)
5,+ Sr a
it may be seen that, since the resistance of the receiving system affects
the decrement Sr in direct proportion, any decrease of R will decrease 5r
and increase S provided, of course, that a is kept constant by suitably
changing k. However, since no matter what is done to R the value of 6,
(transmitter decrement) cannot be changed by the receiving operator,
Fig. 68.—Showing arrangement of a buzzer circuit loosely coupled to the antenna, for
the testing of the crystal rectifier. With the buzzer in operation the antenna
oscillates at its natural frequency and so acts on the receiving circuit as would a
signal. Care must be taken to prevent induction from the buzzer circuit getting
into the K-Ci circuit directly as in this case the test is valueless; the buzzer will
then be heard in the phones even though the crystal is short-circuited.
it follows that, when 5r is made very small, there is hardly any gain in
selectivity obtainable by making it smaller, because, even if Sr were zero,
there would still remain 5, to be reckoned with in connection with the
value of the selectivity. The conclusion to be derived from the above
is that it is uneconomical to try to make the receiving system of extremely
1 In addition to this condition the resistance introduced into the circuit by the
detector and phones should be just equal to the resistance of the entire circuit, exclusive
of the detector and phones.
WAVE-LENGTHS AND RANGES IN SPARK TELEGRAPHY 357
low resistance unless the decrement of the transmitting set is also made
correspondingly small.
Another point to be noted is that in most receivers provision is made
for adjustment of the crystal detector so as to make sure of a sensitive
spot thereon. This is done by arranging the receiving circuit somewhat
as shown in Fig. 68, where a buzzer is used to excite by impulse (and by
means of coils M and N) the antenna circuit, so as to produce therein
currents of a frequency equal to the natural frequency of the antenna cir
cuit; the currents in the latter are transferred by means of H -K to the
detector circuit, and the detector may thereby be adjusted for a sensitive
point.
Wave-lengths and Ranges in Spark Telegraphy.—The wave-lengths
used in spark telegraphy vary from about 50 to about 6000 meters. The
range under 200 is allotted to amateurs; 200 to 600 is generally used for
aeroplane sets; 450 to 800 for ship sets, 900 to 1500 for moderate-size
land stations, and over 1500 for the largest land stations. The laws of
the United States specify the following wave-lengths:
High-power stations over 1600 meters.
Navy 600 to 1600 meters.
Ship stations 300, 450, 600 meters.
Amateurs below 200 meters.
The power used is \ to % kw. for amateur and aeroplane sets, 1 to 10 kw.
for ship sets, 5 to 20 kw. for moderate size land stations and up to 100 kw.
or more for the largest land stations.
The range covered may be approximately determined by means of
the Austin formula given below, which applies to daylight transmission :
0.001 5d
/r=4.25X^-*Xe vT (17)1
Xd
where
/r=the current in receiving antenna in amperes;
/,= the current in transmitting antenna in amperes;
hi and A2 = effective heights of transmitting and receiving antennas, respect
ively, in kilometers;
X = wave length in kilometers;
d = distance between the two antennas in kilometers.
In the above formula the effective resistance of the entire receiving system
1 See Chapter IX for further discussion of transmitting formula;. Papers discussing
this formula are given by Austin in Bulletin of Bureau of Standards, Vol. 7, No. 3, 1911,
and Vol. II, No. 1, 1914, also by Libby in Proc. I. R. E., Vol. 5, No. 1, Feb., 1917.
Recent tests by Vallauri throw doubt on the validity of this equation, he having obtained
currents about ten times as large as those predicted from this formula.
358 SPARK TELEGRAPHY [Chap. V
is assumed- to be 25 ohms. In view of the fact that the distance (d) occurs
as an exponent it is difficult, more particularly for large distances, to solve
the above equation directly for d. The following may, however, be done.
Knowing hi, /12, Is and X, plot a curve showing the relation between d and
I,. The value of d, obtained from the curve, corresponding to an I,
which will give the minimum audibility (this depends on the type of
l:<0
120 CURVE SHOWING RELATION BETWEEN CURRENT
IN RECEIVING ANTENNA AND DISTANCE
110 FROM TRANSMITTING ANTENNA
\ OBTAINED BY MEANS OF AUSTIN-COHEN'S FORMUU
100 \
\\ H, isllt r f Receiving
— & of Tr In 111 i ,s \llHl nil K 11*- el
Cu rrt nl iniTr insmittiiis \n tel 11.1 = a lip !res
90 W 1V( •k IISth = 6 )U lie er 1
so Cu rv. is A 3PI I U ik tu D; r- isl t rm i-i lis io 1 b\ 1 KM I1S 4
U: 111 KM \\ IIV es
—
S 30
ta
" 20
10 —
O.0X0 d
Substituting different values of d in this last equation we obtain the cor
responding values of 7r and are, therefore, able to plot the curve of Fig. 69.
SMALL SPARK TRANSMITTER 359
Fia. 70.—Side view of a small spark set made by the Wireless Improvement O*.
360 SPARK TELEGRAPHY [Chap. V
Via. 72.—General view of the spark transmitter used at the U. S. Government station
at Arlington for broadcasting time signals and weather reports.
Fig. 73.—Showing the construction of the synchronous rotating gap of the Arlington
transmitter.
362 SPARK TELEGRAPHY [Chap. V
5 amperes in the antenna and assuming the total resistance of the antenna
to be 8 ohms, would be given by:
High-frequency power = 8X52 = 200 watts.
Assuming efficiency of the transmitting set from alternator to antenna
= 25 per cent.
200
Alternator output = -== = 800 watts.
case of a low-powered outfit practically all of the apparatus, with the excep
tion of the hand key for sending, may be mounted directly on a panel. A
neat design for a 500-watt, quenched-spark transmitter is shown in Figs. 70
and 71; the legends on the cuts makes them self-explanatory. The larger
land stations of course require large switch boards and auxiliary appa
ratus, in fact the outfit really comprises a complete isolated power plant
equipment.
In Fig. 72 is shown the arrangement of apparatus of the Arlington
spark set, used for sending out time signals; Fig. 73 gives a closer view
of the rotating sychronous spark gap and Fig. 74 gives a complete cir
cuit diagram of this station.
CHAPTER VI
which evaporate was known to vary with the latent heat of evaporation
of the substance and temperature according to the equation,
N = AVTe~*f
where
2V = number of atoms evaporating per second per sq. cm. of surface;
T = absolute temperature, ordinarily called degrees Kelvin ;
a = latent heat of evaporation;
A = a constant.
Richardson was the first to draw an analog between the evaporation of
atoms and possible evaporation of electrons from a hot metal. Reason
ing from the above equation he came to the conclusion that the number
of electrons evaporating per second (current) could be expressed by the
equation
b
i = ayfTe 2T (1)
in which
i = current of emission per sq. cm. of hot surface;
T — absolute temperature of hot metal ;
6 = latent heat of evaporation of electrons = 105,000;
a=a constant.
As this predicted current was due to the thermal activity of the emit
ting surface Richardson suggested the term thermionic current, a name
which is at present used to some extent; the term electron current is also
used, but this is really not distinctive, because all currents, arising from
whatsoever cause, are due to the flow of electrons.
The emission of electrons predicted by Eq. (1) would give currents
from a heated tungsten filament about as shown in Fig. 1; it is evident
that very large currents might be expected from a tungsten filament at
temperatures well within the safe operating region.1 Of course, ordi
narily there is no current of such magnitude due to emitted electrons;
although the number of electrons indicated in Fig. 1 is really emitted,
they at once re-enter the surface so that on the whole there are no electrons
leaving the hot surface. As soon as an electron leaves the filament it
(the filament) is left charged positively and so attracts the emitted elec
tron; thus there are as many electrons falling back into the filament as
are expelled by the internal thermal agitation.
1The melting-point for tungsten is 3270° C; reckoning the safe operating temper
ature as that which gives the filament 2000 hours' life, the safe temperature increases
somewhat with the diameter of the filament, being perhaps 2200° C. for a filament
.01 cm. diameter and 2300° C. for one .04 cm. diameter.
366 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Suppose, however, that there is, close to the heated filament, a posi
tively charged metal plate; an expelled electron will have two forces
acting on it, one tending to make it fall back into the filament, and the
other pulling it toward the positively charged plate. Which force has
the preponderating effect will depend, of course, upon the value of the
positive plate potential; if this is made sufficiently high, all of the electrons
IRREGULARITIES IN ELECTRON EVAPORATION 367
emitted from the hot surface will be drawn to the plate, none of them
re-entering the hot emitting surface.
The value of the current under this condition is called the saturation
current; this value of current measured for different filament temper
atures should satisfy Richardson's equation because all of the electrons
emitted go over to the plate.
As early as 1902 Richardson published experimental results confirm
ing his theory. Many other experimenters published results seemingly
contradicting the relations given in Eq. (1), and for several years Richard
son's theory was the subject of dispute.
It seems that very minor changes in the amount of gas in the tube
used, or the condition of the surface of the hot metal, completely nullified
the results obtained, and such has been found to be the case. H. A. Wilson
found, e.g., that the emission from a hot platinum filament might be
reduced to 1/250,000 of its normal amount by first heating the filament
in oxygen, or boiling it in nitric acid; also he found that the presence
of a slight amount of hydrogen around the heated filament completely
destroyed the effects of the oxygen and nitric acid. On the other hand
it is found that the electron emission from tungsten is very much increased
by such an impurity as thorium; if a small percentage of thorium is
present in a tungsten filament the emission is many times as great as
though pure tungsten were used.
As a result of Wilson's experiment it was evident that the condition
of the hot surface was of utmost importance in determining the emission;
the layer of oxygen-filled platinum on the surface practically prevented
emission. Yet a year afterward Wehnelt showed that if a platinum
filament was coated with lime (calcium oxide) the emission of elec
trons at a given temperature was vastly greater than from the platinum
itself.
Langmuir's experiments, performed with tungsten filaments in ex
tremely high vacuum, proved without doubt the truth of Richardson's
prediction and indicated that the various experimenters whose tests had
showed the opposite had not been careful enough in the manipulation
of their experiments and in the interpretation of the results. He found
that the higher the vacuum the more consistently did experiment and
theory agree, whereas others had concluded that gas was absolutely essen
tial if the thermionic current was to be obtained. In one of Langmuir's
tests he showed that the presence of only .000001 mm. pressure of oxygen
was sufficient practically to stop the emission of electrons from a hot tung
sten filament. It seems then that the condition of the surface of the hot
electrode affects the emission of electrons much as the evaporation of
water is prevented by covering the surface with a thin layer of oil or
similar substance.
368 VACUUM TUBES AND THEIR OPERATION [Chap. VI
50
■10
4X1013 which had sufficient velocity to carry them away from the fila
ment an appreciable fraction of a centimeter.
From the previous analysis of electron emission from a hot body it
will be realized that the condition close to the surface of a hot filament
resembles very much the atmosphere surrounding the earth, a depth of
earth atmosphere of one kilometer corresponding to a depth of " electron
atmosphere " of about 0.01 millimeter. Just as the earth's atmosphere
becomes less dense with increase of distance from the surface, does the
POWER REQUIRED FOR ELECTRON EMISSION 371
From what experimental data the author has been able to obtain him
self it seems as though these figures are rather optimistic; when operated
at the temperatures given in the above table it seems as though the life
of the filament is considerably less than the life of 2000 hours estimated
by Dushman.
Two-electrode Vacuum Tube.—The property of hot bodies in vacuo
permitting passage of electrons to a cold electrode in the same vessel was
originally called the Edison effect; it was noticed in incandescent lamps
as early as 1884. In 1896 Fleming gave the results of a series of experi
ments in thermionic currents through vacuo, but it is evident in the light
of our present knowledge that a large part of the current measured by
him was due to conduction by the ionized gas in the tube he was using.
He found some characteristics which were really due to the electron emis-
'2100° Kelvin =2100° C. absolute.
* See article by Dushman in General Electric Review, March, 1915.
372 VACUUM TUBES AND THEIR OPERATION [Chap. VI
_ sion, notably the unilateral (one direction only) conductivity of the appa
ratus, the non-linear relation between the plate potential (with respect to
the filament) and the plate current, and the fact that a large separation
of plate and filament tended to reduce the amount of plate current obtain
able. He found, however, that the plate current was unstable and that
the better the vacuum the less the plate current became; both of these
effects show that ionized gas was largely responsible for carrying the plate
current. The unilateral conductivity of a vacuum tube having two elec
trades, one hot and the other cold, was utilized by Fleming for the detec
tion of damped high-frequency waves and was patented by him in 1905
This patent was a very important one in the field of radio telegraphy; it
goes by the name of the " Fleming valve " patent. A cut showing a
Fig. 5.—One type of Fleming valve, used on early Marconi receiving sets as detector.
(generally about 2 lbs. absolute of argon), and this gas is ionized by the
electrons from the hot filament; the carrier of the plate current is in this
case also ionized gas for the main part, the number of electrons emitted
from the hot filament being sufficient to carry perhaps 1/500 of the cur
rent to the plate.
The kenotron is a rectifying tube which really operates as a thermionic
valve; the tube is exhausted as thoroughly as possible, so much so that
whatever gas may be present plays an unimportant role in the functioning
of the device. The plate current is never greater than that actually
emitted by the hot filament. These rectifying tubes are made in large
sizes, sufficient to rectify several kilowatts of power; the vacuum in these
is so high that no appreciable current is carried in the reversed direction
(electrons from plate to filament) even if 100,000 volts is impressed.
In small sizes they have
been used as voltage regulators
for self-excited generators, the
speed of which is variable. By
having a differential wind
ing on the field poles, which is
supplied with current through
a regulator tube, and connect
ing the filament of this regula
tor tube across a low-voltage
winding on the armature, a
small generator may be made
to maintain practically con- Regulator tube
Stant voltage over a wide f,0 6.—Use of a two-electrode tube as a voltage
range of speed variation. The regulator for a variable speed generator,
scheme of connection is shown
in Fig. 6, and the reasons for the tube maintaining such constant voltage
over such a wide speed range will appear from an examination of the
characteristics curves of such a tube.
Characteristic Curves of a Two-electrode Vacuum Tube—Value of
Saturation Current.—If the filament current of a kenotron is maintained
constant and plate voltage varied, readings being taken of plate voltage
(with respect to the filament) and plate current, curves will be obtained
having the shape shown in Fig. 7 ; here three curves are shown for three
different filament currents as noted on the curve sheet. The tube from
which these curves were obtained is shown in Fig. 8; the plate is a cylinder
about .5 cm. by 1.5 cm. and the filament is a helix inside this cylindrical
plate.
Curve 1, Fig. 7, shows the variation of plate current for a filament cur
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CHARACTERISTICS OF TWO-ELECTRODE TUBES 375
attracted, to some extent, by the plate for the condition shown in Fig. 10,
but the attraction is negligibly small.
It has been shown by Child 1 that when the emission of the electrons
from the filament is much greater than that required by the plate current,
the plate current may be expected to vary according to the relation
. . . (2)
in which
Ef= potential of plate with respect to filament;
x — distance between filament and plate.
If the plate is cylindrical in form with the hot filament placed in its
axis this relation becomes,
Platfe current if
two electrode tube
Dotted linfe y 2x
7/
2 3 5 10 20 30 40 50 GO
Plate volts
Fig. 11.—Curve 3 of Fig. 7 transposed to logarithmic coordinates.
The author built a tube as shown in Fig. 13 in which the spiral tungsten
filament A used for heating was entirely enclosed in a tungsten thimble
B; this thimble constituted the hot surface from which the electrons were
emitted. Such a construction gives a uniform potential gradient between
the emitting surface B and the cylindrical plate C and so permits experi
mentation under the conditions assumed in theory. With this construc
tion it is not possible to get the tungsten thimble as hot as the filament
EFFECT OF POTENTIAL DROP ALONG FILAMENT 379
charge limiting the plate current. It is evident that the filament used
in this tube gives practically no emission with currents less than 1.0
ampere. With a plate voltage of 100 the plate current rose rapidly with
increase in filament current reaching 135 milliamperes at a filament
current of 1.40 amperes.
When the plate voltage was dropped to 50 and the same variation of
filament current carried out the plate current reached a value of only 48
milliamperes at 7/ =1.40 amperes. With plate voltages of 20 and 5 the
maximum plate currents were 10.6 milli
amperes and 1 milliampere respectively.
Now with //= 1.40 the emission is 135
milliamperes as shown in curve 1; with
the plate at a positive potential of 5
volts (with respect to negative end of
filament) only 1 milliampere was ob
Plate tained, that is, only 1/135 of the elec
trons emitted by the filament reached
the plate, the rest re-entering this fila
ment due to the space charge overcoming
the comparatively weak field from the plate.
Speaking in terms of the idea de
picted in Fig. 10 we can say that the
fines of force from the plate penetrated
but a short way into the electron atmos
1+ 0.6 phere; the great mass of the emitted
Fiq. 14.—The emission of electrons electrons which, it must be remembered,
from various parts of the same fila- stay very close to the filament, never
ment differs very much; because feel the tractive effect of the positive
of the current to the plate, the plate. Those few having exceptionalTy
filament current (hence filament
temperature) is much greater at high outward velocity (due to their
one end of the filament than at velocity of emission and suitable col
the other. lisions with the other electrons in the
electron atmosphere) reach the outer
regions of the atmosphere and so get attracted to the plate.
Even for the lower values of filament current (Fig. 15) the four values
of plate voltage do not give the same plate current as might be expected.
This is due to the fact that the IR drop in the filament is appreciable;
in the special tube pictured in Fig. 13 all curves coincide in the lower parts.
In comparing the curves of Fig. 15 with those of Fig. 7 it is to be
noticed that although they have the same general shape they have entirely
different meanings. In Fig. 7 the flat parts of the curves indicate that
saturation current has been obtained and in the lower curved portions
the space charge is limiting the current; in Fig. 15 the lower curved por-
EFFECT OF FILAMENT TEMPERATURE ON ELECTRON EMISSION 381
20
than the internal grid. In one type of outside grid tube tried by the
author the control worked for a few seconds and then the accumulation
of electrodes on the inside walls of the tube made it stop functioning.
The inner walls of the glass must be made partially conducting to
prevent this accumulation of charge.
The inside control electrode need not be placed between the filament
and plate; it will work to some extent even if it is on the side of the fila
ment opposite to that on which the plate is situated. Its action in such
a tube is not as efficient in controlling the
plate current as in the normal placement ;
in the analyses to follow it will be sup
posed that the gird is inside the tube be
tween the filament and plate and the
curves given to illustrate the text will be
records obtained from such tubes.
Potential Distribution in the Three-
electrode Tube.—The three-electrode tube
functions because of the effect of the grid
on the potential distribution between the
filament and plate; it is therefore neces
sary to have a clear idea of this potential.
In Fig. 16 is shown by the dotted line
(a) this potential distribution between
two metal plates, one marked F to repre
sent the filament, the other marked P to
Fig. 16.—Two metal plates, one Ep represent the plate. The filament is sup
volts higher potential than the posed at zero potential and the plate at
other, have a uniform potential positive potential Ep. With a uniform
gradient between them, the po field distribution as shown in the upper
tential being about as shown by part of the figure the potential between
dotted line a; if plate F is covered
with an electron atmosphere the plate and filament falls off uniformly.
potential is changed to the form In the actual tube such a uniform po
shown by line fc. tential gradient does not obtain; owing
to the comparatively small surface of the /
filament the potential falls more rapidly near the filament than near
the plate.
If we now suppose an electron atmosphere to cover the surface of F
the potential distribution is changed to some such form as indicated by
the full line (b) in Fig. 16. The potential gradient becomes much
lower in the vicinity of F because most of the field of P ends on electrons
in the vicinity of F and so never reaches F; in fact if the emission is much
greater than the plate current (practically always the case with three-
electrode tubes in normal operation) the potential gradient very close
THE THREE-ELECTRODE TUBE 383
to the plate. A positive grid then increases the plate current, plate poten
tial remaining fixed.
A negatively charged grid will result in a potential distribution some
what as shown by curve c of Fig. 17; if the grid is as negative as shown
by the curve the plate current will be reduced to practically zero, because
none of the electrons (except a very few which are emitted with exception
ally high velocity) can move against the negative potential gradient
between F and G. It must be noticed of course that the potential curve
on such a line as indicated by M —N (Fig. 17) will be different from that
on such a line as M' —N'; the grid potential will not be so effective on
the line M' —N' as on a line lying closer to one of the grid wires.
It will be appreciated at once that this effect of the grid in controlling
the flow of electrons to the plate will depend on various features of con
struction of the tube.1 The grid will exercise the most control when its
wires are very fine and close together, and when it completely surrounds
the filament. Unless the grid is considerably larger (in length and breadth)
than the space occupied by the filament many of the electrons will go from
the filament around the grid and thus arrive at the plate without having
been subjected completely to the controlling action of the grid.
This idea is illustrated in Fig. 17A ; the construction shown in a will
permit the grid to exert a much greater control over the electron stream
than will the construction shown in b.
1 The question of the shielding action of a grid is taken up in Maxwell's " Electricity
and Magnetism," Vol. 1; the case worked out is for a flat plate and flat filament, of
infinite extent. In an article in Proc. I.R.E., Vol. 8, No.l, J. M. Miller shows how
closely Maxwell's theory applies to the construction of an ordinary tube.
In an article published in Vol. 15, No. 4, of The Physical Review, R. W. King shows
how the value of the controlling effect of the grid depends upon the parameters of the
tube. The theoretical voltage amplification factor of the tube mo (see p. 417 for sig
nificance of this constant) is shown to be expressible as
2iran
in which
a = distance between grid and plate;
n = number of grid wires per cm. ;
r= radius of the grid wire.
In the derivation of the above formula the grid, hot filament surface, and plate have all
been assumed as infinite parallel planes; although actual tubes depart very far from
this requirement experimentally determined values of mo for several tubes of widely
different construction check with the calculated value quite well.
The interesting point in both Miller's and King's analyses is that the distance between
the grid and filament plays no part in determining the value of mo; the closenesr of thf
grid to the plate is apparently the controlling factor.
HYDRAULIC MODEL OF THREE-ELECTRODE TUBE 385
ment, A being the filament and C the plate, C being at higher level
than A , as must
be the potential
of the plate with
respect to that
of the filament.
A stick D has
several parallel
wooden pinsfast-
ened to it and
the lower ends
of these pins are
fastened (by
tacks) to the rub
ber sheet close
to pipe A, as
shown. When
D is moved up
and down, the
Fig. 19.—Hydraulic model of the three-electrode tube. lower ends of its
pins lift up and
down those parts of the rubber sheets to which they are attached; in
Fig. 19 is shown a- sketch of the rubber sheet with the bar D lifted, and
in Fig. 20 is shown
the form of the
rubber sheet when
the bar D is de
pressed. If the
pressure of the air
in the pipe A is
properly adjusted
the flow of air
bubbles up the un
der side of the rub
bersheet resembles
(more closely than
any analogy the
author has seen)
the flow of elec
trons in a three- Fig. 20.—Hydraulic model of the three-electrode tube.
electrode tube.
The action of the bar D with its attached pins, producing small hills
and valleys in the rubber sheet, illustrates well the action of the grid.
USE OF THE THREE-ELECTRODE TUBE 387
The depression of the pins, making it more difficult for the air to pass up
along the sheet, illustrates a negative grid, and when the pins are lifted up
the increased flow of air corresponds to the increased plate current with
positive grid.1
The effect of the space charge is not simulated very well by the model;
the accumulation of air between the " grid " (row of pins, d, d, d) acts to
prevent other bubbles of air coming through the small holes in the " fila
ment " (pipe A) but this action is not strictly analogous to the mutual
repulsion of the electrons in the actual space charge effect.
Fields of Use of Three-electrode Tube.—Detector, Amplifier, Gener
ator or Converter.—The three-electrode tube was first used as a detector
of radio signals from spark stations; it was much more sensitive than its
competitors, the magnetic detector, Fleming valve, etc., and so rapidly
displaced these as a detector. In its original form as manufactured by
Deforest a potential of about 30 volts was used on the plate; the normal
plate current was a few hundred microamperes. Although these original
tubes were rather erratic in their behavior, and not uniform in their
characteristics (one tube not being like another) by careful adjustment
of filament current and plate voltage, they were nearly as good detectors
as the later types.
As the grid potential of a three-electrode tube controls the plate cur
rent (the power for which is supplied by a local battery) it is evidently
applicable as a relay, the signal voltage controlling the delivery from the
local power supply. When properly adjusted the grid circuit takes an
extremely small power to operate, so that compared to the amount of
power used in the grid circuit the amount controlled in the plate circuit
may be thousands of times as great.
If the grid circuit is adjusted to take no power itself the power ampli
fication is infinite; it must be remembered, however, that to operate the
grid circuit certain coils, condensers, and resistances are required; taking
the losses in these necessary associated circuits into account the power
amplification is not infinite, but it is very large even then. Thus a certain
tube used in telephone circuits as an amplifying repeater has a power
amplification of about one thousand times.
If an alternating potential difference is impressed on the grid of a tube
the plate current periodically increases and decreases. This pulsating cur
rent in the plate circuit may be made to produce fluctuations in the grid
potential by means of a suitable transformer, the primary of which is con
nected in the plate circuit and the secondary connected between the fila-
1 By having the pins, d, d, etc., in the form of tubes open at their lower ends and
having corresponding holes in the rubber sheet, some of the air bubbles will run up these
tubes when handle D is lifted, thus imitating the action of the positive grid attracting
some of the electrons, causing grid current.
388 VACUUM TUBES AND THEIR OPERATION [Chap. VI
The material used for the grids and plates is generally nickel or tungsten,
or molybdenum; the tubes designed for generating much power are likely
to have all metal parts, filament, grid, and plate of tungsten.
In Fig. 21 are shown some of the more common tubes; A and B are
power tubes of 50- and 250-watt ratings, respectively; C and D are small-
power tubes designed for an alternating-current output of about 4 watts,
E, F and G serve as either detectors or amplifiers; H is a Deforest audion
of the original type, J is a cylindrical tube made for amateur use; J is
a modern Marconi tube; K and L are two amplifying bulbs, the latter
having extremely fine grid and very small plate (a nearly invisible zig
zag wire) ; M is a special power tube with grid brought out at tip of the
Fig. 21.—Various types of tubes used in getting the experimental data given in this
chapter.
there was a deal of gas left in the bulb at the completion of the evacuation
process and this gas made the tubes very erratic and undependable in
their behavior.1 Not only would various bulbs, supposedly similar, have
very different characteristics, but any one bulb would not act consistently,
and many tricks had to be employed to make the bulbs perform to the
best advantage.
An exact study of the effect of gas in a vacuum tube cannot be given
here; only those points which bear directly on the operation of the tube
in radio practice will be outlined. The student is referred to some such
book as Thomson's " Conduction of Electricity through Gases " for a
deeper analysis than will be attempted here.
A cold electrode in a vacuum tube, unless subjected to considerable
electron bombardment, will not give off electrons in appreciable quan
tities; thus in a two-electrode tube if the plate is made negative with
respect to the filament no current will flow, because if the plate is made
negative any current which flows from plate to filament must be caused
by electrons leaving the cold plate. Experiment demonstrates the truth
of this statement; if other possible carriers of current are eliminated (such
as actual leaks inside or outside the tube, or gas inside the tube) the amount
of current which will flow is too small to be measured. We may safely
conclude that when a cold electrode (either grid or plate) of a tube shows
current in such direction as to indicate electrons flowing from it, inside
the tube, the tube has in it gas which is serving as a conductor of current.2
This statement neglects the possibility of secondary emission of electrons
due to excessive bombardment by electrons coming from the filament;
this effect will be treated in a later paragraph.
Ordinarily a gas is a good insulator and will not carry current, but
when under rather low pressure it may be made to carry very large cur
rent if by some means it becomes ionized. By this term is meant the
breaking up of the normal gas atom into two parts, a free electron and
positively charged nucleus; this breaking up of a gas atom corresponds
to the " break-down " of any ordinary insulator when it is subjected to
too high a potential gradient.
In a Geissler tube the gas becomes ionized (showing the well-known
blue glow) only when rather high potentials are used, generally several
thousand volts. Now in the vacuum tube used for radio such high voltage
1 It is quit* evident,, however, that Fleming appreciated the necessity of a high
vacuum to make the tubes constant in behavior; the superiority of present evacuation
is due not so much to any conception of its importance, perhaps, as to the better pumps
now available.
1 It must be remembered that even with the highest vacuum obtainable there is
still a tremendous number of gas molecules in the evacuated space; it is likely that
in highest vacuum tubes used to-day (10~8 mm. of mercury) there are of the order of
108 gas molecules per cubic centimeter.
392 VACUUM TUBES AND THEIR OPERATION [Chap. VI
is practically never used; ionization of the gas in the tube may occur with
voltages as low as thirty or forty. This is due to the fact that the hot
filament furnishes the electrons which by their motion (caused by the
positive plate potential) serve to start the ionization of the gas atoms.
In a Geissler tube no such means is at hand for starting the ionization,
hence the comparatively high voltage required to show the effect.
The role played by the electrons emitted from the filament in pro
ducing ionization is easily shown by a simple test. If a tube which is
known to be faulty is subjected to normal plate potential with cold fila
ment, no plate current will flow and the tube will show no signs of ioniza
tion. Now if the filament current is gradually increased emission of
electrons will commence and a slight plate current will flow; at a certain
filament temperature, depending upon how much gas there is in the tube,
the familiar blue haze will appear in the bulb, accompanied generally by
a very large increase in the plate current, thus showing that the filament
must be emitting a certain minimum number of electrons before appreci
able ionization of the gas occurs.
If but a small amount of gas is present the pale blue glow may be so
weak as to be invisible, but the presence of appreciable quantity of gas
is always shown by erratic changes in the plate current.
Some oxide-coated power tubes show a bright fluorescence on the
plate when being used, generally in the form of a pattern of the grid.
It is easy to mistake this effect for ionization because of the blue color
from the fluorescing plate; if the plate is hidden from the eye (by the hand
or a piece of cardboard) it will be seen that there is no blue glow in the
space inside the tube. The intensity of the effect of fluorescence depends
upon the condition of the surface of the plate, which is generally covered
with more or less oxide.
Danger to a Tube from Ionization.—When a tube ionizes the con
sequences resulting depend upon the type of tube being used and upon
how quickly the condition is removed. In the case of a detecting tube,
or amplifying tube, the state of ionization will generally stop the function
ing of the tube, its characteristics being entirely different when the tube
is filled with a semi-conductor (the ionized gas) than those of a normal
electron tube. If either the plate voltage or filament current is reduced
the ionization will disappear and the tube may operate as well (or possibly
better) than) it did before ionizing.
In the case of a power tube the situation is different; unless either
the filament current or plate potential is immediately reduced the tube
may be completely spoiled. Ionization practically never occurs in a tung
sten tube because of the high degree of vacuum ordinarily used; the oxide
filament tube is much more likely to suffer from it. In these tubes there
is always a lot of gas in the metal parts of the tube, filament, grid, and
METHOD OF EVACUATING TUBES 393
plate; now when ionization starts the electrons of the ionized gas travel
to the plate, it being positive, but the positive nuclei travel to the filament
and subject it to a bombardment.
This bombardment results in extra heating of the filament, generally
in one spot, which extra heating tends to aggravate itself and burn the
filament out at this point. The hotter the filament the greater the electron
emission, and also gas is likely to be emitted from the filament at this
hot spot; where the gas and electron emission both increase the ionization
increases, increasing the bombardment of the filament at this spot, and
thus by the cumulative action burning it out. At the time the filament
burns out it releases a lot of gas which, becoming ionized, may permit
the passage of such a large current from the plate as to result in a miniature
" explosion " inside the tube, completely wrecking the parts and break
ing the bulb.
When a power bulb with oxide filament once ionizes it is practically
valueless1 until re-exhausted; the ionization itself will probably result in
the emission of extra gas from the bombarded parts, so that the tube has
more gas in it after ionization than before.
Evacuation of a Vacuum Tube.—Because of the deleterious effects of
gas the electron tube must be very carefully freed from any appreciable
quantity of it. With modern pumps the getting out of the gas from the
space inside the bulb is very simple and rapid but this is not sufficient.
Metals, oxides, and glass absorb a deal of gas which gradually comes out;
so that a tube pumped " clean " will soon show gas because of its emission
from the parts of the tube. This emission is very slow at ordinary temper
atures,' so that a tube might be pumped a long time without getting suffi
cient gas from the parts to prevent further emission. If, however, the
glass and metal parts are heated, the gas is expelled from them very
rapidly, and this is the scheme used in evacuating tubes; the whole tube
is subjected to a " baking " process while connected to the pumps.
This heating should be carried much higher than any temperature at
which the tube may operate; thus if in practice the plates and filament
operate at dull-red heat they should be run for several minutes at a bright-
red heat during evacuation. This overheating of the parts is regularly
done with tungsten tubes but it cannot be carried out to the same degree
with the oxide-coated filaments. The coated filament is easily spoiled
if subjected to too high a temperature, and this limits the possibility of
complete evacuation. For this reason, as previously mentioned, the oxide-
coated power tubes are much more subject to destructive ionization during
operation than arc the tungsten tubes.
1 It may be used, however, for generating a small amount of power, providing the
plate voltage is kept sufficiently low; thus a 300-volt tube which has ionized badly may
sometimes be used by reducing the plate voltage to perhaps 250.
394 VACUUM TUBES AND THEIR OPERATION [Chap. VI
ence of the ionized gas reduced the limiting action of the space charge to
practically zero, thus permitting the plate current to increase at once to
the value fixed by the emission from the filament; second, the ionized
Kf'O 1200
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Fig. 23.—Disappearance of gas from a tube; curves were taken in the order 1-2-3;
ionization showed on the first curve, to a lesser extent in the second and not at all
in the third.
gas acts as a conductor, giving a current in addition to that afforded by the
emission from the filament. With higher filament currents the ioniza
tion set in at lower voltages as indicated on the curve sheet.
396 VACUUM TUBES AND THEIR OPERATION [Chap. VI
In Fig. 23 arc shown three curves from the same tube, one taken after
the other. Curve 1 was taken first ; ionization set in with a plate potential
of 40 volts, causing a large increase in plate current, which value was
maintained for one minute. The plate voltage was then reduced to zero
and again increased, and with same filament current as before; ioniza
tion set in at 60 volts, indicating that during the maintenance of the ioniza
tion current previously, some of the gas had been occluded in the glass
walls of the tube or elsewhere. This idea is substantiated by the fact that
when ionization did set in (somewhat above 60 volts) the current jumped
10 16 20 30 35 40 45 60 65 65 70 75 80
Volts on platu
Fig. 24.—In this tube the effect of the gas present was to so alter the emitting
properties of the filament that the saturation current was appreciably different
with increasing and decreasing plate voltages, showing probably change in
emissivity of the filament.
gas present; a kind of " hysteresis " cycle occurs, the current not going
through the same values for decreasing plate voltage as for increasing
plate voltage. At voltages higher than fifteen this tube showed a drooping
current-voltage curve, which means that its a.c. resistance (for limited
values of impressed alternating e.m.f.) is negative; as long as it held this
shapes may be obtained. Fig. 25 shows an effect of this kind and for each
of the plate voltages used a " hump " occurs in the plate current curve.
800
2 10 12 3
Grid potential
Fia. 25A.—Showing the effect of a small amount of gas in producing a well-defined
"hump" in the plate current curve.
The position of this hump shifts to different grid voltage for the different
plate voltages used in the test.
DETECTION OF GAS IN A TUBE — 399
10 8 6 4 2—0 +
Grid potential (to negative end of filaments) in volts
Fig. 26.—Even in the very high vacuum tubes the grid shows a reversed current when
its potential is negative; these curves are for a type P pliotron having a high degree
of evacuation.
it is seen that for plate voltage of 100 the reversed grid current is
much less than it is for a plate voltage of 200; this is due to the lower
plate current at the lower plate voltage producing less intense ionization
1 It must be remembered that when the grid is subjected to very high frequency varia
tions in its potential it is quite likely that the plate current does not vary in the manner
indicated by the curve obtained in direct current test, such as that given in Fig. 25.4 .
400 VACUUM TUBES AND THEIR OPERATION [Chap. VI
of the gas present. As the grid potential was increased (in the nega
tive direction) the grid current decreased instead of increasing as might
be expected. This is due to the decrease of plate current with the lower
grid potentials.
A tube having considerable gas in it may be made extremely sensitive
as a detector if adjusted with a plate or grid voltage nearly sufficient to
produce ionization; the slight increase in grid potential due to the incom
ing signal may then cause ionization to occur with a resultant great increase
in the plate current. Such tubes are not reliable enough to be of any
great practical importance, however; the modern high-vacuum tube if
properly connected in cascade with the others, may produce the same
amount of amplification and at the same time have the necessary reli
ability of action.
Tungsten Filaments and Oxide-coated Filament.—As noted in the
first paragraph of this chapter, a pure metal such as tungsten must operate
at a very high temperature before an appreciable emission of electrons
takes place; to get the amount of emission required for a power tube
the tungsten must be at a dazzling white heat. In first operating tubes
of this type the experimenter will get an incorrect idea of their behavior
unless meters are used, and the filament is run right up to its rated current.
Tubes using a Wehnelt cathode, or oxide-coated filament, on the other
hand, must not be operated at a high temperature or they will be spoiled.
These filaments are made of thin platinum strip, coated with a mixture
of various oxides (barium, strontium, and calcium) together with a suit
able cement; in order to make the oxide coating adhere more tenaciously
the platinum strip is generally twisted about itself. These filaments
should never be operated at a temperature higher than that required to
give a bright cherry-red color; the detector and amplifier bulbs generally
operate satisfactorily at a much lower temperature than this.
To get the same emission from a tungsten filament as from an oxide-
coated filament requires about twice the amount of power; where the cost
or difficulty of obtaining power is of prime importance, therefore, the
oxide-coated tube is superior. For detector and amplifier tubes used in
army field work for " standby " service, being in continued use, this ques
tion of power supply is of more importance almost than any other; the
power for heating the filaments must be transported generally in the
form of portable storage batteries and that tube requiring the fewest
renewals of batteries is the best, even though some of its other character
istics may not be as good.
Power tubes, on the other hand, use a considerable amount of power
in their plate circuits, as much or more than that used for heating the
filament so that the filament power docs not have the same relative impor
tance as it does for the detector and amplifier bulbs in which the filament
CHARACTERISTIC CURVES OF THREE-ELECTRODE TUBES 401
requires perhaps 3 watts for heating, whereas the plate circuit requires
but .01 watt. So far as power consumption of the tube is concerned,
therefore, the lower filament power of the oxide tube does not offer such
great advantage, in fact, it seems to the author that the oxide filament is
not the equal of the tungstens filament for power tubes. The vacuum
attained in oxide filament tubes is never as good, or as permanent, as that
commonly used with tungsten filaments, and this fact leads to their very
frequent failure. The gas present ionizes and this ionization (if there
is appreciable gas present) completely spoils their operation as generators.
It sometimes happens that a tube ionizes, due to excessive potential
gradients, and when the high plate voltage is removed, the tube acts as
well as before, but, on the other hand, the result of the ionization frequently
results in a burnt-out filament and completely spoiled tube.
With a tungsten tube, on the other hand, even if ionization occurs,
the effect will soon disappear if the plate voltage is held up to its normal
value; the effect of the exceedingly hot tungsten filament is to use up,
in some way or other, the gas causing the ionization. In such a tube
the vacuum is likely to improve the more the tube is used.
Characteristic Curves for Three-electrode Tubes.—The so-called
" static " characteristic curves of a three-electrode tube show how the plate
current and grid current vary as the grid potential is varied over a sufficient
range to cause this plate current to vary from its maximum operating
value to zero, the plate potential being constant while the series of points
for the curve is being obtained. The same curves are taken for several
values of plate potential.
Another set of curves is sometimes used showing the variation of ' >■ ' '
plate and grid currents as the plate potential is varied from zero to its
maximum safe value, the grid potential remaining constant, a series of
such curves is obtained for various grid potentials.
Another, and probably more useful, set of curves show how the plate
and grid currents vary as the grid potential is varied, the plate potential
varying, during the process of getting the curve, in the same way it does
when the tube is actually used in a detecting or generating circuit. When
being used the three-electrode tube always has an impedance of some kind
in series with the plate circuit. The value of the voltage used in the
plate circuit is constant, not varying as the grid potential is varied, by
signal or otherwise; it is therefore evident that as the grid potential
varies, thus varying the current in the plate circuit, the plate potential
must vary because it is equal to the plate circuit voltage minus the drop
in the series impedance, and this drop varies with the grid potential.
This last set of curves is the one which most readily permits the pre
diction of the behavior of the tube. A resistance should be put in the
plate circuit equal to that which is used when the tube is actually operating;
402 VACUUM TUBES AND THEIR OPERATION [Chap. VI
a plate circuit voltage should be used such that when the grid is set at
the same potential as its average potential under operating conditions
the plate current is the same as its average operating value. The plate-
circuit voltage is frequently called the " B " battery voltage.
It has become customary in speaking of grid potential to refer the grid
to the negative end of the filament; unless otherwise stated all the curves
shown in this text are so given. In case the characteristics are desired
when the grid is connected to the positive end of the filament it is only
Grid potential
Fig. 27.—An old Deforest audion, after being well evacuated and baked, showed just
as regular characteristics as the modern tube.
necessary to move the " zero grid potential " along, on the curve sheets
as given, by an amount equal to the IR drop in the filament.
In Fig. 27 is shown a set of plate-current curves from an old Deforest
audion, after it had been re-evacuated to take off all possible gas. The
plate circuit had no added resistance except that of the B battery, which
was so low that the variation in plate current did not appreciably affect
the plate potential. On the curve sheet is shown the locus of the " free
grid potential," i.e., the potential at which the grid set itself when its
CHARACTERISTIC CURVES FROM TYPICAL TUBES 403
current, but also how, as the plate voltage increases, the grid current is
reduced. The sum of the grid current and plate current gives, for all
values of plate voltage, the difference between the two filament currents.
The resistance of the filament of a vacuum tube under such conditions is
16 < vo U
3.0 Va t.iu- 9 ai IPI fyi IK butt
1 MmI : pdten tla i indichtet
( urvL'S
L 18(
100 volU
i I
2.0
S 6
c
I3
O
o 2 TO volt o —
3c
1.0
eg rid
po Lilt'ial /
not a simple function of volts and amperes; it involves all the theory
of a long, leaky, telegraph line.
The safe filament current for these large power tubes is always rated
in terms of the maximum current, that is, the end of the filament where
oixsraaxovuvHO saAHno woaa ivomax saanx so*
406 VACUUM TUBES AND THEIR OPERATION [Chap. VI
i
CHARACTERISTIC CURVES FROM TYPICAL CURVES 407
the plate current and battery heating current combine to give a current
greater than normal battery current.
In Fig. 32 are shown curves for the same tube as used for Fig. 30; the
filament current (larger value) was held at 3.60 amperes and various
- —
E
A 1 3.S
J 1
yJIp
li!■ |lf-VWAAAV
a3
— 1 1 J 1 1 3.3
u T,7
3.2
3.1
J. ■
20 40 60
80 100 20 10 60 200
Plate voltage
Fig. 31.—Showing the effect of the plate voltage upon the filament current of a power
tube, the voltage impressed on the filament being constant. The change in grid
current produced by increasing plate potential is also shown.
voltages were impressed on the plate. With low plate voltage it is seen
that when the grid becomes positive the plate current undergoes a rapid
decrease. This combination of high positive grid voltage and low plate
voltage occurs when the tube is used for generating power and results
\
while varying the plate voltage. For all these curves the grid currents
were only a few microamperes. In this tube it is evident that 1 volt
on the grid has the same effect on plate current as 1 1 volts on the plate.
In Fig. 34 are shown similar curves for a P-10 pliotron, values having
been obtained for low plate voltage and high positive grid voltages and in
J
CHARACTERISTIC CURVES FROM TYPICAL TUBES 409
1W 200 300 400 600 600 700 800 900 1000 1100 1200
Plato voltage
Fig. 33.—Static characteristics of a Type P tube for various fixed grid potentials and
variable plate voltage. The curve in the upper part of the diagram shows the
limit of operation of the tube.
410 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Fig. 35 are shown some typical curves for a finer-mesh grid (P-30). In
this tube the grid voltage is twenty-two times as effective as the plate
voltage in determining plate current. It will be noticed how quickly
the grid current rises as the
plate potential decreases be
yond a certain limit.
Potential of the Free Grid
of a Three-electrode Tube-
When the grid of a vacuum
tube is entirely disconnected
from other circuits it is said
to be " free," meaning that it
is free to assume any potential
circumstances may demand.
Actually a grid is never really
free, because there is always
some leakage from the grid to
the plate and filament even in
tubes with extremely high
vacuum. If the value of this
leak resistance is perhaps 50
megohms the grid may be reck
oned as free, although in many
tubes a much greater resistance
exists and the grids are corre
spondingly more " free."
It is almost an axiom in
vacuum-tube operation that a
grid should never be left free.
Consistent operation of the
tube is almost impossible unless
the resistance between the grid
Fig. 34.—Similar to the curves of Fig. 33, this
tube having a grid with coarser mesh. and filament is of definite value,
and sufficiently low; it seldom
exceeds one megohm in ordinary detecting or amplifying sets.
In Fig. 36 is shown a connection in which a free grid is used; tube 1
is repeating into tube 2, the fluctuations of plate voltage of 1 being
impressed on the grid of 2. The grid of 2 cannot be connected directly
to the plate of 1 because this plate is at comparatively high positive
potential, due to its B battery. By putting an insulating condenser C
between the plate of 1 and grid of 2 the fluctuations of plate voltage repeat
through the condenser into the grid, but the grid is insulated from the
high positive continuous e.m.f. of the plate of 1.
CHARACTERISTIC CURVES FROM TYPICAL TUBES 411
Fro. 35.—Similar to the curves of Fig. 33, this tube having a grid with finer mesh.
ance leak of one megohm or less (as indicated by the dotted line connec
tion) is always used, to keep the grid, normally, at a suitable potential.
Some of the effects produced by a free grid will be indicated by the
412 VACUUM TUBES AND THEIR OPERATION (Chap. VI
B hattery
Fig. 36.—A circuit illustrating the meaning of the term "free grid," the grid of the
second tube is electrically free to assume any potential that circumstances may
demand.
1
I'D Oil la] of !ree ■1, i rttl re -pcCf t > negat Ire eni ol lil; mo nt.
M 3USI ml bj -t; tic l-ol rai (or
\s
f V
i )
10 20 30 40 51
Volts from plate to negative end of filament
Fio. 37.—Variations in free grid potential for various plate voltages and filament
rents; measurements by a highly insulated sensitive static voltmeter.
zero, for various filament temperatures. • The higher the plate voltage
the closer the grid potential approaches zero potential, i.e., that of the
FREE GRID POTENTIAL 413
negative end of the filament. With zero plate voltage the grid goes neg
ative as much as 2 volts, due undoubtedly to the accumulation of electrons
which have left the filament with enough initial velocity to carry them
as far as the grid.
In Fig. 38 are shown the free grid potentials of ten different tubes
all of them having some gas (although not enough to produce visible
ionization with the plate potentials used). In getting these curves the
filament current was brought to its normal value with plate at the desired
voltage, the grid being connected to the negative end of the filament.
The grid was then disconnected from everything and the plate current
noted ; by then connecting the grid to a suitable potentiometer and vary
ing its potential the same value of plate current was obtained. A volt
meter connected across the potentiometer served to show this grid poten
tial which, as it gave the same plate current, must be that of the free grid.
The potential of the free grid depends entirely on the order in which
the successive adjustments are carried out, thus if the grid is left free,
filament current brought to normal and then plate potential brought to
normal an entirely different value for free grid potential may be obtained
than would be if the plate were first put at its proper potential and then
the filament current brought to normal.
In Fig. 39 is shown the curve obtained (with free grid) by holding
the plate at 150 volts, increasing the filament current from a low value
to a high value and then decreasing the filament current through the same
range. A peculiar loop is obtained explained by the fact that as the plate
potential was applied before there was a liberal supply of electrons in the
vicinity of the grid the grid went positive. This positive grid gave com
paratively large values of plate current from A up to the point B on the
curve sheet; here the grid suddenly lost most of its positive charge due
to bombardment by many electrons, and became nearly zero in potential
with a consequent decrease in the plate current. From C to D and back
to C the grid had nearly the same potential for increasing as for decreasing
filament current, but from C to E the grid potential was much lower than
it was for the corresponding values of filament current, when increasing
values were being taken. At E the grid suddenly increases its potential
a small amount and for the remainder of the cycle it has about the same
potential as it had for increasing filament current; other tubes showed
exactly the same effect.
In Fig. 40 are shown the potentials of the free grid of a telephone
amplifying tube. For low values of filament current the free grid assumes
a potential about half that of the plate, then as the filament current is
increased the grid potential decreases gradually until a critical value of
filament current is reached. At this critical filament current (i.e., critical
supply of electrons) the grid potential suddenly falls to a comparatively
-4-»42 plate
-2-0 pfew
grd
free
the
itested,
with
always
for
tubes
sFig.
For
38.
onetcvraen—atrsiaeldnag;l
8
1
N10
S
6
7
9
4
No.o. -.600
I=1=
.35Q.350.360.460480.500.=3-50
vgrid
plate
of
pthe
ofree
in
olterange
goes
srinatgievna.gel
GRID
POF
FREE
ROETSNPTEICATL
WITH pgrid
toaby
Mreopatdselunrticedal
FOF
NENDIELGAMTEINVTE
TO
inplate
cuhrnoaengte
potential
Orid
FREE GRID POTENTIAL 415
B
Piute vo ts - 150
Telep l"l le ep ,..t er Hi e
9-
jfl
D
F
A
Filament current
Fig. 39.—A peculiar cycle obtainable from a tube having a free grid; as the filament
current was increased and then decreased the plate current went around the loop as
indicated by the arrow heads; plate potential was kept constant.
except under unusual conditions, as, e.g., curve A of Fig. 32. Unless
we are specifically interested in the losses in the grid circuit the grid current
may be neglected. Furthermore, unless the conditions are such that
saturation current is reached (plate current using all the electrons emitted
from the filament) the filament current does not affect the plate current
to a great extent. We shall therefore examine in this section, the rela
tions between plate current and grid and plate potentials, neglecting
grid currents and the effect of too small a filament current.
pmoxiova saanx qnv HiaHX Noixvaado '*™o\ ia
'oij —8aiMoqg aqi .reqiwad suopouBA ui aaaj pu8 iBiiua^od sb ^uani^ig iii.u.in.i S8M
ipasuajoui joj siqj p?pads aqivi oq^ aaaj pu8 panmssn aAiiisod psrjnaiod japon
j|u •Buoiiypnoo
EQUATION OF PLATE CURRENT
We have seen that the plate current depends upon both plate voltage
and grid voltage, to some power higher than the first, and that the grid
potential is much more effective in controlling the current than is the
plate potential. We may therefore write,
(5)
where 7P= plate current in amperes;
A =a constant depending upon type of tube;
Ep= potential of plate to negative end of filament;
Eg = potential of grid to negative end of filament;
Ho= relative effectiveness factor of Ee;
x = an unknown exponent, possibly variable.
Langmuir has given this equation with the value of x as 1.5; Van der
Bijl has given the equation with the value of i as 2.0, having also an
added quantity inside the parenthesis, a small constant in which are taker
care of such factors as velocity of emission of electrons, contact difference
of potential of the electrodes, etc.
The quantity no is the theoretical voltage amplifying power of the
tube; it is ordinarily taken as a constant, its value depending solely upon
the geometry of the tube. Many tests show this to be true for the ordinary
use of the tube; it may be that with very low plate voltage and high grid
voltage no changes some
what, but in the ordinary
working range of Eg and
Ep it is practically con
stant. As previously stated,
it varies in different types
of tubes from 2 to 200 or I AW-H'|
more. VWVW r, I
When many determina M/WW
tions of no are to be made, wwwv—
it is worth while to arrange
some apparatus as shown m- s
in Fig. 41, a scheme due to Fig. 41.—An arrangement of apparatus for rapidly
J. M. Miller. The resist- determining the voltage amplification factor of a
ance R2 is preferably 10 tuDe-
ohms and Ri is a decade
resistance box having units, 10-ohm, 100-ohm, and 1000-ohm units; the
1000-ohm units are used very seldom, but few tubes having high enough
values of /jo to require them.
An ammeter Ai serves to read the filament current, and milliam-
meter An serves for plate current. This meter should have two or three
418 VACUUM TUBES AND THEIR OPERATION [Chap. VI
scales, so that for various types of tubes to be tested the plate current
will give indications well up on the scale. The filament battery should
be perhaps 6 volts and Ed and Ec should have voltages suitable for the
tubes to be tested.
With S open Eb, Ee, and If are put at their proper values and the
reading of A2 is noted. Then <S is closed, permitting current J to flow
around the circuit E, Ri, R2, E, the reading of A2 will in general change;
by properly adjusting Ri, however, it will be found that the reading of
A2 (which is the plate current) does not change when switch <S is closed.
The ratio of Ri to R2 for this adjustment gives no.
By examination of Fig. 41 it will be seen that depressing key S raises
the voltage impressed on the plate by an amount IRi, and depresses the
voltage of the grid by an amount IR2. From inspection of Eq. (5) it
is evident that if Ip does not change when <S is closed,
(A£„+MoA#,) =0,
where AEP and AEe are the changes in Ev and E, due to closing switch S.
We therefore have the relation
or
at —10 volts, the plate current follows the square law very closely
throughout the range of the graph. A greater negative potential makes
1000
NO
VT
Ef 800
0I
400
>
3.00 300
2.00 200
1.00
I I I I I I I I I I I 1 i ' i I I I I I I I I | 0
89 10 123456789 20 123456789 30 123456789 40
Plate volts
Fio. 43.—Curves similar to those of Fig. 42, the tube used having an oxide-coated
filament.
the plate current vary with higher power of plate voltage for the lower
values of plate potential; this is to be expected from inspection of Eq. (5).
Different tubes of the same type will not follow exactly the same law
of plate current variation, due probably to small differences in the struc
FORM OF PLATE-CURRENT CURVE 421
ture. In Fig. 46 are shown the results of tests on twenty-four tubes all
having the same rating; twelve had oxide coated filaments with a filament
IR drop of 2.6 volts and the other twelve had tungsten filaments with
an IR drop of 3.6 volts. The curves for the individual tubes ran in gen
eral, parallel to the boundaries of the cross-sectioned areas, as indicated
on this curve sheet
1000
800
G00
400
Curve A- VT 11-1/= 1 .10 E
Curve B-VT 1-1/= 1 ,10 E
//
/ 1 I
200 1
o
1 cE
J' I'
T ioo au
/ 1 to
80a
7 7
/ / 60
/
V = 2: / 10
/
/
/
/ —
/
/ I
Plate volts
Fig. 44.—The curves of Figs. 42 and 43 transposed to logarithmic coordinates; this
graph shows that the exponent for Eq. (5) is neither 1.5 nor 2, but is a variable for
both tubes.
continuous current; we shall first consider the output circuit. The ratio
of plate voltage to plate current is generally called the output impedance.
As there can be no appreciable lag in the motion of the electrons behind
the impressed electric field, it might seem more appropriate to speak of
output resistance instead of output impedance. But it is to be remembered
that the plate current is influenced by the grid as well as by the plate,
1 2 4 6 8 10 20 40 60
Plate voltage
Fig. 46.—Logarithmic plots of 24 typical detector tubes, 12 with tungsten filaments
and 12 with oxide-coated filaments. The curves for the individual tubes lay inside
the areas as noted.
and it may well be that variation of plate current is not in phase with
the variation of plate potential. From this viewpoint the plate filament
circuit has impedance, not merely resistance.
If, however, we maintain the grid at zero potential (or any other fixed
potential) the plate current will vary with plate voltage only and we may
speak of plate circuit resistance. With constant grid potential and vary
424 VACUUM TUBES AND THEIR OPERATION [Chap. VI
ing plate potential the values of plate current determine this resistance
of the plate circuit, Rop, for continuous currents. Such a curve for a tungs
ten filament detecting tube is shown in Fig. 47; on the same curve sheet
is shown a curve of mo for this tube, from which it may be seen that the
value of no is practically constant,
t,U Iy.T 11
1, •Jl 1' except for very low plate voltages.
\ B » * nb
0 fit, .1 •1 The value of Rop continually increases
\\
as Ep is diminished.
\ The value of the alternating cur
\
rent resistance, Rp, is determined by
.»
the ratio of ^5p, the grid voltage be
ing maintained at zero; we may write
Ip=aE/
W
dEv
\ or
\ dlr axEp*
\\
vs But the continuous current resist
——j a
ance is
1
IP aEp*-1
From these we get the relation,
(7)
(•■MI44IM14I 40 " x
Fig. 47.—Curves of w and Rop of a small Jn Fig. 48 are shown the curves
ta^fl»^tate;feTato^^ of Rp and Rop for an oxide-filament
is obtained by finding the quotient of
Ep by in a continuous-current test. amphfying tube; the points indicat
ed by circles on the Rp curve were
obtained by the alternating current measurement and those indicated
by crosses were obtained by dividing the points on the R0P curve by the
proper value of x. On the same curve sheet is shown the value of yo
for this tube; it is nearly constant in the working range of the tube (Er
between 20 and 40 volts) and falls off with the lower plate voltages,
whereas the curve of Fig. 47 showed an increasing juo with lower plate
voltages.
The value of Rp is found experimentally by the scheme outlined in
Fig. 49, originated by J. M. Miller; the same arrangement serves to
measure yo by alternating-current test providing the phone resistance
is negligible compared to the tube resistance. Fig. 50 shows a curve of
juo obtained by the method; it shows mo to be independent of filament
aoNivxsisira jio axvw xinoHio / S2fr
420 VACUUM TUBES AND THEIR OPERATION [Chap. VI
current. With S2 open and Si closed the ratio of n to ri. is varied until
no signal is heard in the telephone and we then have
r-2
Mo=-. (8)
n
E,r-^- = noE,
Rp+R
MEASUREMENT OF AMPLIFICATION CONSTANT 427
Solving this equation for Rp we get the relation given in Eq. (9) above.
In case the resistance R does not permit a balance to be obtained, it
being too small, the ratio of — can be suitably altered.
The relation between I„ and E„ is not a linear one and it is therefore
evident that RP must vary throughout the cycle of change in E,. The
value of Rp is therefore represented correctly only by a constant (the
■ 1
£ f *
1
b
„ 1—
—* 1 P ^
L'OI Sti nt U ( hn s
va id f. r bala 1C(
_
Value of fllament current
Fig. 50.—Value of of a small amplifying tube, obtained by the scheme outlined in
Fig. 49; this shows m, to be nearly independent of the filament current.
value of which we call RP) and a series of harmonic terms; these harmonic
terms become more pronounced as Eg is varied through wider ranges.
In the measurement of Rp by the method outlined above it will be
found that complete silence cannot be obtained at the balance point; the
note heard in the telephone is complex and only the fundamental note
can be balanced. A balance will generally be most easily obtained if
comparatively low values of E„ are used, say not more than 0.1 volt;
moreover it will be found that the value obtained for Rp varies with E„
becoming greater for high values, as explained on p. 499.
428 VACUUM TUBES AND THEIR OPERATION [Chap. VI
cycles. The scheme used is illustrated in Fig. 51; the same setting of
the bridge permitted the measurement of both capacity and resistance
of the tube input circuit. The 50,000-cycle power was supplied to the
bridge by wire A, the other side being grounded. The condensers C„
and Ct, are adjusted to balance the bridge when the (3) and (4) arms are
open, to neutralize any spurious capacity in the bridge ratio arms and
are left set after once being balanced (unless ratio is changed). Suitable
high-resistance leaks are shunted across Ci and C2, these resistances being
free from appreciable distributed capacity. Certain precautions have
to be observed in using such a bridge as noted in an article by the author
in the Proc. I.R.E.1
In Figs. 52-55 are shown the variation in the input circuit of a small
detecting tube rated at 1.1 amperes filament current and 20-40 volts in
the plate. Unless the tube is defective the conductance is practically
zero until about 0.8 ampere is used for heating the filament. It then
rises rapidly until with normal filament current the conductance is about
12 micromhos, showing an input resistance of about 80,000 ohms. The
values of Ep and E, used are noted on the curve sheet.
In Fig. 53 is shown the variation of the input conductance as plate
voltage was varied; this decrease in conductance with increasing plate
T\ I"' V. r. 1
III itnvr vs te vo
IU J5 O.V
v =1. Ec=-- Erf
5 10 15 £0 25 SO 35
Plate volts
Fig. 53.—Variation of input circuit conductance with plate voltage.
t
12
pe V.T.1
1.10 0.2
10
—' _ 8*3
a
3
'I
1.3 .9 .8 .7.6 .5 .4 .3 .2 .1 0
Value of Ec (negative)
Fio. 54.—Variation of input circuit conductance with grid potential.
— ■—
12
ao
1 1
ryje V.T.
/= 1.10 = -.05 r 0
'—
—
.1 .2 .3
.4 .5 .6 .7 .8 J 1.0
Value of E„(ellective)
Fig. 55.—Variation of input circuit conductance with amplitude of voltage impressed
on the input circuit.
or amplifier; if the tube is to be used as detector the input circuit resist
ance may very seriously affect the selectivity of the receiving circuit,
because of its damping effect on the signal.
432 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Mr.
INO. Filament Plate Plate Type of Intended
Current. Voltage Current. Filament. Service.
1 1.1 20-40 6X10-* Oxide Detector and
Amplifier
2 1.1 20-10 4X10-* Tungsten Detector and
Amplifier
3 1.30 130 7X10~* Oxide Amplifier
4 1.75 350 5X10-* Tungsten Power
5 1.35 300 4Xl0-» Oxide Power
6 6.5 500 15X10-* Tungsten Power
7 3.6 1000 25X10-' Tungsten Power
The capacity of these tubes was measured in the bridge shown in Fig.
51, at 50 kilocycles and the results were as follows, the capacities being
in 10-12 farads:
Now when a tube is being used, for whatever purpose, the plate and
filament are connected together through the B battery and whatever
external impedance is introduced in the plate circuit, and the input cir
cuit is from grid to filament; it is therefore evident that the capacity
of the input circuit is that between the grid as one plate of the condenser
and the plate and fila- qaAAAA/WV s~~
ment connected together \_
as the other plate of the
condenser.
From the values given
in the above table the
input circuit capacity Fig. 56.—Possible arrangement of the wires of a three-
of the average tube is electrode tube where they go through the press.
small enough to be neg
lected, and it very frequently has been, judging from the values of capac
ities used in certain amplifying sets. But the values of capacity of the
input circuit previously given are what the author has called the
" geometrical capacity " of the input circuit; the actual capacity is very
different from the values given.
In practically all circuits involving the use of a vacuum tube it is
required to have an impedance of some sort in the plate circuit; this
impedance may be a resist-
ance, a choke coil, or the
Ill
primary winding of a trans
former, and the value of this
impedance is generally of the
same magnitude as the a.c.
resistance of the plate circuit
of the tube, Rp, or somewhat
greater.
When such an impedance
is used in series with the B
Fig. 57.—Forms of plate current and plate potential battery the voltage on the
when a sine wave of voltage is impressed between plate Ep varies when the
the grid and filament. When the resistance in the
plate circuit is very high the fluctuation in plate grid voltage E„ is varied and
potential is nearly n„ times as great as the volt the amount of fluctuation in
age impressed on the grid. Ep is generally much greater
than E„. If an impedance
is used in the plate circuit, which is very high compared to the tube
resistance, the fluctuation of Ep is nearly equal to voEs. It is always
somewhat less than this value, and we put it equal to y.E, where n lies
between zero and jin, depending on the plate circuit impedance.
Let us suppose a resistance, R, used in the plate circuit; it is at once
434 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Ctami=Co-p+(h-+l)Co-P (10)
Thus the effective capacity of the input circuit is not only much
than the geometrical capacity, but it varies with any factors which affect
li, the voltage amplification factor of the tube and circuit.
Due to the mutual capacity of the grid-filament condenser and grid-
plate condenser, and also to the fact that the two voltages Ep and E,
are not exactly 180° apart, the capacity of the input circuit of a tube
will actually be somewhat less than that predicted from Eq. (10).
This mutual capacity of the two condensers brings in another very
interesting phenomenon: the field of the grid-plate condenser may so
react on the grid-filament condenser as to give a voltage in this condenser
in phase with the impressed e.m.f. of this condenser (i.e., the e.m.f.
impressed on the input circuit) so as to give the input circuit a negative
conductance. Such an effect would result in the plate circuit reacting
CAPACITY OF INPUT CIRCUIT 435
on the input circuit to augment any voltage impressed on the input cir
cuit.
Using the bridge scheme illustrated in Fig. 51, the capacities and con
ductances of the input circuits of several of the tubes tabulated on p. 432
were measured at 50,000 cycles. In Fig. 59 are shown the capacity and
CO
V-aC
-)
3W
5 50 3
B
f| 40 3
I
/
Tu !»• No. 1 3 a
/ I 1 ~ 1.1 ) Ep = 2( (for ill ml )<•» of R )
/ "3
/ I >'= x I o " E • : .' 5 2( ■III L'ti a
/ 'Z 20<3
r
C
10
20 30 40 ,60 70
Plate cirouit resistance In 10 ohms
Fig. 59.—Capacity and conductance of tube VI 1 as the resistance in the plate circuit
is varied; the u of the tube is shown also, so that the dependence of capacity upon
n may be noted.
10 20 30 40 50 80 70
Plate circuit reactance in 10 3ohms
Fig. 60.—Capacity and conductance of the input circuit of detector tube "Vll, 05 the
plate circuit reactance is varied. Note that the input conductance is positive
throughout a certain range of the reactance.
As the capacity Co-f of this tube was 10.4, and the capacity Co-p
was 14.4 mm/, and the value of m is 4.65 for #=80 kilohms, it might be
expected that the input capacity would be equal to (10.4+ (4.65+ 1)14.4)
CAPACITY AND CONDUCTANCE OF THE INPUT CIRCUIT 437
= 91.6 mm/- The discrepancy between the measured and predicted values
is undoubtedly due, in part, to the mutual capacity of Ca-p and Ca-p.
The conductance of the input circuit was positive for all values of plate
circuit resistance and gradually increased as R was increased.
In Fig. 60 are shown the capacity and conductance for the same tube,
the plate circuit impedance being an inductance with a reactance-resist
ance ratio between 25 and 50. In this case the increase in capacity is
greater than when an equal amount of resistance was used in the plate
circuit. Thus, with a reactance in the plate circuit of 50 kilohms the
input circuit has a capacity of 82 nnf, whereas a resistance of 50 kilohms
gave an input capacity of only 65 nnf. This difference in behavior of
reactance and resistance is due to the fact that the n of the circuit is
greater in one case than in the other, as will be explained later.
That any capacity present between the grid and plate, and which
is not in the field of the grid-filament condenser, is increased by the factor
(/x-f-1) was proved by actually connecting a capacity of 20 nnf across
the plate-grid terminals of the tube and noting the increase in the effective
capacity of the input circuit, the n of the circuit being 4.2. The capacity
of the input circuit increased by 102 nnf, whereas calculation would
make it increase by (4.2+1) X 20, or 104 nnf.
The conductance of the input circuit of the tube was negative through
out a certain range of plate circuit reactance, thus indicating transfer
of power from the plate circuit
back to the grid circuit, with no
other coupling between the grid
and plate circuits than what ex
isted in the tube itself. This
curve shows that the three elec
trode tube is not inherently a
" one-way repeater," as has been
commonly supposed; the output
circuit does control the input
circuit to an appreciable extent, Fio. 61.—In such a circuit as this, with effi
cient coils used in both circuits, with suit
sufficient in fact to maintain the able values of the capacities the tube will
tube in operation as a generator maintain itself in an oscillatory state, due
of alternating-current power when to the negative conductance as shown in
it is connected to the proper cir Fig. 60.
cuit. If the grid circuit and plate
circuit are each tuned to the same frequency, as indicated in Fig. 61,
the tuning condensers are sufficiently small (and the coils fairly efficient),
the coupling of the two circuits inside the tube may be sufficient to
maintain the tube in the oscillating state, alternating currents flowing
in circuits L2C2 and LiC\.
438 VACUUM TUBES AND THEIR OPERATION [Chap. VI
1 1 1
Curve A- Ca r.u It} grid o e ro nu
,. B- Co llil ct.UK- c rid to CTC und
'id e :VU. :i N
) IX .64 X 0 E jg E r
— 10
1 LI
10 80 30 40 30 Plate
(JO circuit
70 80resistance
90 in 10010s 110
ohms 120 130 140 130 100
10 5
9
-10
-go
1-50
10 20 30 40 # 50 60
Plate circuit reactance ta 10 ohms
Fig. 63.—Curves similar to those of Fig. 62, the plate circuit having a variable react
ance instead of resistance.
ally by Ballantine,1 who shows that for resistive plate circuit the effective
input capacity decreases with an increase in frequency and the input
conductance increases with an increase in frequency. For reactive plate
circuit the effect of frequency may be to either decrease or increase the
'Stuart Ballantine, "The Thermionic Amplifier," Physical Review, Vol. XV, No. 5.
440 VACUUM TUBES AND THEIR OPERATION [Chap. VI
0 1 2 3 4 5 6 T 8 9 10 11 12 13 14 15 16
Beslstance in plate circuit In 10 ohraa.
Fig. 64.—Variation in conductance and capacity of the input circuit of a small power
tube (V7t) as plate circuit resistance is varied.
wave trains A may be from .005 to .0005 second ; the duration of a waye
train B may be from .00001 to .001 second, and the time of one cycle,
C, may be from .0000001 to .00003 second.
The function of the detector is to produce in the telephone, fluctuation
of current, of frequency fixed by the time A, as large as possible with a
given amplitude of signal voltage. The scheme of connections used when
20 30 40
Plate circuit reactance in 103 ohms
Fig. 65.—Curves similar to those of Fig. 64, the plate circuit having a variable reactance
instead of resistance."
thus lower in potential than the negative end of the filament by an amount
IfR, generally one volt or less, whereas in (6) a battery C is inserted in
series with the input circuit to properly lower the grid potential. In
case a careful adjustment of this potential is desired (generally not neces-
——J | | 000
'i ill ■ 7
— H 200 2
■3. ;5 E »■ ,)<>( 0 E 1, =-.C
— J9
—
!
— ■fi 100
4 5 6 7 8 9 10 11
Plate circuit reactance in 10 3 ohms
Fig. 66.—Variation of conductance and capacity of the input circuit of a large
tube as plate circuit reactance is varied.
received is 600 meters, the tuning condenser Ci (Fig. 68) being set at
200 nnf. A conductance of 10-5 mhos is equivalent to a shunt resistance
The author arranged a tube circuit so that its input voltage and plate
current could be recorded on an oscillogram, when a damped sine wave
of about 100 cycles (having the general form of an actual wave train from
a highly damped spark station) was impressed on the input circuit; some
of the films obtained are presented herewith. In Fig. 71 are shown the
input voltage, plate current and telephone current when the grid was
Fig. 70.—Analysis of the action of the three-electrode tube as detector of damped wave
signals; assuming a certain variation in grid potential the resulting fluctuation in
plate current can be plotted from the plate current, grid potential curve of the tube.
made normally 2.5 volts negative with respect to the filament. A large
capacity condenser was shunted around the coil representing the tele
phone of an ordinary receiving set so that the " high-frequency " current
was not forced to flow through this coil. This condenser charged up
during the first part of the wave train more rapidly than it discharged
through the coil, so that its charge increased. Then as the wave train
THREE-ELECTRODE TUBE AS DETECTOR 445
446 VACUUM TUBES AND THEIR OPERATION [Chat. VI
With no signal lov =f(Eot) and when the signal voltage AEe is impressed
on the grid
I„+AI, =f(E„+AE,)
THREE-ELECTRODE TUBE AS DETECTOR
THREE-ELECTRODE TUBE AS DETECTOR 449
450 VACUUM TUBES AND THEIR OPERATION [Chap. VI
If Alp is periodic the average value of the first term AE„ -j^r is zero so
arif
that the average value of Alp becomes equal to the average value of
AE 2 d2I
—~ \. Now, if AE„ is a sine function of time of the form, E sin pt,
we have for the average value of the change in plate current
d2T 1 /*r K2 H2T
^^W'tW- ■ ■ ■ (12)
The increment in plate current therefore varies with the square of the
signal strength, a defect practically all rectifying devices have. At a
d2I
point of inflection of the Iv—Eg curve, -rfr-|=0 and the rectifying power
is lost. The increment in plate current will be negative or positive accord-
dl 2
ing to the sign of ^gr2> 8,8 illustrated in the foregoing films.
It might seem that the best point to operate on the plate current
curve is where the radius of curvature is greatest, but this is not quite so.
If z = radius of curvature,
Z~ dHp
d2Ip
dE2
so that
vhSz^L (i3)
dE/ z
It is evident that if the radius of curvature is not changing rapidly the
value of yir has importance in determining the rectifying power, the
aE0
greater the slope the greater is the rectifying action.
As shown in Figs. 71 and 74 there are two points where the detecting
power is about the same, one with negative grid and one with positive
grid {A and C of Fig. 72). The negative grid is to be preferred to the
positive, because of the high conductance of the input circuit with a posi
tive grid, and consequent excessive damping of the receiving circuit as
explained on p. 443.
The curve of Fig. 70 is obtained by maintaining plate voltage constant;
if there is a high resistance or reactance in scries with the B battery, the
ACTION OF GRID CONDENSER 451
——
10 00 —
y 00
—8 DO T
——
a D0«i
c>
M
5 JO V 1
£] (- .10
i >h
uu
3 00
1
2 oo
e x 10
e — 1 00
£
—1.0 -.8 -.6 -4 —.2 0 +.2 +.4 +6 +.8 +1.0 +1.2 +1.4 +-1.6
Grid potential
Fig. 77.—Plate current and grid current curves for a VTl detector tube.
If the leak resistance is 106 ohms cot <t> must be 106 when the scales
of potentials and currents are in corresponding units as, e.g., volts and
amperes. As the scale of current in Fig. 79 is 10s smaller than that of
potential, the angle 4> in this diagram is so drawn that cot 0 = 10. If
a leak resistance of only 5 X 105 ohms were used, the normal value of grid
potential E„ would be as shown at C", obtained by making cot <f>=5.
When an alternating e.m.f. is now impressed on this input circuit,
the grid will start to fluctuate about its normal value of potential, E0<l;
ACTION OF GRID CONDENSER 453
its potential will be increased and decreased from the value Eog equally
for the first cycle. Due to the form of the Ie—Es curve, however, the
increase in current, when the impressed e.m.f. is positive is greater than
the decrease in current when the impressed e.m.f. goes negative, and this
rectifying action tends to increase the number of electrons accumulated
on that side to the condenser C (Fig. 76) , which is connected to the grid.
But this accumulation of electrons must depress the potential of the grid
10 i)0
—9 JO
—8 00 h,
■j D0-<
1 VT 1
E ■a
t> DO r1 .10
.j DO
— a / —
i
■
\ 11
■i 00
00
-1.0 -.8 -.8 -.K -.2 0 +.2 +.4 +.6 +.8 +1.0 +1.2 +1.4. 41.6
Grid potential
Fig. 78.—Curves similar to those of Fig. 77 for a supposedly identical tube.
below its normal value, and so cause a decrease in the plate current. The
amount of this decrease in plate current for a given alternating e.m.f.
impressed on the input circuit, is a measure of the efficiency of the tube
as a detector, so we shall investigate this point more fully.
Before starting this analysis it is well to point out that whereas a tube
may detect by either an increase or decrease in plate current when no
grid condenser is used, with the grid condenser a signal always produces
a decrease in plate current, never an increase.
At the end of the wave train the grid condenser C (Fig. 76) will be
454 VACUUM TUBES AND THEIR OPERATION [Chap. VI
charged (negatively on the side connected to the grid) and this charge
must leak off before the next wave train arrives, otherwise the tube will
not respond to a signal as well as it should. The time taken for the
/
/
/
V :ur e
g C >t<t = r
th VSti rd "or -C.l
C >tip '.F
~- H
1
Em
+ hF
-.4 -2 .0 +.2 t.4 +.6 +.8 +1.0 *2 +.4 +.6 +8 +2.0
Grid potential
Fig. 79.—A diagram for determining the normal grid potential of a tube connected as in
Fig. 76 ; the leak resistance is supposed connected to the positive end of the filament
and the IR drop in the filament is assumed as 2 volts.
inside the tube and r is the leakage inside the tube itself. The values
of C and - (tube conductance) for various tubes were given in Figs. 59-
66; the impedance between D and B, Fig. 80, is therefore calculable
when R is given. Designating this impedance by Zt, we then find that the
voltage impressed on the grid of the tube is equal to the input voltage
Zt
(across points A-B, Fig. 80) multiplied by the fraction —- the
(z'+=c)
addition and division being carried out vectorially.
In addition to the features just analyzed we must remember that the
impedance between points A-B is to be kept high as this input circuit
is connected directly across the tuning condenser of the receiving set.
With the detecting tubes commonly used (characteristics about like tube
No. 1, page 432) it seems that C =5X10-'° and R = 106 give the best results.
For tubes having smaller internal capacity lower values of C and higher
values of R are better suited; thus the detecting tube shown at J, Fig.
21, is generally used with C=4X10-10 and fl=4Xl06.
Analysis of Detector Action with Grid Condenser.—Let the voltage
between the grid and the negative end of the filament (which we call
zero potential) be a, then
I„R+E„ = a (14)
where Iog and E0, are the normal values of grid current and potential
respectively, when no signal is being impressed.
When a signal is impressed on the input circuit, the grid is acted upon
by a voltage E sin pt; the grid current will pulsate in value about its
normal value, but owing to the form of the Ig—E, curve the increase in
grid current is greater than the decrease, so that there is an average increase
E2 d2I
in the grid current which is equal to as was previously proved for
the plate current—see Eq. (12). This increase in grid current must pass
through the resistance R, so that the equation for grid potential when
the signal is being impressed is,
I\R+~ fgiH+E',=a (15)
Also we have E'„, being the new average value of grid potential when
signal is being impressed on the grid, and /'„ corresponding to E't (see
Fig. 81),
1/' g - J —\F
— l00 l±Ug ^ ,
so that from Eqs. (14) and (15), we may get the relation,
dh\ „ . E2 d2I
AE'dt)R+T dE? *+p.-b--'-*-o-
456 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Imr-AE.^R+% gjB-AH.-I.B-0,
So that
d2I,
jfk <•«)
R+dE,
Grid potential
Fig. 81.—Change in grid potential due to the increased drop in the leak resistance when
a signal is impressed on the tube.
dE
If II is small compared to -~, this simplifies to
(XI g
d2I,
_E2dEl
(17)
dE,
The decrease in plate current caused by this, drop in grid potential
depends upon the shape of the Iv—E, curve, or ^=r. The real measure of
aJb,
the detecting efficiency of a tube is therefore,
d2I,
dlv E2 dE2 dl.
AI,=AE, (18)
dE, 4 dl, dE,'
dE,
ANALYSIS OF ACTION OF CONDENSER 457
■00
700
roo
GOO 1
Dcte •to r tube A
400 20 1,-1.10
300
5
200 20'o
I, *ja
100 10 t
0 - -1 i 1 1 +1 +2 +i +1 +j
C Iri( [til 1
900
BOO
700
600
GOO
SuO 'I,
100 10 ur
3c
o
0 +.1 +.2 +.3 1 +. +. i f 7 + B +.9 + 1 0
Grid Potential
Fia. 82.—Characteristic curves of two detector tubes. Using Eq. (18) it is found that to
change the average plate current by one microampere requires a signal voltage of
.059 volt for tube A and .052 volt for tube B. Without grid condensers the tubes
require about three times as much grid voltage for the same change in plate current.
in the grid condenser. The solution in Eq. (18) supposes the signal has
persisted long enough for the steady state to be reached ; if a damped sine
458 VACUUM TUBES AND THEIR OPERATION [Chap. VI
wave is impressed, the detection efficiency will depend upon the decre
ment, size of grid condenser, etc., as analyzed on p. 401. The solution
obtained in (18) also neglects the difference in value of . | at the two
grid voltages E00 and E'e.
■
- 1
w Bh ut Brid e OIK. en ■ex
til 8 t ibt re !tl leu very
w •11 or tin ;u Ju tment 2
ol I'll ■ve i A -A': lio : sc w •11
10 t'l rvi ■ E -B 30
2 1
10
I
//
•6 .4 .3
.1 0.2 .1 .2 .3 .4 .5
Gr iil potential
Fio. 83.—Even with very low plate voltage and filament, current some tubes detect
very well; with half normal filament current and a plate potential cf only 1 or
2 volts this oxide coated tab;; requires only about .3 volt signal to give one micro
ampere change in plate current.
In Fig. 82 are shown the grid and plate currents of two detecting tubes
such as were used by the Signal Corps. If no grid condenser were used
with these tubes we find (using Eq. (12)) that to produce an increase
ANALYSIS OF ACTION OF CONDENSER 459
1 B 0 6
Grid |>o(cuUul
Fio. 84.—With low plate voltages it makes a great deal of tlillerence whether the grid
is connected to the positive or negative end of the filament ; platu current indicated
by circles and grid current by crosses.
tive end) curves of /„ and Ip were obtained as in Fig. 83. With no grid
condenser and £=2.6 volts, the detecting action was much better than
might be expected with filament current and plate voltage so far away
from their rated values. By Eq. (12) for curves A an input voltage of
0.28 is required to give a charge of 1 microampere in the average value
of the plate current and for curves B a voltage of 0.34 was required.
In Fig. 84 is shown the great difference in the form and magnitude
of In and Tv when the junction of grid-filament circuit is changed from the
negative end of the filament to the positive end; the difference is very
much exaggerated here because of the low value of the voltage of the
battery in the plate circuit.
In Fig. 85 are shown the characteristics of an old Deforest detecting
bulb, the filament being at the rated value for this type of bulb. It will
be readily appreciated that such a tube would act peculiarly as different
adjustments were made. Thus with a plate voltage between 30 and
50 the tube would not detect, with or without grid condenser. With
EFFECT OF DECREMENT ON DETECTOR ACTION 461
20 volts in the plate the tube gave very good detection with or without
grid condenser; with ten volts on the plate the tube gave fair detection
with grid condenser and none at all without grid condenser.
Effect of Frequency and Decrement of Signal.—The previous analyses
have not taken into account the amount of electricity available for charg
ing condenser C; only relative reactances, etc., have been considered.
But it is evident that if the condenser is to be charged the grid current
must supply the electrons required, and it maybe that the current is not
sufficiently large to do this, in the short time the signal is impressed.
Suppose the signal voltage has the form shown in Fig. 86; it reaches
its maximum in three cy
cles and then rapidly de
creases. If possible the
grid condenser C should be
charged up to a potential
fixed by the maximum
value of this signal. To Fig. 86.—In analyzing the effect of the decrement of
make the problem simple the signal on the detecting action we assume the
we will suppose the ampli first three cycles of a wave-train have the same
tude of the voltage to have amplitude, the maximum value of the signal voltage.
its maximum value during
the first three cycles and examine the possibility of the condenser C
having reached the value of potential fixed by Eq. (16).
If the condenser is to have its potential changed by AE, the required
quantity of electricity is (&E,XC). The current available for charging
E2 d2L
the condenser is (very nearly) — ^ 2 and for three cycles this makes
3TE2 d2I,
available a quantity of electricity q - —^— ■ Now if is negligible
dl
compared to we get from Eq. (16)
E2 d2I° dE>
' ~ 4 dE,2 dl,'
So, as q = CAE, we may put
E2 d2Ig dE, 3TE2 d2I,
C—
4 dE, dl. " 4 dE,2'
from which we conclude that the largest condenser which can be used, and
still be fully charged, is fixed by the relation C = 3 T
If -^ = 5X10~6 (which is about the value obtained from Fig. 78, when
dE,
E» is — 0.6 volt) and T is 2 X 10-6 (which is the period of a 600-meter wave),
EFFECT OF DECREMENT ON DETECTOR ACTION 463
Fig. 88.—By increasing the value of the grid leak the form of the plate current curve
may be changed; in this film all conditions were the same as those of Fig. 87 except
the value of the grid leak resistance had been approximately trebled.
charged; the " telephones " (in this case a coil of high inductance) were
shunted by a large capacity so that the " high-frequency " fluctuations
in plate current did not pass through them, but the low-frequency change
in plate current did pass through them, giving a current of the form
shown.
By increasing the value of the leak resistance about three times the
time required for the grid condenser to discharge was increased and so
the plate current was held at its lowered value for a longer interval of
time; the currents then had the forms shown in Fig. 88.
Zero
Fia. 89.—This diagram shows in (6) a correct representation of the grid potential when
signal (a) is impressed and in (c) an incorrect representation. The average
potential of the grid will not be further depressed unless during the previous cycle
the grid is forced to a potential higher than its "free" potential.
plate voltage being ten or less. Such a tube would probably have an
alternating-current resistance in the plate circuit of perhaps 10s ohms, so
the telephones could not be efficiently introduced directly in the plate
circuit; a step-down transformer or another low impedance tube would
be required to supply the telephones.
The advantages of using a tube with comparatively low emission from
the filament come from its limitation on the strength of disturbances
which may occur. Atmospheric disturbances constitute the present limit
ing condition of radio; irregular cracks and hisses are produced in the
phones, perhaps hundreds of times louder than the signal and so make
the signal unreadable. If these disturbances can be limited in strength,
so that they are not more than five or ten times the signal strength, a
good operator will read right through them; with the present tubes these
disturbances may be thousands of times as strong as the signal. Graph
(a) of Fig. 90 illustrates the present detector tube; normal plate current
may be 500-1000 microamperes and the total emission may be 5000
microamperes. A strong signal (such as an atmospheric pulse) may
decrease the plate current to zero or increase it to 5000 microamperes,
whereas the signal is probably not changing it by more than one Or two
microamperes. The effect of strong disturbing noises such as static is
to deafen the operator's ear for the weaker signal.
If the tube used for detector has the characteristic shown in graph
b of Fig. 90, the effect of stronger pulses of e.m.f. impressed on the grid
is much less; the saturation current of the tube does not permit a large
increase of plate current, no matter how high a positive potential may
THREE-ELECTRODE TUBE AS OSCILLATOR 467
be impressed on the grid and the reduction of the plate current to zero
by a negative potential in the grid cannot produce as great a disturbing
noise as for the other tube, because the normal plate current for tube
(6) is only 1/20 as much as it is for tube (a).
A tube having the characteristic shown in (6) would probably not
be as efficient a detector as tube (a), but this defect would be remedied
by a suitable amplification. Another advantage of tube (£>) would be
its comparatively small internal capacity, because its parts could be much
smaller than the present detecting tube; the feature above would make
the smaller tube preferable, because the capacity of the input circuit
of a tube is a serious factor in the design of amplifiers, especially those
used for amplifying high-frequency currents.
The Three-electrode Tube as a Source of Alternating Current. Gen
eral Field of Application.—A three-electrode tube, if connected to a cir
cuit having a natural period of oscillation, will, if certain conditions are
satisfied, generate alternating-current
power of the frequency fixed by the L
and C of the circuio to which it is con
nected. The action is nearly analogous
to that of a violin bow; although the
force and velocity of the bow are essen
tially constant the peculiar friction
between the bow and string enables
the string to absorb more power from
the bow when string and bow are mov
ing in the same direction than is given
back to the bow by the string when the
motions of bow and string are in oppo
site direction. If the frictional force Velocity
between string and bow is plotted as Fia. 91.—Frictional force between a
a function of the relative velocity of violin string and bow, as a function
of their relative velocities, the great
the two, the graph will have the form er the difference in their velocities
given in Fig. 91 ; curve (a) is for the the less is the frictional force be
bow without resin and curve (b) shows tween them. Putting resin on the
the change in this friction after resin bow changes curve a to curve b.
has been put on the bow.
The muscles of the arm actuating the bow constitute a source of con
tinuous power; it is obviously impossible for an arm muscle to supply
(directly) power to a string vibrating 1000 times a second. The arm
supplies energy to the bow at an essentially constant rate, the reactions
between the bow and string serve to utilize this power to maintain the
string in a state of rapid vibration.
The system which drives the balance wheel of a watch is also some-
468 VACUUM TUBES AND THEIR OPERATION [Chap. VI
about its normal value, I„p, and the plate voltage will also fluctuate
about its normal value, Eop. The actual plate current may be considered
as made up of the constant value Iop which flows through L, and does
not appreciably vary as Es is varied, and an alternating component Ip,
which flows in the plate circuit by the path C, R, C\. The plate voltage
similarly will be considered as made up of a constant term Eep on which
is superimposed the alternating voltage Ep; at any instant the actual
plate voltage will be equal to Eb — iPR, where i, is the instantaneous
Fig. S3.—Theoretical curves of voltages and currents in a tube; actually the plat*
voltage does not go through such wide variations.
materially from the sinusoidal forms here shown. It is, however, dif
ficult to write the theory of the various circuits for any but sinusoidal
functions, and we shall assume that Ip and Ep are such, unless specific
mention is made to the contrary. We shall call the oscillations normal
when Ip is sinusoidal or approximately so, that is for (/„) max — Or <C 1 op.
Output, Efficiency and Internal Losses, for Normal Oscillation.—
The effect of the load resistance R on the output of a tube could be pre
dicted by noticing that the alternating current IP really flows through
R and the tube resistance, RP, in series; as R is decreased Ip increases,
just as the load current from any alternator increases when the resistance
of its load circuit is decreased. The voltage Eg impressed on the grid
circuit generates in the plate circuit an alternating current through Rp
and R in series.
If sufficient excitation is supplied to the grid circuit to force the actual
plate current to vary between zero and 2I0P, the maximum value of the
alternating current, Im, though R and Rp (in series) is Iop. The alternating
current power delivered to the external circuit is
p»=¥*-Ki^)2* (19)
Emo being the maximum value of the voltage impressed on the grid.
If now R = Rp, we have,
P^^2 (20)
But the input to the plate circuit is Eovlop, the value of which we assume,
is independent of the magnitude of the external resistance R. It there
fore follows that a separately excited tube having sinusoidal variations in
the plate current has a maximum efficiency of 50 per cent, and that this occurs
for the same condition as gives maximum output, i.e., R = Rp.
This theoretical limit of efficiency is never reached, because the plate
current cannot be made to execute harmonic changes and still be forced
472 VACUUM TUBES AND THEIR OPERATION [Chap. VI
to zero value. The reason for this is the variation in no when the plate
voltage becomes very small and the grid voltage large (in positive value) ;
neither does mo hold constant when the plate voltage is very high and with
a high negative potential on the grid.
Of course the efficiency factor of 50 per cent neglects the losses in the
grid, or exciting circuit, which really should be charged up to the tube,
and also the power required to heat the filament. These two factors
very materially reduce the possible efficiency of the tube as a generator.
As mentioned above, this limiting figure of 50 per cent for efficiency
holds only for sinusoidal plate current ; it is possible to so operate the tube
that the plate current is much distorted and at the same time the effi
ciency is increased to perhaps 85 per cent or more. This case w ill be taken
up later in this chapter.
A large-power tube was connected as indicated in Fig. 92 and the
effect of variation in R was noted. The grid excitation E„ was kept
sufficiently low so that the tube was not being worked near its limiting
output for any value of R used.
The results are given in Fig. 94, and serve well to show how the power
output varies with the resistance of the load circuit; the magnitude of
the alternating current generated by the tube is also shown on the
curve sheet. It is apparent that this tube should be used with
a load circuit resistance close to 1000 ohms if maximum power is to be
obtained.
The effect of continued operation on the characteristics of the tube
is shown by the dotted curve; it shows the output (for exactly the same
conditions as were used for the solid curve) after the tube had been oper
ating for twenty minutes. The temperature of the filament depends not
only on the filament current, but also on the temperature of the plates;
the hotter the plates the higher will be the filament temperature for a
given filament current, and of course the more will be the emission of
electrons.
For the lower values of R (less than 500 ohms) it will be noticed that
the alt ernating current exceeds 0.707 of the current supplied by the machine
in the plate circuit; with sinusoidal current in the load circuit this con
dition could not occur; it must therefore be that the current in the load
circuit was distorted in form when the lower values of load circuit resist
ance were used.
The curves do not show faithfully the characteristics of the tube as
a generator for the higher values of the load circuit resistance becaiise
the choke coil used in the plate current circuit had an impedance of only
8000 ohms, so that the supply current was far from constant for the higher
values of R. This supply circuit acted as a partial short circuit for the
load circuit, more so as R increased in value.
POWER LOST ON PLATES 473
[
.-
—
r — —
/ /> -
E■-- —
c= r JW ■r
i'/
rated as 250 watts on the plate, the product Ebhp must not exceed 250
when the tube is not oscillating, but if the tube is generating alternating-
current power, and conditions are adjusted for maximum output (sinu
soidal variations of I„ assumed) the input, Ebhp, may be safely increased
to practically double the rating, or 500 watts.
Another way of obtaining the amount of power used on the plate is
to write the expression for E'VI'V from Fig. 92 (where E'v and V v are
the voltage between plate and filament, and current through tube, respect
ively) and find its average value. It is
1 CT
Power expended on olates = ^ J E'pl'pdt. Now as Ev and Ip are 180°
current occurs), we have for the power used on the plates (where £'yand
I'P are fluctuating as much as shown in Fig. 93),
I CT
Power = ^ I (E0+EB sin pt) (/<,+/op sin {pl-\-ir))di
IpRp IpR
. A a/ A
* 0 ^
Y
of the coil in the plate circuit is negligible the angle of lead of E, with
pL
respect to is fixed by the angle whose tangent is
It,'
In case the reactance in the plate circuit is large and negative
(which would be the case in
Fig. 92 if C is decreased so that
X its reactance is appreciable) the
phase relations are as shown in
Fig. 97; the plate current now
0 leads the exciting voltage E,
\ V \ and lags bohind the plate volt
age Ep, by some angle between
\V \\ 90° and 180°.
The grid voltage required
to produce a certain current,
Fig. 97.—Phase relations of voltages in the Ip, through the condenser C,
tube circuit of Fig. 92, the load circuit hav shunting the choke coil in the
ing resistance and capacitive reactance. plate circuit, is given by the
equation,
(26)
Mo
If there is power used in the circuit through which IP flows, it must
be taken care of by a suitable resistance in series with C; Eq. (26) must
then have its resistance term increased by the value of the equivalent
series resistance.
In Figs. 98, 99, and 100 are shown oscillographic .proofs of the fore
going statements; the voltages and currents are not pure sine waves
and so do not obey exactly the relations just obtained on the assumption
that all currents and voltages were sine waves. The distortion in Ip is
explained by the fact that Rp varies through the cycle; its average value
for the conditions existing when the films of Figs. 98, 99, and 100 were
obtained was about 2500 ohms.
Effect of Phase Relations on the Possible Power Output of a Tube
Generator.—From the foregoing analysis it is evident that a tube gener
ator can act on its output circuit with a voltage Ep, the maximum value
of which is somewhat less than the normal plate voltage E0P; also that it
can supply to the output circuit an alternating current IP, the maximum
value of which is somewhat less than the normal plate current I0P- If
I and E represent the effective values of voltage and current which the
tube furnishes to its output circuit, it is evident that the maximum power
output will occur when the load circuit is such as to bring / and E in phase
PHASE RELATIONS IN OSCILLATING TUBES 477
and that the output is then equal to EI, which is also equal (in the limiting
case of maximum output) to %E0VI0p.
Now if the load circuit is such that E and I are in phase, it is evident
that its impedance must be resistance only, furthermore the value of this
resistance must be equal to Ell, which is also the alternating-current
resistance of the plate circuit of the tube. The truth of this statement
was shown in Fig. 94.
For such a circuit as that given in Fig. 92, the magnitude of current
Ip must be directly proportional to E„, as indicated by Eq. (25). Due
Fio. 98.—Oscillogram of grid voltage, plate voltage, and plate current, corresponding
to conditions of Fig. 95.
There is shown also in Fig. 101 the value of the current taken by the
grid ; as long as the grid was not forced positive with respect to the filament
the reading of the continuous current ammeter in the grid circuit was zero,
but when the value of alternating voltage impressed on the gird exceeded
-~= of the normal negative grid potential, E^, the grid was positive for a
small portion of the cycle and so took current. The variation of the reading
of the grid ammeter is shown by the curve marked /„; it was zero until
Fig. 99.—Oscillogram of plate voltage, grid voltage, and plate current, corresponding
to conditions of Fig. 96.
Fig. 100.—Oscillogram of plate voltage, grid voltage, and plate current corresponding
to conditions of Fig. 97.
problem can be readily specified. In Fig. 102 are shown the filament,
plate, and grid terminals 1, 2, and 3; the filament battery and plate cir
cuit battery (or machine) are omitted, as they do not enter directly into
the determination of the conditions for self-excitation of the tube.
If the normal plate voltage and plate current are Eop and 10„ respect
ively, we know that the tube can, when operating properly, generate an
amount of power somewhat less than ^Eoplop', let us call this available power
P. If this power is supplied to a circuit of L, C and R, in series, it will
produce a current fixed in magnitude by the relation P = PR. This
current, /, will produce an alternating voltage between the terminals of
480 VACUUM TUBES AND THEIR OPERATION [Chap. VI
L, the effective value of which is equal to IuL, where o> is nearly equal
. 1
to - -,— .
Vlc
When generating the amount of power P the potential of point 2 must
be fluctuating in voltage (with respect to the filament) by an amount
approximately equal to E^. The potential of point 3 must be fluctuating,
with respect to the filament, by an amount EmB, such that noEme is about
equal to 2Eop, as shown in Fig. 95.
-
SO ry je |P- 10 ilk trn n
E, = 1 00 E. = - 12; R = 1 WO I 3.05 .—■
70 a Powe r
1 JT~
00 h.
SO I
.2 lUin d
„s=
'o-
H I. - I*. <
20 E 2—
5
10 §1
/
1
0 2 4 G 28 4100 G 8 200 2 4 6 8 300
Value of Efl(ctrective1
Flo. 101.—Variation of output current and power as the exciting voltage on the grid is
increased; the circuit was arranged as shown in Fig. 92. Variations of /& and the
average grid current are also shown.
or
\ lop
on the assumption that R0p=2Rr.i
true if the input and output circuits of the tube had negligible capacities)
we find,
L4-5 = V2RRpLC (29)
And for the proper grid excitation, we should have,
L4-6=—V2RRpLC (30)
no
As an illustration of how these approximate relations are applied to
an actual circuit, we suppose a set designed to generate a frequency of
1 In case Rp is greater than this LM must be correspondingly increased; thus if
Rp = Hop then we must have
uL^VRRp-
As previously mentioned /i„ varies with the amount of excitation on the grid; a
curve showing the variation in Rp is given in Fig. 115, p. 499.
482 VACUUM TUBES AND THEIR OPERATION [Chap. VI
000,000 cycles per second (500-meter wave), the capacity C being .0004
nf. The total resistance of the oscillating circuit is 10 ohms, the no of
the tube to be used is 4 and Rp is 3000 ohms. Using the relation X = 1885
VLC, we find
LC = .0705,
and therefore L = I76fih.
Then we find, L4-5 = 65M and for L4-6, we find 32/xh. If the tube can
supply 4 watts of power, the current in this oscillating circuit would be
= 0.632 ampere.
If Rp = 3000, we have -f- = 6000, and also we have EopIop = 8. From these
I op
two equations, we find that EOJ)=220 and 7OiJ=.037. From the above
values, we have
01L4-5I = (2*6 X 10s) X (65 X 10-6) X .632 = 153,
this being the effective value of the voltage impressed on the plate. But
this is equal to £op4-v/2, as we have already assumed necessary for gen-
E I
erating a power equal to
This elementary analysis serves for an approximate solution of the
circuit; the filament would be connected to point 4, somewhat lower than
the middle- of the coil and points 5 and 6 should be adjustable by multi
point switches. Normally there should be 65/xA between points 4 and 5
for the plate connection, and 32 /Ji between points 4 and 6 for the grid
connection.
The foregoing calculations have been made on the assumption that
the alternating-current output of the tube was 50 per cent of the input.
Actually on a small tube like this 25 per cent efficiency would be more
likely than 50 per cent; this would decrease the value of / and so require
an increase in the required values of L^-q and Lis.
As the alternating component of the plate current Iv is practically
90° out of phase with the power circuit current /, the required phase dif
ference of 180° between Ep and Eg will not be obtained if /„ is appreciable
compared to I. This shift in phase of Ep as the ratio -j- increases, very
materially reduces the possible output of the tube.
If it should happen that R and Rp are so high that the Las required
is more than about two-thirds of the whole coil L, the conditions required
by Eqs. (27) and (28) could not be satisfied by this circuit, so it would not
oscillate.
DETECTION OF CONTINUOUS WAVE SIGNALS 483
E 2 E' 2 } d2I
—y~ H—~- -[-average value of EmE'm sin ait sin pt 1 "
dE2'
484 VACUUM TUBES AND THEIR OPERATION [Chap. VI
The first two terms give the increase in the plate current which is con
stant, as long as the excitation is applied; their effect would produce an
increase in the value of the plate current as read by a continuous-current
ammeter in the plate circuit, but they would not produce a readable sig
nal in the phones, giving only a slight click in the phones when the excita
tion is put on the grid and another when it is taken off.
Whatever audible signal is obtained must come from the third term;
this may be written in the expanded form
cPI
hE^E'wicos («-p)<-cos (u+p)t) ^g-f.
The average value of both these cosine terms is zero, but cos (to— p)t
may fluctuate so slowly as to produce an audible signal in the phones, and
'■'WWWWVW
detector of signals for undamped, than for damped, waves, its sensitive
ness not decreasing with the stiongth of signal so rapidly for one as it docs
for the other. Eq. (31) shows also that the response to a given signal
varies with E'„ the amplitude of the local oscillations, so long as the vari
d2Ip
ation of E't does not change the value of
This increase in response with the strength of the local oscillations
is similar in character to the increase in response of a telephone receiver
due to the use of the perma
nent magnet. It is not a
characteristic peculiar to a Crystal detector
actuated by single
vacuum tube, but holds for frequency
any detecting device in which
the response varies with square
of the impressed force (when
a single frequency is im
pressed). A crystal rectifier
has a nearly parabolic rela
tion between the current strength of signal
through it and the impressed Fig. 104.—Rectifying action of a crystal actuated
voltage (see Fig. 60, p. 347) by a single frequency,
and the curve of response as
a function of the signal strength is as shown in Fig. 104, when it is used
to detect spark signals. If, however, the crystal is used to detect con
tinuous-wave signals by use of an auxiliary source of continuous wave
To continuous excitation (Fig. 105), its response
wave generator follows the same law as obtained
increased the response falls and may reach practically zero for excessively
large values of E'e.
This same characteristic holds for the vacuum tube used as a beat
receiver, the static charac
teristic of a tube being as
Response of crystal indicated in Fig. 108; if
detector used for
beat reception the amplitude of the lo
cally generated e.m.f. is
0C, the response (for given
signal strength) will be
about twice as strong as
if E'„ had the amplitude
OB only, whereas a value
of E', equal to 0D would
result in a signal perhaps
_ less than for E',=0B.
Strenirtli of Signal If E', is increased to the
Fig. 106.—Rectifying action of a crystal used as indi- value OE the response to
cated in Fig. 105. the signal will be practi
cally zero.
Detection with Grid Condenser.—In case a condenser is used in series
with the grid of the tube being used as a beat receiver Eq. (18) must be
used in predicting the
detection efficiency. The
question is somewhat
more involved than for
the tube with no grid con
denser, because the nor
mal grid potential (aver
age value with no signal
coming in) varies with
the value of E'„ the
potential decreasing as
E'g is increased in value.
As all three of the deriv
atives used in Eq. (18) Fig. 107.—Rectifying action of a crystal detector as a
vary as the normal grid function of the amplitude of the locally impressed
potential is varied an voltage, the signal voltage being of constant
exact expression for the plitude.
detection factor must be
rather complex. As the tube is used in practice the most sensitive con
dition is easily found as will be described in a succeeding paragraph, deal
ing with the self-excited, oscillating tube as detector.
CIRCUITS USED FOR SELF-EXCITATION 487
and (36
To make Eq. (36) true the grid circuit must be so adjusted that no
current flows in it as the voltage, e„, goes through its cycle of values;
this requires that at no time throughout the
> /\ cycle must the grid be positive with respect
-L - < / \ I to the filament, and that the capacity of
the grid-filament circuit is negligible. The
first condition can be brought about by
using a proper value of Ee (Fig. 109), but
the second condition cannot be brought
about by any adjustment of the tube cir
cuit. In some cases this capacity is of ex
treme importance; for very high-frequency
circuits it may be one of the limiting fac
tors of operation. It must be borne in
mind that the capacity to be considered is
Fig. 109.—A commonly employed not the geometrical capacity of the tube,
circuit for producing oscilla- but the effective capacity as explained on
tions; the frequency is fixed by page 432 et seq. (An oscillating tube
the coMtonte of the plate circuit furnishes maximum power when the ex-
and the value of M is the critical , , . . . .. , . . . ,
factor for production or non- ternal stance in the plate circuit is equal
production of oscillations. to Rp, so in calculating the probable effect
of the grid-filament capacity of an oscil
lating circuit the proper value of n to use in Eq. (10), p. 434, is /io/2 )
We have also
12>
dt'
CIRCUITS USED FOR SELF-EXCITATION 489
Fio. 110.—A sinusoidal variation in grid potential will produce a sinusoidal variation
in plate current only if the fluctuation in plate current occurs over a limited range.
490 VACUUM TUBES AND THEIR OPERATION IChap. VI
fc-C&f+CLtSf (37)
By combining the foregoing equations to eliminate e„, e„ ip, and ?2, we get.
Fig. 111.—Due to the upper and lower curves of the plate current curve of Fig. 110
the actual alternating component of the plate current is flat topped (sine-wave
shape shown by dotted lines).
1 For an analysis of an equation of this kind see the first few pages of Chapter IV.
CIRCUITS USED FOR SELF-EXCITATION 491
to increase itself; this occurs if M is negative and its value such that
M > — (Li+CRiRp). The plate current then tends to increase or decrease
MO
(according to the sense of this disturbance) and does so as long as the
characteristic curve (Fig. 110) is straight.
In the case the constants of Eq. (38) are such as to make its roots
imaginary, we have,
[Rl+cr-^Li+»oM)]2~^(1+1?)< a • • • (40)
a = "2L7[fli+ck(Ll+MoM)]' (42)
and ti
W = 2iV^(1+f)-[^+^(Ll+"oM)]2- • • (43)
Rz.+~-(L1+?oM)<0,
that is, when M is negative and its absolute value is such that,
(47)
/--4= (48)
If the coupling between the grid and plate circuits is made tighter than
required for the limiting value, the frequency is somewhat decreased.
If we suppose Eq. (48) to give the frequency the critical value of M
may be written in the form,
-M-^l+^if^u). • • • (49)
that me,>ep, it is possible to have ip 180° out of phase with ep, so that R'p
may be negative, whereas Rp is always positive.1 We have then as the
condition, for self-sustained oscillations
Ra-b+R'p=0. . . (50)
From Eq. (50), Chapter I, we find that at resonance,
If we use the approximate relation C =~tjj » ^1- (53) yields the solution,
_M = W1+*^l\ (54)
When RL+~D-(L1+noM)=0,
1 This difference between Rp and R'p may be indicated by writing Rp = —r- and
Sip
de
R'p for the latter case it must be remembered that as c„ changes e„ undergoes
alp
de
simultaneous changes which may result in the total derivative —r- being negative whereas
dlp
&€
the partial derivative —r is always positive.
blp
494 VACUUM TUBES AND THEIR OPERATION [Chap. VI
*v 4('+t)-» <55)
The solution of this is ii = h sin oil, in which
tit'
In practically all radio coils is so large that <> may be put equal to
90° without much error, so that,
ep= -IiVTiL2+(u,Li)2 sin (*<+*■ /2) (57)
From (56) and (57) it is evident that ep and e, are practically 180°
out of phase, a condition we have previously shown necessary for oscillation.
The plate current is fixed by the condition,
€„ = - RLii - (Li+noM) ~.
As e„ = Rpip, we have,
72f. . Li+tioM dii RL T . L\+noM ,
1>-—X1~~~R~ dt=-R,IlSin wt 727~ w/l 008 "*
in which
tan \p = ^ .
CIRCUITS USED FOR SELF-EXCITATION 495
As M is negative and noM is greater in absolute value than L%, the angle
4? is nearly — 2-
Then
Imp and 7 i being the maximum possible va'ues of the effective values of
ip and i\, and this value of Imp must be equal to Iop. So we put,
496 VACUUM TUBES AND THEIR OPERATION [Chap. VI
10pRp
or Iml
ml ~ ^/}^x,2+w2(Ll+Moilf)2,
and assuming
Iml :
R, Jc 1
RP2
which for the average tube is practically the same as,
E
gives, I„i =
Iml=E"\Zl (60)
Eqs. (59) and (60) then constitute two limits on the possible amplitude
of Zi ; whichever gives the lower value will determine the maximum value
of Ii. The best condition makes the two limits the same which occurs
when
Eop 1 Li .
7 =73- 77 (61)
lop Kl l>
The symbols I„p and Eop have been used to indicate the limiting values
of ip and e„, so that Eq. (61) is properly written, using effective values of
voltage and current.
maximum value Ep _ 1 L\ .
maximum value Ip RL C
But from Eq. (50), Chapter /,
1 h
Rl »
C ~K'
ing for its value upon the amount of change in the plate current. The
discussion of Rp on page 471 ct scq. and the measurements recorded in
Fig. 94 had to do with Rp for very small variations in plate current, and
in such a case Rop is about twice as
great as Rp.
For the conditions obtaining when
Eqs. (61) and (62) are applicable,
the plate current is supposed to vary
from zero to 2 Ittp, and furthermore
the relation between J, and (Ep+noE„)
is supposed to be linear; for such
E
conditions Rp = R»p = -j*-. The differ-
ence in Rp with weak excitation and
strong excitation is indicated in Fig.
114; the full-line curve represents
the actual relation between Ip and Et,
Fig. 114.—If the Rp of a tube is to be when tnere & no resistance in series
constant the relation between Ip and with the plate circuit and the dotted
(Ep+poE,,) must be a straight line as curve shows the assumed relation on
indicated in the dotted graph; actually thg bagig of E (33) The dotted
the solid line curve gives the plate .. . » „ / , • . A\
current, hence it is evident that Rp ^ CUrve V™ for R" <at P0mt A>
must vary with the magnitude of flue- E
tuation of (Ep+noEg).
l op
AE
whereas the full line curve gives for Rp at the point A a value of
E
about half as great as -j*.
1 op
Of course, it is not possible to excite a tube to the limits set by Eqs.
(59) and (61), so Rp actually never increases to the value
Em
RP
as the intensity of the oscillations varies; the value of Rp for the ordinary
tube will undergo changes about as shown in Fig. 115.
Stability of Oscillations.—In the average circuit the value of the
oscillating current is greatest when the coupling is as weak as can lie
permitted and still maintain oscillations. For this condition, however,
the stability of the circuit is very poor; the slightest decrease in either
// or E„ is likely to stop the oscillations. Also for this condition it is
necessary to readjust the coupling for every change in the oscillating
circuit; if either RL, L\, or C is increased the oscillation will cease. To
VARIATION OF PLATE CIRCUIT RESISTANCE 499
If the plate current hp has been adjusted equal to half the saturation
current, for the values of // and E„v used, a continuous-current ammeter
will indicate no change in the value of the plate current when oscillations
start. In general, however, there will be a change; when oscillations
start the average plate current will generally increase if the circuit is
such that no condenser is used in series with the grid and will decrease
if such a condenser is used. Conditions may occur in which this general
statement is not true.
Adjustments to Give Maximum Output of Tube.—With a circuit
arranged as in Fig. 109, there are two adjustments to carry out before
the tube will give its maximum out
put; the grid must have the proper
excitation and the plate circuit resist
ance must equal the tube resistance.
The circuit of Fig. 109 is reproduced,
with slight modification, in Fig. 118.
The oscillating circuit Li, Rl, C, is
many times an antenna, with loading
coil, so it is evident that Rl itself
is not adjustable, yet the resistance
between points A and 0 must be made
equal to the tube resistance.
The plate circuit inductance is Fig. 118.—To make the circuit shown in
made with taps as indicated in Fig. Fig. 109 useful, the inductance in the
118; point B is adjusted to give the oscillatory circuit must be fitted with
two sets of taps as indicated here; the
right frequency to the oscillating mutual induction between the two
circuit, and then point A is adjusted coils Lt and Lv must also be adjust
to give the plate circuit the right able.
resistance. Neglecting the effect of
the plate current compared to the oscillating current (an ordinary radio
set makes Ip equal to about 1/20 of /), we have,
a
Ro-a=Rl\r~l) -~sT RlL
E0,
If R0-a is to be equal to Rp = -f* (for conditions of maximum power)
lop
we so adjust tap A that
Eqj, _ Lp2
lop RlLiC
or L,-^E»*lMC (63)
Also we know that ec, and ec, are fixed by the relation — C2 ^^ = 12, and
— Ci -1 = iz- By the use of these relations, and deriving Eq. (65), we get
the equations,
, d2ii T d?h , Ddi2 , i<i
Llw+Mw=L*w+Rti+c; <67>
- (68)
We can write
(60)
CIRCUITS USED FOR SELF-EXCITATION 505
Eqs. (67), (68) and (69) permit the precise determination of n, 12, and
13, but it is evident that the solution would be tedious and the solution
can be easily guessed. If oscillations occur at all they will be sinusoidal
and as they are all supplied with power from the same source (the plate
circuit) we can write,
n=Ji sin ut, 12 — I2 sin (co£+02), 13 = ^3 sin (to<+03).
By deriving these expressions and substituting in Eqs. (67), (68) and (69),
and for each equation thus obtained, equating the coefficents of cos ut and
sin ait, we find
Rp(h+ h cos (f>2+h cos <t>3) — u(wLz+M)l3 sin <l>3=0. . . (70)
Rv{h sin fo+h sin <f>3) + <j>(Li+noM)Ii+ui(n0L3+M)l3 cos <fo =0. (71)
uLh+uMh cos <t>3 = (^oL2—-^-^h cos fa+hR sin <f>2- ■ (72)
j{Lx-M){nQL3+M)'
=0. (77)
506 VACUUM TUBES AND THEIR OPERATION [Chap. VI
The frequency might be calculated from Eq. (76), and this frequency
carried into Eq. (77) would permit the calculation of the critical coupling
for oscillations. From inspection of Fig. Ill it is evident there will be
two possible frequencies and of course each of these must be used in
solving Eq. (77). This general solution is lengthy, so we will investi
gate only two of the more important cases.
In case Ci=0 and 1/2=0, the circuit degenerates into that of Fig.
.109 and so our general Eqs. (76) and (77) should reduce to the simpler
forms obtained for this case. Eq. (76), becomes (if we put Ci =La =0)
r
'2'
and if this value of a> is substituted in Eq. (77), in addition to the condition
that Ci =1/2 =0, we find as the condition for oscillation,
ff +—^-(Li+moM) =0,
Hp'- 2
which we have already obtained from the circuit of Fig. 109.
In case M =0 and L2 =0, Eq. (76) becomes,
-^—uC2+ —j 0 (78)
This is evidently the condition for zero reactive current in the three-
branched plate circuit, one branch having L\, another having C2, and the
third having L3 and Ci in series. Eq. (78) may be put into the form
-i-[LlC2+(U+LdCi]\+LlC2UCx=Q. . . . (79)
If we put [LiC2+(L>3+ Li)Ci] =a, and L1C2L3C1 =b we can write the two
positive roots of this equation,
CIRCUITS USED FOR SELF-EXCITATION 507
Of these two roots for w one is greater than ana* the other is less
than j—ft- We shall show that the only possible oscillation is the lower
\ L3L1
one of the two.
If we substitute M =0 and L2 =0 in Eq. (77), we find that the critical
conditions for maintaining oscillations as given by,
R+ 7 Ll . v /l+-^V-\-0, . . . (80)
the condition for oscillation making the left-hand member less than zero.
The condition for oscillations is then determined by the inequality
uLl 1 (RRJ>C2+MoLa)+Li+RR]jC2<0. . . . (81)
. (83)
Eq. (81) also serves to further limit C\, because from it we get the
relation,
r ~1 L\+RPRC2 (fu.
Ul>W2 L1L3(w>+l)+R,RC2(Li+I*) w
(85)
a>C2 V ...rr m L
(no+lMULa-M2)-
R- *0. (86)
RPC2\ u(Li+l*-2M)-
03C2
The capacity coupling serves to increase the magnetic coupling if M
is negative and if w{Lz — M) — ^r<0. Even if M is positive the con
dition for oscillations may be still maintained by
using sufficient capacity coupling.
It is to be noted that even if no actual con
denser Ci is used in the circuit, there is always
such a capacity present in the tube itself, due to
capacity between the actual grid and plate, as well
as that of the lead-in wires connecting to them.
At very high frequencies this internal tube capacity
may very seriously affect the behavior of the tube;
in certain tubes of foreign manufacture the lead-in
wires of the plate and grid are kept as far from
Fig. 122. This circuit is each other as the structure of the tube permits
similar to that of Fig. with the idea of minimizing this internal capacity.
120, but simplified by (gee tube (0) of Fig. 21, page 389.)
eliminating the dummy Another circuit which may be used is shown
antenna circuit.
in Fig. 122. For this case, we have,
-Llli-Mlt-
T di2 , ,■ ai\
d.i\
and as
Rpip=ep+noel!,
CIRCUITS USED FOR SELF-EXCITATION 509
Wlien the reactance across the machine or battery furnishing the plate
voltage is negligible (it should always be made so by shunting with a large
capacity, if necessary), we have
... (88)
and as ta = —
we can write (88) in the form,
<*»
+ (Li+^oM)^R2+(w(L2-M)—^y^=0. . (91)
If in (90) we neglect the terms ~ and R2, we get for the natural period
itp
of the circuit,
o>= . 1 (92)
V(Li+L2-2A/)C
And using this value of 01 in Eq. (91), which determines the critical con
dition for oscillation,
fi[2WIa-^+i?(Ia-h^^ (93)
R{R'+R)<~(L1+La)C • (95)
— , ,' • (W)
VC(la+i'l)'
R+^/l^oM-1^1^*.]^ (99)
R,c\ ye
C{L2+LlR-J
R
from which, using (98) and neglecting terms involving -5-,we get,
lip
r+*>M{mJ*+M)
and this can be satisfied only if M is negative and its absolute value is
greater than n0L,2. The condition imposed by (100) will be satisfied if
M is negative and its absolute value lies between the two roots of Eq.
(100). So the absolute value of M is limited by the relation,
The condition is evidently different from that existing when the oscillating
circuit was in series with the plate. In that case if M exceeded its critical
value the value of the oscillating current was reduced, but there was no
upper limit for the permissible value of M. With the oscillating circuit
in series with the grid, however, the oscillations will cease if the absolute
value of M exceeds a certain critical value.
Circuits of Very High Frequency.1—Vacuum-tube circuits will gener
ate any frequency between one per second or less to many millions per
second; the low frequencies require very high values of L and C, but
1 Many other circuits than the few here analyzed have been designed and used. The
reader is referred to an article by L. A. Hazeltine in Proc. I.R.E., April, 1918, one by
W. C. White in G. E. Review for September, 1916, and one by G. C. Southworth in the
Radio Review for September, 1920. Southworth has been able to obtain frequencies
as high as 3 X 10s cycles per second.
512 VACUUM TUBES AND THEIR OPERATION [Chap. VI
actual connection being as shown on the curve sheet given in Fig. 178,
p. (570).
With Lp, of this figure, below a critical value, the main circuit, Lr-Lp-
C-L—R, will not oscillate; it is quite likely, however, that when the main
circuit is not oscillating, high-frequency currents will be generated in the
circuit made up of L„ and L„ in series with the internal capacity of the
tube. Thus, with L„=200 ph, L„=400 fih, L=8000 fth, C = .0O2 rf, the
ammeter I (Fig. 178) gave no indication, but the meter Iv showed that
the tube was oscillating violently. Test with wave-meter showed the
circuit, L„-L,-tube-capacity, to be generating a ■ H
complex current of fundamental wave-length equal j.
to 800 meters; this is about the natural frequency
of the circuit.
The desired wave-length, of about 6000 meters,
was not started until Lp was adjusted in excess of
1200 fih; the frequency changed suddenly from one
value to the other, as Lp was varied through its
critical value. There is a tendency in such a cir
cuit, however, to maintain the existing oscillation;
thus if Lp was increased, the high-frequency oscil
lation persisted until Lp exceeded 1200 ph. As L„
Fio. 126.—In a circuit of
was decreased, however, the high-frequency oscil this kind (often called
lation did not start until Lp was made less than a Meissner circuit)
1000 ixh, so that with Lp = 1100 ph, either 900 meter spurious oscillations
or 6000 meter oscillations might exist, depending may be set up in the
upon whether Lp had been decreased from a high circuit indicated by
the arrow, the main
value to 1100 ph, or had been brought up to the oscillatory circuit re
value from something lower. maining unexcited.
An interesting condition was found in this test:
if the condenser across machine En was taken out the high-frequency
oscillations was very persistent, whereas the 6000-meter oscillation
would not start, no matter what value Lp might have. Evidently for
the lower frequency the machine offered a high-inductive reactance and
resistance, whereas for the high-frequency current it acted like a con
denser of low impedance.
The undesired high-frequency current for the circuit above described
was completely eliminated by introducing a suitable resistance directly
in series with the grid, as indicated at A in Fig. 178; 100 ohms sufficed
to diminish their amplitude considerably and 2000 ohms at this point
resulted in such high losses for the 800-meter wave that it could not
sustain itself. This high resistance had a negligible effect on the 6000-
meter oscillation, because of the comparatively small charging current
flowing to the grid at this frequency.
514 VACUUM TUBES AND THEIR OPERATION [Chap. VI
term d2i
-v-f is really a measure of the assymetry of the change in plate cur-
Q>€g
rent when E, is positive and when it is negative; in other words, it measures
1 Changing the plate-circuit inpedance changes the effective value of the tube capacity
(and hence its effect on the frequency of oscillation), because the n of the tube and
circuit has been changed; the yuo of the tube, however, has not been altered by changing
the plate-circuit impedance.
OSCILLATING TUBE AS DETECTOR 515
the excess of the increase of plate current for positive E„ over the decrease
for negative Et. So long as the relation between Iv and Eg is parabolic
di2
the value of -j—| is constant, but for this condition the tube resistance Rp
is also constant. We have previously shown, however, that to make a tube
oscillate, the coupling (of whatever kind is used) must be increased beyond
a certain critical value, and that after this value is past the oscillations
start and automatically increase in amplitude, until the plate resistance Rv
is sufficiently increased to restore a certain balance which was destroyed
by increasing M. This change of resistance was analyzed in discussing
Fig. 114. The plate current in an autodyne receiver will fluctuate over
the straight part of the full-line curve of this figure if the value of M
(between L\ and L2 of Fig. 127) is kept sufficiently low: if it is increased
much beyond its critical value the fluctuation in plate current will extend
over the upper and lower bends of the curves.
The tube will act best as a detector of continuous-wave signals for that
coupling of Li and Li (Fig. 127) which results in the greatest product
(Pi
of E'e-r-^- This product will generally be a maximum for the weakest
(l€g
coupling which will maintain the tube in the oscillating state; such is
nearly always found to be the case in practice. If the coupling between
L2 and L3 is held constant and the coupling between L2 and L\ is dimin
ished, the signal strength will be a maximum for the weakest possible
coupling. In carrying out this test it is necessary continually to change
C to keep the beat note of constant pitch, because of the effect df Li on
the value of the effective self-induction of L2.
Three possible conditions of the adjustment of a beat receiver are shown
in Fig. 128. In (a) the coupling is so adjusted (tight) that the grid poten
tial, with no incoming signal, fluctuates between A and B; the plate cur
rent fluctuates with a frequency nearly the same as that of the signal,
between the values AG and BH, its average value being 01. This cur
rent 01 flows through the phones and the high-frequency alternating
component of the plate current is carried by the condenser shunting the
phones. In case no actual condenser is used to shunt the phones this
current will utilize the capacity of the phone cords or the distributed
capacity of the windings to by-pass the high inductance circuit of the wind
ings themselves.
When the signal voltage E, is superimposed on the grid it alternately
increases and decreases the amplitude of the grid fluctuations of poten
tial; the value of grid potential now fluctuates with variable amplitude,
the amplitude being fixed by the limiting values EF and DC, the fre
quency of these cycles of variation of amplitude being equal to the
difference in frequency of E„ and E'„.
516 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Fig. 128.—This diagram shows the effect of the strength of the local oscillations on the
signal strength; the audio frequency current through the phones, which gives the
audible signal, is indicated by the wavy dashed line in each diagram. In (a) the
local oscillations are too violent to give a good signal, in (ft) the signal is somewhat
improved and in (c) it is best. It is doubtful if the local oscillation could be cut
down as much as indicated in (c) without stopping the oscillations altogether.
For all three diagrams the amplitude of the high-frequency signal voltage is the
same.
OSCILLATING TUBE AS DETECTOR 517
The plate current will now be of the form shown in the right-hand
part of the diagram, and the average value of this high-frequency plate
current will be as shown by the dashed line shown at K, L, M, etc., and
it is this pulsating current which, flowing through the telephone receivers,
gives the signal.
In diagram (6) of Fig. 128 is shown the effect on the signal strength
of reducing somewhat the amplitude of the locally generated oscillations
E'„ which occurs as a result of decreasing the coupling between L\ and
U in Fig. 127 (dotted line of Fig. 112). Although E't is less than in
diagram (a), the value of the signal current (shown again by the
dashed line) is greater for (6) than it is for (a).
In diagram (c) of Fig. 128 is shown the result of still further decreasing
the value of the local oscillation E'g; it is likely that M could not be suf-
Tube A TubeB
9SF
Fig. 129.—In order to control easily the strength of the local oscillations impressed on
the detecting tube it is best to have a separate oscillator and couple this properly
to the detector, Tube A. In this diagram Tube B is the oscillator; it is coupled
to the detector by the two coils L» and L.t
ficiently reduced to make the tube oscillate in this fashion without stopping
the oscillations altogether. The signal current is, however, greater for
this condition than for either of the two other values of E'Q shown at
(a) and (6).
Use of a Separate Tube for Generating the Local Oscillation?.—In
order to use the vacuum tube as detector most efficiently it is necessary
to have the amplitude of the voltage E't under control, and this can best
be done by using a separate tube for generating the voltage E'e, in addition
to the detecting tube. The scheme of connection is then as shown in
Fig. 129. The local oscillations are generated in tube B, their frequency
being fixed approximately by L4, L5, and C\, and intensity by the coupling
between L5 and L%. This coupling should be considerably greater than
the critical value, so that as conditions in the circuit are changed the
oscillations of tube B are not stopped.
518 VACUUM TUBES AND THEIR OPERATION [Chap. VI
The value of E'g impressed on the grid of the detecting tube A can
be controlled by varying the mutual inductance between L3 and La,
either by moving the coils with respect to one another or by changing
the value of either of them. The value of M should be so adjusted that
the condition obtained is that shown in Fig. 128, diagram (c).
The antenna circuit and L2C2 circuit are each tuned for the frequency
of the incoming signal, and the coupling between L\ and L2 is adjusted
as near the critical value as possible. We have shown that the effect
of the coupling between L2 and L\ is to decrease the resistance of the
L2C2 circuit, and this resistance may be made to approach zero, if the
coupling is suitably adjusted. Further, the L2C2 circuit can be exactly
tuned for the incoming signal, so that the- reactance is zero also, hence
the impedance of the L2C2
circuit may be made to
approach very close to zero,
so that the current caused
to flow by a weak signal
may be perhaps a hundred
or more times greater than
it would be if the coupling
L1 — L2 were not used. 1
The impedance of the
L2C2 circuit, as a function
of the impressed frequen
.99 x 10s 1x10* 1.01 x 10s cy, has the form shown in
Frequency Fig. 130; it is evident from
Fia. 130.—By properly adjusting the coupling of coils this curve that not only
Li and Ls of Fig. 129 (keeping the coupling too low
to produce oscillations in Ls— C2) the resistance of is the circuit of Fig. 129
the circuit L% — Ci may be made to approach zero. one to amplify signal
This curve shows how the impedance of the Li — C% strength, but also that
circuit will then vary with frequency of impressed this amplification is very
signal. selective. With a low
resistance coil for L2 and
a well-insulated condenser, and the grid circuit of the tube adjusted
to absorb but little power, the selectivity is extremely sharp.
Effect of Condenser in Series with the Grid on the Critical Coupling.—
In the foregoing analyses of the conditions required for self-excitation
of tubes no mention was made of the effect of a condenser in series with
the grid, as affecting the possibility of oscillation. In some common
oscillating circuits it is necessary to use a grid condenser to insulate the
grid from a high positive potential; such a one is shown in Fig. 131. " !'K'
1 An experimental investigation of the magnification obtainable in such circuits was
carried out by E. H. Armstrong and reported in Proc. I.R.E., Vol. 5, No. 2, April, 1917.
OSCILLATING TUBE AS DETECTOR 519
and easy to make. If grid condenser is used the distinctness of this pluck
ing sound is by no means as pronounced as is the case for no grid con
denser; for some values of capacity and leak resistance it is almost impos
sible to hear it at all, even though the critical coupling is known and
especial care is used in listening.
In the case of no grid condenser the finger test gives very distinct
indication of the oscillating condition; with the moistened thumb placed
on a filament connection (binding post) a finger is touched to the grid
connection of the tube, thus grounding the grid to an extent sufficient
to stop oscillations.2 The cessation of oscillations is accompanied by
a sharp click in the receivers and when the finger is removed from the grid
connection the starting of oscillations, with accompanying change in plate
current, is indicated by another click, generally less distinct than the first.
For coupling of the tickler coil considerably in excess of the critical value,
the two clicks (starting and stopping oscillations) are of about the same
intensity.
With grid condenser and leak the finger test does not give reliable
results, except to the experienced operator; even with no oscillations
two clicks are heard when the finger is touched to the grid connection and
when it is removed therefrom. With the tube not oscillating the grid is
practically always positive, with respect to the potential of the negative end
of the filament; when the grid is grounded by the finger, thus suddenly
bringing it to the same potential as the filament, a sudden change occurs in
the plate current with resultant click in the receiver; when the finger is
removed the grid at once resumes its normal positive potential and so
again gives a change in plate current and click in the phones. As has
been previously noted, when grid condenser is used the grid leak resist
ance is best connected by the positive end of the filament; such has
been assumed in statements just made.
The same two clicks are observed if the tube is oscillating, and there is
not much difference between the clicks in the two cases. This is especially
true if the grid condenser is small and electron supply in the vicinity of
the grid plentiful; if, for example, with an ordinary detecting tube the
grid condenser is 100 nnf (a commonly used value) and filament temper
ature normal, even a good operator may not distinguish any difference
in the clicks for the oscillatory and non-oscillatory condition.
If, however, the grid condenser is much larger, say 5000 nnf or larger,
there is a marked difference to be noticed; with oscillations the two clicks
have nearly the same intensity, but with no oscillations the click heard
upon removing the finger from the grid connection is much softer than
5 On most receiving sets it will be found that, even though the grid connection
directly at the tube is not accessible, some screw or binding post connected to the grid,
is available.
522 VACUUM TUBES AND THEIR OPERATION [Chap. VI
the one heard when making contact with the grid. When the tube is
not oscillating it takes an appreciable time to charge the grid condenser
to its normal potential and the accompanying change in plate current
is slow, thus giving a weak sound; the larger the grid condenser and the
lower the filament temperature, the longer will this charging time be and
correspondingly weaker is the click in the receivers.
The tests for the oscillating condition can then be summarized as
follows:
Coupling Test.—No Grid Condenser.—Distinct sound (plucking string)
when critical coupling is exceeded.
With Grid Condenser.—The click occurring when critical coupling is
exceeded is not distinct unless the grid condenser is large (several milli-
microfarads) and the filament temperature subnormal.
Finger Test.—No Grid Condenser.—Two distinct clicks when tube
is oscillating and none at all when tube is not oscillating.
With Grid Condenser.—Two distinct clicks of nearly equal intensity
if tube is oscillating; if tube is not oscillating the click upon touching; the
grid connection is more pronounced than that when releasing the grid,
the distinction being more pronounced with larger grid condensers.
Peculiarities of Adjustment of Oscillating Detectors.—When first
working with oscillating detectors certain apparent discrepancies will be
encountered. Thus if the tuned grid circuit uses one of the coils of a loose
coupler and the other coil of the coupler, or a section of it, is used for the
tickler coil, it may be found that when the coils are separated, oscillations
occur, no matter which way the tickler coil is connected in the plate circuit.
It may also be found that oscillations occur when the coils are quite widely
separated and that as the coils are brought nearer together the oscilla
tions cease, an apparent contradiction to the analysis previously given.
With the coils arranged as shown in Fig. 132, it is apparent that the
magnetic coupling of Li and L2 is weak, but it may well be that the two
coils of the coupler
permit enough elec
trostatic coupling of
the plate and grid
circuits to produce
oscillations, and this
Fio. 132.—If an ordinary coupler is used in making testa for eyen if the connec-
oscillations some peculiar results may be obtained. tion of L\ is re
versed. Now if the
sense of the magnetic coupling of L\ and L2 is incorrect for producing
oscillations, the electrostatic coupling of the two circuits will be neutral
ized as the two coils are brought closer together, and when they get
close enough, the coupling due to both effects will be less than the
PECULIAR NOISES WITH OSCILLATING DETECTOR 523
critical value and so oscillations will stop. In case the tickler coil con
sists of only a few concentrated turns this effect will not be noticed.
When the coupling of plate and grid circuits is accomplished by rotating
one coil inside the other, it will often be found that setting the coils at
right angles to one another, which of course makes M =0, will not stop
oscillations and that the coils must be rotated considerably past the 90°
point before the oscillations stop. This is because of the electrostatic
coupling introduced by the proximity of the two coils; enough reversed
magnetic coupling must be introduced so that the total coupling, induc
tive plus capacitive, is less than the critical value for the circuit. This
effect is mentioned, and analyzed on p. 504.
Peculiar Noises Occurring in an Oscillating Detector Circuit.—If
the oscillating detector circuit has no condenser in series with the grid
its behavior is very regular, but if a grid condenser is used all sorts of
queer noises may be heard in the phones, unless the adjustment is care
fully carried out. The noise may vary from a series of regular " clicks,"
separated from each other by several seconds, to a high shrill signal; on
carrying out further adjustments, the note may become so high as to be
inaudible, so that the operator has no convenient way of telling that the
action of the tube is irregular and that readjustment is required.
The condition practically always occurs as a result of too tight coupling
of the tickler coil, too high a resistance for the grid leak, or a combination
of both. The noise is due to the starting and stopping of oscillations, the
musical pitch having nothing to do with the frequency of oscillation, but
being fixed by the rapidity with which
one group of oscillations follows the
next.
The oscillations start, thus charging
the grid condenser and reducing the
mean potential of the grid and so
changing the Rp of the tube; but the
condition for oscillation for the circuit
given in Eq. (101) depends upon Rp,
and it is evident from inspection of
this equation that if R„ increases, the d c
Plate voltage.
value of M required for oscillation is
Fio. 133.—When oscillations start, in
increased. In Fig. 133 is shown the a circuit using a condenser in series
relation between Ep and IP, for two with the grid, the plate-current curve
values of Eo,; the curve OA is for may change from OA to DB, due to
Eo,=0, and the curve DB is for E„e at the decrease in average potential of
some negative value. The slope of the grid, when oscillations start.
this curve serves as a measure of Rp, the value of Rp being actually
given by the cotangent of the slope, when the scales for Ep and Ip are
524 VACUUM TUBES AND THEIR OPERATION [Chap. VI
The squealing noise will nearly always be produced if, after the proper
value of M has been obtained for a certain setting of the tuning condenser
C (Fig. 123) the capacity of this condenser is much decreased. Decreasing
C increases w and so, according to Eq. (101), makes a lower value of M
permissible; with the ordinary detecting-tube circuit, having grid con
denser, it is practically always necessary to use the lowest value of M
compatible with the requirements of Eq. (101) if steady oscillations are
to be produced. A value of M much greater than this will not only cut
down the sensitiveness of the tube as a detector, but is always likely to
produce noises.
Use of Regenerative Circuit for Spark Reception.—A tube circuit
arranged with " tickler " or other form of coupling for the detection of
continuous-wave signals is also adapted for the reception of spark, or
damped-wave, signals; with the antenna circuit and the local circuit (L2 — C
of Fig. 127) tuned accurately to the incoming signal the tickler coupling
can be increased to a value slightly less than that required for producing
oscillations. The increase in intensity of the signal by using a suitable
value of coupling can be increased thousands of times over the value it
would have if no tickler coupling were used.
It has been shown that the effect of the coupling is to reduce the
resistance of the L2 — C circuit to a very low value (Fig. 130) so that a
certain e.m.f. impressed on this circuit, from the antenna circuit, will
produce a current perhaps 100 times as great as would normally be the
case. The change in the plate current (which gives the signal in the
phones) is proportional to the square of the voltage impressed on the grid,
as given in Eq. (18), and so will increase greatly as the resistance of the
L2 — C circuit is made to approach zero by suitable tickler coupling. If
e.g., the actual resistance of L2 — C is 10 ohms and by means of tickler
coupling the effective resistance is reduced to 0.1 ohm, the current in
L2 — C is increased 100 times, the voltage impressed on the grid
is increased 100 times, and the signal current, A/p, is increased
104 times.
The effect on the signal strength as the mutual inductance between
Li and L2 (Fig. 127) varies is shown in Fig. 134; as M is increased the
signal intensity rapidly increases, retaining its normal musical quality,
until such a coupling is reached, OA, that oscillations start. The resulting
noise in the telephone when the tube is oscillating, is of " scratchy "
quality being caused by a kind of beat phenomenon between continuous
waves locally generated and the incoming damped waves; as the phase
relations between the successive wave trains and the continuous oscilla
tions of the tube are of haphazard values, and as the amplitude of the
spark signals is variable throughout each wave-train, the resulting vari
ation in amplitude of the plate current is of very irregular character, thus
52G VACUUM TUBES AND THEIR OPERATION [Chap. VI
producing the scratchy note for couplings indicated by the dotted line
in Fig. 134.
Regenerative Circuit for Short-wave Spark Reception.—For short-wave
reception, say less than 400 meters, probably the most satisfactory type
of circuit is one which uses no other coupling between the grid and plate
circuits than that due to the capacity coupling in the tube itself. In
this scheme the " tickler " coil of Fig. 127 is replaced by a small vari
ometer, not coupled to the L2 — C circuit at all; the required amount of
inductance in this variometer varies with the wave-length, type of tube,
etc., but is generally less than 1 milli
henry. It is best to add in the Li—C
circuit another variometer about the
same as that used in the plate circuit,
thus making it possible to tune the closed
circuit with very small value of C.
The L2—C circuit is carefully tuned
to the incoming signal and the regenera
tive action is brought to its maximum
permissible value by suitably adjusting
the variometer in the plate circuit. As
the plate inductance is increased, a slight
Increasing M further adjustment of the closed tuned
Fio. 134.—If the tickler coil is used circuit is generally required in order to
when reserving spark signals (of get maximum sensitiveness,
sufficiently low decrement) the Behavior of a Regenerative Receiver
signal will increase very rapidly Regarding Sound of Signal, etc.—There
as tickler is increased until this . . ,. .
passes its critical value; the tube -are many interesting phenomena con-
starts to oscillate and then the nected with the adjustments of this re-
signal, although very loud, loses generative circuit other than those already
its characteristic musical note and mentioned, When M is made just greai
becomes "mushy" in quality. enough to produce oscillations (slightly
greater than OA, Fig. 134) the detecting
efficiency of the circuit is greatly increased, so much so that spark signals
so weak as to be entirely inaudible with tickler coupling just less than
the critical value become quite loud when oscillations start. In this
case the listening operator gets no clue to the identity of the sending
station from the spark note because the signal is inaudible until the
tube is oscillating, and then the distinctive spark note is not present.
If such a weak signal is coming in and the closed circuit is properly tuned
to it (with tickler coupling about equal to its critical value), a peculiar
effect is produced by the adjustment of the antenna circuit. With this
circuit much detuned of course the signal is inaudible; as the antenna
loading coil, or similar adjustment, is increased the signal becomes audible
BEHAVIOR OF REGENERATIVE RECEIVER 527
Fig. 136.—It is impossible to work tubes in parallel, with their filaments in series,
because of the greatly different filament currents resulting in the different tubes.
be used in the filament circuit, yet the filament current must be fairly
large because the plate current must not be more than about 15 per cent
of the filament current, and this plate current must be a considerable
fraction of an ampere unless excessively high voltages are used.
As the ordinary electrical power supply is 110 volts, it might seem
that if tubes are to operate in a group several filaments might be con
nected in series, thus saving in power assumption; thus five 20-volt
filaments might be operated on a 110-volt line and still leave enough volt
OPERATION OF POWER TUBES IN PARALLEL 529
scheme for using two kenotrons (rectifiers), A and 7?, connected to a high-
voltage winding in such a way that the plate of the three-electrode gener
ator C receives unidirectional pulses which serve in place of a continuous
current supply. By the use of suitable condensers, D, and choke coils,
E, the power supplied to the plate of C may be made as uniform (free from
pulsation) as may be desired.
The four transformer coils shown, F the primary, G and H low-volt
age secondaries and /, high-voltage secondary will all be wound on the
same core; the low-voltage winding H must be protected from the other
windings and core by high-voltage insulation because it assumes a high
positive potential as soon as operation of the set begins. If the voltage
desired in the plate of tube C is 2500 volts the winding J should have a
voltage rating of 5000 or 6000 volts (effective).
Fia. 139.—Illustrating the action of the rectifier tubes, in connection with condensers
D-D (Fig. 138) to give the variable unidirectional voltage a-b-c-d.
Instead of using several condensers and choke coils to smooth out the
pulses of e.m.f. supplied to the plate of the power tube a single condenser,
of sufficient capacity, might be used without choke coils The required
size of the condenser can be readily calculated if we assume the permissible
variation in voltage applied to the plate.
Let us suppose the voltage furnished by one half of transformer I
is given by the equation e = Em sin wt and is shown in Fig. 139 at curve 1;
this voltage is operative in one rectifier circuit and the voltage operative
in the other rectifier circuit is shown at curve 2. The average voltage
impressed on the plate of the power tube is shown by the dotted line V0,
and the actual voltage is shown by the broken line a-b-c-d. At time h
the condenser D (Fig. 138) begins to charge because the voltage operating
in rectifier A circuit becomes larger than the potential difference of the
condenser plates. Neglecting the voltage required to cause saturation
current to flow in the rectifier (which will generally be small compared
to the voltage V„ and Em) we suppose t he charging current of the condenser,
ALTERNATING CURRENT SUPPLY FOR PLATE CIRCUIT 531
/oX7r = /eX0 or 6
we have,
From this relation we get as the required capacity of the condenser, after
using the value of 8 given above
(102)
Em = -^=2050 volts.
the operator notices at once that the tube is not oscillating the plates
will rapidly become overheated and the tube perhaps spoiled. To avoid
this contingency a separate exciting tube may be used, this tube furnish
ing only enough power to operate its own circuit and supply the losses
in the grid circuits of the group of power tubes. Such a scheme is shown
in Fig. 140; the exciter tube A is adjusted with tight coupling between
Z/2 and L\, so that it oscillates under any condition which may occur, and
the power tubes M, N, etc., are each excited by a common connection
to tube A. By adjustment of the condensers C\—C2, etc., the output of
each power tube may be controlled, this control being in addition to that
Load Circuit
Fia. 140.—When many tubes are to operate in parallel it is generally best to excite them
from a separate tube A, self-oscillating, controlling the amount of excitation by
condensers Ci— Cj, etc.
afforded by the filament current. The frequency of the exciter circuit
must of course be that required for resonance in the load circuit of these
power tubes.
In case the individual control of the excitation is not desired a common
adjustable condenser may be inserted in the exciter lead where indicated
by the dotted lines at X; this condenser should have a reactance about
equal to the impedance of the combined input circuits of the power tubes.
Although the largest tubes made to-day permit a power consumption
in the plates of not more than 250 watts, thereby limiting the power out
put to about twice this amount, it seems likely that tubes of much greater
capacity will soon be obtainable; water-cooled plates are an obvious
necessity and a steel tube, instead of glass, with continuous pumping
by a mercury-vapor pump during use, seem to be likely developments.
Another scheme for using an exciter tube for maintaining the power
tube in oscillation is shown in Fig. 141. In this case the exciter tube
534 VACUUM TUBES AND THEIR OPERATION [Chap. VI
4^
electron current away from the surface to which the first electron is
traveling.
The number of electrons taking part in this reversed current depends
upon the number caused by the secondary emission
and upon the potential of the surface attracting them.
Suppose the arrangement of electrodes as given in
Fig. 142; the grid is at higher potential than the
plate and so attracts most of the electrons caused by
the normal thermal emission from filament F. How
ever, some of these electrons will go through the
interstices of G and impinge on P, causing secondary
Fio. 142.—Connection
emission where they strike. As G is at higher po of a three-electrode
tential than P, the electrons due to secondary emis tube to get the
sion are likely to go to G instead of re-entering P. characteristics of the
If the potential of G is held constant (contact B dynatron.
remaining fixed) and the potential of P is gradually
increased from zero by moving contact A to the right, the various
happenings will be about as shown in Fig. 143 Curve 0— A shows the
/B electron current to P
due to emission from F;
curve 0-B shows the
amount of secondary
emission from P, due to
electrons of current OA ;
curve C shows the frac
tional part of the second
ary emission which is at
tracted to G; curve O-D
shows the electron cur
rent away from P due
to secondary emission,
and curve OEFGH
shows the actual electron
current to P, all of these
curves being plotted for
increasing plate poten
tial.
The peculiarity of
Fig. 143.—Curves of various currents occurring in the that part of the curve
operation of the dynatron. from E to G is the basis
of action of the dyna-
tron; an increasing plate potential results in a decrease in plate
current, in other vorr's, an alternating-current test of the resistance
536 VACUUM TUBES AND THEIR OPERATION [Chap. VI
i =io — . (103)
r
where i = plate current;
io = value of plate current obtained by
projecting the curve GFE back
to v =o as shown in Fig. 143;
r= internal resistance of the tube,
determined from the slope of
F'of Thi^XTrode thG GFE CUrV6'
tube w l'dynlZn. Transposing the terms of Eq. (103) we have
v =r(i0 — i)
If the voltage of the battery B (Fig. 144) is E and the drop across the
resistance R is V, then
E = V+v = Ri+r(i0-i) =(R-r)i+ri0 = (fi r)F+rt0.
Then
dV R
(104)
dE R-r
As R-r may be made small, it is evident that a small increase in E, the
voltage used in the plate circuit, may result in a much larger change in
the voltage drop across R. It has been possible to regulate the tube so
that an increase of one volt in E has resulted in a change of the potential
difference across R of 100 volts, thus giving a voltage amplification of
100 times.
The dynatron may be used as regenerative detector, oscillating detector
of continuous waves, or as a generator of alternating-current power just
as can the ordinary three-electrode tube; it is not evident, however, that
it has any advantage over the three-electrode tube as ordinarily used.
It is possible to add a fourth electrode to a dynatron and thus make
it act as a normal three-electrode tube in addition to the effects obtained
from secondary emission. A possible connection of such a tube (called
the pliodynatron) is shown in Fig. 145. By suitably adjusting the two
e.m.f.'s OB and OA, the circuit may be made to oscillate at a frequency
7Yioa«is shjax jo saanx Z8S
0OOH-
+■ 006
H 008+
\ 1' UUL
1 "i (
V du <J! tll\ "1
s o p. J III XII. 1 / n y lilll
jojj gnoUBA pjtnd hrjioA S3 // • 009+
/ i 000
srl/ /
i/ QC S}|0.1 + oot
008+
—
003+
:_ + 001
0
001-
——
08- Of— 08- 0Z- 01- 0 + 01 - OZ 06- 0E- - 09 - 09 01- 08- - 06 001-
PHO IBnno)od
•oij -$fi — uohbuXq so^suapttitnp u; ws Arempjo auoqdap^ M}TOdoj •aqn^
538 VACUUM TUBES AND THEIR OPERATION [Chap. VI
-BO -40 - 30 - 20 -10 0 +10 1 20 +30 +40 +50 + 60 +70 +80 +90
Grid potential
Fig. 147.—Dynatron characteristics in an ordinary telephone repeater tube.
nary telephone amplifying tube operated outside its normal range. This
tube normally operates with a negative grid, but by carrying the grid
through sufficiently high positive potent ials the form of its current is made
to resemble that of the dynatron very closely. The tube was not pumped
to as high a vacuum as are the dynatron and pliotron, so that there was
more gas present in this tube, but the regularity of the curves and the
fact that they could be duplicated as many times as desired shows that
THREE-ELECTRODE TUBE AS POWER CONVERTER 539
however much gas there was present, it was playing a minor role in the
action of the tube.
Detailed Study of the Three-electrode Tube as a Power Converter.—
The foregoing analyses of the conditions for oscillation of a three-electrode
tube have all been based on the assumption that the plate current in the
oscillatory condition could be sufficiently well represented by a constant
current with a sine-wave current superimposed, and on this basis we
have shown that the theoretical maximum output of the tube was one-
900
8)1
Ai ipl fy nj.' tul
h = 1.<HI 11 II) p TUO
c irv •s ( tsrid .mi rei t BOO
for varioii< plat oltase
^nn
—
——— 100
h 5 vi .Its j
803
s / 00 vol S j/ 1
— la9 200
/is 5 v olti/1
1 r B T 100
■z
1 R s ss ■
.,11 0
1
J.
- — LOO
X) ■oil
200
-60 -60 -40 -30 -20 -10 0 tlO +20 +30 +40 + 50 +60 +70 +80 +90 +100
Grid potential
Fia. 148.—Dynatron characteristics in an ordinary telephone repeater tube.
half of the input; the fact was also mentioned that the conditions demanded
for this efficiency of 50 per cent could not be realized, so that we were
forced to conclude that the maximum efficiency of a tube generator was
about 40 per cent.
The author with the assistance of Mr. H. Trap Friis 1 carried out a
detailed study of the tube generator for both separate and self-excitation,
and it was found that the efficiency might become very much higher
when the proper adjustments were made; part of the results of this study
1 Proceedings of A.I.E.E., Vol. 38, No. 10, Oct., 1919.
540 VACUUM TUBES AND THEIR OPERATION [Chap. VI
will be given here, as they show exactly how a tube functions. The nota
tion used in this analysis is somewhat different from that used so far
because the previous symbols are not applicable. The plate current can
not be represented by Iop-\-Imp sin ut, as has been previously assumed;
it consists of a series of pulses so that an infinite series of sine terms would
be required to represent the alternating component. The plate voltage
also does not have exactly a sinusoidal variation. We therefore represent
the instantaneous value of the actual plate voltage by ep, grid voltage
by e,, plate current by i„, grid current by it, etc., instead of representing
each by a constant plus a sine term.
Oscillograms were taken to show the various quantities entering into
the operation of the tube and circuit, the frequency of the alternating
current being between 100 and 200 cycles; later the circuit constants
were diminished sufficiently to raise the frequency to 100,000 cycles, to
show that the re
sults obtained at
the lower frequency
(which allowed ac
curate oscillographic
records to be ob
tained) were valid
at radio frequencies.
The first effect
studied was the
change in form of
e, and ip as the
excitation of the
grid was increased,
Fia. 149.—Connection of power tube for study of its using a separately
characteristics. excited circuit as
indicated in Fig. 149.
The reactance of Ci was 62 ohms and of L\ was 8700 ohms; the value
of R was 1000 ohms and the resistance of Li was 190 ohms. The no of
the tube used was 3.9.
With comparatively low values of Ec and E, a record was taken of
e», e,, and ip, and is given in Fig. 150; it is seen that the fluctuations in
Cp and ip were nearly sinusoidal so that the results of the previous analysis
would hold good for this condition. Upon increasing e„ to six times
its value the forms of ep and ip are made to differ widely from sine forms,
however, as shown in Fig. 151.
An interesting point is shown by the film; the value of R used was
1000 ohms and this is the value which gives, for this tube, maximum out
put for low values of E„, as shown in Fig. 94. This value 1000 ohms
THREE-ELECTRODE TUBE AS POWER CONVERTER 541
must therefore be the tube resistance Rp for the low value of E„. But
with large excitation used in Fig. 151 the plate current evidently fluctuated
as much as possible (from zero to saturation current) and the fluctuation
in ep is less than half of Eb, indicating that R should be more than doubled
if maximum output is to be obtained from the tube. This it will be remem
bered has been predicted as necessary when iv fluctuates between zero and
saturation current, and ep fluctuates between the limiting values of zero and
2 E0p. With a resistance load of the kind shown in Fig. 149 it is evident
that such a wide variation in the value of ep is impossible; the load cir-
Fio. 150.—Nearly sinusoidal variations in ep and ip for low grid excitation. 2?&=900
h = .25, £e = 120, E„ = 50, Frequency = 140, fl = 1000, C = 18.4 microfarads.
cuit must contain inductance and capacity to cause eP to fluctuate so
widely. This point is taken up later on in this section.
If R is still further reduced the distortion in ep and ip will appear with
much lower values of Eg; in Fig. 152 is shown a record for a value of
Eg of 100 volts with R only 100 ohms. The fluctuation in ep is now
hardly noticeable although ip fluctuates, with distorted form, from zero
to saturation current as before. The current taken by the grid in Figs.
150 and 152 was zero; in Fig. 151 the grid swings positive 300 volts so
we might expect a large grid current, but it is shown to be small. This
is due to the fact that the plate is at rather high potential (650 volts)
during the time the grid is positive, so that but few electrons go to the
grid.
542 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Fig. 151 shows also the fluctuation of h; in spite of the large induct
ance L\ (which was 10 henries) there is considerable variation in h- This
must of course always be the case; the value of Li ~ must at any instant
at
be equal to the difference between Eb and Cp.
Fig. 151.—Distortions occurring with higher grid excitations. i?j>=900, /& = .34,
EC = \2Q, Eg = 300,/= 140, tt = 1000, C = 18.4M/.
In Fig. 153 are shown the curves of ep, iv, and e„ for two values of
R, all other conditions being the same; it may be seen that the amount
of distortion in iP is reduced as the value of R is increased. In getting
these two films the value of L\ was kept constant, with the result that
a THREE-ELECTRODE TUBE AS POWER CONVERTER 543
Fig 152.—Witn low load circuit resistance distortions occur for even low grid excitation.
E» = 900, /4 = .34, £c = 120, tf, = 100,/=140, fl=100, C = lS.4tpf.
Fig. 153.—Showing effect of load resistance on forms of voltage and current, other con
ditions constant. For both films £6=900, £c = 120, £, = 100 and /= 140. For
left-hand film h = .295, R = 1000. For other Ib = .272, It = 201 n.
544 VACUUM TUBES AND THEIR OPERATION [Chap. VI
Fia. 154.—Connection of the power tube to a tuned output circuit, showing where oscil
lograph vibrators were introduced and directions of current assumed as positive
(above zero line in oscillograms).
for each condition the forms and phases of currents and e.m.f.'s. The
tests were run at low frequency so that oscillograph records might be
obtained; the results obtained were duplicated later in a high frequency
run.
Fig. 154 shows the circuit used; simpler ones may be used, but the
laboratory apparatus at hand was best suited to this one. The diagram
also shows where the oscillograph vibrators were introduced and the
direction of currents assumed as positive; if, on a film, a current is shown
below its zero line, it was flowing in the opposite direction to that shown
in the diagram. If the frequency of the exciting voltage, E„, is chosen
the same as the resonant frequency of the load circuit
THREE-ELECTRODE TUBE AS POWER CONVERTER 545
the tube when the output is forced as high as possible. They did bring
out the fact, however, that the filament ammeter, if a continuous-current
instrument, does not read correctly the filament current when the tube
is generating alternating-current power. The ammeter indicated 3.65
amperes when getting the curves of Fig. 156 and the total emission for such
a current is evidently about 0.5 ampere. Now when the tube was oscillut
THREE-ELECTRODE TUBE AS POWER CONVERTER 547
ing, the filament ammeter reading 3.65 amperes, the total emission was
about 0.8 ampere, showing that the filament temperature was much hotter
than when not oscillating. Holding the voltage across the filament constant
(approximately the condition when the tube is oscillating) the set of curves
Amp.
1+ I —v
E A" cf* 3.6
J R^OQ—f
3.2«
3.0
0 80 1B0 210
E b Plate Voltage
Pio. 157.—This set of curves shows how the filament current changed as the plate
voltage was increased; even with 3.75 amperes in that end of the filament carrying
the larger current the emission was only .5 ampere, whereas when oscillating this
same tube gave an emission of .8 ampere with an indicated filament current of only
3.65 amperes.
given in Fig. 157 were obtained. The grid was held at a positive potential
of 100 volts and the plate voltage suitably varied. The electron current
to the plate increases the filament current at one end and decreases it
at the other; the relative values of increase and decrease will be deter-
THREE-ELECTRODE TUBE AS POWER CONVERTER 549
mined largely by the resistance used in series with the filament battery.
It can be seen that even with the larger filament current as great as 3.75
amperes the emission was only 0.5 ampere.
From some preliminary oscillograph records we knew that in oper
ation the total emission was about 0.8 ampere when the filament ammeter
read 3.65 amperes. A brief test showed that the filament current required
5
- >o
'o
cu
1
.7 ^>
r h
c
£.6
O
Cl
aC
m I F=4.0 Am P.
g"4
T \\
IF=3.6 i Amp.
v I,
» I'M
80 no 100 200 240 280 320 GO Vo-UJ
Ej Plate Volt.«3
Fig. 160.—As the curves of Fig. 159 are important, and they were obtained by extra
polation, they were verified for. correctness of form by picking off from Fig. 158 a
similar set of curves for a filament current of 3.65 amperes; evidently these curves
are of the same form as those of Fig. 159.
Fia. 161.—In this figure various forms of plate current have been assumed and (plate
voltage remaining fixed in shape) the resulting efficiencies calculated.
552 VACUUM TUBES AND THEIR OPERATION [Chap. VI
whereas it took about 1000 volts; although the plate current is small
with a grid negative more than 300 volts this small current has a marked
effect on loss of power on the plate, because of the very high plate voltage
during that part of the cycle when this small current is flowing to the
plate.
Experimental Proof of Foregoing Theory.—To test the validity of
the ideas presented above a series of runs were made with the tube, using
the circuit given in Fig. 154 and the results therefrom are shown in Table
I. The frequency was kept at the resonant value for the output circuit
and each time a set of readings was taken the value of R was changed
properly to maintain the current in the oscillating circuit constant. This
Amp.
.2
4* 1 E(,=1<X 0 Volts
□
1-15
2CS \ 1^ = 8.65 Amp.
E
*.l
n*
0
-200 -300 -100 -500 Volts
Ec Grid Voltage
Fig. 163.—The tube used in the tests did not have a constant value for ^i0; theoretically
a negative potential of 260 volts should have reduced the plate current to zero.
This tube would have required about 1000 volts (negative) on the grid to completely
cut off the plate current.
was necessary in order to keep the form of the voltage ep constant as the
values of Ee and E„ were varied. While it was not thus pointed out
in discussing the current forms of Figs. 161 and 162, the values of Ec
and E„ are the factors which bring about the change of current form as
the form of ep is maintained constant. The form of current shown in
(a) Fig. 161 was obtained with relatively low Ec and E„ the value of
each of these being increased for the succeeding diagrams of the figure.
In Fig. 164 are shown the efficiency curves for the various runs of
Table I and on the curve sheet are given the calculated values of the
maximum positive grid potential for that condition in each run which
gave maximum efficiency, as indicated at a, b, c, d, etc. For the com
paratively low value of current in the oscillating circuit which obtained
THREE-ELECTRODE TUBE AS POWER CONVETER 555
TABLE I
Eb -1000 volts. G«=2MF. Ci -3.91mP. ~=H0. L, =9.SH. //=3.65Amp.
E, 7. Output Output
Run. Be effective Input effective R ,_ Input
volts. volts. watts. amps. ohms. watts. %
120 220 334 0.98 149 143 42.8
150 220 298 1.00 149 149 50.0
180 220 214 1.02 119 124 51.5
210 220 186 1.00 89 89 47.8
250 220 119 0.96 42 39 32.8
150 260 302 1 00 149 149 49.3
180 260 273 1.03 149 158 58.0
210 260 241 0 99 149 149 60.5
240 260 197 0.99 119 117 59.5
270 260 161 0.96 89 82 51.0
150 300 302 1.00 149 149 49.3
180 300 283 1.02 149 155 54.8
210 300 261 1.02 149 155 60.0
240 300 246 1.00 149 149 60.8
270 300 212 0.98 134 129 60.8
A 180 340- 291 1.01 149 152 52.3
210 340 278 1 03 149 158 56.8
240 340 265 1.04 149 161 60.8
270 340 244 1.01 149 152 62.4
■ B 300 340 229 0 99 149 146 63.8
330 340 186 0.99 119 117 63.0
270 400 260 1.02 149 155 59.7
300 400 250 1.03 149 158 66 3
330 400 235 1 02 149 155 66.0
360 400 222 1.00 149 149 67.3
390 400 197 0 96 134 124 63.0
420 400 150 1.02 89 93 61.8
C 450 400 126 0.98 74 71 56.3
D 410 460 228 1.02 149 155 68.0
420 500 245 1.05 149 164 67.0
450 500 237 1.04 149 161 68.0
480 500 222 1.01 149 152 68.6
510 500 195 1.04 119 129 66.2
540 500 176 1.02 104 108 61.5
570 500 157 1.04 89 96 61.2
556 VACUUM TUBES AND THEIR OPERATION [Chap. VI
during these tests the form of plate voltage is somewhat different from
a sine wave, and the variation of best grid potential may have been due
to this cause. The increase in efficiency with increase of E, and Ec is
as would be expected from the analysis given for Fig. 161.
Fio. 164.—Efficiency curves plotted from Table I; the values of positive grid potential
for maximum efficiency in each run is calculated and recorded. This agrees well
with the predicted "best grid potential."
A series of runs was then carried out (results given in Table II) to study
the effect of varying the value of the minimum plate voltage, other con
ditions remaining the same; this was accomplished by varying R, thus
cutting down the value of the oscillating current and hence the variation
of voltage across the condenser C\, Fig. 154. The variation of potential
TABLE II
£6 = 1000 volte. Ct-2„F. d=3.91^F. ~=138. U =9.85. I/=3.65Amp.
ep E0 I: Output Output
Run. min. Ec effective Input effective R -JiiV * Input
volts. volte. volts watts . amps. ohms. watts. %
A 30 270 300 134 1.12 37 46.5 34.7
100 270 300 179 1.10 85 103 57.5
160 270 300 204 1.02 117 122 59.8
250 270 300 217 0.91 149 123 56.8
B 490 270 300 25.5 0.60 297 107 . 42.0
THREE-ELECTRODE TUBE AS POWER CONVERTER 557
the record shown in Fig. 167; in fitting the various films together care
was taken to see that they had their proper respective phases. The
white fine drawn vertically through all the records gives a fine of equi-
phase.
This set of curves gives the complete story of the circuit and tube.
The plate current is very nearly the form shown in Fig. 162, and the plate
potential is nearly of the form shown in condition (a) of the same figure.
The slight depression in the peak value iv is due to the grid taking some
current, this depression coinciding in time with the peak of grid current.
The form of the positive alternation of the i curve is not like those pre-
viously given, due to the fact that it has been assumed that 7» was con
stant whereas it actually had considerable fluctuation, as shown in the
record. If the coil used for L\ had more inductance this variation in
h would be diminished; we had only 10 henries with a resistance of 189
ohms, the coil being air core. In practice an iron core coil of greater
inductance would be used, but we did not want to introduce any other
sources of distortion than the tube itself.
The form of current in condenser Ci differs from that in condenser
C2 because of the effect of i which will practically all flow through C\
for the circuit as arranged.
The grid current has just the form and magnitude predictable from
THREE-ELECTRODE TUBE AS POWER CONVERTER 559
Fig. 159; the amount of current taken by the grid in this test and the
values of E„ and Ec used caused a loss of power on the grid (due to
bombardment) of about 10 watts.
Fig. 167.—Oscillogram of all the currents and voltages for Run B—Table I; the white
line represents the same phase on all films. The calculated efficiency from the eviv
and evi areas agrees well with the calculated efficiency.
The two filament currents, if and i'f, have forms which might be pre
dicted from curves similar to those given in Fig. 157; in that end of the
filament carrying the larger current the continuous current ammeter
measuring the current indicated only 3.05 amperes, whereas the current
560 VACUUM TUBES AND THEIR OPERATION [Chap. VI
meters in the test. The value of 63.8 per cent given in Table I was the
value obtained when the oscillograph circuits were not connected, the
closing of the circuits changed the conditions enough to drop the efficiency
to 59.5 per cent.
Fig. 168 shows the form of ip which is predicted from Fig. 159 after the
forms and magnitudes of ep and e„ have been assumed; this form of ip
is very close to the actual form given in the oscillogram of Fig. 167.
The result of our tests and analysis have then shown that the efficiency
of a tube as a converter can be accurately predicted from the three sets
of curves given in Figs. 156, 159, and 163 after we have determined, from
the curves of Fig. 159, what the best minimum plate potential is and
also what the maximum positive potential of the grid should be.
lie,
Fig. 169.—Arrangement of the tube circuit for self-excitation; the machine Ec main
tains the grid at the proper average potential.
To get a fair efficiency (60 per cent or better) the value of h should
not be greater than 25 per cent of the saturation current of the tube;
with the efficiency known and the safe radiation of power from the plate
being known the proper value of Et, is fixed.
Self-excited Tube.—Using the circuit and constants used in getting
the records of Fig. 167 an attempt was made to run the tube self-exciting
by changing the connections slightly as shown in Fig. 169. The choke
coil Z/2 serves to prevent the grid from being short-circuited to the filament
(for the a.c. excitation) through the machine Ec. The voltage for exci
tation was obtained from the drop across the condenser C2, the insulating
condenser C3 being necessary to prevent short-circuiting the machine
Ei,. With this connection the grid does not get quite as much excita
tion as shown by the curve eCj in Fig. 167, because an appreciable part
562 VACUUM TUBES AND THEIR OPERATION [Chap. VI
of this voltage is used in overcoming the reactance drop in C3. (In this
calculation the capacity of the grid circuit of the tube itself must l>e con
sidered; in some of the Type P tubes this capacity is as high as 500 mif,
when the load circuit has its proper impedance for maximum output-
see p. 442.)
The circuit of Fig. 169 refused to act as it did for the separate excita
tion, giving a small output at a low efficiency; a more careful exami
nation of the record in Fig. 167 gave the reason. The alternating com
ponents of e„ and e„ must be exactly 180° out of phase if the maximum
output and efficiency are to obtain, as becomes at once evident if the
construction of Fig. 161 be carried out for any other than the 180° rela-
Fig. 172.—In this case of the self-exciting tube the plate voltage did not fall sufficiently
low to give best efficiency; it measures on the film 300 volts where as Fig. 165 shows
the proper minimum plate potential to be KM) volts.
THREE-ELECTRODE TUBE AS POWER CONVERTER 565
Fig. 173.—Separately excited tube—Eb = 1040, /(, = .170, Ec=270, £„=300, R=37.
Input = 106 watts. Output = 50, Efficiency = 47%.
volts, 72 =8.0 ohms. The current produced in the oscillating circuit was
4.40 amperes, resulting in an efficiency of 57 per cent.
Fig. 172 shows the currents and voltages in this self-exciting circuit,
and it is at once evident why such a comparatively low efficiency was
obtained; the minimum plate voltage, instead of being 200 volts, as it
should for this tube, was 300 volts. For this figure the curve of plate
current included also the alternating component of the grid current, hence
the absence of the depression at the peak value.
The current through the plate-current vibrator reversed during part
of the cycle, due to the fact that this vibrator carried in addition to the
plate and grid currents, an alternating current which resulted from the
voltage across the condenser Ci acting through the reactance of coil La and
THREE-ELECTRODE TUBE AS POWER CONVERTER 567
condenser C2, Fig. 169. This current is shown as ix in Fig. 172; when
the plate current is corrected by this small amount it is seen that the plate
current does not reverse, as we know it cannot with the conditions as
they existed in this test.
Action of the Tube at High Frequency.—It was desired to show that
the action of the tube was just the same at high frequency as at the low
frequencies used, so a circuit was arranged similar to that of Fig. 169,
with smaller values of capacity and inductance. The choke coils L\
and Li used in the previous tests would act as condensers of comparatively
low reactance at the high frequency to be used so they also had to be
The conditions obtaining when Fig. 177 was taken show the best
adjustments for efficiency which we were able to get with the Type P
tube; the high efficiency was obtained without unduly decreasing the
output. If this form of plate current could be maintained and the value
of Ed be increased to 3000 volts the calculated efficiency becomes So
per cent; this is probably as good as could be done with sine wave
shapes of ep and eg, but it seems as though, by suitably deforming both
of them, giving them both flat tops, the efficiency could be considerably
increased over this value.
M
Fig. 176.—Conditions as given in Run C, Table I.
Tests similar to those described in this paper were carried out using
a much smaller tube, that styled by the U. S. A. Signal Corps type VT-2.
The results obtained with the large tube were duplicated almost exactly
in so far as efficiency was concerned. It was found possible to so adjust
the values of Ec and Ec that the tube gave an output of 6.3 watts with
an efficiency of 70 per cent, the voltage used in the plate circuit being
the rated value, namely 300 volts. It was found possible to get over
7 watts output with the plate loss considerably lower than its safe rated
value; if the plate voltage had been increased to perhaps 400 volts the
tube output might have been raised to 10 watts while still having the
plate loss within its safe value.
These tests were all carried out with a separately excited tube; with
THREE-ELECTRODE TUBE AS POWER CONVERTER 569
the tube self-excited the efficiency was not obtained higher than 61 per
cent, with a plate voltage of 300. This run gave an output of 5.6 watts
output with a current h of 0.305 ampere; the frequency was 400,000
cycles, the value of R was 53 ohms, the oscillating current 0.325 ampere,
Ci and C2 being 1360 and 770 micro-micro-farads, respectively. The
value of Ec was 40 volts.
With the conditions of a self-excited circuit adjusted for the best
conditions as previously outlined difficulty may be encountered in start
ing the circuit to oscillate, a shock of some kind being generally required
to start oscillations. Because of this possible difficulty it may be the best
Fig. 177—Best conditions for high efficiency. Eb = 1040, h = .286, Ec - 410, E, - 460,
ft = 149, Input =227 watts, Output = 155, Efficiency =68%.
practice' to run these tubes separately excited, using one tube (so adjusted
that it oscillates readily) for exciting others as indicated in Figs. 140-141,
pp. 533-534. It may well be that with a higher resistance in the oscil
lating circuit more output can be obtained from two tubes if one only
is used as a generator, the other being used as exciter only. Certainly
if more than two tubes are to be used it will be well to use one as exciter
for supplying the grid voltage for the others.
Characteristics of the Circuit of Fig. 122.—Using the circuit shown in
Fig. 122, a series of runs was made to investigate the effect of changing
the constants of the circuit and some of the results are shown in Figs. 178
570 VACUUM TUBES AND THEIR OPERATION [Ghap. VI
and 179; the legends and diagrams on the curve sheets make them self-
explanatory. For these tests three pliotrons (type P-30) were operated
in parallel, all grids being connected together as also were the plates; the
plate current recorded on the curve sheets is that of one tube.
It may be seen, from Fig. 178, curve 3, for example, that for efficient
coils and condensers of the type used here it is possible to get as much
as 16,000 volt amperes from one tube, with only 800 volts on the plate
and normal filament current. The behavior of the tubes, as regards
0123456789 1000 1 2 3 4
Value of Lp in to-5 henries
Fig. 178.—Amount of high-frequency power obtainable from three Type P plitrons in
parallel and effect of changes in La.
stability, conditions for maximum output, etc., agree fairly well with the
theoretical predictions.
Characteristics of the Three-electrode Tube as an Amplifier.—As the
voltage impressed on the input circuit of a tube causes a change in the
plate current which may be flowing through an inductance or resistance
in the external plate circuit, and as it is evident that the drop across this
external circuit may be many times greater than the e.m.f. impressed on
the grid, the device may be used as a voltage amplifier. The amplified
voltage in the output circuit will have very nearly the same form as the
input voltage, sufficiently so that the currents due to speech may be
THREE-ELECTRODE TUBE AS AMPLIFIER 571
I ! ! I I I ! ! I I I I I 1 1 I ! I I I I I I I ! I I I—!—!—!—!—1
100 -Mi :juU 400 500 ooo TOO S0J UOO 1000 1100 1200 1300 1100 1300 lbOO
Value of Lpln microhenries
Fig. 179.—Showing the effect of varying the plate circuit inductance with fixed value
of Lg. Region of oscillation indicated by solid lines; outside these limits tubes
refused to oscillate.
dance in the plate circuit and the resistance of the tube itself. If we call
the alternating component of the plate current Ip we have the relation,
(105)
in which R is the external resistance of the plate circuit. The drop across
R (which is the only available part of the amplified voltage, the rest being
used up inside the tube itself) is IPR and this is evidently given by
R
IPR = EV = £>o p.r,.
572 VACUUM TUBES AND THEIR OPERATION [Chap. VI
From this we get the actual voltage amplification due to the tube, which
is designated as p,
R
"-*°i£+i2 (106)
wave of current in the plate circuit and so will not produce a sine wave
of voltage across a resistance in the plate circuit.
fication constant of the Signal Corps VT-1 tube taken under various
conditions. It is seen that the factor fi increases as R increases, for all
conditions.
Curve 1 was taken with a constant " B " battery voltage; under
this condition the plate voltage decreased as R was increased due to
the resistance drop in R. But a decreased plate voltage resulted in an
increase in Rp, so that for this condition as R was increased, it approached
Rp very slowly due to the increase in Rp with increase in R.
1U
Flo. 182.—Showing effect on the amplifying power of a tube of holding the grid at
different average potentials, making the grid more negative increases the tube
resistance, hence requiring a higher external resistance to get the same amount of
amplification.
T> pu u
If =1. ill
,Tnal esi ice in
\platC V re ■ it = :20, MO oh US
—
\
\ \
\ \ 0 v .u- in i! tatter
/]_ □Z \ K n
i \
/ \
I / / \
0 v ilt I
\
/ / \
/ / \
/ / / — \
< < u J v ilt i
_ —
1 \
1 i■ r
I i \ 1 \
\\ 1151 vdlts
100 ¥ ilti
Value of E0
Fig. 183.—Variation in amplifjdng power with different grid potentials and different
plate circuit voltages.
1000
3 4 5 6 7
Volts impressed on grid (values effeotive)
Fig. 184.—The quality of amplification (distortionless or not) is shown by a test of this
kind. The tube used requires an external resistance in series with the plate of at
least 150,000 ohms to givi distortionless amplification.
THREE-ELECTRODE TUBE AS AMPLIFIER 577
The first term gives the steady value of plate current with no input volt
age, the second the true amplification current, the third a double-frequency
distortion current, and the fourth a steady increase in the value of ip,
while Ems sin wt is acting. The third term has the same coefficient as
the fourth and the fourth term will register on a direct current ammeter
in the plate circuit. Hence the quality of amplification of a tube (distor
tionless or not) may be judged by the indication of the plate ammeter
as the input voltage is impressed. Fig. 184 shows this effect and also
the effect of added resistance in the plate circuit in decreasing the distor
tion. With 150,000 ohms added in the plate circuit, this tube would
give essentially distortionless amplification for input voltage as high as
5 volts.
In case a reactance is used in the plate circuit, for repeating, instead
of resistance, it will be found that the value of n is greater than for a
corresponding value of resistance. Thus if an inductive reactance (of
negligible resistance) is used in the plate circuit, the value of the react
ance being equal to the tube resistance, a value of n is obtained equal to
0.7 £io instead of 0.5 mo as was obtained for resistance. This follows at
once by considering the voltage relations in a tube circuit, as given in
Fig. 96, p. 475.
CHAPTER VII
CONTINUOUS-WAVE TELEGRAPHY
reached at much greater distances from the sending station than with
the spark transmitter.1 Also, for the same range, less power is required
than with the spark transmitter, and the transmission efficiency thus
improved.
3. Antenna Voltages Decreased.—Since the energy is radiated in a
continuous stream, when a signal is being sent, and not in groups, it follows
that for a given power in the antenna the amplitude of the oscillations
need not be so great. For example, if we assume 1000 sparks per second,
a decrement of .1, and a 300-meter wave, the time per second during which
energy is radiated 2 is:
mission, very much higher than could be obtained with the damped-
wave type. In addition may be mentioned the very important part
which continuous waves have played in the development of radio telephony
(see Chapter VIII), for which it is essential. Because of these advantages,
it is probable that continuous-wave telegraphy will ultimately supersede
and replace entirely the damped-wave systems; in the large stations,
this change already has been made or is being made at the present time.
High-frequency Undamped-wave Generators.—Continuous high-fre
quency osculations may be produced by any one of the several schemes
described below. All of these have been commercially developed and
applied, and are listed in the order of their importance (this relative rating
being for high-power stations only) at the present date (1920). It is
probable that the first three means of generation will find increasing
development in the future, while the fourth and fifth will be superseded
by one form of the first three methods. The development and impor
tance of vacuum tubes as generators of high-frequency oscillations has
been very rapid within recent years, and it is likely that this source of
high-frequency power will ultimately replace all others.
The several means of high-frequency power generation are as follows:
(1) Poulsen Arc;
(2) Alexanderson Alternator;
(3) Goldschmidt Alternator;
(4) Iron in saturated cores;
(5) Marconi Series of Spark Gaps;
(6) Oscillating Tubes.
Poulsen Arc.—A great deal of work has recently been done in an effort
to determine with exactness the action and theory of this type of generator,
the best presentation being that of P. O. Pedersen 1 to which the reader
is referred. In the discussion which follows, we have referred largely
to his paper and to certain earlier theory as developed by Barkhausen.
to which Pedersen also makes reference. Much of the laboratory work
done in the past is not applicable to the modern arc generator, due to the
wide divergence of the test arc and the generator as designed and con
structed for commercial service.
Elementary Theory.—Instability of the Arc.—Consider the ordinary
arc circuit indicated in Fig. 1 with the resistance R omitted for the present.
The conduction of current through the arc is simply a case of conduction
through an ionized gas, in this case vaporized carbon or copper at a very
high temperature. Initially, this arc stream of ionized gas is not present,
so that to start the current flow in the above circuit, it is necessary to bring
the two electrodes in contact. The intense heat developed by the current
1 "On the Poulsen Arc and Its Theory," Proc. I.R.E., Vol. 5, p. 255, 1917.
THE OSCILLATING ARC 581
a variation in the current flowing through it, and the arc supply is there
fore not strictly a constant-current source. This variation may be made
extremely small, however, by using large inductance values.
A Simple Explanation of the Operation of the Oscillating Arc.—If a
condenser, in series with an inductance, is connected to a source of electric
energy, of voltage E, the current which flows after closing the switch is
an oscillatory one,1 its frequency being fixed by the natural period of the
oscillatory circuit and its magnitude depending upon the voltage E,
and the ratio C/L. This oscillatory current dies away due to the damping,
and the condenser is finally charged to a potential difference E, and there
is no current in the circuit.
Suppose an arc, connected as in Fig. 4, is burning steadily (switch in
the oscillatory circuit being open), with a difference of voltage across the
two electrodes equal to E. When the switch is closed the current flowing
in the L, C, R circuit is given by 2
(1)
through the arc and thus gives it greater than normal value. This results
in a decrease in voliage across the arc, thus tending to facilitate the dis
charge of the condenser, thus producing a greater discharge current than
would have occurred if the arc voltage had held constant.
It will thus be seen that the voltage-current characteristic of the arc
tends to give a greater current in the condenser during both the charge
and discharge periods, than would occur if the arc voltage were independent
of the current through the arc.
Now the current flowing into the oscillatory circuit is supplied when
the arc voltage is higher than normal and the current flows out of the
oscillatory circuit (against the influence of the arc voltage) when the arc
voltage is less than normal. As energy is being supplied to the oscillatory
circuit during the charge and extracted during the discharge, from the
conditions just cited it is evident that more energy is supplied to the oscil
latory circuit from the arc supply circuit during the charge than is given up
to the arc during the discharge. Unless too great a resistance is present
in the oscillatory circuit this action results in a building up of the current
in the oscillatory circuit, and this building up will increase until the maxi
mum value of the oscillatory current is practically equal to the generator
current, Io-
This action is shown by curves A of Fig. (5); the curves of which
are nearly self-explanatory; the current in the oscillatory circuit is reck
oned positive when it is flowing in the direction indicated in Fig. 4.
THE OSCILLATING ARC 585
The lower curve of Fig. 5 is the product of the current i and the voltage
acting on the oscillatory circuit. Area A gives the energy supplied to
the oscillatory circuit by the arc during the first alternation, and area
B gives the energy supplied by the oscillatory circuit to the arc during
the second alternation. The difference, A-B, gives the energy supplied
to the oscillatory circuit during the complete cycle, and if this is greater
than the PR loss in the oscillatory circuit during the cycle the oscil
latory current will continue to increase until some other factor controls the
action.
The excess of area A over area B depends upon the arc characteristic,
being greater as the characteristic curve (Fig. 2) becomes steeper; as to
whether or not the "excess is sufficient to build up oscillations depends
upon the resistance of the oscillatory circuit. These two factors control
completely the operation of the arc; it must be remembered, however,
that the relation between arc voltage and arc current used in plotting
Fig. 5 must be determined from the oscillatory state because the static
characteristic gives too great a difference in areas A and B. The vari
ation between the static characteristic and dynamic characteristic increases
with frequency, in such a way that at high frequency (say 500,000 cycles
per second) the difference between areas A and B is not sufficient to pro
duce much oscillatory power.
A simple arrangement of apparatus which has nearly the same action
as the arc is shown in Fig. 6. A source of e.m.f. is connected to a resist
ance R which is fitted with a sliding
contact, B. Between the lower point of
the resistance R and the contact B is
connected an oscillatory circuit consisting
of L and C in series.
Suppose that, with B in the middle of
R, switch S is closed; current will im
mediately start to flow as indicated by i, Fig. 6.—A simple circuit which may
charging condenser C. Now as C starts be made to operate the same as
to charge contact B is moved up on R, an oscillating arc.
thereby increasing the voltage impressed
on the L-C circuit. The motion of B is so regulated that it reaches B' in
an interval just equal to one-quarter of the natural period of L-C; it
then starts to move down on R and reaches point B" in an interval
equal to one-half of the natural period of L-C. Thereafter the contact
oscillates between B' and B", making a complete cycle in a time equal
to the natural period of L-C.
Such an arrangement will result in the building up of a large oscillating
current in the L-C circuit, the magnitude being limited only by the volt
age E and the resistance of the oscillatory circuit.
586 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
Fia. 8.—Supposed action of an oscillatory arc, the length of which is much less than
normal.
up to 1000 kw. (input) utilize what has been designated as the " normal
Poulsen arc." In this arc the ratio of direct current in the supply circuit
to the radio frequency current (effective value) is always equal to the
V2, or:
Iic = V2lac
where lac is the effective value of the current in the oscillatory circuit.
The normal arc therefore represents the division limit between oscil
lations of type I and type II, its characteristics being somewhat similar
to those of type I, as shown in Fig. 9.2
Professor Pedersen in his paper previously referred to emphasizes
the importance of the extinction voltage on the characteristics of the nor
mal arc. As the arc current approaches the zero value, the arc voltage
suddenly rises, as shown in the above figure. The arc must be able to
develop this voltage if operation is to be efficient. Previous theory has
1 Zenneck, "Wireless Telegraphy," p. 237.
» Ibid., p. 236.
THE OSCILLATING ARC 589
field consists in blowing out the arc and allowing a new arc to form at the
beginning of the next period, it is evident that its intensity will depend
on the frequency to be generated. Pedersen has found the proper field
intensity to be approximately proportional to the frequency. Thus with
an arc drawing about 20 amperes from the supply line, and an oscillatory
circuit with a ratio of Vl/C about 300, Pedersen found the most suitable
field strength to be given by the relation (H+400)X =5000, in which H
is in gausses and X in kilometers. With a hydrogen atmosphere it seemed
that a field about one-fifth as large as this was proper.
Action of the Gaseous Atmosphere.—The hydrogen or coal gas in
which the arc usually operates assists in cooling the electrodes, and thus
when the arc current falls to zero, the cooling action of the gas promotes
a rapid increase in the arc resistance (deionization). It also affects the
static characteristic, making it steeper than in air, as shown in Fig. 26,
page 141.
The reason for the hydrogen atmosphere thus steepening the curve
is not known, but the effect of this increase in slope upon the arc operation
is evidently to cause the arc voltage variation (which in turn acts to
charge the condenser) to be more sensitive and of greater amplitude for
a given arc current variation. The radio frequency energy input is thus
increased.
The foregoing features of construction are embodied in all modern
arc generators. Fig. 11 illustrates a 500 kw. arc (input rating), which
is much less than the maximum capacity to which generators of this
type have been built up to the present time.
Generators of 1000 kw. capacity are of the same general construction,
but somewhat smaller in size. The arc chamber is equipped with a water-
cooled jacket to assist in cooling the chamber, while the copper anode
has circulating water supplied to it by means of flexible pipe connections.
The negative electrode is usually of carbon, although graphite is being
largely used for the higher capacity arcs. The anode, as shown in the
figure, is equipped with handwheels to permit the accurate adjustment
of the gap length. The smaller wheels shown are used for clamping the
electrode into its proper position. The enormous size of magnetic circuit
apparently required for these large capacity generators is indicated in
Fig. 11 as well as in Fig. 12, which shows the generator with the electrodes
and arc chambers removed; the circuit shown in the latter figure is for
a 500 kw. arc, the upper pole piece having been removed.
Arc generators are most efficiently used at the longer wave-lengths
and are therefore usually operated at 3000 meters or above, 6000 meters
being the wave-length generally used. In some cases the wave-length
is as high as 18,000 meters. The capacities range from 100 kw. or less
up to 1000 kw.; 350 kw. arcs are generally used for high-power land
592 CONTINUOUS-WAVE TELEGRAPHY [Chap. VTI
Fig. 11.—A 500 kw. Poulsen are converter; over the operator's head is the anode ter
minal and on the right is shown the pipe for carrying off the exhaust gases from
the arc chamber. (Proc. I. R. E. Vol. 7., No. 5).
Fig. 12.—Magnetic field structure for a 500 kw. converter; the proper form of pole
piece has been subject of considerable study. (Proc. I. R. E. Vol. 7., No. 5.)
and the sets have a transmission range of perhaps 2000 miles in the day
time. Just recently small arcs (2 kw. input) have been constructed,
THE HIGH-FREQUENCY ALTERNATOR 593
which when fed from a 600-volt line seem to operate satisfactorily for
wave-lengths as short as 800 meters.
High-frequency Alternator.—The generation of high-frequency cur
rents by means of machines similar in their principles of construction
to the huge alternators which supply the modern central-station loads,
has doubtless occurred to the student. The extremely high frequencies
required, however, necessitate machines of special design which require
a high grade of engineering skill in their construction. Alternators for
supplying loads of commercial frequency may be any one of the three
following types :
I. The armature is the rotating element, the d.c. field being stationary.
This arrangement is similar to that employed on all d.c. generators but
is rarely used on alternators, particularly the large sizes.
II. The field rotates with respect to the armature, which is fixed in
position. This construction possesses several advantages over type I,
particularly due to the lesser insulation requirements of the field winding
and its greater simplicity as compared to the armature winding. This
construction is universal on all modern alternators.
III. Both the field and armature windings are stationary in space,
the flux linking the armature winding being periodically varied by means
of an inductor, revolving in the air gap. This inductor is essentially a
disk whose periphery has been divided into sections, alternate sections
possessing a high magnetic reluctance, while the intermediate sections,
which are made of steel, possess a relatively low reluctance. This type
is practically unused in the low-frequency machines of commercial engineer
ing, but possesses several inherent advantages which make it the most
satisfactory of the alternators designed for high-frequency generation.
Since both windings are fixed, in position, their proper insulation is much
simplified. Very serious difficulty is encountered when it is attempted
to place an insulated winding on the revolving member (rotor), due to the
high peripheral speeds and consequently high centrifugal stresses involved.
Design of the High-frequency Alternator.—That a special construction
and design is required may be seen from the following: If we consider
a machine of the inductor type having a maximum permissible speed of
20,000 r.p.m. and a required frequency of 100,000 cycles per second, the
rotor diameter being assumed 30 centimeters, the distance through which
a point on the rotor moves in generating one cycle is
20,000
tX30X
60
= 0.31 cm.
100,000
Therefore, in this small space we must have a section of high reluctance
(for instance, bronze) and a section of low reluctance (steel) so that a
594 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
to. 14.—Developed view of the winding and rotor of the machine shown in Fig. 13.
<r parallel, whichever may be most suitable for the conditions involved,
t should be remembered that two similar windings are placed in the
lole tip on the near side of the air gap, which are not shown in the figure.
Thus the operator has four or more separate windings which he may con-
lect in any arrangement most desirable for his conditions. On the alter-
lator at the New Brunswick station, each coil has its terminals brought
rat, there being 64 such coils.
On the normal inductor generator, the number of armature slots is
ilways equal to the effective number of poles. In the Alexanderson
liachine the number of armature slots may be two-thirds the number of
soles. This is a distinct advantage, as more space and more thorough
nsulation is thus permitted for the winding. Thus in the figure, we have
between the lines xx, twelve armature slots and nine inductor spokes,
596 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
which represent eighteen effective poles, or the armature slots are two-
thirds the effective poles.
The greater the flux variation I — I the greater will be the generated
voltage. By decreasing the air gap the effect of the inductor on the flux
becomes more pronounced and thus the generated voltages increase.
On a certain machine, with a minimum permissible air gap of .004 inch
(for each of the two gaps), the voltage generated was nearly 300 volts.
With the air gaps increased to .015 inch each, the voltage decreased to
150. (Eccles.) Similarly, the output capacity increases as the air gap is
decreased and vice versa.
The highest frequency for which these machines have been constructed
at the present time (1920) is 200,000 cycles per second with a capacity
of about 1 kw. Machines of 50 kw. and greater have been constructed,
the frequency, however, being lower for these higher capacity machines,
usually about 50,000 cycles. A 2-kw., 100,000-cycle generator is indicated
in Fig. 15, showing the driving motor, normally operating at 2000 r.p.m.,
connected through special 1 : 10 gears to drive the alternator shaft at
20,000 r.p.m. This general arrangement is followed on all alternators of
this type, the gear ratio decreasing as the capacity increases. On some
machines the driving motor is connected to the low-speed gear shaft by
means of a chain connection. A view of one armature of a 2-kw., 100,000-
cycle machine is shown in Fig. 15.4.
As might well be supposed, the high-speed machines are not as reliable
in operation or as easy to maintain as a low-frequency machine of the same
power. The bearings of the machine shown in Fig. 15 are flexibly fastened
to the bed plate of the machine so that as the armature shaft expands
each bearing will move away from the rotor disk equally, thus maintain
ing the two air gaps equal. Forced oil feed must be used for the bearings
and for the larger machines, pipes carrying cooling water are liberally
distributed throughout the structure of the machine.
The high peripheral speed of the disk results in a very rapid circulation
of air through the two air gaps, causing considerable noise and power
consumption. The small machine shown in Fig. 15 requires about 7 h.p.
to turn the disk at rated speed, the machine not being loaded.
These high-frequency inductor alternators require suitable tuning
condensers to neutralize their internal reactance before they can deliver
appreciable power; a small 200,000-cycle machine will scarcely deflect
a voltmeter across its terminals unless a proper condenser is connected
across the armature terminals.
Connection to the Antenna.—The armature winding may be directly
connected to the antenna as shown in Fig. 16a, or it may be inductively
coupled as shown in Fig. 166, by using an oscillation transformer. In
THE ALEXANDERSON ALTERNATOR 597
either case the antenna circuit must be tuned to the frequency of the
alternator if maximum output is to be obtained. If the 2-kw. 100,000-
High frequency
generator, q Driving
20,000 np.m. ^ j motor 2poo r.p.m.
if
^Oi7 pump
Fig. \5A.—A view of a section of one armature of the machine in Fig. 15.
the coil were standing still. Reviewing the above, two frequencies may
be considered as being generated in the coil, viz.,
fi=N — Nr (produced by </>')
fi =N+Nr (produced by <t>")
since N,=N,
this becomes /i =0
■ h=2N
2t
18-A-Norruul Construction
j
\<t>=<t> + <t>" ^*-*'+*"!
/ \
- >e \ /
18-B Construction
by means of Conjugate
Vectors
Fig. 18.—A stationary, pulsating, magnetic field maybe represented by two rotating
fields each constant in strength, rotating in opposite directions. Each rotating
field has one half the strength of the stationary pulsating field.
f2=N+Nr=2N
By thus employing tuned circuits, the magnitude of the current flow pro
duced will be a maximum and is limited only by the effective resistance
of the circuit. This ef-
fective resistance includes
the losses due to hystere Choke coil
sis and eddy currents as
well as dielectric losses.
Since e.m.f.'s of sev
eral frequencies are con J
i —
cerned, circuits must be I
available which are tuned
to each of these frequen
cies. Fig. 21 indicates
the arrangement em
ployed by Goldschmidt,
for a quadrupling of the
generated frequency, di Fig. 21.—In order to get currents of appreciable ampli
tudes of the various frequencies generated in a "re
rect current being sup flection" type machine the rotor and stator must be
plied to the stator. supplied with suitably tuned circuits, one for each
The rotor R revolves frequency generated.
at the required speed in
the d.c. field produced by the stator winding <S, supplied by means of
the storage battery B. There is thus induced in R an e.m.f. of fre
quency N, the value of which is given by
NPXRPM
N-- where JVp=the number of poles.
120
This e.m.f. will cause a current of corresponding frequency to flow in the
circuit R, Ci, L\, C"i, the values of the capacities and L\ being adjusted
so that the circuit is tuned to this frequency. C\ compensates for the
inductance of the rotor, while L\ and C"i compensate each other, and the
drop across them is thus very small. This current induces an e.m.f. of
frequencies 2 N and 0 in the stator circuit S, C2, L2, C'2, in which the values
of C2, L2 and C'2 are adjusted to resonance for the frequency 2N. C2
compensates for the inductance of the stator winding, while L2 and C'2
compensate each other, and therefore practically no drop exists across
this portion of the circuit. The double-frequency current induces an
e.m.f. of frequencies 3 AT and N in the rotor, and triple-frequency current
604 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
flows in the circuit R, Ci, C3, which is tuned to resonance for this frequency.
Practically no current of frequency N will pass through C3, since Li, C\,
represents almost a short circuit path across Cz for this frequency.
The triple-frequency current flowing in the rotor circuit R, Ci, C3,
induces in the stator e.m.f.'s of frequencies 4N and 2N, and currents of cor
responding frequencies flow in the circuits S, C2, CA and S, C2, L2, C'2,
respectively, each of which are tuned to resonance. The condenser CA
represents the antenna through which we thus have a current flowing
whose frequency is four times the frequency (N) of the current initially
generated. If it were desired to utilize the triple-frequency current, the
antenna would be connected to the rotor in place of C3, while La and C'2
could be omitted from the stator circuit. By suitably arranging other
circuits higher frequencies could be obtained but such an arrangement is
not employed to any extent commercially, as the quadruple-frequency
machine is more efficient and fulfills all requirements.
For the complete Goldschmidt machine as described in the preceding
discussion, we may tabulate the generated frequencies, as before—
Stator Rotor
0 N
2Ar and 0 3 AT and N
4tf and 2N
Pio. 22.—Rotor and stator e.m.f.'s of a single-phase induction motor. The rotor e.m f.
may be separated into its two components as shown by the dashed line. One fre
quency is equal to that impressed on the stator plus the frequency of rotation
and the other frequency is the difference of the two.
Fig. 23.—When the rotor was run at practically synchronous speed the amplitude of
the differential frequency was practically zero, leaving in the rotor only the additive
frequency.
606 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
and thus additional losses are caused which may be minimized by reducing
the gap.
On the largest machines we thus find extremely small air gaps, being
about .08 cm. on a 100 kw. machine (normal rating). The rotor of
this machine weighs about 5 tons and is 1.25 meters in diameter, which
indicates the extreme precision and care required for the proper construc
tion of this type of generator. Trouble may be experienced if the rotor
expands under the effects of temperature rise produced by continuous
operation. This will cause an increasing output (almost inversely pro
portional to the gap length) as the gap decreases until the rotor suddenly
makes contact with the stator and jams tight, resulting in the destruction
of the machine.
It is also important that the rotor and stator slots be strictly parallel
to the shaft and to each other. That is, there should be no skewing, as
otherwise the e.m.f.'s induced throughout the length of one conductor of
the winding will not be in the same phase, and a decreased voltage (and
thus a decreased output) results. A divergence of 1 millimeter in 1 meter
length would cause a decrease of 20 per cent in the total output.
Typical Installation.—The largest alternators of this type have a
maximum output of 200 kw. with a normal output of 100 kw., one of
which is located at Hanover, Germany, the other at Tuckerton, N. J.
These machines are of the four-reflection type, with direct-current supply
to the stator and having 400 poles. For an output frequency of 50,000,
which means an initial frequency of 12,500, the motor drives the generator
at 3750 r.p.m. This motor is rated at 4000 r.p.m., 250 h.p., 220 volts,
and is supplied from two direct-current generators in Ward Leonard con
nection, to secure the necessary flexibility of speed control and ease of
starting. The generator is directly connected to this motor by means
of a flexible coupling.
The antenna at the Hanover Station consists of a double-cone system,
the aerial wires being supported by a single steel tower 250 meters high.
The aerial system is made up of 36 bronze cables of 8 mm. diameter, the
outer ends of these cables being attached through insulators to poles
12 meters high which are arranged in a circle around the tower, the radius
of this circle being about 450 meters. The tower is insulated at the base
and half way up by means of heavy glass insulators and in addition is
supported by steel guy wires, sectioned by insulators.
Frequency Transformation.—The design and construction of such
alternators as described above, which provide at their terminals, e.m.f.'s
of frequency sufficiently high to be used directly for radio-transmission,
requires the highest type of engineering skill if the many complex problems
involved in their construction are to be solved successfully. Alternators of
somewhat lower frequency, however, say 10,000 cycles per second, can be
608 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
this voltage and the total flux <£, which must be developed in the two
transformers to develop the
required c.e.m.f., as shown in
Fig. 26A.
Since the total flux <j> is
a maximum when the primary
current is a maximum, the Altera*
component fluxes, which exist
in each transformer, and which
add up to give this total flux,
must each be a maximum at
this instant. Since B satur Fia. 25.—Use of two saturated arcs to triple the
ates at about one-half the frequency.
current value required for A,
we can plot the component fluxes as shown in Fig. 26 B. The pri
mary current, which has not been indicated, is approximately sinusoidal
in form. The two fluxes <i>a and 4b,
by their variation cause e.nxf.'s E&
and Eb2 to be induced in their
respective secondary windings, the
wave form of these e.m.f.'s being
indicated in Fig. 26C.
The two secondary windings are
so connected together that the volt
age across the load circuit {L—C,
Fig. 25) is obtained by taking the
difference of E„2 and Em; in Fig.
26D this line voltage (Em—Em) is
shown and it is evident that the
e.m.f. is principally a triple-fre
quency one. The load circuit,
which includes the radiating antenna
and its loading coil (if any), must
be tuned to this triple-frequency
e.m.f., if an appreciable output is to
be obtained.
Frequency Doubler.—An arrange
ment for doubling the frequency first
suggested by Epstein in 1902 and sub-
Fia. 26.—Analysis of action of the ar- sequently developed by Joly and Val-
rangement of Fig. 25. louri, is indicated in Fig. 27. Both
transformers are identical, and each
is equipped with a tertiary circuit, supplied from the storage battery B.
610 CONTINUOUS-WAVE TELEGRAPHY [Chap. VU
r3 ;::>r,
To
1 ■1
Alternator
I 1
Fig. 33.—The "wabbling neutral" scheme of tripling frequency; the center point of 3
K-connected iron core coils is connected to the antenna and the center point of
3 y-connected air core coils is connected to ground. The three-phase power
supply is otherwise ungrounded.
STATIC FREQUENCY CHANGERS 615
/XAXVX/\\
\ / A/VWV
\ /
t-o
■XVX/XXVX
\ w /
\* /
>> //
3-0 /
/\X\/X/\X\/
Fig. 34.—Curves of flux and e.m.f. to analyze the action of the wabbling neutral; in
curves 8 the voltage forms eo-i and eo_a are shown without their third harmonies,
these being shown separately in the X axis.
with three air-core coils. The two neutrals were then connected together
and the resulting current in the connection was nearly a pure sine wave
of triple frequency.
Application of Rectifier Elements to Frequency Changers.—Another
type of frequency changer is that utilizing a rectifying element in the pri
mary circuit. The action is due fundamentally to the fact that the flux
in the iron core is always set up in the same direction, regardless of reversal
of the supply current. Fig. 36 indicates a typical connection, while
37 indicates the voltage and flux relations obtained.
Fig. 35.—Oscillogram showing the third harmonic obtainable from the curcuit of
Fig. 33.
Fig. 38 indicates an arrangement utilized by Zenneck and others.
This operates exactly similar to the arrangement of Fig. 36, but makes
use of four valves to secure unidirectional current through the one primary
winding. Current is permitted to flow only in the direction indicated
by the arrows in the valve elements ; an inspection of the figure will indi
cate their operation. Fig. 37 is also applicable to the operation of this
circuit.
Marconi Multi-gap Generator.—By properly timing the discharge
periods of related spark circuits, each circuit acting inductively on a
common secondary circuit, undamped high-frequency oscillations may
be obtained in the secondary circuit. This principle has been utilized
by Marconi in the construction of a multi-gap generator, the connections
of which are indicated in Fig. 39.
MARCONI MULTI-GAP GENERATOR 617
The synchronous gaps D\, D2, Dz, etc., are all rigidly keyed to the same
shaft, but are displaced properly with respect to one
another so that the discharge in the several circuits
occurs at different intervals. The result is graphically
illustrated by the curves shown in Fig. 40. It is essential,
if efficient operation is to be obtained, that the several
circuits are discharged in proper sequence and at exactly fa
the right instant, so that the component oscillations
acting on the common antenna circuit will produce a
constant amplitude high-frequency current as shown.
This is accomplished by the proper displacement of
the several disk discharges on the shaft and is also
Flo. 36.—A fre
insured by means of an auxiliary disk resembling a toothed quency doubler
wheel, which acts as a " trigger " to cause the main dis using iron core
charge to occur at exactly the proper instant. This is and rectifiers.
not shown in the diagram.
It is evident that the speed of rotation of the discharger disks is fixed
by the radio frequency generated and for this reason the generator is
particularly adapted to long wave-lengths.
If we assume a generator with ten disks,
each having 40 studs, and the shaft
revolved at 50 r.p.s. the interval between
two condenser discharges is
M rtfef rfef
Choke
Colls
if p.
_=_ J2-D.C. 5000 V. 1
J_ Generators _
— L in Series C.— C»—r
"n . T [
Cut In
Method
- Key Open - Key Closed ■
II
Compensated
Method
III
Modulated
Method m—m
i
Fig. 41.—Methods of transmitting signals from continous wave stations.
^/mvm#wwll
-Key ope -Key closed-
condition the alternator voltage is very small and is able to send but very
little current through the antenna circuit. Therefore the radiated energy
will decrease to a very small value, essentially zero. When the key is
depressed (open position), the iron is no longer saturated and the impe
dance of Li increases to a high
value. The alternator current will
then flow through the antenna
circuit in preference to the shunt
circuit, and energy will be radi
ated.
At the New Brunswick station
this variable, iron-cored impe
dance is connected in a tuned
circuit (tuned when the key is
open) which is coupled to the
Fio. 46.—A method of sending by generator antenna and alternator as shown
which employs a magnetically controlled in Fig. 47. When the key is
short-circuit on the machine. closed, the local circuit is detuned
and the energy input into this
circuit becomes very small, the major portion of the energy thus being
diverted to the antenna circuit. The transformer indicated in the figure
is an integral part of the alternator and is shown supported in two sec
tions above and on either side of the alternator in Fig. 17, p. 599.
For either scheme of
control, the energy ra
diation is essentially as
shown in Fig. 41-1. The
use of a chopper or buz
zer in the exciter circuit
may not be entirely
satisfactory, due to the
inability of the machine
voltage to follow accu
rately the rapid varia
tions of field current pro
duced. There is no Fig. 47.—In the application of the scheme indicated in
doubt, however, that Fig. 46 it is found advisable to use the circuit arrange
satisfactory results could ment shown above.
be obtained by inserting
the interrupter in the key circuit of Fig. 47 Radiation in this case
would be nearly as indicated in Fig. 41-111.
Methods of Sending Applicable to the Goldschmidt Alternator.—As
with the Alexanderson alternator, the generated frequency for this machine
CONTINUOUS-WAVE SIGNALING METHODS 625
is fixed by its speed, and therefore wave-changing methods are not appli
cable. Signaling is accomplished by means of the " cut-in " method
using field excitation control, the connections are indicated in Fig. 48.
In addition to opening and closing the exciter circuit, the key also simulta
neously cuts out or in a portion of the driving motor field resistance. Thus,
any tendency of the alternator to suffer a drop in speed, when the exciter
key is closed, and the Driving
Motor
load applied, is com
pensated for by the
cutting in of a certain
amount of motor field
resistance, which will
tend to raise the
D.C. Supply
speed. In addition,
the heavy weight and
inertia of the rotating
element effectually aid Fig. 48.—Scheme of sending signals with the Goldschmidt
in maintaining con- alternator using a motor speed control in addition,
stant speed, and under
operating conditions the variation in wave-length is claimed to be less than
one-tenth of 1 per cent.
The above discussion describes the only method which has yet been
used for controlling the output of this alternator. Switching to a dummy
antenna, or some form of shunt circuit, as described for the Alexanderson
machine, would also be applicable, but the present method seems to be
completely satisfactory.
Methods of Sending which May be Used when Frequency Trans
formers are Used.—Since these transformers must be associated with
some form of high-frequency alternator, whose frequency is rigidly fixed
by its speed, the same methods as described above for the Alexanderson
and Goldschmidt machines will apply. On low-power sets the key may be
connected to open the supply circuit directly, while on large-power sets
the circuit may be opened indirectly by auxiliary relays actuated by the
sending key. The antenna current would then be as shown in Fig. 41-1.
The key may also have associated with it some form of interrupter or
chopper, resulting in current variation as shown in Fig. 41-111.
For the larger installations, the energy would be controlled by means
of the exciter supply due to the smaller power involved. Cut-in send
ing would be the most feasible, although switching to a dummy antenna
or connecting a variable impedance across the alternator terminals as
in the case of the Alexanderson machine could also be used.
Energy Radiation Control when Marconi Generator is Used.—For a
generator of this type, switching to a dummy antenna would be a satis
CONTINUOUS-WAVE TELEGRAPHY [Chap. VU
factory means of varying the radiated energy, the " cut-in " method of
sending thus being used. Some form of absorbing circuit across the
generator terminals might also be used to give similar results. The key
might be placed in the common generator lead at point X, Fig. 39, p. 618,
or point Y, opening the supply or antenna circuit respectively. An inter
rupter element may be associated with either of these three means, giving
the " modulated " method of sending as shown in Fig. 41-111. It would
be undesirable to employ a wave-changing scheme, as this would require
circuit- variations in each of the four primary circuits involved, with
resultant complexity of connections, etc. On larger installations, it would
be preferable to place the key in the exciter circuit of the d.c. generators,
in preference to the point X. This would probably be the most satis
factory means of control for the same reasons as stated above in connec
tion with high-frequency alternator installations.
Control of Radiated Energy when the Oscillating-tube Generator
is Used.—The radiation of energy from an antenna supplied from an
oscillating-tube generator may be in accordance with any one of the
three methods indicated in Fig. 41. The method employed for small
sets is usually a direct opening of the antenna circuit by means of the
key, which may or may not be associated with an interrupter (usually
a buzzer for small field sets) to obtain the modulated method of sending.
The wave-length change may be
obtained by short circuiting a por
tion of the antenna circuit induct
ance. Since the power generated
by these circuits is as yet com
paratively small, there is no neces
sity for auxiliary relay equipment
to be associated with the key.
The most feasible control scheme,
however, is one which controls the
"grid potential " of the oscillating
tube; by making this sufficiently
negative the tube stops generating
power as described in Chapter VI,
and illustrated in Fig. 117, p. 500.
„ ,
Fig. 49.—An arrangement whereby the . ,. Fig. . 49 shows the diagram
... . of
output of this small tube transmitter can connections for a small oscillating
be controlled by either one of three tube set, which utilizes three of the
methods. above-named methods of sending.
The oscillating circuit involved
were described in Chapter VI, p. 513, and the student is referred there
for a discussion of their action.
CONTINUOUS-WAVE SIGNALING METHODS 627
Receiver
Circuit
Voltage
Current
through
Phones
OjlUl Oetectorjl
Receiver
Circuit
Voltage
Current
through
Phones
Receiver
Circuit
Voltage
If the set is sending on the " modulated " method, the signal is received
exactly as in the case of a spark signal. The action is indicated in Fk.
53. This shows the mean current through the phones to vary at audit
frequency (chopper or buzzer frequency) when the key is held closed,
and the signal is thus made audible to the observer.
CONTINUOUS-WAVE RECEPTION 631
cycles are not interrupted at the same point, but the point of interruption
will shift as shown in Fig. 57.
The telephone will thus be periodically impulsed by the audio frequency
component of the resultant current flowing through the phones as indi
cated by the dotted curves in Fig. 57. The frequency of this current
is the difference between the frequency of the wheel and the incoming
signal. Thus, for the machine considered above, and an incoming fre-
Speed
below
Synchronous
Value
Telephone Speed
above
Current Synchronous
Value
Fig. 57.—The tone wheel run either higher or lower than synchronous speed will act to
give a musical note signal, the pitch being fixed by the difference between the
actual speed of the tone wheel and synchronous speed.
quency of 50,000, the speed would be as shown below for a desired audio
frequency of 1000 cycles per second.
f=fi -h - 1000 =50,000-49,000 running below synchronism
/ =/2—/i - 1000 = 51,000 — 50,000 running above synchronism
where /i = frequency of incoming energy;
/2 = frequency of interruptions caused by the tone wheel
The note may thus be easily adjusted to give maximum audibility by alter
ing the speed of the tone wheel.
This device operates in some respects similarly to the heterodyne
receivers discussed below, although no local frequency is generated. The
pitch of the note received does, however, depend on the speed of the tone
wheel, which permits its adjustment to give a musical note which can
easily be heard through static and minimizes interference to some extent.
This is evident when it is considered that the interfering station must
radiate practically the same wave-length as the station whose message
it is desired to receive if much interference is to occur. A very slight
difference in the wave-length causes a relatively large difference in pitch
of the resultant note, and the interference is thus easily identified and
may be eliminated by properly altering the speed of the tone wheel.
This receiver was specially developed for use in connection with the
Goldschmidt system of undamped wave-transmission, and was used to
some extent in the stations utilizing this system, notably those at Hanover,
Germany, and Tuckerton, N. J., U. S. A.
Rotating Plate Condenser.—Another scheme for the reception of
undamped wave signals is shown in Fig. 58.
The movable plates of condenser C2 are rapidly rotated by a small
motor or similar means so as
3 to cause the circuit L2 — C1 to
be in tune for a small interval
of time during each revolution.
While in tune the current in
the detector-phone circuit will
be much greater than at other
times and a series of impulses,
one for each revolution, is thus
exerted on the telephone dia
phragm. The action is some
Fio. 58.—By rotating the plates of the tuning what similar to that of the
condenser, the use of a crystal detector makes
a continuous-wave signal audible, the pitch of chopper, but differs in that no
the note being fixed by the rotational speed circuits are interrupted.
of the condenser. Heterodyne Receiver or
" Beat " Receiver.—The receiv
ers described above have all been applied to the reception of undamped
wave signals in the past, but at the present time have been superseded
by receivers involving the generation of local high-frequency currents
by means of oscillating vacuum tubes. The advantages of this type of
receiver over the earlier schemes are :
1. Ease of operation.
2. Simplicity.
CONTINUOUS-WAVE RECEPTION 635
3—1
Fig. 59.—The oscillating tube as receiver; it uses the beat note idea and is used to-day
universally.
while the latter may be called the " self-heterodyne " or " autodyne "
method of reception.
Self-heterodyne Receiver or Autodyne.—The self-heterodyne receiver,
utilizing an oscillating vacuum tube as a generator and detector, is
undoubtedly the most important of recent developments in the field of
radio, and will be described somewhat in detail. A possible connection
for the receiving set is indicated in Fig. 59.
If the various oscillation requirements of the tube have been satisfied,
the tube will oscillate at a frequency determined by the constants of the
local circuit, L2, Li, C, and a current of this frequency will flow in the local
circuit.2 This is known as the local high-frequency current, and is indi-
1 See Chapter VI, p. 483, for mathematical analysis.
1 For analysis of conditions required for oscillation see Chapter VI, p. 510.
636 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
cated by curve a, Fig. 60. Assume its frequency to be 1,000,000 cycles /sec.
Now consider that the transmitter is operated on the " cut-in " method
and is radiating at a frequency of 999,000 cycles /sec. A portion of this
energy strikes the receiving antenna, which is tuned to it, and a maxi
mum current is caused to flow in the antenna. This, in turn, induces
an e.m.f. in the coil Z>2 and causes a current whose frequency is 999,000
to flow in the local oscillating circuit. This current is called the incoming
high-frequency current and is shown in curve 6. (It should be noted
that the antenna and local oscillating circuits are slightly detuned.)
The two high-frequency currents, flowing in the same circuit, com
bine to give the resultant current indicated in curve c, which shows the
periodic Variation in amplitude produced. These periodic variations in
amplitude are called " beats," and the beat frequency is always the dif
ference between the component frequencies. (A " beat cycle " consists
of one complete rise and fall in amplitude). For the values assumed above
the beat frequency would thus be 1,000,000-999,000 = 1000 cycles /sec.
It is to be particularly noted that the frequency of alternation of this
resultant current 1 is the mean of the two component frequencies, namely,
999,500 for the values assumed. The resultant current is therefore a
radio frequency current.
The drop across condenser C will have the same form as the current
curve {i^'e=2~J^) ^ identical with the variation in grid voltage Et.
The effect of this variation in grid voltage upon the plate current
depends on the point of the characteristic curve at which the tube is being
operated. If it is assumed that operation is on the lower bend, the plate
current will vary as shown on curve d. This variation may be resolved
into two components as shown in curves e and /, e flowing through the
bridging condenser, while / flows through the phones. The latter com
ponent varies at beat frequency, and if this frequency is high enough, a
musical note is produced in the phones, which is maintained as long as
the key is held closed at the transmitter. Opening the key leaves only
the local high-frequency current flowing and no variation of plate current
at beat frequency is produced, hence no note is heard in the phones.
If the tube stops oscillating and the incoming signal is maintained, the
same result is obtained.
If it is assumed that the tube is oscillating symmetrically with respect to
the upper and lower bends of its characteristic curve, the mean plate cur
rent remains unchanged (giving no current of audible frequency) although
a beat frequency variation in amplitude is produced. This means that
1 On the basis of measuring frequency by the time between successive zero values.
At the points of minimum amplitude the phase reverses as explained in Chapter IV,
p. 241.
CONTINUOUS-WAVE RECEPTION 637
Local
High Frequency
Current
Incoming
High Frequency fcr
Current
Resulted Ion of
High Frequency
Current
Plate
Current
Alternating
Component of
Plate Current
Plate
Current
The above discussion indicates that the receiving tube must perform
simultaneously the functions of oscillation and rectification. Failure
of either would result in no signals being received. These functions,
which are performed by the one piece of apparatus in the self-heterodyne
638 CONTINUOUS-WAVE TELEGRAPHY [Chap. VII
ing case, a metal plate should be placed in front of the condenser and
electrically connected to the moving plates. See Fig. 59A. This pre
caution prevents any change in frequency due to the proximity of the
observer's hand or body near the condenser and is extremely important
on short wave-length receivers.1
Effect of Upper Harmonics.—Since the vacuum tube does not generate
a pure sine current of fundamental frequency, but also produces upper
harmonics, a unique phenomenon is observed when the heterodyne receiver
is close to an oscillating tube transmitter, as may be the case in the labo
ratory.
Harmonic Harmonic
Fig. 62.—A diagram for analyzing the peculiar noises heard when an oscillating tube
receiver is close to a continuous-wave transmitter.
The operator, when in doubt, should vary his local frequency over wide
limits, and select that adjustment giving maximum audibility.
Possibility of Receiving Undamped-wave Signals with an Ordinary
Crystal.—An ordinary damped-wave receiver, using a crystal or simple
Fig. 64.—Back view of the set shown in Fig. 63; toroidal transmitting coils were used
to eliminate local interference. The magnetically operated key is seen in the opened
box.
is on the bend. It has also been noted that the use of a grid condenser
improves the detecting action and does not require that the tube be oper
ated on the bend of the curve. In fact, the detection is best when the
tube is operated on the straight portion. For these reasons the grid
condenser is also used in connection with the heterodyne receiver.1
Fig. 66.—Back view of the set shown in Fig. 65; with 1500 volts supplied to the plate
circuit this set generates 1 kw. of high-frequency power.
RADIO-TELEPHONY
and the amplitude of the current supplied by the alternator must neces
sarily increase; the reverse takes place when the diaphragm is displaced
outwardly.
Fig. 2.—When no sound impinges on the microphone the amplitude of the high-frequency
current supplied to the antenna is constant.
Fig. 3.—If a sound wave actuates the microphone, its inward and outward displacement
varying the resistance in the antenna circuit, results in a highly-frequency current
in the antenna of variable amplitude, called a modulated high-frequency current.
tudes, the percentage change be alike for the amplitudes of all the component
frequencies. This principle is of very great practical importance not only
in radio-telephony, but in wire-telephony as well.
We have already shown how harmonic vibrations of the microphone
diaphragm having a single frequency, such as those caused by a tuning
fork, may be reproduced in the receiver diaphragm. It is plain that the
amplitude of the displacement of the receiver diaphragm depends upon the
intensity of the electromagnetic field on reaching the receiving antenna
and upon the constants of the receiving circuit, including the sensitiveness
of the rectifier and of the telephone receiver, as well as the amount of
coupling between the open and closed circuits, the damping thereof, and
also whether the rectified current is amplified by a suitable amplifier or
not. Of course the intensity of the electromagnetic field at the receiving
antenna is a function of the distance between the transmitting and receiving
antennas, the wave-length corresponding to the carrier frequency, the
height of the two antennas and the absorption of energy due to the inter
vening medium, which is in turn a function of the wave-length; hence,
no matter what the value of the modulating frequency or the frequency
of the transmitter diaphragm, the per cent change in amplitude as related
to the displacement of the receiver diaphragm must be the same for all
values of modulating frequency, because the percentage of radiated energy
which reaches the receiving antenna is dependent upon the carrier fre
quency and not upon the modulating frequency. Again, as regards the
effect of the constants of the receiving circuit upon the amplitude of the
receiver diaphragm displacement the receiving circuit may be so chosen
and adjusted that it will affect all modulating frequencies within the speech
range to the same extent.
It follows from the above that, if the transmitting diaphragm be
spoken into, the displacement of the diaphragm corresponding to each
of the possible harmonic components of its vibrations will be reproduced
in the receiver diaphrag-n with practically the same percentage change in
amplitude, and hence speech will be correctly reproduced.
The carrier frequency should be much higher than the highest important
speech frequency, which is in the neighborhood of 5000 cycles per second;
therefore, the carrier frequency should be at least above, say, 15,000
cycles per sec. and, as a matter of fact, in actual practice it is seldom lower
than 100,000 cycles per sec, and a frequency as high as 6,000,000 cycles
per sec. has been used.
It might be thought that this carrier frequency may be dispensed
with and the vibrations of the telephone diaphragm may be caused to
produce antenna currents of audio frequency, by means of a circuit arrange
ment somewhat as shown in Fig. 9, where the microphone M would, on
being spoken into, produce audio frequency currents in the antenna,
654 RADIO-TELEPHONY [Chap. VU
through the means of the transformer T. This system would fail, became
it would require a prohibitively large antenna in order that the audio
frequency currents might cause
=1 sufficient energy to be radiated
for successful transmission over a
reasonable distance; hence the use
of the "high-frequency carrier." 1
It is hardly necessary to em
phasize the fact that the genera
tor of the high-frequency carrier
must be such as to cause by
itself no change in the amplitude
of the high-frequency carrier:
otherwise this would be heard
in the receiver, together with the
speech, and would interfere with
the latter. In other words, the
high-frequency generator must
Fia. 9.—Such a scheme as this, dispensing with
the carrier frequency, cannot be used because not interfere with the modulation
practically no power can be radiated from of the high-frequency current as
an antenna with currents of voice frequency. brought about by the microphone
transmitter.
Sources of Power.—The sources of power which may be used are
those which will produce undamped high-frequency currents. (See p. 580.
Chapter VII.) Of these various sources the following have been most
generally used for radio-telephony:
The Poulsen Arc.
The Alexanderson or Fessenden Alternator.
The Oscillating Vacuum Tube.
All of the above have been fully described in Chapters VI and VII, and we
shall, in this chapter, study the manner only in which each of them may
be connected for successful radio transmission of speech.
Before going any further we will first briefly describe various types
of telephone transmitters and will later discuss the manner of using them
in radio-telephone circuits.
Transmitters.—The transmitters used for radio-telephone are broadly
divided into two general classes on the basis of their current carrying
capacity, i.e. :
(a) Low-current or low-capacity transmitters.
(b) High-current or high-capacity transmitters.
The low-current transmitter for radio-telephony does not differ from
1 It is shown in Chapter IX, that the power radiated from a simple antenna
with the square of the frequency.
THE MICROPHONE TRANSMITTE 655
the transmitter used in wire telephony, and its most common type will
here be described. This type is known as the solid-back carbon trans
mitter. The simple schematic diagram of Fig. 10 illustrates its construction
when stripped of details. It consists of an elastic diaphragm A mounted
upon the rubber ring FF, which is in turn held against E, the diaphragm
being mechanically connected to the carbon block B' . B' is placed opposite
another carbon block B in a chamber filled with small carbon granules C ;
this chamber is closed by means of the mica
washer G and the insulating nut H. The 3
two carbon blocks B and B' form the two
electrical terminals of the transmitter; the
wall of the chamber containing the granules -4——.
is covered with a strip of paper designated
by D; if a source of e.m.f. be connected
to B and B' it will send a current from B
through the carbon granules and to B', or
vice versa. On speaking into the trans
mitter the diaphragm is caused to vibrate,
and these vibrations are mechanically trans
ferred to the block B' so that the latter's
pressure upon the carbon granules is made
to vary; this varies the resistance between
B and B', and hence it varies also the cur
rent in the circuit wherein the transmitter
is connected.
Such an arrangement is very sensitive to Fia. 10.—Internal construction of
changes in pressure on the diaphragm and is theL °rdinary microphone; the
i . ■ , ■, , mi carbon granules between plates
known as a microphone transmitter. The B and R, are the ^ J ^
current carried by such a transmitter is very variable resistance,
small because of the fact that a limit is soon
reached beyond which " arcs " are developed between granules, the
contact points of which become red hot, and the transmitter becomes
useless. The current-carrying capacity of an ordinary transmitter is
about 0.1 ampere, and its average resistance when not spoken into is 50
to 100 ohms, so that the power capacity is a maximum of 0.12X100 or
1 watt. Some special microphone transmitters " low resistance," may be
obtained which have a resistance of 10 to 20 ohms and a current-carrying
capacity of 0.5 ampere, or a maximum power capacity equal to 0.52X20
or 5 watts.
The high-current or high-capacity transmitter has received a good
deal of attention at the hands of radio engineers and inventors, and many
types have been developed, the most important of which will be very
briefly described. The reader is referred for more information upon
656 RADIO-TELEPHONY ICha?. vm
Fio. ll.-A simple type of liquid P*1™^ vary the area of contact betwa
jet microphone, designed to give
itself and the jet and thus vary the resist-
low resistance and high power- ance between C and A. The capacity of
absorbing capacity. guch a transmitter is quite high, in so fir
as the only Umitation is the eventual bofl
ing of the liquid; it has been constructed to take care of 400 watts
Thus, low-capacity transmitters may be constructed of 1 to 5 wait
capacity and 100 to 10 ohms resistance respectively, while high-capacity
transmitters have been constructed of 50- to 500-watt capacity and of
about 8 to 4 ohms resistance, respectively.
Conditions for Best Modulation.—We will again note that the speech
transmission is brought about simply by changing the amplitude of the
transmitting antenna current (modulation of antenna current) ; in other
words, if the amplitude of the antenna current should be changed but
little by the operation of the telephone transmitter, speech would be
transmitted but poorly and to a short distance, while the opposite is true
In other words, the range and quality of transmission does not quite
depend upon the amount of current in the transmitting antenna, but
upon the change in this current or the extent of the modulation. Hence,
a radio-phone system should be so designed as to enable the telephone
transmitter, when spoken into, to produce the maximum possible chaM'
in the antenna current. This corresponds to a condition where the antenna
current amplitude is caused to reach a miminum of zero, and a maximum
which is dependent upon the characteristic of the rectifier in the receiving
' See "Radio-Telephony," by A. N. Goldsmith.
ANALYSIS OF MODULATION 657
1
•
Fia. 13.—The current of Fig. 12, in combination with such a rectifier as that assumed in
Fig. 6, would give a rectified current as shown by the points A ; its average value
would be a sine-wave current. If an ordinary rectifier is used the rectified current
is as shown by the solid line curves, the average value of which is shown by the
dotted curve which is not a simple harmonic current but is more complex in form.
off a note, which, though of the same pitch as that impinging upon the
transmitting microphone, would be of a more complex quality.
To remedy the objectionable condition brought about by the combina
tion of a harmonically modulated transmitting antenna current and a
rectifier giving a current proportional to the square of the impressed
' Fig. 14.—A type of modulated current in which the square of the amplitude varies as a
sine wave.
Ic
3
o
■30
V
Fig. 15.—Such a current (as that shown in Fig. 14) in the transmitting antenna, with an
ordinary type of detector will give in the receiving circuit a rectified current as shown
by curves A, the average value of which is curve B, a sine-wave current.
be similar in quality to that acting at the transmitter, either of the two
following conditions must be satisfied:
(a) If the receiver circuit rectifies proportionally to the first power of
the voltage impressed upon it, then the difference between the amplitude
of the antenna current with the microphone in operation and that with
the microphone idle should vary in direct proportion to the pressure of
the sound waves on the microphone, or, in symbols
I — Io=kp (1)
where /= amplitude of the antenna current with the trans
mitter in operation;
Io =amplitude of the antenna current with the trans
mitter idle;
k =a constant of proportionality;
p = the pressure of the sound waves upon the microphone.
(&) If the receiver circuit rectifies proportionally to the square of the
voltage impressed upon it then the difference between the square of the ampli
660 RADIO-TELEPHONY [Chap. Vffi
tude of the antenna current with the microphone in operation and that
with the microphone idle should vary in direct proportion to the pressure
of the sound waves on the microphone, or, in symbols :
P-Io2=k'p, ft
where I, Jo, p have the same significance as in Eq. (1) and k' = another
constant of proportionality.
Of course, in practice, neither of the two conditions set forth above
is fully and entirely satisfied throughout the entire range of pressure
impressed upon the microphone diaphragm, and the speech transmission
is, therefore, never ideal.
Percentage of Modulation.—The percentage of modulation is expressed
by means of the following equation:
Jf=^X100, (3
*o
where Jo = amplitude of antenna current with microphone idle;
D\ — difference between Io and minimum antenna current
amplitude;
M = percentage of modulation.
In the ideal case of a " completely modulated " antenna current Di=h
and M - 100 per cent.
Of course, in designing a radio-phone transmitter, the aim is to make
the percentage of modulation as large as possible without, at the same
time, interfering with the quality of the transmission.
In view of this the idle resistance of the telephone transmitter and
the change in the resistance must be carefully chosen with respect
to the resistance of the rest of the system. Thus, considering the simpfc
circuit represented by Fig. 1, p. 647, it is plain that if the idle resistance
of the telephone transmitter were much lower than that of the balance
of the circuit, then any change in the former could not appreciably affect
the total resistance and, hence, could not effectively modulate; on the
other hand, if the reverse were the case the antenna power radiation
would be very small, since the largest percentage of the alternator power
output would be absorbed by the transmitter. Thus, there must be a
best telephone transmitter resistance and this was shown by Seibt to
be equal to that of the rest of the antenna circuit.
In many of the systems of radio-telephony the telephone transmitter
is not placed directly in the antenna circuit, but, in practically even
case, it is so connected that, by speaking into it, an effect is product
which is equivalent to changing the resistance of the antenna circuit
the telephone transmitter resistance may, in these cases, be transferred
ANALYSIS OF MODULATION 661
since it carries either the antenna current or the, current in the oscillating
circuit of the Poulsen arc. In case (6) the transmitter need only be of
low capacity—high resistance, since it only carries the field current of
the alternator. However, in this case a certain change in the resistance
of the transmitter may not produce a proportional change in the ampli
tude of the antenna current (a requirement for good modulation) unless
the magnetic field of the alternator is far from saturated and the self-
induction of the field circuit is sufficiently low.
Fio. 16:—Various simple schemes for connecting the microphone to the source of power
to produce modulation; none of these is used in the better types of radio-telephone
transmitters, however.
Fig. 19. —A scheme of modulation due to Heising in which a separate tube is used to
accomplish modulation; the scheme has been extensively used in small transmitters
with the vibrations of the telephone transmitter. Again, since the poten
tial difference impressed upon the plate of the oscillator (i.e., that across
Q and 0) is being varied, it finally follows that the amplitude of the antenna
current will thereby be varied, since the amplitude of the antenna current
increases with increase of the plate voltage. Thus, the vibrations of the
telephone transmitter are finally reproduced in the antenna as variations
in the amplitude of the antenna current or, in other words, the antenna
current is thereby modulated.
The function of the coil D may be more clearly seen if the coil were
assumed to be short-circuited. Under these conditions, no matter how
much the modulator plate current were caused to vary by the action of
the transmitter, the potential difference across the points Q and 0 would
remain constant, and no change would be effected in the amplitude of
antenna current.
The function of the choke coil A, which should be an air core coil,
is to prevent the plate circuit of the modulator tube from taking from the
antenna circuit any of the high-frequency power which the oscillator tube
is supplying to it; the proper amount of inductance for coil A depends
upon the types of tubes used, but, in general, its reactance should be con
siderably greater than the plate-circuit resistance of the modulator tube.
Analysis of Heising Scheme of Modulation.—This scheme of modu
lation is probably better than any other so far suggested, and we are
therefore giving a more complete analysis of its operation.
Let us first suppose that the coil D, Fig. 19, has so much reactance
that no appreciable change of current through it occurs due to the action
of the microphone. We will assume, as has been done before, that the
microphone is actuated by a sine wave of sound, and furthermore, that the
sine wave of sound gives a sine wave of e.m.f. across the secondary termi
nals of the transformer S. (In order that the possible variation in the
impedance of the grid-filament circuit of the modulating tube may not pro
duce distortion of the terminal voltage of the transformer secondary, a
high resistance R of constant value is permanently connected across the
secondary to give the load circuit of the transformer an essentially constant
impedance.) The potential variations of the modulator grid will cause
its plate current to pass through sinusoidal variations, and will thus
make the plate circuit of the modulator behave like a variable resistance
connected across the points Q and 0 in multiple with the plate circuit
of the oscillator tube. This is schematically indicated in Fig. 20, where
ftniod represents the variable resistance of the oscillator plate circuit and
Rom represents the resistance of the oscillator plate circuit. Let
/mod = current in plate circuit of modulator;
Iok = current in plate circuit of oscillator;
Id = current supplied by the plate battery.
0(36 RADIO-TELEPHONY [Chap. VIII
If we now suppose that /mod is, due to the vibrations of the microphone
diaphragm, caused to change from zero to twice its average value, then,
since we have assumed that the coil L
has such reactance as to keep h essen
tially constant, it follows that the cur
rent Ian must increase and decrease
about its average value- to the same
extent as does /mod- Of course, as the
value of /oec is changed in response to the
vibrations of the microphone diaphragm,
Fig. 20.—Simple representation of the the power given to the antenna in the
Heising scheme of modulation. form of high-frequency current must be
changed and so must the amplitude of
the antenna current; in other words, modulation of the antenna current
is made to take place.
The variations of some of the quantities involved in this scheme of
modulation are represented in Fig. 21, where the various curves are self-
explanatory; the current /«<> for any instant is obtained by subtracting
from the essentially constant h the value of Imoa at that instant.
Now, if we investigate the variation in the power supplied to the oscil
lator, it will be noted, by referring to Fig. 20, that, since Rok is a constant
resistance the current through which is changing from zero to twice its
average value, then the power expended in Rok must vary from zero to
four times its average value. But since the power expended in Rok is
equal to the current multiplied by the voltage across it, it follows that
not only must the current, lax, vary from zero to twice its average value,
but the voltage across it must also do the same; that is, the voltage across
the points Q-O, Fig. 19, must vary from zero to twice its average value.
This result would seem to be contradictory to our assumption pre
viously made that the current h is constant; for if h is constant there
can be no change whatever in the voltage across Q and 0. But, as a matter
of fact, h does vary, though the amount of this variation may be small
if the inductance of the coil D (Fig. 19) is large; thus it might easily be
that a variation in h of only 20 per cent at the modulating frequency
would cause the voltage across Q and 0 to change from zero to double
its average value. In some actual radiophone sets employing this circuit
we have the following :
Average value of h = 0.08 ampere
Inductance of coil D = 2 henries.
Voltage of plate battery =300
If, then, a maximum variation in h of 20 per cent should take place at
a modulating frequency of 1000 cycles per sec. we would have:
Maximum voltage drop over D =2tX 1000X2X0.2X0.08=200
HE1SING SCHEME FOR MODULATION 667
Fig. 23.—Current through coil L* changes the permeability of both the inside cores,
thus changing the effective inductance of Li and Li, both of which are connected
in parallel with the generator.
coil Lz is thereby changed, the impedance of the coils L1-L2 will be
changed, and the antenna current will thus be modulated.
The adjustment of the value of the direct current in L3, with the trans
mitter inoperative, has an extremely important bearing upon the oper
ation. To begin with, it must be noted that this current may be adjusted
so that:
ALEXANDERSON SCHEME FOR MODULATION 671
Fio. 25.—The circuit of Fig. 23 is found to function better if proper condensers are
■utilized as indicated in this diagram.
Eq. (2) is similar to Eq. (1) except that the amplitude of the current is
now (Jo+ J'o cos ai<), instead of just Jo.
Eq. (2) may be changed as follows:
t - Jo sin ait+I'o sin wt cos a>it =
J' I'
= Jo sin wt+~ sin ut cos a)i<-f-^ sin ut cos out
ANALYSIS OF MODULATED WAVE 675
j>
^.nd, adding and subtracting -~ cos wt sin wit, we have :
i I'o ■ . . I'o . ■
H—5- sin oit cos wit —5- cos cot sin wit,
»r:
7' I'
i=Io sin sin (w+«i)<+-2^ sin (a>— «i)< ... (5)
)r, letting
. / = frequency corresponding to w;
fi = frequency corresponding to m,
Thus, if /= 300,000
ind /i = 1,000,
hen the three frequencies will be:
300,000, 301,000, 299,000,
tfhich means a difference between the smallest and largest frequencies
)f 2000 cycles or about two-thirds of 1 per cent of the frequency of the
inmodulated wave (carrier wave). On the other hand if:
/= 20,000 (X = 15,000 meters)
ind fi = 1,000
then the three frequencies would be :
20,000, 21,000 19,000
which means a difference between the smallest and largest frequencies
of about 10 per cent of the frequency of unmodulated wave.
676 RADIO-TELEPHONY [Chap. VIII
e.m.f. the current will be more sustained than the impressed e.m.f. itself.
If, for example, a highly damped pulse of e.m.f. is impressed upon a cir
cuit of low decrement and the same natural frequency as the e.m.f., the
current will be about as shown in Fig. 31; the current builds up slowly
and dies down slowly. We can conclude that any changes in the ampli
tude of the e.m.f. impressed on such a circuit will be followed but slowly
by corresponding changes in current. It follows that if a modulated
high frequency e.m.f. similar to that shown in Fig. 30 is impressed on a
low-decrement circuit, of the same natural frequency as that of the
impressed e.m.f., though a large amplitude current will flow in the circuit,
the changes in the amplitude of this current caused by the changes in the
impressed e.m.f. amplitude will be comparatively small. If, on the other
hand, the decrement of the circuit is very materially increased, by adding
resistance, the current produced by the action of the modulated e.m.f will be
much smaller in amplitude than before, but the fluctuations in amplitude of
the current will follow very closely those of the modulated e.m.f.
An extreme case of this effect is illustrated in Fig. 32, wherein the
impressed e.m.f. (curve a) is assumed to be made up of two distinct damped-
wave trains. In curve (6) is shown the current set up by this e.m.f. in
a low-decrement circuit, and in curve (c) is shown the current set up in
a high-decrement circuit. Quite evidently, the current in the latter case
very closely resembles the e m.f. acting on the circuit, whereas the much
larger current in the case of the low-decrement circuit is very far from being
similar in form to the e.m.f.
The modulated e.m.f. involved in radio-telephony circuits would act
on high- and low-decrement circuits in a manner similar to that indicated
for the damped e.m.f. of Fig. 32; the low-decrement circuit would have
large currents set up in it, but the variations in amplitude of these currents
would not follow the variations in the impressed e.m.f. amplitude, whereas
the high-decrement circuit would have much smaller currents (same L
and C supposed as for low-decrement circuit) but the variations in ampli
tude would more accurately follow those of the impressed modulated
e.m.f. Since the voice sounds are conveyed by the variations in the ampli
tude of the current and not by the magnitude of the current itself it is
evident that the high-resistance circuit would be the one to use for suc
cessful radio-telephony.
Applying this general idea to an actual case of speech transmission,
we come to the conclusion that the decrements of the transmitting antenna,
the receiving antenna, and closed-tuned circuit at the receiver must all
be higher than the highest decrement occurring in the modulated e.m.f.
Thus in Fig. 30 the e.m.f. (which is supposed accurately to represent the
voice sounds) has its more rapid change in amplitude from A to B; in
ten cycles its amplitude decreases in the ratio of 1 : 10, which corresponds
RADIO-TELEPHONY [Chap. VIII
Fig. 32.—A aeries of damped waves of e.m.f. acting on a low resistance receiving circuit
produce a current as indicated in (6), evidently not of the same form as the e.m.f.
a high-resistance circuit will have currents as shown in (c) which current closely
resembles the e.m.f. causing it.
length used is 300 meters, the number of cycles from A to B would be 100;
a decrease in amplitude to one-tenth of its initial value in 100 cycles cor
responds to a decrement of 0.023, which would be practically never obtained
in either of the antenna circuits and could only be obtained in the closed-
tuned circuit of the receiving set by having a tickler coupling to the plate
circuit.
Multiplex Radio-telephony.—It is possible to carry on, by means of
a scheme of " double modulation," seveial radio-phone conversations
MULTIPLEX RADIO-TELEPHONY 681
in the same area and using exactly the same high-frequency carrier wave
for all stations; the extra complications of the scheme are worth while
only in regions of congested communication.
The general idea of the scheme is conventionally indicated in Fig. 33,
wherein A is a modulator and B is a long wave-oscillator; C is a modu
lator and D is a short wave-oscillator; the
connections of a tube-transmitting set utiliz
ing this idea are shown in Fig. 34. From >
5
these two diagrams it is evident that the
antenna sends out a " doubly modulated "
high-frequency wave, that is, the amplitude
of the high-frequency wave follows a curve -a
which is a voice-modulated long-wave radio-
frequency. Thus generator B, Fig. 33, might
generate oscillations of 25,000, and the ampli s
tude of this 25,000-cycle current is voice-
modulated by the action of A. This vari
able amplitude, 25,000-cycle wave, controls,
through the action of modulator C, the am 3O
plitude of the high-frequency current generated
by D and sent out from the antenna.
Fig. 34 shows how the Heising modulation
scheme may be made to function for multi ■2
+->
plex transmission, and Fig. 35 shows the general '3
.3
reception scheme for multiplex telephony. The
antenna circuit and the closed circuit, Li-Ci,
are tuned to the high frequency generated by
the oscillator exciting the transmitting anten .3
-3
na. The action of the grid condenser and 1
leak is to produce in the plate circuit a pul .0
sating current, the form of which is the same a
>e
as the envelope of the high-frequency wave
received by Li-Ci. This envelope is itself of f
inaudible frequency, it being perhaps a voice- si
frequency modulated, 25,000-cycle current. 6
This 25,000-cycle current acts on the tuned cir iZ
cuit L2-C2 coupled to the plate circuit of the first
tube. The grid condenser and leak of this second detecting tube act to
produce in the plate circuit of this tube (in which the telephones are con
nected) a pulsating current of the form of the envelope of the 25,000-
cycle current. This envelope is, however, of voice frequency, and there
fore makes audible the speech carried by the doubly modulated high-
frequency wave.
682 RADIO-TELEPHONY [Chap. VIII
wave, etc. The selecting of the proper message at the receiving station
is done by the tuning of the L2-C2 circuit (Fig. 35) ; as this is tuned to
the various long-wave frequencies being used, the conversations from the
several transmitting stations become audible. All receiving stations tune
their respective antennas and
L1-C1 circuits to the same high Si
frequency carrier current. *
By using several high-fre cci)
quency carrier waves, far enough jac.
apart in frequency so that no
interference is encountered, and
using several long wave-modula
tions of each of these, it might -c3c
be possible to carry on, in the E
same area, without serious inter .a3
ference, perhaps fifty different -ac
conversations.
Another scheme for carrying _l >2
on multiplex telephony uses an
antenna tuned to several differ t. a be
B
Si. MM
ent frequencies and coupled to
this antenna the same number
of ordinary singly-modulated
transmitting sets; it seems that
this scheme may be made to
work satisfactorily.1 Q
Amounts of Power Required
z,u
to Cover Distances.—As regards
the distance range of radio- -aa
telephonic transmission it must o
be remembered that the re Cj
sponse at the receiving end is £
due not to the total power in the
transmitting antenna, but to <
the variation of this power;
therefore, it might, as a general
statement, be said that those
formulae would apply to radio-
telephonic transmission which apply to undamped-wave telegraph
transmission as given on p. 738, with the proviso that, in these formu-
1 See Proc. I.R.E., Vol. VIII, No. 6, for report on the feasibility of such a scheme,
article by Ryan, Tolmie, and Bach, entitled " Multiplex Radio Telegraphy and Teleph
ony."
684 RADIO-TELEPHONY [Chap. VIII
lae, the change in antenna current must be substituted for the antenna
current itself. Furthermore, while in the case of telegraphic transmission
the signals may be very faint and yet be understood by an experienced
operator, in the case of radio-telephone transmission, the signals must
be several times more audible, in order that speech may be fully under
stood, especially by an inexperienced operator.
Practically, the following have been found to be the dependable trans
mission ranges for a fair modulation, i.e., not less than 50 per cent:
Receiving
Apparatus
Fio. 37.—Scheme for simultaneous transmission and reception using two antennae,
spaced a considerable distance from one another and tuned to different wave-lengths.
other for receiving; each operator can then talk and listen at the same
time, as is done in ordinary wire telephony. Attempts have been made
to use a single antenna for simultaneous transmission and reception, but
the results are not reported to have been very satisfactory. One possible
scheme uses in the transmitting circuit two antennae of identical char
acteristics, one a real antenna and one a dummy; adjustments are so
carried out that half the power from the transmitter goes through each
antenna. The receiving coil of the receiving circuit is coupled to both
antennae equally so that when transmitting practically no voltage is
induced in the receiving circuit. When the distant station is transmitting
only the real antenna is excited so that the signal is received all right. A
brief description of such a set is given in the Radio Review, Vol. I, No. 15,
by M. B. Sleeper.
SIMULTANEOUS RECEPTION AND TRANSMISSION 687
Modulated To
High Frequency Receiving
Currents Circuit
Fig. 38.—The scheme for balancing out of the receiving antenna the strong
induced by the local transmitting antenna.
mitting antenna are opposed and balanced out by means of e.m.f.'s induced
directly by the transmitting into the receiving circuit.
(6) Those wherein filters are used to minimize the effect of the e.m.f.'s
produced by the local transmitter.
(c) The " Barrage Receiver " invented by E. F. W. Alexanderson.
To class (a) belongs the simple magnetic balancing-out scheme 1
illustrated by Fig. 38, where the e.m.f.'s induced from antenna Ai into
the antenna A2 are opposed by the e.m.f.'s induced in coil D by the currents
in B. Of course the phases of these two sets of cm.f.'s may not be exactly
Transmitting Receiving
antenna antenna
To receiving
circuit
■ Modulated
highcurrents
frequency
Fio. 39.—A scheme whereby the action of condensers Ci and Cj is utilized to eliminate
from the receiving antenna the strong signals from the local transmitting antenna.
Modulated gj -7T
high frequency cx c,
currents
:c,
Modulated
High Frequency
Currents
Fig. 41.—Another scheme for balancing at the local signal, by suitable coupling of the
detector circuit.
In this diagram
Ct represents the equivalent capacity to the ground of the trans
mitting antenna;
Cr represents the equivalent capacity to the ground of the receiving
antenna;
Cm represents the mutual capacity between the two antennas.
It will now be noted that starting at the point D we have the following
two multiple circuits to ground: DC1BC2G and DFCmHC/J. It, there-
690 RADIO-TELEPHONY [Chap. VIII
To Receiving Circuit!
Fig. 44.—Alexandereon's so-called "Barrage receiver," it is an attempt to rotating
fields as phase changers to neutralize the local signals.
692 RADIO-TELEPHONY [Chap. VIII
Fig. 45.—View of the construction of the set shown in Fig. 46; the set uses the Heising
scheme of modulation, and has besides the receiving detector tube, two low-
frequency amplifying tubes, coupled by iron core inductances.
put represents che largest present commercial set. An idea of the arrange
ment of apparatus in a small set (output about 4 watts), may be had from
Figs. 45 and 46, which show an outfit designed for communication over
(I')2
W, = -5— ergs per cu. cm.
from the conductors of the toroid. It is plain that if the current is reduced
to zero the field collapses and in so doing it moves with respect to the
conductors on the toroid and induces an electromotive force therein,
thus producing an electric
field. In this case, since the /
magnetic field is very near Pi
to the conductors, the mo @nnnn mam®
tion of all of the magnetic
field with respect to the con
ductors takes place at the Fia. 8.—Two closely adjacent charged plates illus
same time, all of the energy trate well a closed electric field.
given to the field is returned
to the circuit, and no phenomena take place other than the well-known
one of electromagnetic induction.
Similarly Fig. 8 represents the two plates Pi and P2 of a condenser.
The charging of the condenser produces an electric field, which is limited
practically to the space between the plates. If the condenser plates are
short - circuited,
the electric field
will collapse and
here, as in the
case of the to
roid, since the
electric field is
very close to the
plates, practically
all of the energy
in the field will
be returned to
the circuit.
x 'r " b- /^-r' If, on the
Electee lines Magnetic \\ne%," other hand, we
study the case
Fio. 9.—A pair of wires disposed as shown here, excited by a high
frequency alternator, illustrates what are called open magnetic and of changing mag
electric fields; these fields reach out (with appreciable strength) netic and elec
to distances greater than the dimensions of the circuit itself. tric fields which
are distributed
to comparatively great distances away from the seat of these fields,
we meet with a new phenomenon, i.e., radiation of electromagnetic
waves. Thus, consider the case of the two conductors of Fig. 9, to
which there is connected the high-frequency alternator A. The voltage
part of the total magnetic field, however, it may generally be neglected without much
error.
700 ANTENNAS AND RADIATION [Chap. EX
it takes time for the field to travel any distance, it follows that the phase
of the field will be different at each point; in other words we shall, as
already outlined in Chapter III, have a wave constituting an electro
magnetic disturbance in the medium, so that while at a certain instant
of time the electric field in a certain portion of the space may be repre
sented by (a) Fig. 10, the maximum intensities occurring at 1, 2, 3, a little
later the electric field will appear as at (6), the maximum intensity now
occurring at 1', 2', 3', and the wave of electric disturbance having traveled
the distance from 1 to 1'. The above also applies to the magnetic field,
Electiic field
1 2
Fia. 10.—Electric and magnetic fields associated with a wave of radiation at two suc
cessive instants of time; magnetic field c occurs with electric field a, dense magnetic
field occurring where dense electric field is and vice versa—The magnetic and electric
fields are in time phase and space quadrature,
Since in the case under discussion the electric field is produced by the
motion of the magnetic field and the latter is produced by the motion
of the electric field, it follows that the H and £. of Eq. (3) are the same
as the H and E- of Eq. (4), and may be substituted therein. Thus, from (3)
H =yXl08,
and substituting in (4) /
108
or o-^,
and of course the second equation becomes the same as the first, i.e.,
108
or i = VHXW-8.
In our case V, the velocity of magnetic field and of the electric field, is
the velocity of light; since the velocity of light is 3X1010 cms. per sec.
we may substitute this in Eq. (3) and thus obtain
t =300 # (5)
From this relation we conclude that a magnetic field, of intensity
represented by one gauss, when moving with the velocity of light, gener
ates an electric field, at right angles to itself and to the motion, of the
intensity of 300 volts per centimeter.
From our brief qualitative consideration of the phenomena around
an antenna carrying an alternating current it follows that we may consider
the space about an antenna as occupied by two components of electric
and magnetic fields. One of these is continually moving backwards and
forwards from the antenna, so that energy is alternately given to it by
the antenna and returned by it to the antenna. Because of this back
wards and forwards motion the average displacement of this component
of either field is zero, and may therefore be known as the " stationary "
component, also known as the " induction " field; it is this component
with which students of electrical engineering are more familiar, in so far
as it is this which produces the well-known phenomena of induction
(either magnetic or electrostatic).
The other component of either field is the one which, once having
left the antenna, is prevented from returning to it and is thereafter urged
away from the antenna and continually travels outward from this with
the velocity of light. This component, while fundamentally of the same
nature as the stationary component, it is yet very different in so far as
704 ANTENNA AND RADIATION [Chap. IX
This point is illustrated in Fig. 11; in (a) are shown the magnitudes
of the actual electric and magnetic fields at various distances from the
radiator (points supposed in the equatorial plane) and in (6) and (c) are
shown the induction and radiation components of the actual field. The
electric and magnetic fields are, for all conditions, in space quadrature (i.e.,
at right angles with one another) but the time phase between the two
fields varies as indicated in the diagram.
H H
Actual fields, at first decreasing rapidly with distance, and
then more slowly, time phase between E and^H decrease*
from nearly 90°at (1) to 0°at (5)
Js Jt M
Induction fields decreasing rapidly with distance, time
phase between E and H for all points -90°
J2 Js J* J' .
< *H H H
Radiation fields decreasing slowly with distance, time,
phase between E and H for all points — 0°
, *■ Increasing distance from antenna
Fig. 11.—Actual electric and magnetic fields at different points in the vicinity of an
antenna shown in a; these actual fields decrease in magnitude with distance from
the antenna and at the same time come more nearly into time phase. The compo
nents of the fields which are 90° out of phase (in time) are called the induction
fields, shown at 6 while the components which are in time phase with each other
constitute the radiation fields, the latter decrease with the first power of the dis
tance while the former decrease with the second power of the distance.
The above discussion has been given on the basis of the antenna and
counterpoise represented by Fig. 1, but it applies equally well no matter
what the counterpoise and no matter what the nature of the source which
produces alternating currents in the antenna.
Radiated Field at any Distance from Antenna.—Before taking this
up we will discuss very briefly the distribution of the current in an aerial.
In the case of the aerial shown in Fig. 12 it is plain that, since the current
in the wire CD flows only to charge the capacity of the wire, the effective
706 ANTENNiE AND RADIATION [Chap. IX
A = -TrjfeC0SwK) ®
1 The normal development of the equation of radiation field requires more mathe
matical background than the average radio engineer possesses and it is not thought well
to introduce it here; a short analysis of the problem is given in Berg's "Electrical
LAWS OF RADIATION 707
□
t—;Im sin wt
- Eqrartorial plane-
.G'
Fig. 14.—With uniform current in wire CD the magnetic field due to this current, is
given as above.
the phase angle is different for points at different distances since this angle
is equal to to y. Substituting u=2irf and V = X/ we have:
Since the " radiation " component of the electric fields bears a fixed rela-
to the " radiation " component of the magnetic field as given by Eq. (5),
we may write:
600W/m / ( 2tt(A
e = 300A = cos (««-—j , (8)
From Eqs. (7) and (8) we obtain the effective values of the radiation com
ponents of the two fields. Thus, if :
Engineering, Advanced Course," p. 278 et seq. Eq. (20), p. 289, of that volume is
the same as the Eq. (6) given above, it being noted that Berg has used h to signify
one-half the length of the oscillator.
708 ANTENNAE AND RADIATION [Chap. IX
H= (9)
lOXd
GOOttZJ
(10)
10Xd
where I = effective value of the current in aerial, in amperes.
Eqs. (9) and (10) show that the effective value of either field varies
directly with the effective value of current in the aerial and with the height
of the aerial and inversely as the wave-length and distance from the aerial.
Now consider the case represented by a loop of wire as shown in Fig.
15. Assume, similarly to the previous case, that the capacity of the con-
Fia. 15.—In the case of a coil antenna the magnetic field at P is calculated by adding the
two fields due to CD and FG, it being noted that the currents are opposite in direc
tion.
It will be noted that the amplitude of these two fields is practically the
same, since, for great distances, d is practically equal to d+s, but the
phases of the fields are different by the amount
1 2ts ,.
7r —— radians.
\
The resultant field (h) is given by:
, ... 2wllm /, 27rd\ 2rfZ, / 2*(d+s)\
A=/ll+/l2 = __— Cos ^__j+iox(d+8)Coa («< —j-
^=-ioxrsinx (15)
„ — T OAVfield at P due to CD
0 ^ t 0g, .. .. «. .. .. FG
_ 8 OC=re8ultant field, obtained
/X ^ adding (vectorially) OB'
to OA
Fig. 16.—The field due to wire CD is shown by vector OA ; that due to FG is shown by
OB' nearly 180° out of phase with OH. The actual field is obtained by adding
vectorially OB' and OH, it being noted that they differ in phase by ^r— .
and if s
710 ANTENNjE AND RADIATION [Chap. IX
It may then be seen that if the distance between the two wires of the
loop is exactly equal to one wave-length, the resultant field at all points in
the plane of the loop is zero, while if the distance between the two wires is
o one-half a wave-length the resultant
field in the plane of the loop is equal
•Y to twice that of one wire. In other
words the resultant at any one point
Ml is due to fields of the same amplitude
but different phase, the latter depend
Fiq. 17.—At a point Y in the equatorial ing upon the distance between the
plane of the coil, equidistant from
both wires C-D and FG the radiation wires, since in one case the field has to
field is zero. travel a greater distance than in the
case of the other wire. Thus, if the
two wires were close together the resultant field at any point would be
zero.
Again, if a point be chosen such as Y, Fig. 17, in a plane perpendicular
Fia. 18.—The distribution of radiation field in the equatorial plane of a coil antenna.
to the plane of the loop and equidistant from both wires, it is plain that
the fields at Y due to either CD or FG must be 180° out of phase, since
they have to travel the same distance, and the result is that the resultant
EXCITATION OF ANTENNA 711
field at Y is zero. For points other than those such as point Y of Fig.
17 and point P- of Fig. 15 the
maximum value of the field for
a certain distance from the aerial
varies from zero at Y to a maxi High frequency alternator
mum at P.
If a curve were plotted to 1*ouIsen arc
polar coordinates, showing the Tube oscillator
effective values of the magnetic
field intensity at all the points
around the circumference of a 19 —Excitation of antenna by magnetic
circle having the loop as a center, coupling to generator,
we would obtain a diagram as
shown in Fig. 18, the intensity of the field at any point P along the cir
cumference PQR being represented by the line Oa. It may be easily
shown that the intensity of the field
varies harmonically from zero at points
R and R' to maxima at points T and 7",
and, therefore, the curves OBC and ODF
should be circles with a diameter equal
Audio to the intensity of the field in the direc
frequency tion 7*7". Such a loop will, then, radi
alternator
ate most energy in the direction T 7" in
the plane of the coil and practically
Fia. 20.—Simplest schemes for spark none m the direction RR'.
telegraphy excitation. Methods of Producing Current in
the Antenna.—So far we have dis
cussed simple antennae energized by means of an alternator placed directly
in series with the aerial; but it has already been stated that an antenna
may be energized by means
other than this one. Thus
the diagrams of Figs. 19, 20,
and 21 give various methods
of energizing the antenna,
all of which methods have
already been studied. Fig.
19 shows the alternator in
ductively coupled to the
antenna circuit, instead of Fig. 21.—Ordinary scheme of excitation for spark
having the alternator directly telegraphy.
in the antenna circuit. This
has the advantage of eliminating some of the harmonics of the alter
nator, so that the current in the antenna is now nearby harmonic. It
712 ANTENNA AND RADIATION [Chap. IX
Umbrella type
Fia. 22.—Umbrella antenna.
spark gap is directly in the antenna, while in Fig. 21 the spark gap is
placed in the so-called closed oscillating circuit. The disadvantage of
placing the spark gap directly in the antenna is due to the fact that such
a gap has considerable resistance, especially in the case of high-power,
high-voltage sets where the gap distance must be large, and when so used
will make the decrement of the antenna proper very high, which is
"T" type
—rr.
i
Fig. 23.—Antenna of the T type.
Fig. 28.—Umbrella antenna of this form is a poor radiator; the spreaders come to low.
the currents in the vertical and horizontal portions of the antenna, which
occurs on one side of the antenna to a much greater extent than on the
other. This would, of course, take place to a greater extent the larger
the horizontal portion of the aerial relative to the vertical portion. The
Clifden station of the Marconi Co. has a vertical portion about 60 meters
high and a horizontal portion about 2000 meters long; it is said to have
a large directional effect. In " L" type aerials as used on board ships,
however, the horizontal portion is never very much longer than the verti
718 ANTENNAE AND RADIATION [Chap. LX
1 It must be pointed out here that the radiation resistance of each vertical wire of
the multiple-tuned antenna cannot be calculated as though the wire stood alone, using
e.g. Eq. (21), p. 737. The presence of the other vertical wires, also carrying current,
will affect this radiation resistance, the amount of this effect depending upon the prox
imity of the various vertical wires, and upon the relative phases of their currents.
720 ANTENNA AND RADIATION [Chap. DC
Thus, in the case of the multiple-tuned antenna the intensity of the radiated
field at any point is the resultant of the fields due to each of the vertical
wires and, if suitably designed and adjusted, the resultant field in certain
directions may be made a minimum and in others a maximum, thus pro
ducing a directional effect.1
An elementary analysis shows the normal operation of this antenna to
be but slightly directive, the maximum radiation taking place at right
angles to the length of the antenna. If directive radiation is obtained by
phase shifting in the different vertical wires, the radiation resistance of
the antenna as a whole falls to a small fraction of its normal value.
" Coil Antenna."—This has already been discussed on p. 708, where
it was shown that such an aerial has a very decided directional effect,
and that the intensity of the field in the plane of the coil, where it is a
maximum, is a function of the distance between the two vertical sides
of the coil and is greatest when this distance is equal to one-half a wave
length. A comparison may here be made of the single vertical wire
with uniform current throughout and of the coil antenna with uniform
current throughout. Thus, from Eqs. (9) and (14) on pp. 708-709 for
the effective values of the intensity of the magnetic field at any distance
from antenna we have:
u ioxd w
for coil of one turn. Of course, if the coil aerial has more turns' than
one the intensity of the field is directly proportional to the number of turns,
provided that the current is uniform throughout.
If N = number of turns
H=-roxdsinT (14a)
= 2N sin —.
A
In order to make the two fields the same we must have
. ITS 1
SmX=2iV'i
1
or s =- sin -l .
7T 2JV
Below is given a table showing the value of s for different values of N.
TABLE I
Distance between sides of a coil aerial of the same height as a
corresponding single vertical wire aerial necessary to make the
fields from the two aerials alike.
N 8
1 0.17 X
2 0 .08 X
3 0.053 X
5 0.032 X
10 0.016 X
100 0 0016 X
It is understood that the coil aerial field has, in the above discussion,
been considered which exists in the plane of the coil, i.e., the plane of
maximum field intensity. The above table shows that for a single turn
coil aerial the width must be as large as 0.17X in order for it to have an
effect equivalent to that of a single wire of the same height. But with
a larger N the width may be made much smaller, so that with a 100
turns the width need only be a few meters, even with large wave-lengths.
However, with a large number of turns the question of the capacity
between turns and the effective resistance of the coil plays an important
part.
If the capacity from turn to turn is large (i.e., the turns close together)
the current will not be uniform throughout, and, furthermore, the phase
of the current at every point will be different, a condition which is not
conducive to best results as regards radiation. Hence the turns should
be separated by a considerable distance from one another. This may be
stated by saying that the capacity of the coil itself should be such
as to make the fundamental wave-length of the coil no larger than
722 ANTENNAE AND RADIATION [Chap. IX
To detector
And amplifier
Fig. 33.—Use of a coil receiving antenna; by throwing the switch down the coil acts
as a simple antenna, the coil L being used for tuning. When it is desired to get
the directional effect of the coil the switch is thrown up.
for general reception, the loop merely acting as a low antenna, timing
being accomplished by the variometer,' L. When the desired signal is
received the switch may be thrown upwards and the directive effect of
the coil thus be obtained.
For wave-lengths from 10,000-20,000 meters a square coil about
6 meters on a side with 50 turns spaced 4 cm. apart is suitable.
Because of the comparatively low receptive power of loop antennae
the receiver (detector) used must be the most sensitive available; the
use of such a detector with a good amplifier is possible because of the com
paratively low intensity of the " strays " picked up by a loop.
TYPES OF ANTENNjE 723
(1) Those which may be used only when the ship is in flight.
(2) Those which may be used at any time whether the ship is
in flight or not.
The first class includes by far the most effective type of aircraft aerial;
in this case the aerial is a trailing wire dangling from the aircraft while
the counterpoise consists
of all the metal parts of All metal work
the craft electrically con |of ship, carefully
connected to
nected together. The trail gether
ing wire is made up of a Receiving or
transmitting set
length of phosphor bronze
or silver bronze wire rang
ing between 150 and 300
feet with a weight attached
at its free end and dang
ling from the aircraftsome-
what as shown in Fig. 32.
| Weight
The transmitting or receiv
ing apparatus is connected Fia. 34.—Arrangement of apparatus on aeroplane
between the trailing an antenna;.
tenna wire and the metal
parts of the craft which, as already stated, form the counterpoise; this is
schematically shown in Fig. 34; when the aircraft approaches ground
the aerial wire is reeled in, the reeling-in apparatus being operated either
by hand or by a small electric motor.
Such an arrangement as the one above described has been used with
success on practically all types of aircraft, including lighter than air
ships. Its only disadvantage seems to lie in the fact that in the case
of a forced landing, and, more especially, in the case of an aeroplane
being compelled to dive or to " loop-the-loop " the presence of the trailing
antenna wire might prove disastrous unless it were reeled in very quickly.
724 ANTENNA AND RADIATION [Chap. IX
(a) The skid-fin antenna is nothing more than an inverted " L-an-
tenna " the top of which is mounted a few feet above the uppermost
plane and covers in length
and width practically the
entire wing, somewhat as
Wire net work
A B C D suitably shown by A BCD in Fig.
insulated from 35, where the wire DF is
rest of aeroplane
the leading-in wire and
connects directly to the
transmitter or receiver;
the counter-poise consists
as usual of all the metal
parts electrically connect
ed together. Such an
antenna has been exten
Aeroplane antenna of the skid-fin type. sively used by U. S.
Navy aeroplanes. It must
be understood that because neither the length of the leading-in wire
nor that of the top wires can be made very large, and also because
of the small separation between the antenna proper and the counterpoise
the aerial is not a very good radiator, and, in general, aircraft carrying
a skid-fin antenna also carry a trailing wire antenna. It may be said,
in a general way, that the transmitting range of a skid-fin antenna is
about one-half that of a dangling wire antenna for the same aircraft and
transmitting apparatus.
When the metal work of a ship is used for counterpoise it must be
TYPES OF ANTENNAE 725
all very carefully bonded together, otherwise sparks may occur, when
transmitting, which are, of course, an unnecessary fire risk.
(b) Coil aerials have been used more especially for receiving purposes,
in view of their ability to detect the direction from which the waves may
be coming. They are made up of several turns and of such dimensions
as will enable them to fit in between the two wings of a biplane, some
what as shown diagrammatically by B, Fig. 36. In this case no counter
poise is necessary. When the coil is used as a transmitter the greatest
radiated field will be in the plane of the coil, similarly if the coil is used
for receiving it will respond most vigorously to signals coming from the
direction of A or C. In order to either send or receive in certain direc
tions the coil may be rotated or else the aeroplane itself may be veered
around until the plane of the coil points in the desired direction. In
order to avoid either one or the other of these operations another coil
may be used with its plane at right angles to the first, in which case the
Upper wing
B
f / ^_
Y C
To
receiver
.Lower wing
Fio. 36.—Coil type antenna installed between the wings of an aeroplane: the coil sides
are placed behind the struts between the wings.
operator need do no more than move small coils within his easy reach;
this will be more fully explained later, in the section on direction finders,
p. 766.
The range of transmission of coil antennae is small, but they are used
for receiving from very great distances. Some aeroplanes carry a trailing
wire for long-distance transmission while in flight, a skid-fin antenna
while stationary, and a coil aerial for directional reception.
(c) The T-aerial for airships is schematically illustrated in Fig. 37,
where AB is the leading-in wire and CD the top of the " T." The
counterpoise consists of the metal parts of the suspended car, including
engine, etc. Such an antenna has practically the same transmitting
characteristics as a " T " antenna of the same dimensions used on the
ground; and because the wire AB is quite long and the wires CD may
be made very long as well, the range of the antenna is comparatively
large. It need hardly be stated that the construction of such an aerial
is such as to permit it to be used with equal effectiveness whether the air
726 ANTENNA AND RADIATION [Chap. IX
ship is in flight or not, and is a great improvement over the trailing wire
antenna at first used on such ships. Care must, of course, be observed
regarding the fire risk of the installation.
Underwater Antennae.—The problem of underwater antennae is
especially important in connection with submarines. Up to a few years
ago communication by radio with a submarine, while submerged, was
considered very unsatisfactory, because use was being made of antennae
similar to ground antennae such as the " T " type or inverted "L.';
These antennae, even if made of heavily insulated wire, are more or less
likely to be short-circuited by the water (particularly salt water) more
especially because, as will be made fully discussed on p. 752, the highest
potential is, when transmitting with such antennae, present at the very
end of the wires, where it is most difficult to guard against the short-
Fig. 37.—In a dirigible balloon a T type antenna is used, the counterpoise consisting of
all the metal work around the engines, etc.
the submarine loop the wires AB and A B' are the radiators while CD
and CD' radiate very little energy since they are very close together and
the fields created by them practically neutralize each other; of course
in which
wave, just at the surface of the ocean;
Hz = intensity of magnetic field x cm. below surface;
en = 2ir X frequency ;
/x = permeability of sea water = unity;
p - resistivity of sea water in abohm sper cm.3 = approxi-
mately 10u.
top of the loop 16 feet below the surface of the water at a wave-length
of 6000 meters and 200 miles from the transmitting station, while for
a wave-length of 2500 meters and the same distance signals could only
be heard with the top of the loop 8 feet below the surface of water.
If we assume that the loop was such that the " mean depth " was
5 feet lower than the top of the loop, so that in one case the effective
depth was 21 feet in the first case and 13 feet in the other the experimental
results agree very well with those predicted from Eq. (15). Thus we have
\2500X2l",y°-
antenna; it is opened and the receiving appara- point such as A (Fig. 42) and
tus put in the break. the receiver inserted therein.
Again, a living tree has been used as an antenna for receiving. The
receiver is, in this case, shown connected as in Fig. 43, where A is a nail
driven into the trunk of the tree as high up as possible. It seems as if,
here, the actual receiving of the waves was mostly effected by the leading-
in wire AB, while the upper
most parts of the tree serve
to increase the capacity of the
antenna and also to intercept,
to a certain extent, electro
magnetic waves which induce
currents in the electrically
conducting juicesofthe treeas
well as in the leading-in wire.
In general it may be
stated that almost any sys
tem of electrical conductors
more or less removed from
ground and insulated there •To receiver
from is capable of ab
sorbing energy from an
electromagnetic wave pass Fig. 43.—A tree has been recommended for an an
ing by it and, when used tenna; experiments seem to show, however, that
in connection with the mod the tree is practically nothing but a support for
ern highly sensitive vacuum- the upper end of the wire, the real receiving being
done by wire A-B.
tube detectors, may be easily
made to detect the presence of waves.
Law of Radiation of Power from an Antenna.2—Upon consulting the
literature there will be found many formulae which are supposed to give
1 See articles by A. H. Taylor, I. R. E., Vol. 7, Nos. 4 and 6.
2 For a thorough mathematical discussion, see Pierce, "Electric Oscillations and
Electric Waves."
LAW OF RADIATION 731
Equatorial plane
Earth
Fig. 44.—The energy radiated from an antenna is to be calculated from the law given
the strength of magnetic field at P, in terms of the antenna constants.
so far that the induction field is negligible. Our first assumption is that
the effective value of the amplitude of the current in the vertical part
of the antenna is at all points the same; this is nearly true for the ordinary
antenna, in which the capacity of the vertical wire is small compared to
the capacity of the network of wires generally used for the top of the
antenna. This assumption will give us a radiation somewhat greater
than the true value. The next assumption we make is that the actual
height of the antenna, I, represents the distance between the positive
and negative charges of the antenna, the flow of which causes the antenna
current J. In case of a ship antenna the height I is from the water to
the top of the antenna. In case of a land antenna, with possibly a poor
ground, it is likely that the average distance between the charges of the
antenna is greater than the distance from the top of the antenna to the
ground, so that it might seem that in this case we should take a distance
greater than the actual height, if the theory of the doublet is to be appli
cable.
732 ANTENNA AND RADIATION [Chap. IX
This is indicated in Fig. 45; it may be, for such a ground condition,
that the distance V (average distance between charges) is considerably
greater than I. We
shall neglect this ex
tra height (I' — I), how
ever, as it is not only
indeterminable, but it
contributes but little
Surface of earth to the radiation reach
r Dry + "*" + earth ing the distant point,
+ P; the electromag
++
Moist carth + + netic energy sent off
+
+ + -r- + + + from thissubterranean
+
part of the antenna
Fio. 45.—In an actual antenna there is undoubtedly a verti could only reach P
cal motion of the charges in the earth under the antenna ;
this subterranean current will contribute practically no by traveling through
radiation at distant points because of absorption in the the earth's crust, in
earth's surface. which case the atten
uation is so rapid that
the amount of energy arriving at P by this path will be negligible compared
to that reaching P from that part of the antenna specified by the height I.
We shall therefore assume that Eq. (9) represents accurately the radi
ation field at point P, the symbols having the definite meaning given
below.
2rllm
lOXcT
in which IIm maximum value of magnetic field at P, in gilberts
per cm.;
Z=actual height of antenna, in cm., from ground to top,
for flat-topped antenna;
Im = maximum value of current (in amperes) in antenna,
this value being assumed the same throughout the
height of the antenna;
X = wave-length radiated, in cm.;
d = distance from antenna to point P, in cm.
Now the energy per cu. cm. at P, due to this magnetic field, is equal
to Hm2/8nr, and as the electric field set up at P by this moving magnetic
field must be of such magnitude that it represents the same energy per
cu. cm. as that possessed by the magnetic field, the total energy per cu.
cm. (maximum value) must be Hm2/Air. As the electromagnetic wave
travels past point P with the velocity of light, the electric and magnetic
fields at this point both go through sinusoidal variations, so that the
LAW OF RADIATION 733
average value of the energy per cu. cm., in terms of the maximum value
of magnetic intensity, must be equal to one-half of the maximum energy,
If we now consider the effective value of the magnetic field at the point
P, we have (as Hm2 = 2H2, H being the effective value) the average
energy of the radiation field at P equal to i/2/4ir, the energy being in
ergs per cu. cm.
This energy of radiation travels past point P with the velocity of
light, V, so that the energy streaming past P per sq. cm. (plane of the
sq. cm. being perpendicular to distance d) per second is equal to H2V /4x.
Using now Eq. (9) to express H and substituting I (effective current) for
Im, we get
Energy, in ergs, per sq. cm. per sec. = 2 ^ ^J — = ■ (16)
The area of the sphere is 4ird2 so we have, for the total radiation from
the oscillator
Total radiation, in ergs per second
/rPPV\A „
lO2*2 -
Or we have, watts
2/2
(17)
by the whole surface of the supposed sphere if we are to get the total
radiation from the filament. To be sure, the lower half of the sphere
(below the surface A) actually gets inappreciable illumination, due to
reflection at the surface and to absorption in the material below A, but
this fact in no way alters the radiation from the filament, it merely redis
tributes the lumens after they have left the filament, and increases to some
extent the illumination in the upper hemisphere. The surface of the earth
Fig. 48.—Ir. calculating the power radiated from a coil we assume a sinusoidal distribu
tion of H in both equatorial and meridian planes.
acts in the same way towards the radio waves as does the surface A to
the light rays striking upon it.
In the case of a coil the formula for radiation may be at once obtained
by using the proper value for H in the previous deduction for the ordi
nary antenna. We suppose a coil of one turn the length of whose vertical
sides is I, and the width between these sides is s; the value of H in the
equatorial plane is
/4irll \ . ITS
The formulation of the total radiation for the coil requires the knowl
edge of the distribution in the meridian plane as well as the equatorial
plane. Assuming both these distributions sinusoidal,1 as indicated in
Fig. 48, we find the average value of H2 and thus we get the total radiation
from the coil
Watts =2407r2 ~ sin2 ™ (18)
and the square of the current, and an inverse function of the square of
the wave-length.
We will illustrate the influence of the wave-length upon the power
radiated by means of an example. Assume a simple antenna for which
I = 10,000 cms. = 100 meters
/ = 20 amperes
then if X = 1000 meters (/ = 300,000 cycles per sec.)
i no2 v 202
Power = 120*2 X — =4800 watts,
=120r£ (21)
= 240^^- (22)
vertical wire (no top wires) will have a resistance only41 per cent of the valut
given by Eq. (17) when oscillating at its natural period and if much load
ing is used, so that the amplitude of current decreases uniformly from bas?
to top of antenna the radiation resistance will be but 25 per cent of the
value calculated from Eq. (17).
In the case of the coil antenna, radiating up and down, as well
horizontally, the radiation resistance is probably much greater than tie
value given by Eq. (18), for a square coil perhaps twice as much.
Current in Receiving Antenna.—It is important to be able to cal
culate the current in the receiving antenna, because the value of this
current determines whether or not it is possible to hear the signals whid
cause such a current to flow in the receiving antenna. It must be here
stated that were it not for the interference of the so-called " strays '
(see p. 193) it would be possible, due to the extreme refinement and sensi
tiveness of modern detecting apparatus, to hear signals, no matter hew
illttllJitl- £
Oncoming:
small the currents in the receiving antenna. In view of the " strays."'
however, which also produce currents in the receiving antenna, the signal
currents must be larger than would otherwise be necessary, so that the
" strays " may interfere with the signals as little as possible; since tin
" strays " currents have considerable magnitude it follows that attention
must be paid to making the signal currents large. Hence the importance
of knowing the factors affecting the signal current in the receiving antenna.
We will determine this for a simple antenna and for a coil antenna.
Received Current in Simple Antenna.1—Consider the antenna repre
sented by Fig. 49 in the path of electromagnetic waves moving, as
1 In an article by Bennett, in the Journal of the A. I. E. E., for Nov. and Dec., 1920.
various properties of antenna; are analyzed and exact expressions for them derived
Among other things, he shows that an antenna having negligible resistance (other
than radiation), the amount of power which can be abstracted by a receiving antenna t
equal to about 6% of the amount flowing through an area (parallel to the wave from
equal to (X)s square meters, X being in meters.
MAGNITUDE OF RECEIVED CURRENT 739
Ir-^ (23)
It now becomes necessary to substitute for t its value in terms of the trans
mitting antenna constants.
From Eqs. (10) and (15) we have:
_ WwU
l" Xd '
'-Tar <24)
for a simple transmitting antenna;
T \20irNllrI . TTS
I'=-MR—am\ (25)
for a coil transmitter of N turns and a width 8 with the receiving antenna
in the plane of the coil.
1 These solutions hold only for the steady state; they are not good until the transient
condition is past.
740 ANTENNA AND RADIATION [Chap. DC
B*
Oncoming
Then, if D and D' represent the assumed positive direction of the poten
tial difference established across AB and A'B' and, if:
we have :
The total electromotive force within the entire coil is equal to the vector
difference of l&_ and Z£i. Since AB and A'B' are at practically the same
distance from the radiating antenna, the values of l£_ and will be the
same, but their phases will differ. Hence, total electromotive force within
the coil is obtained by taking the vector difference of the e.m.f.'s in the
two sides of the coil, as shown in Fig 51.
We then have
2l&_ sin ~ = electromotive force in coil
MAGNITUDE OF RECEIVED CURRENT 741
7r = ^sin^ (26)
for a single turn coil.
In case the receiving coil has A7, turns Eq. (26) becomes
7,=^sin^ (27)
for a coil of Nr turns.
And substituting for L the expressions obtained from Eq&. (10) and
(15) we finally have the following:
h- UR 8mT (28)
Fig. 51.—The effective induced e.m.f. of a receiving coil antenna is obtained by subtract
ing vectorically the e.m.f. 's. induced in the two sides.
for a transmitter coil of width s and placed with its plane in that of the
receiving coil.
For the sake of convenience all receiving formulas are collected below ;
it is assumed that: the vertical wires of the receiving antenna are parallel
to the electric field of the oncoming wave, that the transmitting antenna
current is undamped and of uniform amplitude throughout, that there
is no energy absorption by the medium, that the receiving circuits are
tuned to the transmitting frequency, and that the planes of the coils
742 ANTENNAE AND RADIATION [Chap. IX
'•=w (30)
Coil to antenna
. 376JVZW .its foU
Antenna to coil
7'=H^sinT (32)
Coil to coil
/,-752yJ Bin ^ anf (33)
In case the angle ^- is sufficiently small that the angle may be sub-
A
stituted for its sine these formulae become somewhat simpler in form.
We have
Coil to antenna or antenna to coil
. 1180A7UT .
Coil to coil
. 7450NNrU*8rI i
\Mit~- (35)
In every one of the preceding formulae it is to be noted that the received
current is:
A direct function of receiving and transmitting antenna heights,
and the transmitting antenna current.
An inverse function of the wave-length, to the first, second, or third
power the distance and the resistance of the receiving antenna
circuit.
Returning to the matter of the effect of " strays " it is apparent that
if the received signal current is made large by suitably arranging the
receiving antenna constants, then the " strays " current will at the same
time be made large, and thus reception may be poor. On the other hand,
if the receiving antenna constants are poor and the transmitting antenna
constants very good, then the received signal current will be large while
the " strays " current will be small, with consequent improvement in
1 It is to be pointed out that whereas the constants in these formulae are given to
the third significant figure, the actual received current may differ from the predicted
value greatly; refraction and reflection of the waves play an important role in trans
mission.
COMPARISON OF ANTENNA TYPES 743
Factor is
When there is absorption 2
-0.000047-^=
Factor is « v*.
R=12(h2^ (19)
for simple antenna
72 s2
22 = 240^-^ (20)
if these masts were replaced by wooden or concrete masts the latter might
suffer considerable dielectric loss.
Since eddy currents and the loss due thereto increases with an increase
of the frequency it follows that the effective resistance representing this
loss increases with the frequency or decreases with an increase of the wave
length.
(5) The loss due to the leakage currents flowing between the aerial
and the counterpoise should be kept down by using suitable insulators
between the antenna wires and the supports and also between the lead-in
wire and any walls through which it passes so that the resistance of the
leakage paths may be made as high as possible. The resistance of the
leakage paths is, of course, very much diminished in wet weather and,
especially, where sprays from a rough sea reach the aerial. It has already
been pointed out that in the case of submarines the ordinary antenna is
very inefficient, except on a smooth sea, because of the salt-water sprays
producing large leakage currents to ground and thus absorbing the largest
part of the energy given to the antenna.
Since the loss due to leakage is a direct function of the (voltage)2
and the latter is inversely proportional to the frequency (for a given
current) it follows that the effective resistance correponding to leakage
loss varies inversely as the square of the frequency and directly as the
square of the wave-length.
(6) The loss due to corona takes place at high voltages and is due
to the partial ionization of the air about the antenna wires, which causes
the air to become a partial conductor and carry a current. At night the
corona effect is visible through the glow which accompanies it. The
corona does not begin to take place except at a certain definite voltage,
which, however, varies with the shape and size of the conductors; this
critical voltage is smallest where the conductors are small and at points
and corners. Once the critical voltage has passed, a large amount of
energy loss may take place due to corona. As a matter of fact this phenom
enon is to a certain extent a limitation upon the amount of power which
may be radiated by an antenna in so far as, for an antenna of certain
dimensions, the greater the power given thereto the greater must be the
voltage and hence the greater the corona loss; thus, for a certain antenna
there is a limit to the power input, beyond which it is inadvisable to go
because a large amount of power is wasted due to corona loss, and little
is gained as far as power radiated is concerned.
This limit is reached when the voltage at the ends of the antenna is
in the neighborhood of 150,000 volts.1 This is one reason why the use
of very large radiating systems for large stations is imperative in order
1 As mentioned before this limit, depends upon how well the antenna conductors are
kept free from sharp points and edges.
COMPONENTS OF ANTENNA RESISTANCE 749
that the large capacity resulting therefrom may keep the voltage below
the limit of corona loss even for large amounts of power input. The
effective resistance representing this loss is for a fixed current an inverse
function of the frequency and a direct function of the wave-length, for
voltages above the critical value.
From the above we have, then, that for a certain antenna and for a
fixed current therein :
Radiation resistance is an inverse function of (X)2;
Resistance corresponding to (2) ,(3) and (4) (eddy currents and
skin effect) decreases as X increases;
Resistance corresponding to (1), (5) and (6) (dielectric loss, leakage,
corona) increase with increase in X.
The above relations are roughly indicated in Fig. 52, where the various
components of the antenna resistance have been plotted, together with
Wave length
Fio. 52.—Various components of antenna resistance, showing approximately how they
vary with wave-length.
curves showing the total loss resistance and the total antenna resistance.
From the component curves A, B, and C, we have obtained the total loss
resistance curve, by adding the ordinates of curves B and C, and,
finally, the total antenna resistance, curve H, by adding the ordinates
of the curves A, B, and C. The important point brought out by the
curves is that, because some of the loss resistance components are a direct
function, and others an inverse function, of the wave-length, it follows
that the total loss resistance has a minimum value, as represented by the
point K on curve F. It would seem, then, as if from the point of view
750 ANTENNA AND RADIATION [Chap. IX
while the other curve shows large resistance to the right of the minimum
value. This is accounted for as follows: a trailing-wireantenna is a much bet
ter radiator than a skid-fin antenna, hence the radiation resistance should
be larger in the former and therefore that part of the curve to the left
of the minimum, which is very much affected by the radiation resistance,
should have the larger ordinates in the trailing antenna than in the skid-
fin antenna curve. On the other hand, since the skid-fin antenna is very
close to the aeroplane structure, the dielectric and leakage-loss resistance
should be very much greater than in the trailing-wire antenna, and hence
the ordinates of the resistance curve to the right of the minimum value
should be much larger. The minimum resistance for the skid-fin antenna
is seen to be less than for the other in view of the shorter length of wire
used and hence less ohmic resistance.1
The very large land stations have a minimum antenna resistance
between 1 and 2 ohms; the minimum resistance for the antenna of a
5-kw. set is generally between 5 and 10 ohms. Portable field antenna
sometimes have a resistance as high as 50 ohms.
What has been said of the resistance of an ordinary antenna applies
to a coil radiator as well, except, of course, that the components of the
total resistance are related to one another in a somewhat different way;
and this is true, to a certain extent, of any one type of antenna relative
to any other. The most important thing about a coil radiator is that
its counterpoise or ground resistance is practically eliminated, and hence
a much "less total resistance is obtained. Therefore, a certain voltage
will, when impressed upon a coil radiator, produce a much larger current
than in a simple antenna having the same radiation resistance as the coil ;
hence it is possible to radiate larger amounts of power by means of the
coil than one might at first think; for ordinary-sized coils, however, the
frequency must be very high if appreciable power is to be radiated.
Natural Wave-length of Antenna.—Consider an antenna in its simplest
form, i.e., a long vertical wire connected to the alternator as shown in
Fig. 55. The antenna wire has :
(1) Distributed inductance.
(2) Distributed capacity.
(3) Distributed resistance.
(1) The distributed inductance is due to the ability of every part of
the antenna to develop magnetic lines of force. Assuming the absence
of magnetic material near the antenna, its inductance per unit length
should be practically uniform throughout its height.
1 For a number of curves of aircraft antenna resistance see Johnson's paper in I. R. E.,
Vol. 8, Nos. 1 and 2.
Also see Scientific paper No. 341 of Bureau of Standards, by J. M. Cork.
752 ANTENNAE AND RADIATION [Chap. IX
same throughout the antenna wire of Fig. 55. The current in such a
wire exists because electrons are being made to flow alternately into and
out of a capacity; at the very end of the wire past which there is no capacity
the current must be zero and will grow in value for points farther away
from the end. The flow of this rapidly alternating capacity current
(leading current) through the inductance of the antenna wire produces
an increasing voltage as we proceed towards the end of the wire, a phenom-
, ,B
pTda
\
i
—j
1 f
a b
Fig. 56.
Fig. 56.—If the current at the base of an antenna is held constant while frequency is
changed the distribution of current along the antenna will change; this will change
the amount of magnetic energy associated with the antenna and hence will change
its effective self-induction.
Fig. 57.—By considering the leakage, capacitance, inductance, and resistance of a
small element d, the equations for current and voltage may be obtained. Even if
the resistance and leakage are neglected fairly accurate expressions will be obtained.
enon which is well known to the electrical engineer in the case of long
distance transmission lines. In order more fully to understand the dis
tribution of current and voltage we are giving below the expressions for
the current and voltage in a simplified antenna or, more definitely, an
antenna having uniformly distributed inductance and capacity and no
resistance whatever. Thus, let AB, Fig. 57, represent such an antenna.
Let E =e.m.f. vector at any point P, the effective value of the e.m.f.
being E;
/= current vector at any point P, the effective value of the
current being /;
754 ANTENNAE AND RADIATION [Chap. IX
(42) and (43). At the end of the antenna the current vector is zero
while the voltage vector is a maximum. At the alcernator end E and 7
may have any value, depending upon the value of Vbx and the height
of antenna. The example represented by the curves is not one which
is ever purposely realized in practice, since the antenna would, in this
case, produce a comparatively weak electromagnetic field, in view of the
fact that the current and voltage are positive over certain portions of the
antenna and negative over others; hence
the effect of certain parts of the antenna
would be partly or fully neutralized by
other parts. The curves, however, show
a more or less extreme possibility. The
Fig. 58.
Fig. 58.—A possible form of excitation of an antenna, at a frequency much higher than
its natural frequency.
Fig. 59.—The ordinary form of voltage and current distribution on an unloaded antenna,
excited at its natural wave-length.
more usual case is that represented by Fig. 59; this case will be dis
cussed more fully a little later.
Again, we note from Eqs. (42) and (43) that, since E and I are trigono
metric functions of ad, this quantity must represent a space rate of change
of angle, as distinguished from u, which represents a time rate of change
of angle. Now, looking at the curves of Fig. 58, which represent nothing
756 ANTENNA AND RADIATION [Chap. IX
but so-called stationary waves of e.m.f. and current, the distance between
such points as B and D must be the length of the stationary wave over
the antenna, and this distance must be such as to make
where
Xi = wave-length of stationary waves in centimeters,
or
Xi=£ (44)
a
Since
a = y/bx and b = a>Ci, x = wLi,
a = o3\rLiCi. (45)
If
/ = frequency of alternator in cycles per second,
a=2ir/vT[c7 (46)
Thus, the length of the antenna stationary waves, Xi, is equal to the
velocity of propagation of the waves divided by the frequency; but this
quotient represents the length of the electromagnetic waves, therefore,
the wave-length of the stationary antenna waves is equal to the wave-length
of the electro-magnetic waves in free space.
Now, going back to Eq. (41) on p. 754 we may solve for the value
of -r^, thus:
Io
|2 cot al (48)
Io 0
CURRENT AND VOLTAGE DISTRIBUTION 757
Since Eo and Io are the e.ra.f. and current at the alternator their ratio
must be the effective impedance of the antenna at the point where the
alternator is connected. In our case the expression for this impedance
is always imaginary, and therefore, represents the value of the reactance.
This result was to be expected, since the resistance has been omitted in
our simplified discussion.
Let Xo = antenna reactance at the alternator in ohms.
Then
Xo = — rCotoZ (49)
o
Substituting for
we have
X0 = -yJ£cot2*^l (50)
or
X0 = -^cot^-, (51)
etc. Hence the antenna can be made to resonate at the frequency fi and
at frequencies three times, five times, seven times, etc., fi. On the other
hand, a little to either side of the points 2, 4, 6, etc., the reactance is
infinite and directly at the points 2, 4, 6, etc., the resistance of the antenna,
as measured at the base, becomes infinite so that practically no current
can be caused to pass into the antenna at the frequencies S2, /■», /g, etc.,
which are two times, four times, six times, etc., the first resonating fre
quency f\. It is not out of place to point out here that the first resonating
frequency f\ is such as to produce one-quarter of a stationary wave over
the antenna, as may be easily seen from the discussion of p. 757. This
Fia. 60.—As the frequency impressed on an antenna is varied the reactance (as measured
at the base) goes through the changes indicated here; in case an antenna with appre
ciable resistance had been considered the reactance changes from its high positive
value to high negative value by going through zero values at 2, 4 and 6.
A(
capacity and inductance per unit length of the part BC are different from
those for part A B. However, in view of the fact that for the part BC
the capacity per unit length is kn times 1 that of a single wire, while the
inductance per unit length is ^ times that of a single wire, the product
of these two quantities remains the same, and it is safe to take the dis
tance A BC as again being approximately one-quarter of the fundamental
wave-length of the antenna.
The inaccuracy of this simple rule increases as the form of the aerial
departs from the simple one given in Fig. 60. It has been found experi
mentally that the natural wave-length is connected to the extreme length
1 k is a constant less than unity; it approaches unity as the different wires of the
antenna are spaced farther apart.
760 ANTENNAE AND RADIATION [Chap. IX
the effect of the series inductance is to make the natural frequency of the
entire antenna circuit smaller (larger wave-length) than that of the antenna
alone, and vice versa for the case of the series condenser.
It will be noted that by making the slope of the curve B very great
(large inductance) the antenna circuit may be caused to have a very
much lower fundamental frequency than that of the antenna alone, the
Fig. 64.—The diagram of reactances of an antenna (A), a coil (B), and a condenser
(D), shows how the natural wave-length of an antenna circuit is changed by adding
loading coil or shortening condenser in the base of the antenna.
limit being zero. In the case of the series condenser it will be observed
that no matter how large we make its reactance (how small its capacity)
the maximum frequency obtainable is twice that of the fundamental
frequency of the antenna proper. Thus, if an antenna has a natural
wave-length of, say, 500 meters, it is impossible to change this to any
thing less than 250 meters by placing a condenser in series with the
antenna.
The changes which take place in the natural wave-length of an antenna,
as various coils or condensers are used in series with it, are shown in Figs.
762 ANTENNA AND RADIATION [Chap. DC
4500
4000
3500
k-/.
8000
r
-
2500
C -i§L
2000 >
\ irii Uio 1 ot wa 'el BCl ll w knc ine
s nsrl • U re 1 nte ma 176 ■el en km
1500
1000
500 - -
65, 66, and 67. A single-wire antenna was used in the test, about 175
meters long, having (unloaded) a natural wave-length of 700 meters.
As a variable inductance, in series with the ground connection of the
antenna was changed, the natural wave-length of the loaded antenna
increased as shown in Fig. 65. Then keeping the value of the loading
inductance fixed at 1140 a variable condenser shunted around this
load coil brought about the changes in wave-length shown in Fig. 66.
The effect of putting a " short-wave " condenser in series with the
base of the antenna is shown in Fig. 67 ; it will be seen that with no capacity
in series with the base of the antenna (that is, the lower end of the antenna
1
Na urn1 Wl re tli. ml' ;ul< 1
700
600
e
600 a
8
■9
400
i ^
/yi
300
H I ,nv. t of ser cs c om ens :r
z o 1 W, ive em to i f Bl ten na
200 >-
Sir wir ■ al ten 11 1 70 I let* rs 1, Og
W
100
E =■ , cos ad
cos al
and
I=- sin ad
sin al
Cases (4), (5) and (6), illustrated in Figs. 70, 71, and 72, are analogous
to cases (1), (2) and (3), respectively, except that the distribution of
voltage and current takes place over
the entire antenna length and not
over the vertical part alone. The
result of this is that the vertical part
has a current of more nearly con
stant effective value over the entire
height; of course this result is especi
ally desirable in view of the better
radiation produced by a uniform cur
rent over the vertical wire.
Experimental curves of voltage
and current distribution for a low-
frequency circuit, representing at low
frequency what an antenna docs at
high frequency, bear out the theo
retical predictions already discussed,
except that, whereas in the theoreti Fig. 69.—Voltage and current distribu
cal curves of Figs. 69 and 72 we have tion in simple antenna with shortening
shown the effective value of the volt condenser.
age to actually become zero at points
marked K, this does not happen in the experimental curves.1 The reason
for this lies in the fact that the theoretical curves have been plotted
on the basis of Eq. (37),
which takes no account
of the resistance of cir
cuit, while actually there is
resistance. The effect of
the resistance upon the
effective value of the volt
age along the antenna is,
generally, to make it im
possible for it to become
zero for, at the nodal point,
wmmmr, where the voltage should
Fia. 70.—Voltage and current in unloaded inverted be zero, there is power flow-
L antenna. ing past the nodal point to
supply the losses for the
rest of the antenna, and in order for this to take place the voltage
must be greater than zero. In the case of no resistance the voltage along
1 See Morecroft, "Experiments with long electrical conductors," Proc. I. R. E., Vol.
5, No. 6, Dec., 1917.
766 ANTENNAE AND RADIATION [Chap. IX
the antenna has different effective values, but the same phase for the
same half-wave and changes in phase through 180° at the point where it
passes through its zero value. On the other hand, in the actual case
the voltage all along the
antenna has not only
different effective values,
but different phases as
well, as may be shown by
the vector diagram of Fig.
73 where the vectors rep
resent voltages at differ
ent points of the antenna
of Fig.* 72, the numbered
vectors corresponding
with the numbered posi
tions on the antenna. At
Fig. 71.—Current and voltage in inverted L antenna nodal Points the voltage
having a loading coil. would be very small as
shown at £3; its magni
tude (for a given impressed voltage) becomes smaller as the resistance
of the upper part of the antenna is decreased.
Direction Finders.—This is the name given to receiving antennae
so constructed as to indi
cate the direction from
which the signals are com
ing. The simplest direction
finder is a receiving coil
antenna; it has already
been pointed out on p. 708,
that such a coil when used
as a transmitt er will produce
the maximum intensity of
field in its plane ami the
minimum at right angles
thereto; in a similar manner
the coil will, when receiving,
have the greatest current
produced in its circuit when Fig. 72.—Current and voltage in inverted L antenna
its plane is in the plane of havin8 shortening condenser,
propagation of the waves
and the minimum when its plane i.s perpendicular to the plane of propa
gation of the waves. Thus, if the coil be arranged so that it may be
made to rotate with respect to its vertical axis while signals are being
DIRECTION FINDERS 767
e2 = -Mcos/3^ (56)
770 ANTENNAE AND RADIATION [Chap. E
Substituting in (55) and (56) the values of ix and ia of (53) and (54) we
have:
ei = — oiMIm cos a sin (3 cos ait, (57)
02 = oiMIm sin a cos 0 cos ut, (58)
e=ei+e2 = — uiMIm cos &><(cos a sin 0— sin a cos0). . (59)
The maximum value of e for a given value of a and 0 evidently occurs
when cos ut = 1 or
Max value of e = uMIm (cos a sin /3— sin a cos 0). . . (60)
Since the maximum value of the current flowing in the coil K is directly
proportional to the maximum value of e, and since this latter changes
as the angle 0 is changed, i.e., as the position of K changes, it follows
that the signal strength will vary as K is rotated about its axis.
We may now find the values of 0 which will make the signal strength
zero or a maximum respectively; this will occur when the value of the
parenthesis of Eq. (60) is zero or a maximum.
We can put cos a sin 0 —sin a cos /3 =sin (0 — a) and then get
sin (/3-a) =0 when 0-a=O° or 180°
from which 0 =a or = 180°+a (61)
sin (0 — a) = maximum when 0 — a =90° or 270°
from which 0 = 90° +a or =270° +a. . . (62)
We may therefore state that extinction of the signals will take place
when the normal to the plane of the coil K is parallel to the direction of
the incoming waves, and that maximum strength of signals will resulT
when the normal to the plane of K is at right angles to the direction of
the incoming waves. It will be noted that, in this particular case, where
Di and Th are parallel to A\ and A% respectively, the results are the same
as if the whole system of coils were reduced to the coil K alone used as a
coil antenna; for, when the plane of K is perpendicular to the directioi;
of the waves, the strength of signals is a rninimum, and when the plane
of K points towards the direction of the waves, the strength of signals
is a maximum.
A discussion similar to the one given above may be applied in a similar
manner and with similar results to the case of damped waves. Of course
it is plain that the results expressed by Eqs. (61) and (62) are vitiated
by the existence of any dissimilarity between the circuits A\-Di~Fi and
Ajj-Aj-fV In order to avoid any dissimilarity as much as possible, even
at the expense of sensitiveness, the condensers Fi and F2 are often dis
pensed with, and the circuits are thus made aperiodic.
By fitting coil K with a suitably calibrated dial and rotating the coil
until weakest signals are obtained, the direction of the incoming waves
may be determined with a comparatively small percentage of error. Use
DIRECTION FINDERS 771
has been made of the direction finders for determining the position of a
ship or aircraft of some kind. Thus, in the case of a ship S which is
nearing the port, the ship may get her bearings quite accurately in one of
two ways, as indicated below:1
(a) The ship may be fitted with a directional receiver, and the stations
A, B, C, D may be fitted with non-directional transmitters continually
sending out different
identifying letters. The
operator on board the
ship is assumed to know
the positions of the sta
tions A, B, C and D on
his chart. He would
obtain the angles o, /S, 7
(see Fig. 77) by mani
pulating his directional
receiver. By plotting
the points A, B, C, D
and the angles a, 0, 7
the position of the ship
may be obtained.
(b) The ship may .
be fitted with a non-
directional transmitter
continually sending out
some identifying letter,
and the stations A, B,
C, D may be fitted with
directional receivers.
The operators at A, B,
C, D would, by manip
ulating their direc
tional receivers, obtain f,g 77 —Arrangement of shore station around a port to
the angles which the furnish radio : compass service to incoming ships,
lines SA, SB, SC, SD
make with the north and south line and report these angles by telephone
to a central station F, where the angles are plotted and the position
of the ship is determined. Station F will then transmit the position of
the ship by radio to the operator on board the ship.
1 Ships desiring radio compass service must be fitted to receive on 450 meters in
American ports and 800 meters in European ports; thus a ship sailing from American
ports should now have receiving equipment calibrated at 300 and 600 meters (man
datory) as well as 450 and 800 meters.
772 ANTENNAE AND RADIATION [Chap. DC
This latter method is the one used in the port of New York and Bean
to be preferable to the former, in so far as this requires the presence of a
skillful operator, capable of plotting the ship's position, on board each
ship, whereas in the other case all the plotting is done in one single cen
tral station, where much greater accuracy may be obtained.
So far we have shown how, by means of the single coil antenna or by
means of a goniometer, we may be able to determine the plane parallel
to which the electromagnetic waves are
acting; but we have not yet determined
the exact direction of the mcoming waves.
Thus, we have been able to find that the
waves may be acting along the line AB,
but not whether they are coming from 1
or from B; this determination is techni
cally known as the " elimination of the
180° uncertainty." In most instances the
direction from which the waves are coming
is known, especially in communication
between ship and shore and vice vera;
but sometimes this is not the case.
In order to eliminate the 180° uncer
tainty the single-coil antenna or the double-
coil antenna of a goniometer is accom
<
panied by a vertical-wire antenna locate!
in the axis of the coil or coils, as shorn;
for the case of the single coil antenna of
Fig. 78, where A BCD is the coil antenna
FG the vertical-wire antenna, connectec
to ground in series with the tuning in
ductance H and the key K. The in
*
ductance H is loosely coupled to the col
/ p
N inserted in series with the coil antenm
To detecting The operation of obtaining the direction d
apparatus the incoming waves would be as follow;
Fia. 78.—To eliminate the 180° (1) With key K open and the cgl
uncertainty
. , it, is necessary to ,.use antenna
, ,
turned, mto
. . some position where ■
a simple antenna in connection ^
with the coil antenna. tne signals may be easily heard, tune the
coil antenna circuit to the mcoming wave
frequency by means of condenser P.
(2) Close K, and, without changing condenser P, adjust H until the
circuit of the vertical wire antenna is tuned to the frequency of the incom
ing waves, which will be denoted by maximum noise in the receivers con
nected in the detecting apparatus.
DIRECTION FINDERS 773
(3) Again open key K. Turn the coil antenna until the signals dis
appear or become a minimum. The normal to the plane of the coil when
in this position represents a line parallel to the direction of the incoming
waves.
(4) With key K still open turn the coil antenna 90° from position of
(3). Maximum signal strength will
then be obtained.
(5) With the coil antenna in the
position of (4) depress key K. The
signal strength will either increase or
decrease relative to that of (4), de
pending upon the exact direction from
which the waves are coming. If the
signal strength decreases upon closing
K the waves are coming from a cer
tain direction, and if it increases the
waves are coming from the opposite
direction. Whether it is one direction
or the other may be told by previously
calibrating the entire apparatus.
Waves are used for this calibration
which are known to come from a
definite direction.
The reason for the behavior of the
vertical-wire antenna together with
the coil antenna is as follows: Con- Fig. 79.—Direction of assumed positive
dder Fig. 79 and let the arrows repre- e.m.f. induced in the conductors of
jent the assumed positive directions two antennae of Fig. 78.
jf the electromotive forces in the
.vires AB, FG, CD. Let the direction of the incoming waves be as repre
sented by W, and let the plane of the coil be parallel to the direction
)f the waves.
E=Ei-Ez
It is plain that no matter what the angle a
Fig. 80.—The e.m.f. act the vector E will always be at right angles to 2?2-
ing in the coil antenna The current h will, since the wire antenna is
(Fig. 79) is the vector tuned to the incoming waves, be in phase with the
difference of the e.m.f. e.m.f. E2. The e.m.f. E„ induced in N will be 90°
in its two sides and is behind the current h or 180° from the e.m.f. E.
shown at OE; current
flowing in the simple Since the total e.m.f. producing the current in the
antenna is shown at 011 coil antenna is E—EH, this e.m.f. will, in this case,
and this induces a volt- be OA, less than if the coil antenna alone were
age in the coil antenna acting, when the total e.m.f. would be E.
equal to OEn. Now consider the case when the waves are
coming from the opposite direction to W. Let
the symbols: E!\, E'a, E'z, E', V2, E„' represent quantities correspond
ing to Ei, E2, E3, E, h, En, with the waves from the direction opposite
to W. In this case the waves will
strike conductor CD first, and hence
the e.m.f. produced therein will lead
the e.m.f. 's of FG and AB. The
vector diagram will then be as shown
in Fig. 81. As before E'=E\-E'z
and will be always perpendicular to
E'2. The e.m.f. E'„ will now be in
phase with E' and the total e.m.f.
(E,+Efn) producing the current in
the coil antenna will, in this case, Fig. 81.—This diagram shows how the
be OA, larger than if the coil anten phase relations of the various e.m.f. of
na alone were acting, when the total Fig. 80 change if it is assumed that the
e.m.f. would be E'. signal waves are coming from the oppo
Thus it has been shown that if the site direction to that assumed in Fig. 81.
waves are coming fromTF, Fig. 80, the
action of the current in the vertical-wire antenna is to diminish the current
in the coil antenna (and hence the strength of signals), while if the waves
DIRECTION FINDERS 775
are coming from the opposite direction the action of the vertical-wire
antenna is to increase the strength of the signals. It will be understood
that whether the signal strength is increased or decreased by the action
of the vertical-wire antenna will depend not only upon the direction of
increasing waves, but also upon the direction of the winding on the coils
H and N and the position of these coils relative to each other. This is
the reason why the entire apparatus has to be calibrated beforehand.
In the case of a goniometer the vertical wire antenna is coupled to both
of the coil antenna?, and the manipulation of the apparatus is similar to
that for the single-coil antenna.
Incomplete Extinction of Signals.—Unless special precautions have
been taken coil antennae do not give zero signal, in any position; the
signal goes to a minimum, but is not extinguished. This effect is pro
duced by the coil acting to some extent like a simple antenna. The
two wires leading from the coil to the detecting apparatus unbalance the
coil electrically, one of them going directly to ground (filament circuit
of detecting tube) and the other connecting to ground only through a
very high impedance. This asymmetry is sufficient to prevent a " silent "
setting to be made with the coil, because the antenna effect gives an
e.m.f. 90° out of phase with the coil effect. By a suitable auxiliary cir
cuit it is possible to eliminate this antenna effect, thus getting a more
accurate setting, if necessary.
Reliability of Direction Finders.—The precision with which a direction-
finding receiving coil can be set (under laboratory conditions) is probably
less than 1°; in general an operator can set more precisely for minimum
signal strength than for maximum unless two coils, at right angles to
each other, are used and one of them arranged for commutation. In
this scheme the combination of coils is so placed that one coil (the one
without the commutator) lies approximately in the direction of the
signal, thus being set for maximum reception. The other coil (evidently
set for minimum signal) is connected in series with the first by means of
the commutator. The operator then orients the apparatus until the
commutation of the one coil makes no difference in the signal strength.
The precision of setting with this apparatus is probably much better
than 1°.
It would seem that it is not worth while to increase the precision of
direction finders beyond that now attainable, because of the non-linear
propagation of radio waves. With short waves there is not much devia
tion from straight line propagation, under ordinary conditions; with the
long-wave-signals, however, the propagation seems to be rather erratic.1
With signals from 10,000-20,000 meters long, an apparent change in
1 See Bureau of Standards Scientific Paper No. 353, reporting experiments by
A. H. Taylor.
776 ANTENNA AND RADIATION [Chap. DC
when
is
state"
"steady
ifirst
B
the
how
seaset ptcreiun—strvead;, end.
voltage
The
shows
Fig.
film
Am82.
nxhows
anup Voltage
voltage
the
itand
middle
(C
state)
at
=20,
B
=212,
msteady
popen
heres ed
c
X
'If
Cti/r
frequency-
Xmju**Hj
JB-
£
(reverb)
enS■••■.«
aend
the
of
=345.
rtnitfiecnial
.7*
ir-
'A/a
778 ANTENNA AND RADIATION [Chap. IX
cab/* *, , r*lV£$2f
Fig. 83.—Here the artificial antenna was forced to vibrate at three times its fundamental
frequency; it will now be noted that the voltages at B and C are in opposite phase
in the steady state. From the film it can be seen that the original pulse arrives
at C one-half a cycle after passing point B.
£_ 9 *wet—i
mfoft « /o-o £^
tftf Am/Irs ti ^mk
Fig. 84.—WTiile the steady state is being set up some sections of the antenna may carry
currents greater than the steady state values.
TKANfcSIENT CONDITION IN AN ANTENNA
780 ANTENNA AND RADIATION [Chap. DC
/mdu^emW° = 2^W
It has already been noted that the deflections of the hot-wire ammeter
are proportional to I2, or to the watts (PR) lost in the instrument itself.
For this reason it has been erroneously called a watt-meter, when the scale
is graduated in (amperes)2 and not in amperes. The ammeters used in
modern wave-meters are graduated in either of these ways, in fact, the
(ampere)2 graduation is the more convenient for certain measurements.
It should, however, be clearly kept in mind that the instrument is not
really a watt-meter in the ordinary sense; the scale calibration generally
gives the watts used in the instrument itself.
b. Crystal Detector and Phones.—The hot-wire ammeter is applicable
only when the wave-meter is to be coupled to a circuit of considerable
power, so that appreciable currents are caused to flow in the wave-meter
circuit. When the induced currents are exceedingly small, as when the
wave-meter is coupled to a receiving antenna, or a buzzer-excited wave
generator, only the most sensitive of current indicating devices may be
used. The crystal detector and phones, which have already been de
scribed in connection with the reception of spark signals (see page 339)
786 WAVE-METERS AND THEIR USE [Chap. X
are eminently suited for this purpose, and various schemes for connecting
these into the wave-meter circuit have been tried. These schemes are
shown in Fig. 4, which also shows the relative sensibility of the different
arrangements.1
Scheme No. 1 is probably the most generally used, and its operation
and action is exactly similar to that involved in the reception of spark
signals (see page 339). It illustrates what is known as the " direct "
connection of the detector and phones. Circuit No. 4 represents what is
called the " unilateral " connection, the phones and detector being com-
nected in a closed loop, which is connected to the wave-meter circuit at
one point only. This scheme is not used to any great extent, due to its
poor sensibility, but possesses an advantage in that the calibration of the
wave-meter is not affected appreciably, by the character of the detector-
Fio. 4.—Various schemes of connecting crystal rectifier and telephones for indicating
resonance in a wave-meter excited by a very low-powered source.
phone circuit. Thus in circuit No. 1, the leads going to detector and
phones may possess considerable capacity (as indicated diagrammatically
by the dotted condenser), which capacity is in parallel with the wave-
meter condenser. The wave-meter calibration will thus no longer apply,
since the circuit capacity has been augmented by an uncertain amount,
and the determinations are therefore inaccurate. The amount of error
produced evidently depends on the relative value of the variable wave-
meter capacity, and the external fixed capacity. This error will be a
maximum when the variable condenser is set at the minimum value,
the meter reading being less than the true wave-length which is being
measured. As the variable capacity is increased, the error decreases,
and may become negligible at the larger wave-lengths.
With the " unilateral " connection, however, the wave-meter circuit
constants are unaltered, regardless of the characteristics of the detector-
1 Circular of the Bureau of Standards, No. 74, p. 105.
RESONANCE INDICATORS 787
phone circuit, and any pair of phones with associated leads, etc., may be
employed. The action of this connection is essentially one of electro
magnetic induction. The high-frequency magnetic field linking L links
also the closed loop of the phone detector circuit (the coupling is very
small, however, and this probably accounts for the low sensibility), and
induces in it a radio frequency e.m.f., which will cause rectified radio
frequency wave-trains of current to flow in the loop. Electrostatic effects
also play a considerable r61e in the operation of this detecting scheme.
The connection has an important application to portable or field-type
wave-meters, which may thus be used with phones whose leads vary in
length and other characteristics, i.e., size, insulation, and configuration.
Since the wave-meter is independent of these variations, accurate determi
nations can be made, if the audibility requirements do not necessitate
coupling the wave-meter too closely to the exciting circuit, while varying
degrees of error would occur with connection No. 1, which requires the
wave-meter to be used with the phone-detector circuit with which it was
calibrated, if accuracy is to be obtained.
Circuit Nos. 2, 3, and 5 all operate through the trapping of a charge
on one condenser plate (by means of the rectifier) during the passage
of the wave-train, the condenser then discharging through the phones,
giving an audible click. Thus in circuit No. 2, if we assume that the
detector will permit current to flow downward, but not upward, it is evident
that a positive charge will accumulate on the lower condenser plate during
the passage of a wave-train. After the group has passed, the condenser
discharges downward through the phones (it cannot discharge up through
the detector) and up through the inductance of the wave-meter circuit
until the charges on its plates are neutralized.
The action of circuit No. 3 is similar to that of circuit No. 1.
In circuit No. 5 the charge is trapped on one plate of the condenser
C in the phone-detector circuit. If we again assume the detector to be
conducting for downward-flowing current, then the right-hand plate of
the condenser will accumulate a positive charge. Current will also flow
through it in the opposite direction through the phones, but with difficulty
due to greater impedance of the phones. The condenser charge, caused
by the asymmetrical flow of current, is discharged upward through the
phones (it cannot pass through the detector) and causes the phones to click
once per wave-train as in previous circuits.
Circuit No 6 is better suited to large currents, the telephone and
detector being replaced with a small hot-wire ammeter, when particularly
large currents are to be indicated. If a small power exciting source is
coupled to the wave-meter, the energy transferred from the wave-meter
circuit to the aperiodic detector circuit is too small to give clearly audible
indications, unless the coupling between the exciting circuit and the wave
788 WAVE-METERS AND THEIR USE [Chap. X
Fig. 5.—Two types of thermo-couples for use with comparatively large currents; the
most sensitive couples use an extremely fine welded joint at the contact, and are
mounted in a small evacuated glass bulb.
also affects the sensitivity as this determines the rise in temperature; the
best couples are enclosed in an evacuated glass bulb.
The metals usually used in the couple are constantan and steel, or
constantan and maganin, the former metal being a copper-nickel alloy
while manganin represents an alloy of copper, manganese, and nickel.
The materials are not expensive and their combination possesses perfectly
satisfactory thermoelectric properties. A typical constantan-steel thermo
element would have wires of about 0.02 mm. in diameter and 4 mm. long.
Such an element has a resistance of about 1 ohm and with 15 milliamperes
of high-frequency current flowing through, it will generate about 40
micro-volts. The resistance of the galvanometer used with the couple
should be approximately the same as that of the couple itself; with such
a combination a deflection of 100 mm. would thus be produced on a galvan-
Fig. 6.—The thermo-couple may be connected directly in the wave-meter circuit or may
be connected in the secondary of a transformer having suitable ratio.
small powers arc involved, in which case close coupling may be required
to cause the tube to glow, still further decreasing the accuracy of the
measurement. Actually this scheme is good only for testing on high-
power sets; a buzzer-excited circuit would not produce sufficient current
in the wave-meter to make the tube glow, no matter how tight the coupling.
/. Incandescent Lamp.—This device, in its manner of indicating reso
nance, is similar to the neon tube discussed above. It is, however, con
nected directly in series in the wave-meter circuit, as indicated in the
diagram of connections (Fig. 9). The lamp is a low voltage lamp (2-
or 4-volt battery lamp) and is usually con
nected into the circuit by means of an ordinary
small lamp socket, which is short-circuited
when the lamp is not in use.
This scheme possesses the same advantages . .
and disadvantages which were mentioned in ' a
connection with the neon tube. It also pos- FlG. 9._In wave.mctcrs
sesses the disadvantages of inserting a con- a small, low resistance, in-
siderable additional resistance in the wave- candescent lamp has been
meter circuit, while the neon tube arrangement hsed 88 resonance indicator,
has the disadvantage of connecting a leakage
of uncertain value across the wave-meter condenser, as discussed before
in connection with previous circuits. The effect of the parallel connec
tion of the neon tube is of course to raise the effective series resistance
of the wave-meter circuit somewhat, the amount of increase depending
upon the intensity of glow in the tube. There is little to choose between
the lamp and tube.
Classification of Resonance Indicators.—The above schemes for indi
cating resonance of the wave-meter circuit may be classified as to whether
the results obtained are quantitative or qualitative, and the power of the
circuit to which the wave-meter is coupled. Those schemes which permit
a curve of high-frequency current (or indication proportional thereto) to
be plotted against the wave-length readings on the wave meter condenser,
are considered as quantitative, while those which permit only the resonant
wave-length adjustment to be obtained, are considered qualitative.
Those schemes which indicate visibly are, in general, in the quantitative
class. The neon tube and incandescent lamp are exceptions to this rule,
and are in the qualitative class. The hot-wire ammeter, the thermo
couple and d.c. galvanometer, and crystal and galvanometer, are arrange
ments which will give quantitative results. Audible schemes are usually
qualitative, as illustrated by the crystal and phones. It should be noted
that this device may be made quantitative by shunting the phones with
a variable resistance, as in the audibility meter, but the results obtained
are not accurate. It is also possible to obtain quantitative measurements
792 WAVE-METERS AND THEIR USE [Chap. X
(2)
Now since
C=K"A=ad2,
we have,
C_
-be2, ..... (3)
~~K" K'
794 WAVE-METERS AND THEIR USE [Chap. X
where
a
"W'
Differentiating expressions (2) and
(3) with respect to 0 and equating,
we obtain
Sr-4-—*
or,
r2 =460,
and
r = VWd=2x/bO. . (4)
r22dd
AUTODYNE WAVE-METER 795
then
or
r = Vibe+r22. . (5)
This is the form of condenser used in modern wave-meters, having
practically superseded the semicir
cular form, due to its greater con
venience and accuracy of reading. Fixed
A simpler form, utilizing rect Plates
angular plates, but not having
commercial application, due to
space requirements, is shown in
Fig. 14. Fig. 14.—A simple form of condenser in which
It is readily seen that the in the capacity varies as the square of the
tersected area of the fixed and setting of the movable plates.
movable elements (and thus the
capacity) varies as the square of the distance of movement. Thus the
wave-length scale, placed as shown, would have a uniform marking,
as in the case of the rotating
plate condenser previously de
Circuit in which oscillations scribed.
of unknown wavelength Autodyne Wave-meter.—It
are nowtag.
has been previously shown, in
the description of the " beat "
method of receiving undamped
waves (see page 514), that the
beat frequency reduces to zero
when the incoming and local
high-frequencies are made equal.
^ Therefore if the local high fre-
Fig. 15.—If an oscillating tube circuit (calibrat- quency is known, the incoming
ed for frequency or wave-length of the closed frequency is at once determined,
oscillating circuit) is available it may be used This principle is utilized in the
as a autodyne wave-meter; when the beat s0.callcd autodvne wave-meter
note (heard in the phones) is reduced to zero, .„ , . ~ ,_
^.
the unknown wave-length, .J:,is the
.i. same as that illustrated in Fig. 15.
given by the calibration curve of the oscil The wave-meter must be
lating tube. completely calibrated by means
of known high frequencies, and
this calibration must be frequently checked as the constants of the tube
change with time. It will be noted that the capacity of the tube from
796 WAVE-METERS AND THEIR USE [Chap. X
inductance of the circuit, and hence will not appreciably affect the char
acteristics of the set. This coil may be arranged for mounting directly
on the wave-meter, one terminal being connected to ground, while the
other is connected to the antenna through the oscillation transformer.
The coupling between the small inserted inductance, called a search
coil, and the wave-meter itself, must always be as loose as possible and
yet permit definite indications to be obtained. This is so that the current
in the wave-meter may not produce an appreciable reaction back on the
circuit whose wave-length is being measured, which would cause its own
indications to be in error. This is similar to the case of instruments which
are used to measure pressure: a voltmeter must draw so little current
as to alter inappreciably the electrical pressure at the points to which
it is connected, or a gauge, inserted in a gas tank, must not have so much
Fig. 16.—In measuring the wave-length of a transmitting set, a search coil (gene-ally
one turn) is inserted in the base of the antenna, and the wave meter coupled very
loosely, to the search coil. The Marconi Co. has used an additional "link" circuit
to permit easy adjustment of coupling.
space within itself, as to decrease materially the pressure of the gas which
it is supposed to measure.
The simplest manner of varying the coupling is to vary the distance
between the wave-meter and the search coil. An intermediate circuit
whose coupling to the wave-meter and search coil may be conveniently
varied is also largely employed. This arrangement is shown in Fig. 16,
and is used by the Marconi Company in their station type wave-meter.
It is very important that very loose coupling be employed when making
the initial adjustment of the wave-meter, as otherwise the delicate hot
wire ammeter may be burned out when the resonant adjustment is attained.
The coupling may easily be increased when it is found that the value used
gives deflections which are too small for accuracy. The best adjustment,
is that which results in definite, readable indication with minimum coupling.
When the preliminary adjusting of the wave-meter indicates this con
dition, the adjustment of the set should be carefully repeated, and wave
798 WAVE-METERS AND THEIR USE IChap.X
mine the distribution of all the energy radiated by the set. The procedure
is exactly similar to the foregoing, with the exception that instead of
Doting only the wave-length readings at points of maximum current,
readings are taken, at a number of condenser settings, of both the wave
length and the wave-meter current or " current squared " if the hot-wire
ammeter scale has been calibrated in this way.
Referring to Fig. 16, as the variable condenser is adjusted to the several
wave-lengths in succession, the current in the ammeter will successively
increase as the resonant adjustment is approached, and then decrease as
have already been briefly discussed in Chapter V (see page 326), and are
called the " energy-distribution " curves, since they show the amount
of energy radiated at the different wave-lengths.
Significance of Energy Distribution Curve.—Considering the wave-
meter simply as a calibrated receiving circuit having a very small decre
ment, the curves indicate proportionately the amount of energy which
would be received (and therefore the strength of signal), by each one of
a number of such receiving circuits assumed equidistant from the trans
mitting station, and each tuned to a different wave-length. Thus, that
circuit which is tuned to Xo (assuming M to be loose or medium coupling)
would receive a maximum amount of energy and the strongest signal.
This would be the station for which the signal is intended. The other
receiving stations would also receive some energy; this energy would
decrease, as the adjustment from Xo becomes greater and greater, and
signals so received, represent interference to the receiving station. If
we consider Io2 as the energy required for audibility at the several stations,
then Xi to X2 represents the range of tuning over which interference will
occur if the transmitter coupling M is loose. Similarly, X'i to X'2, and
X"i to X"2 represent the range of wave-lengths over which interference
occurs as the coupling is tightened. It is therefore evident that tight
coupling should be avoided except under emergency conditions (SOS call),
so that interference to other receiving stations, which may be tuned to
wave-lengths in the neighborhood of Xo, h;e minimized.
It should be kept clearly in mind that the set is radiating energy at
all the different wave-lengths, and each receiving station is in tune with
the energy which is causing the signal to be heard. That is, each receiving
circuit picks out its own particular wave-length to which it is tuned,
and its received signal is proportional to the amount of energy which the
transmitter is sending out at that wave-length.
Wave-meter Coupling.—When determining the energy distribution
curves for the set, the coupling between the wave-meter and search coil
should first be adjusted so that a full scale deflection is obtained on the
hot-wire ammeter when the resonant condition is obtained with the trans
mitter coupling (Af, Fig. 16) adjusted to its proper value. This coupling
between the wave-meter and search coil should remain undisturbed
throughout the determination of the several energy distribution curves.
The curves obtained will thus have maximum permissible ordinate values,
making any error in their determination a minimum, and the energy
radiation under the different coupling adjustments will be comparative
in a quantitative as well as a qualitative sense.
Energy Distribution for Undamped Wave-transmitter.—For an
undamped wave-transmitter, the energy is all radiated at the fundamental
wave-length, neglecting the small amount radiated by the upper harmonics,
DETERMINATION OF ENERGY DISTRIBUTION 801
which are relatively weak. If the wave-meter circuit had zero decre
ment, that is, no resistance, the signal would be received by that wave-
meter only, which is tuned to Xo. The energy distribution curve in this
ideal case would be a straight line ordinate at Xo (Fig. 18).
Since the wave meter always possesses a decrement, however small,
the distribution curve will appear as shown by the curve A, Fig. 18.
The greatly decreased interference is indicated by the small difference
between Xi and X2. Assuming receiving circuits with a decrement equal
to that of the wave-meter only those tuned within this range would receive
interference, while the set for which the signal is intended receives a stronger
r.ioh
signal, due to all the energy being radiated by the transmitter at the wave
length (Xo) for which the wave-meter is tuned. The greater selectivity
and efficiency of the undamped wave-set, as indicated by the above
characteristics, are rapidly causing its increasing use in the art, and it
may eventually supersede the damped wave-set altogether.
Determination of Decrement of a Spark Transmitter from Energy
Distribution Curve and Known Decrement of the Wave-meter.—If we
consider a wave-meter circuit coupled loosely to an undamped wave-
generator as shown in Fig. 19, then, when the wave-meter circuit is tuned
to resonance, its reactance ^Lco — is equal to zero and the current
is limited only by the resistance in the circuit, or
. E
802 WAVE-METERS AND THEIR USE [Chap. X
Ceo
High Frequency,
Alternator
R irR
since /--
2*
and
& R2., *2R2{C-C\2
/,- it- _n~^~o- \ c°) T2/cr-cy
P E2 R2 " +82[ C ) '
ir2R2/CT-C\2
R-
&2 \ C }
Solving this expression, we obtain
s=ir%rylij^r2- (8)
a i - C'-(
c \/,2-j
where 5i=the decrement of the circuit under
measurement;
52= the drecrement of the wave-meter
circuit.
This formula is sufficiently accurate for all practical purposes, if
1. 5i + «2 is small compared to 2r.
C —C .
2. — is small compared to unity.
3. If the wave-meter is loosely coupled to the wave-meter circuit.
The procedure for determining 8i, assuming 62 known, may be out
lined as follows :
1. An energy distribution curve is obtained as shown in Fig. 20.
(Coupling between the closed circuit and the antenna circuit of the trans
mitting set assumed to be loose.)
2. The value of C, is then determined from this curve. The value of
1 See Chapter IV, page 272.
804 WAVE-METERS AND THEIR USE |Chap. X
/2
C is preferably obtained for that point of the curve where I2 = since
then
\I2-P '
and the calculation becomes simpler.
3. Knowing CT and C\, as obtained from the curve, and substituting
in the equation
«i+«2=t^V^'
5i+5z (9)
Sl + 52 =w &+£r2\77=P' (10)
since \=KVc and \2=K'C.
.20\-
I 1 I 1 1
500 550 GOO 650 700
Wave-Length in Meters
Fig. 21.—If the coupling of the oscillation transformer is too tight a double-humped
resonance curve is obtained from the wave-meter reading; the resonance curve for
each of the component frequencies of the curves may be obtained by the scheme
shown in Fig. 22.
becomes,
C2-d
$2 = 1 decrement of wave-meter
c2+c\ '
since,
5i=0.
This measurement may conveniently be made by any one of the
several generators of high-frequency continuous oscillations described in
DETERMINATION OF WAVE-METER DECREMENT 807
Chapter VII. The high-powered tube circuit is preferable for this purpose,
due to the frequency being fixed, and the exciting circuit being of sufficient
power to be unaffected by the proximity of the wave-meter circuit. How
ever, in case the tube is not oscillating powerfully, the oscillations may
be affected when the wave-meter is coupled to the circuit. To prevent
this, it is desirable to use very weak coupling and have an ammeter in
the circuit supplying power to the wave-meter circuit. The indication
of this meter should re
main constant through- [ 20
out the decrement de
termination showing his
that the power gener
ated by the tube was .16
not appreciably affect
ed by the wave-meter Kl4
tuning.
The wave - meter .12
coupling, if made too
great, may also affect hlO
the frequency of the -True Energy
tube oscillations as well .08 Distribution
Curve
as their amplitude. The nergy Distribution
effect of this frequency 100 Curve obtained
with interfering
variation on the de conditions
crement determination .04
may be analyzed with
the help of Fig. 23. h.02
If the capacity of
the wave-meter con
denser is less than that Wavemeter Capacity
required for resonance, Fio. 23.—If the wave-meter is coupled too tightly (to a
then a current will low-powered set) the energy distribution curve will be
flow in the wave-meter unreliable because of the reactions of the wave-meter
circuit which is leading on the power circuit.
with respect to the
induced e.m.f. The effect of this leading current on the tube cir
cuit is to increase the apparent inductance, causing the wave-meter
indication to correspond to a point on the resonance curve of a circuit
whose resonant frequency is below that given by Cr. Similarly, a
lagging current in the wave-meter circuit (wave-meter capacity greater
than resonance value) decreases the apparent inductance, the wave-
meter indication corresponding to a point on a resonance curve, the reso
nant frequency of which is above that given by Cr. These effects have
808 WAVE-METERS AND THEIR USE [Chap. X
(12)
DETERMINATION OF WAVE-METER DECREMENT 809
3—
-g-=mdd.
where
A is the active area of the moving plate,
and
6 is the angular displacement.
Also
dA ja
A '
or,
dA =bmtm'de.
But, referring to Fig. 25,
dA=$(P2-r2)d8,
Fixed Plates
where
p is the radius vector from the axis to the enveloping
curve,
and
r is the radius of the circular space occupied by the
separating washers between the plates.
Equating the above expressions for dA, we have,
$(P2-r2)d6 = bmtm,d8
or
p = V26m«"'9+r2, (15)
where b and m are design constants, which determine the minimum and
maximum values of the capacity to be used (b=K'a while m is the same
812 WAVE-METERS AND THEIR USE [Chap. X
element for commercial decrements is very small, and the decrement scale,
if connected directly to the condenser shaft, would be crowded and difficult
to read accurately. Therefore it is usual to gear the scale to the con
denser shaft, the relative angular motion of the decrement scale and
capacity element being about 6 : 1.
The decrement of the meter for all values of C and for each of three
fixed inductance coils which may be used is known from curves supplied
with the instruments. These decrements vary from about .07 to .02, the
larger value corresponding to a large value of C and smallest value of L.
The smaller value is obtained with C at its minimum value and the largest
inductance inserted in the circuit.
Measurement of Resistance.—Knowing Si, the decrement of the
circuit, the resistance is at once known at the frequency of osculation from
the following relations, which have previously teen deduced: ,
tune out the signal, in which case the coupling should be decreased, and
all direct induction effects from the buzzer circuit (to which this con
tinuous note is due) minimized or eliminated by making the buzzer cir
cuit as compact as possible. If no point of maximum note occurs as the
wave-meter condenser is varied, it is probable that the wave-length of
the test circuit is beyond the range of the instrument. The remedy is
evidently to change the known value of inductance (or capacity) in the
test circuit, or to try others of the various coils with which the wave-
meter is equipped.
After the wave-length has been determined, the unknown value of
inductance (or capacity) is given at once by the formula,
Xmetera — 1885"N/Z/C,
L and C being measured in micro units.
Equivalent results are obtained if the wave-meter is employed as the
exciting circuit. The connections are then as shown in Fig. 28. The
wave-length of the wave-meter oscillations is varied until a maximum
note is heard in the phones across the test circuit, under which condition
the natural frequency of both circuits is in agreement.
WAVE-METER USED TO MEASURE L AND C 815
The same precautions are to be observed in this case as for the preced
ing method, with especial reference to the phone circuit connected across'
the test circuit. Long, twisted leads must especially be avoided as these
will cause large error, due to their distributed capacity (conventionally
shown in dotted
lines, Fig. 29) par 3-
ticularly if the test
circuit capacity is
small. It is to be
noted that a wave-
meter will have a
different calibration
when used with a
hot-wire meter for To Vacuum Tube
Generator of
indicator, and when undamped
Oscillations
detector and phones,
or buzzer, is connect
ed in parallel with
its condenser. The
amount of correction Fig. 29.—To measure the natural wave-length of an antenna
required is greatest the antenna is coupled (by a small search coil) to a source
for the lowest set of continuous wave power of variable frequency. When the
tings of the wave- antenna ammeter reads a maximum, the wave-meter is used
meter condenser. to read wave-length of power. If a d.c. generator is used in
the plate circuit of the tube generator the phones and detec
Use of Wave- tor may be used for getting resonance, the commutation
meter to Measure ripples being audible; otherwise an ammeter will be used in
the Constants of an the wave-meter circuit.
Antenna. — Another
important measurement involving the use of the wave-meter is that
of the constants of an antenna. The loading coils, short-wave con
denser and oscillation transformer are first removed from the antenna
816 WAVE-METERS AND THEIR USE [Chap. X
^ = X^=^2 (18)
The following alternative method may also be employed. The known
inductance inserted in the circuit is assumed to be the only inductance
1 In the equations given, the wave-length is expressed in meters, while inductance
and capacity are expessed in microhenries and microfarads respectively.
* This deduction is a very simple one and suffices for ordinary purposes. It must
be noted, however, that actually C0, the same as L0, is not a constant, but varies as dif
ferent values of loading are used. For an analysis of this point see Morecroft, "Some
Experiments with Long Electrical Conductors," Proc. I. R. E., Dec., 1917, and Miller
"Electrical Oscillations in Antenna- and Inductance Coils, Proc. I. R. E. (June, 1919),
also discussion of Miller's paper in Proc. I. R. E., Dec., 1919.
WAVE-METER USED TO MEASURE ANTENNA CONSTANTS 817
18852 Li 18852
°r 2
Fig. 30.—In case a very short spark gap, a low-powered induction coil, and very weak
coupling are used the phones and crystal detector may be used for getting resonance
in the wave-meter, otherwise the ammeter will be used to indicate resonance.
Since
Xi=XoVl-X,
and
X2 = XoVl+X.
we have,
l-K
X22~ l+K'
X,2+X,2Ji: =
(X^+Xx2)^ x22-x,2
X22-Xi2
K = x22+x,2- •
X2 + X1
Since X, is approximately equal to
and
X22+X!2
X,2 is approximately equal to
we have,
(X2-X,)(X2+X,) (X2-X,)(2Xr)
2Xr2 2X,2
or
X2 — Xi _ X2 — Xi
(21
x, x2+xr
The latter forms are somewhat simpler than the more accurate expres
sion, as no squared terms are involved. They are, however, accural
enough for most commercial determinations. The last form is perhaps
the most desirable, as it eliminates all measurement of Xr.
(6) The second method is as follows : The oscillation transformer pri
mary and secondary are connected in series in the closed circuit as shorn
in Fig. 33.
Step-up power
transformer
Fig. 33.—Unless a very short spark gap (hence low power) is used the hot-wire ammetc;
(or similar indicator) would be used in place of the phones and detector.
are then set up in this circuit as in the normal operation of the transmitter
and the wave-length noted. Calling this wave-length Xi, L', the total
inductance in the circuit, is obtained from
1885^!
The connections to one coil are then reversed and the readings repeated.
In this case,
L''=mh-rLl*2M+L2-
Therefore
L'-L"=AM
T'— T"
M=^±- (22)
or
L"-U
4 '
according as L' is greater than L" or vice versa.
Then when the set is in normal operation, using loading coils, etc.,
we find the coupling coefficient from the relation
M
VL1L2,
where Li is the total inductance in the primary circuit under
normal operation;
Li2t is the total inductance in the secondary circuit under
normal operation, i.e., the inductance of the oscil
lation transformer secondary + the effective induc
tance of the antenna+the inductance of the loading
coil (if inserted).
The above methods are exactly equivalent in result and may be used
indiscriminately. Method (6) is perhaps the better, since the consider
able amount of data needed to plot accurately an energy distribution
curve is not required. Sometimes, however, this curve is required as illus
trating an operating characteristic of the set, and the coupling is then
most simply determined by the relationships developed in Method (a).
How to Improvise a Wave-meter.—The varied and important uses
of the wave-meter as described on the preceding pages have made it a
fundamental and essential part of any radio laboratory or station equip
ment. Now and then occasions may arise where this instrument may
not be available, through loss, damage, etc., and in this case, a " home
made " instrument must be devised. Also, a large majority of amateur
operators prefer to construct their own meters for the enjoyment and
822 WAVE-METERS AND THEIR USE [Chap. X
experience which such constructive work brings to them. For these rea
sons it has been considered desirable to give a brief outline of the pro
cedure to be followed.
One of the first points to be decided is: What shall be the maximum
wave-length which the wave-meter to be designed is to measure? We
will assume this to be 2000 meters. A suitable veriable condenser must
next be chosen, and as one or more variable condensers are normalh-
available in even the simplest installations we will consider that such con
densers are available in this case. The maximum capacity of the several
condensers should be measured, either electrically, or from their dimen
sions, by means of the expression given on page 165, Eq. (30).
The wave-meter condenser should have about .001 microfarad capacity
per 1000 meters maximum wave-length to be measured. Thus, for this
problem, the capacity should be .002 microfarad and that condenser should
be chosen which possesses at least this capacity.
The maximum wave-length and capacity thus being determined, the
required inductance is readily obtained from
or
2000 = 1885 v/L^X.002
1.125 = LM»X.002
L =563 microhenries.
This inductance should then be designed (generally in the form of a
single layer solenoid) in accordance with the formula given on page 145,
Eq. (11). The coil should be wound with finely stranded wire, the indi
vidual strands being insulated to minimize the resistance of the wave-
meter.
A small hot-wire ammeter (0—100 milliamperes preferable) should
then be obtained and as-
-(a) j . I sembled with the condenser
^~ i ' * and coil, the connections
being made as shown in
Fig. 34.
All connections should
be well made and the cir
cuit made as compactly as
Fia. 34.—A convenient arrangement of terminals possible SO as to minimize
for a wave-meter. ,i • , »
the resistance of the wave-
meter. This equipment may-
then be enclosed in any wooden box of convenient size, with only the
ammeter and condenser index and associated scale visible. Additional
IMPROVISING A WAVE-METER 823
binding posts may be added for phones, detector, and buzzer circuit as
shown.
The wave-meter is then ready ior calibration, which may be accom
plished by coupling the instrument to a transmitter which may be adjusted
to radiate at several known wave-lengths. A few points on the scale may
be approximately determined by using the wave-meter (with detector
and phones as indicating devices), as the closed circuit of a receiving set,
coupled very loosely to the antenna. A few stations of known wave
length may generally be heard in this way, and so a few points of calibra
tion obtained. A curve should then be plotted between the known wave
lengths and corresponding positions of the condenser index (the condenser
scale is usually graduated in degrees or in 100 divisions to the semicircle).
This curve will have an appearance similar to the wave-length curve in
Fig. 11. The decrement of the meter may also be measured by one of the
methods described above, and should not exceed .10 for an average value
of the condenser.
CHAPTER XI
AMPLIFIERS
amount of energy much greater than that actuating the antenna. The
suitability of the three-electrode tube for this purpose is at once evident
from the analysis of its action given in Character VI.
The General Characteristics of Triodes.—These have been quite
thoroughly discussed in Chapter VI; on pages 570 et seq. the possibility
of using a tube as an amplifier was pointed out and an elementary analysis
given.
The " static " relation between the plate current and grid and plate
potentials was shown to be expressible by
/» = A (Et+MoE.?, (1)
and it was also pointed out that, for small variations in the tube poten
tials, the exponent might be treated as unity.
It was further shown that, if a sufficiently small sine wave e.m.f was
k impressed on the grid, the pulsations in the plate current would be sinu
soidal in form, and the constant (1 /A) acquires the significance of " alter
nating current plate circuit resistance."
We then have the equation which was used throughout Chapter
VI in analyzing tube action, i.e. :
I,=-±-(Ep+moE,), (2)
=
u
X=
a. / 5/
1 1 1 1
43210123*
— Grid Voltage +
Fig. 1.—Showing the effect on the plate current—grid potential curve of a tube of
putting external resistance in the plate circuit; a tube which by itself gives char
acteristic A, will give characteristic B if sufficient external resistance is put in the
plate circuit and the voltage in this circuit suitably increased.
ance R is put in series with the filament having such a resistance that
when normal filament flows through it the IR drop is the required amount.
In some multi-stage amplifiers (several tubes repeating one into the other)
the filaments are all connected in series to the A battery, the filament
of the preceding tube may serve as the resistance R, as indicated in Fig.
3. In the operation of
tubes as amplifiers the
following quantities play
a very important part:
(a) A.C. resistance of
plate to filament or out
put circuit of tube.
(6) A.C. resistance of
grid to filament or input
circuit of tube.
Fio. 2.—To keep the grid of an amplifier tube negative
(c) Capacity of grid to either a small battery of dry cells may be used (a)
filament under static con or a resistance inserted in the negative leg of the
ditions and under actual filament may be employed (6).
operating conditions.
All of the above quantities have been fully discussed in Chapter VI, and
the reader will do well, before proceeding with the study of this chapter,
to go over the fundamental principles of three-electrode tubes as outlined
in the beginning of Chapter VI. The fact should here be emphasized
that the capacity of the grid to filament, while small under static con
ditions, may attain com
paratively large values
under actual operating
conditions. Again the
circuit from plate to fila
ment or grid to filament
is made up of a resist-
_ _ , , , ance in multiple with a
Fig. 3.—In case several tubes are used in cascade it is . , ... ,.
possible to connect all filaments in series and connect caPaclty> wmle ordl-
the leak resistances behind the filament of the preced- narily the impedance of
ing tube. This makes the grid of each tube negative either circuit is practi-
with respect to its filament by an amount equal to the cally equal to its resist-
IR drop of the filaments. ance> there are cases
when the frequency is
high enough to make the impedance much less than the resistance. That is,
the capacity reactance of the circuits, shunting the resistance, may be
low enough to determine the impedance of the path.
Effect of External Resistance in the Plate Circuit.—As pointed out
in Chapter VI the function of a triode when used as amplifier is to make
828 AMPLIFIERS [Chap. XI
to produce a varying voltage between the grid and filament of the second
tube, and, similarly, the varying voltage is relayed from the second to the
third tube, etc., until the plate circuit of the last tube is reached, wherein
are placed the telephone receivers or any other device used for making
the signals readable. From this brief description it is plain that the signals
must be " repeated " from one tube into the next. Amplifiers, cither
for low-frequency or for high-frequency, are divided into the following
classes, according to the arrangement used for " repeating."
(1) Transformer-repeating amplifiers.
(2) Resistance-repeating amplifiers.
(3) Inductance-repeating amplifiers.
Tube i Tube 2 Tube 3
-nz-H+H
Si. This e.m.f. is applied to the grid and filament of the second tube,
and thus the varying signal voltage is " repeated " from the first into the
second tube and finally from the second into the third tube, the varying
plate current of which is caused to affect the telephone receivers.
It will be at once apparent that in an arrangement of this kind, while
each tube itself is always amplifying, the advantage of this may be lost
by a poor repeating device. The object to be gained is, of course, to make
the varying voltage between the grid and filament of each tube greater
than for the preceding tube. This requires correct proportioning of the
primary and secondary of the repeating transformers T\, T2; otherwise
the grid-filament voltage of the second tube may be but slightly larger,
or even smaller, than for the first tube. This is not an unusual occurrence
in poorly designed " amplifiers."
We will study the repeating action from the first into the second tube.
For the sake of simplicity we may assume that the repeating transformer
has neither leakage inductance nor resistance and also that the mag
netizing current is zero; this is equivalent to saying that the transformer
is ideal. In so far as the alternating current relations of the circuit are
concerned, such a transformer may, if the secondary is loaded by means
of a non-inductive resistance, be replaced by a fictitious resistance placed
in the primary and equal to the secondary circuit resistance divided by
the square of the ratio of transformation. Let:
E„i = effective value of alternating voltage between grid
and filament of Tube 1 ;
Eg2 = effective value of alternating voltage between grid
and filament of Tube 2;
RPi = plate-filament a.c. resistance of Tube 1;
Rg2 = grid-filament a.c. resistance of Tube 2;
juo = amplifying constant of Tube 1 ;
V= effective value of alternating voltage across primary
of repeating transformer, T\)
n = repeating transformer ratio expressed as the ratio of
secondary to primary voltage.
The above quantities are illustrated in Fig. 7. The action of E„i upon
the plate current of Tube 1 is the same as if an alternating voltage equal
to tM)Eei had been impressed upon the plate circuit, in addition to the
battery e.m.f. This alternating voltage noE0i is impressed upon a circuit
which may be simplified as shown in Fig. 8 and consisting of the plate
resistance of the first tube in series with the equivalent resistance of the
repeating transformer transferred to the primary. This is probably the
simplest way to treat the problem when the coupling between the primary
and secondary of the transformer is tight and the load circuit of the trans
832 AMPLIFIERS [Chap. XI
former is resistive only. For the more general case, i.e., leaky trans
former and reactive secondary load, the action of the tube is best analyzed
by using for the external impedance in the plate circuit the resistance and
reactance of the primary of the transformer as calculated from the general
■equations given on pages 86-87.
From Fig. 8 the following equation is easily derived:
R<n
v ~»fi«=^o—rtr -kfi (7)
~n2Rn + Rn
K "*> H 71- P
- -vwwwwwv-^-w/vwvvwwwv*-
"■7*o£gJ -———
Fig. 7. Fio. 8.
Fig. 7.—Circuit detail of the amplifier shown in Fig. 6.
Fig. 8.—Under ideal conditions (transformer requiring no magnetizing current, having
zero internal impedance, and secondary load resistive only) the circuit of Fig. 7
may be replaced by the one above.
The voltage between grid and filament of the second tube is equal to the
voltage across the transformer primary multiplied by the ratio of trans
formation; thus:
En=nV (8)
and
lMnnRn
(9)
En tfRn+Rf,
Eq. (9) may be written as:
A'
(10)
where
R,,
a=
Rm
It will be noted from Eq. (10) that the ratio -^r varies directly with
.c<m
the amplifying constant of the first tube and it also varies in a complex
manner with Rn/Rn and with n. It will further be noted that:
R
1st. If m and n are kept constant and the ratio -~ increased from
Zip,
TRANSFORMER-REPEATING AMPLIFIER 833
E
a low value, then will constantly increase towards the limiting value
tin
R
imn which will be theoretically reached when -^p- = oo .
Rjn
R
2d. If fio and are kept constant and the value of n changed then
Kn
E
-=p- may be shown to have a maximum when:
En
n2=f-* (11)
^="°2 (12)
If the tubes used for the various stages of amplification are similar, which
is almost always the case, the transformers may have the same ratio
throughout.
The results indicated by Eqs. (11) and (12) have been obtained on the
basis of ideal transformers having neither leakage inductance nor coil
resistance and requiring no magnetizing current. The effect of all of
these in an actual transformer would be such as to alter the best value
of the transformation ratio, and, more than this, to diminish the ideal
ratio E,jEgt as given by Eq. (12). The leakage inductance and coil
resistance of the transformer can be made quite small and negligible as
compared with the resistance Rs, and their effect will, therefore, be but
small. On the other hand, it is very important to make the magnetizing
current very small, or, in other words, to make the no-load reactance of
834 AMPLIFIERS [Chap. XI
the transformer primary very high. This will be made clearer by a study
of the diagram Fig. 9, which is similar to Fig. 8, with the exception of the
introduction of Xo in multiple with R^/n2, where: Xo=re'actance of
transformer primary at no load.
A resistance should, in the above diagram, be inserted in series with
Xo to represent the core losses, but we have omitted it for the sake of
R simplicity and also because in such
"P" transformers the core losses are made
i^^^fTTn negSblyraU- », ti. ♦ * • ■
x„ Ihe diagram snows that Xo is m
™ms^^ 1 multiple with RJn2 and therefore
diminishes the equivalent impedance
of the circuit H-P; if, then, Xo were
K MoEgl *| very low the voltage drop across H-P
. , and, therefore the secondary voltage
Fig. 9.—In order to take care of the ,„ , , , , „ _ . .
magnetising current of the trans- <^*> WOuld te smaU- U 18 ™P°rtant,
former the diagram of Fig. 8 must be then. to make X0 as high as possible,
changed as above, the value of X0 or, in other words the primary must
being equal to the primary reactance, have a very large number of turns,
with secondary open. There ig a pojiritj however, beyond
which it is uneconomical to increase
the value of Xo, since the gain in amplification is too small to make it
worth while. To show this we have worked out the theoretical curves
of Fig. 10, after having assumed the following:
mo =6,
Rv = 10,000.
For Re, of 250,000 ohms the best transformer ratio for an ideal trans-
/250 000
former is found, from Formula (11), to be: ^1 ^ ^ =5, and, similarily
E
Maximum possible value of -=£ for R,, of 1,000,000 = 6X^ = 30.
TRANSFORMER-REPEATING AMPLIFIER 835
6 8 10 12 14 16 18 20 22 24 26 28
No-load reactance of repeating transformer primary in 10* ohms
Fia. 10.—Calculated values of voltage amplification using transformers of different
ratios and two different values of input circuit resistance of the second tube. The
curves show the effect of varying the no-load reactance of the primary of the trans
former abcissa; being no-load reactance in thousand ohms.
ratios of transformation, i.e., 4 and 5 for Rtl of 250,000 and 3 and 4 for
Re, of 1,000,000 ohms. They show:
1st. That for low values of A"n the ratio E,jEtl may be very small,
even smaller than the amplifying factor of the tube, which is in this case
6. Thus, a transformer with low no-load reactance might make the result
of two tubes no better, or even worse, than for one tube alone.
836 AMPLIFIERS [Chap. XI
2d. That for Rlt of 106 ohms the ratio of E,,/Ee, is larger than for
Rlt of 250,000 ohms, for the same transformer ratio, even though the value
of n used for RSl of 250,000 ohms is much nearer the ideal value than for
R„, of 106 ohms.
3d. Beyond certain values of Xo the ratio EaJEQl does not increase
much with increase of Xo. Not only is it of no advantage to increase
the reactance Xo above a certain amount, but it is actually disadvan
tageous. The Xo is, of course, increased by increasing the cross-section
of the core or the number of turns in the primary winding. The former
of these expedients is objectionable because it increases the space require
ments. As regards increasing the number of primary turns, it must be
noted that, if this is done, the secondary turns must be proportionately
increased if the ratio of transformation, n, is to be constant. Now, the
higher the number of transformer turns the higher become the internal
resistance and leakage reactance of the transformer, which have so far
been neglected in our discussion.
A high internal transformer impedance may produce a large internal
drop due to the " load " attached to secondary, i.e., the grid-filament
resistance and reactance of the tube into which the transformer is repeat
ing, and also the internal distributed capacity of the secondary winding
itself; the final result would be that the voltage applied to the grid-filament
might be far less than that calculated on the basis of negligible internal
transformer drop. This may be summed up by stating that, for a given
frequency, the higher the number of turns used the more does the ratio
of terminal voltages (secondary to primary) depart from the turn ratio
n, being only a fractional part of n. In fact, it is possible to increase the
transformer turns to such an extent (more especially if the ratio be high,
say: 10 to 1), that the terminal voltage of the secondary (when used in
the tube circuit) is less than the voltage impressed upon the primary winding.
The above phenomenon may take place if the number of turns is kept
constant and the frequency raised. In practice the value of Xo for an
amplifier to be used at constant audio-frequency is made equal to about
once or twice the value of the plate-filament a.c. resistance.
4th. The higher the ratio of transformation the greater the ampli
fication. In connection with this it will be noted, however, that a point
may be reached beyond which it is uneconomical to increase the ratio,
since the gain in amplification is too small, as for example in the case of
curves A and B for transformer ratios of 4 and 5 respectively. As a matter
of fact if we consider that, for a constant number of primary turns, the
increase in ratio is obtained by increasing the number of secondary turns
and that simultaneously the internal impedance of the transformer and
effect of the distributed capacity of the secondary are increased, it will be
apparent that, due to the large internal drop, the voltage across the sec
TRANSFORMER-REPEATING AMPLIFIER 837
ondary may be smaller for a high than for a low ratio of transformation.
This effect has already been pointed out in connection with the value
of Xo and plays such an important part in connection with the trans
(13)
TRANSFORMERS FOR LOW-FREQUENCY AMPLIFIER 839
The first two components are due to the constants of the electric and
magnetic circuits of the receiver and the losses taking place therein and
840 AMPLIFIERS (Chat. XI
are the effective reactance and resistance measured with the diaphragm
" locked."
The motional reactance and resistance are produced by the motion
of the diaphragm and are to be added to the static reactance and resist
ance respectively. It is plain that the motional resistance is the resist-
Rm + Rp'
and
Pm~h2Rm~{Rl+Rp)2Rm (14)
For maximum response in the receivers the power (Pm) expended in the
motional resistance should be a maximum, and since the expression of
Eq. (14) is a maximum when Rm = Rp, we conclude that if the receiver
had nothing but motional resistance then maximum response would be
obtained by making the motional resistance equal to the plate-filament
a.c. resistance of the last tube.
In the case of a practical receiver containing motional and static resist
ance and reactance it is apparent that the larger we make the number
of turns of copper wire the more we increase all the components of the
impedance, including the motional resistance, and the greater is likely
to be the receiver response. It is, however, difficult to determine theo
retically how far we should go on increasing the number of turns and the
total impedance. In practice, a receiver is generally chosen whose
total impedance is about equal to the a.c. resistance from plate to
filament.
Connections of Transformer-repeating Low-frequency Amplifiers
for the Reception of Damped and of Undamped Waves.—The diagram
of Fig. 6, page 830, shows in a schematic manner a low frequency trans
former repeating amplifier without any connections to any receiving
apparatus. Fig. 13 shows how such an amplifier would be connected
to another tube for the reception of damped waves or of radiophone
negative motional resistance merely signifies that the diaphragm in motion (in the right
motional phase) absorbs less power as eddy currents and hysteresis than if it is locked
and so unable to move.
Fig. 15 shows an autodyne tube receiver for undamped waves and the
manner in which it would be connected to the amplifier. Considering
CONNECTION OF AMPLIFIER TO RECEIVER 843
Fig. 13 it will be noted that the rectifying tube is connected in the standard
manner already discussed in Chapter VI, page 451, with a grid condenser
and leak resistance, and that,
in this case, the telephone re
ceivers, which would ordinarily
be connected to the points Q
and S, have been replaced by
the amplifier. The condenser
C is of a fairly large capacity
(5000 fifif or more) and is used
for the purpose of carrying
whatever high-frequency cur v To Point! Q & S
^ of Amplifier
rents flow in the plate circuit
of the rectifying tube; these
high-frequency currents flow
readily through the low im- -=-
pedance which the condenser fig. 14.—How a crystal detector set would be
C has at high-frequency, while, connected to the amplifier,
on the other hand, the audio
frequency currents which are to be amplified take the path of the primary
of the transformer T. As a matter of fact the repeating transformers
such as T, T\, T2, have such a high distributed capacity, on account of
To Points Q & S
of Amplifier
Fid. 15.—Hott an autodyne tube receiving continuous wave signals would be connected
to the amplifier.
the very large number of layers of wire enclosed in a small space, that
the by-pass capacity C may often be dispensed with, in which case the
distributed capacity of transformer T carries the high-frequency currents.
844 AMPLIFIERS [Chap. XI
The amplifier shown in Fig. 13 has batteries K\, K2, K3 in series with
the grids for the purpose of keeping them at an average negative poten
tial; it will also be noted that a single battery (^2) is being used for the
filaments of all the amplifying tubes, and that the battery B2 feeds the
plates of all the amplifying tubes. Instead of using the grid batteries
K\, K2, Kz the lower ends of the secondaries of the repeating trans
formers may be connected to the filament battery circuit at a point of
suitable negative potential. This has been discussed on page 827 and
is exemplified in the amplifier circuit of Fig. 16, page 845. Figs. 14 and 15
hardly need any explanation and show in every case that the amplifier
is connected in place of the telephone receivers.
Transformer-repeating Amplifiers for High Frequencies.—These are
similar to the amplifiers for audio frequency with the exception of different
electrical constants for the transformers, made necessary by the use of
radio frequencies. A diagram is given in Fig. 16 showing a three-stage
high-frequency transformer-amplifier connected for the reception of
undamped waves. It will be noted that the grid of the first amplifying
tube is connected directly across the receiving tuning condenser. Q and
S are the input terminals of the amplifier while Qi and Si are the output
terminals; the latter are shown connected to an autodine rectifying tube,
and the telephone receivers are placed in the plate circuit of the rectify
ing tube. The grids are maintained at an average negative potential
by making use of proper resistances in series with the negative sides
of the filaments. If grid batteries should be used instead they should
be connected on the lower side of the secondaries of the repeating trans
formers; if connected next to the grid they will increase the free capacity
of the grid connection and thus reduce to some extent the voltage impressed
on the grid itself.
This type of amplifier is not a very efficient one, and, in fact, we might
say that it is almost impossible to construct an efficient amplifier for very
high frequencies. We will discuss the main features and difficulties
encountered in this amplifier, and will find later that these difficulties
exist in all types of high-frequency amplifiers.
The repeating transformers T\, T2, T3 are generally constructed with
out any iron, in order to prevent the excessive eddy current and hysteresis
losses which would take place at radio frequencies.
The optimum electrical constants of the transformers cannot be derived
on the same basis as for the repeating transformers of the low-frequency
amplifiers for the reason that the high-frequency transformers do not
approach, even to a small extent, the ideal transformer without leakage.
Consider the plate and grid circuits of two adjacent amplifying tubes as
represented in Fig. 17. Assume, for the sake of simplicity, that the grid
takes no current, or, in other words that its resistance is infinite. We will
TRANSFORMER AMPLIFIERS FOR HIGH FREQUENCY 845
first discuss the action of the transformer without considering either the dis
tributed capacity of the coils L\ and L2 or the capacity of the grid-filament
circuit of the second tube; all these capacities play a very important part
in the operation of the amplifier and will be taken into consideration later.
846 AMPLIFIERS [Chap. XI
but
fv>En
therefore
E~ =
and
Eg, nouiky/ L\Li
— (15)
K V(w2Li2+/^2)
The ratio EnlEn varies directly with A; and VL2 but it varies in a com
plex manner with Li. If all other quantities are kept constant and Li
only varied, it may be shown that E^/Eg, is a maximum when
a>Li = tfp (16)
If
Rp = 10,000 ohms (previously assumed value)
and
w=3Xl06 (about 600 meters wave-length)
then, for maximum value of EnlEn,
T 10,000 X106 =**00
00ftn microhenries.
. .
— 3 X 106—
TRANSFORMER AMPLIFIERS FOR HIGH FREQUENCY 847
and
This last equation shows that when L1-C1 is tuned to the incoming
frequency the ratio E,JEH varies inversely as vXi ; hence it is advisable
to make L\ very small, a condition which is very desirable, since then
the distributed capacity is negligible. There is, however, a limit to decreas
ing Li, in view of the fact that the resistance of a multiple resonating
circuit such as L\-€\ will, after decreasing L\ below a certain value,
decrease and will thus cause a much lower voltage to be applied across
the points H-J of Fig. 18. This effect can be calculated from Eq. (50),
page 72, from which it may be seen that the effective resistance of the
parallel circuit, at resonance, depends upon the ratio of L to R; the
smaller L is made the lower in the ratio L/R unless large well-stranded
conductors are used. '
As regards Lq, it should be made large, yet if it be so made its dis
tributed capacity may be such as to practically short-circuit the grid-
filament of the second tube and make the ratio E,JEti practically zero.
Hence, it is advisable to keep L2 as small as is consistent with reasonable
amplification. We will illustrate by means of the following example:
Take mo =6;
fc=0.3;
Li = j
1,2=256 fiB.
Then
En 6X0.3XV256
En~ V36 '
which is a small value as compared with 8.5 to 9.5 for audio-frequency
amplifier.
Of course we could increase L2 above 256, but, in so doing, its distrib-
uted capacity would begin to affect the grid voltage adversely and nothin?
would be gained by the increase in L2.
The effect of the grid-filament capacity must now be considered.
This capacity is comparatively small under static conditions but, as shorn
on page 432, Chapter VI, it increases very much under the conditions
present in amplifiers; of course the reactance of this capacity is in parallel
with the grid-filament circuit and causes the voltage across the grid to
fall to a small value, in spite of all the precautions which we may haTe
been taken in designing the repeating transformer. As a matter of fac:
it is shown in Chapter VI that the higher the alternating voltage produced
RESISTANCE REPEATING AMPLIFIER 849
at the output terminals of the tube the lower becomes the capacity react
ance of the input circuit, or, in other words, the better the repeating
transformer the poorer may the amplification be. Thus the capacity
of the input circuit of an amplifying tube, may be 50 to 75 ntf. Assuming
a value of 50 y.nf the reactance of this capacity at 600 meters would be
only 6400 ohms!
This is the most important difficulty encountered in the design and
construction of all high-frequency amplifiers, a difficulty which makes
such amplifiers, especially for short wave-lengths, very difficult to con
struct. The only remedy is to reduce the capacity of the input circuit
or, in other words, to make the area of the grid as small as feasible, and
keep the wires connecting to the grid as far from the other wires of the
tube as possible and use a tube having a low /zo- Some very small tubes
have been built for high-frequency amplifiers with these ideas incorpo
rated.1 The fio of such tubes is generally low, probably not more
than 3.
In case tuned plate circuits are used for a high-frequency amplifier
it is evident that unless all the tuning condensers are controlled by one
handle the adjustment of the amplifier for signals of various frequencies
would be tedious and difficult.
Resistance-repeating Amplifiers.—We will first discuss this type of
amplifier relative to audio-frequency amplification. The diagram of Fig.
19 shows such an amplifier for three stages. The incoming signal voltage
is applied to the points QS and is caused to affect the grid of Tube 1
through the means of the high resistance R. The grid and filament of
Tube 1 are connected across the resistance R through the comparatively
large condenser Ci; a leak resistance r\ is connected from the grid to the
filament. The purpose of the leak resistance and of the condenser Ci
will be explained later, but it will be presently understood that any vari
ations of potential difference across R will be impressed upon the input
circuit of Tube 1 with the exception of any drop of potential which may
take place in the condenser &.
The variations of the grid potential of Tube 1 will cause a correspond
ing variation of the plate current in this tube, and hence a varying differ
ence of potential will exist across the high resistance Ri. Since the point
o is at constant potential it is plain that the potential difference between
the points k and o will be varied and, as the battery resistance is com
paratively low, the variation of this potential difference must necessarily
be very nearly the same as that across Ri.
The grid and filament of Tube 2 are connected across k and o through
the comparatively large condenser C2, and, therefore, any variation in
the potential difference across k and o will be impressed upon the grid
1 Such a tube is shown at 0 in Fig. 21 of Chapter VI, page 389.
850 AMPLIFIERS [Chap. XI
of Tube 2, or, in other words the signal will be repeated into the second
tube by means of the repeating resistance Ri.
In a similar manner the signal will be repeated from Tube 2 to 3,
where it will be picked up on the receivers. The purpose of the grid
condensers C2 and C3
is to insulate the grids
of Tubes 2 and 3 re
spectively from the
batteries B\ and B2.
Thus, if condenser C2
were removed it is
plain that the grid of
Tube 2 would then be
connected to battery
B\ through the resist
ance Ri, and the
battery would impress
such a high positive
potential upon the
grid as to probably
spoil the tube. A
similar reasoning ap
plies to the case of
grid condenser C\ in
so far as it insulates
the grid of tube 1 from
anyhigh direct electro
motive force which
may be to the left of
the points QS; some
times, as will be shown
later, it is possible to
dispense with the grid
condenser Ci and the
resistances ri and R
for the first tube.
As regards the leak
resistances n, r2, t$
they are made neces
sary by the use of the insulating grid condensers Ci, C2, and C3. It has
already been found in Chapter VI, page 410, that, when a condenser is
connected in series with the grid, if the grid is very highly insulated, the
operation of the tube is very uncertain. The accumulation of electrons
RESISTANCE-REPEATING AMPLIFIER 851
h = f^r (18)
Again, assuming that the reactance C2 is very low as compared with that
of the grid-filament of tube 2, there will be a negligible drop of potential
over C2 and the voltage of the grid to filament for Tube 2 will be given by:
-g&«L (19)
and
Ef, mRt (2Q)
En Rp-\-R\
Eq. (19) shows that the ratio EtJEti increases continously with increase
of Ri and it approaches a maximum which will be reached when R\ is so
large that Rp may be neglected; this maximum will be given by:
E
Maximum possible value of -^r=no (21)
852 AMPLIFIERS [Chap. XI
This result is to be compared with that given by Eq. (12) and applying
to the case of a repeating transformer amplifier, for which:
E 7}
Maximum possible -jr = mo .'. (21a)
&n 2
i4
p
i
3
C3|,
o
p.
■1)
<o2
cs
0 10 20 30 40
Repeating resistance in Thousand Ohms
Fig. 20.—Variation in the amplifying power of a resistance-repeating tube as the value
of the external resistance used in the plate circuit is varied.
In order to study more fully the relation expressed by Eq. (20) we have
plotted curve, Fig. 20, for which:
mo =6
Rp = 10,000.
The curve shows that it is hardly worth while to increase Ri beyond
about 30,000 ohms for this particular tube, for the gain in EHiESl is
RESISTANCE-REPEATING AMPLIFIER 853
thereafter too small for even very large increases of Ri. Futhermore,
it must not be forgotten that the insertion of a resistance in series with
the plate requires a corresponding increase in the voltage of the B battery
as previously pointed out. As a matter of fact such a tube would prob
ably not be used with more than 20,000 ohms in the plate circuit. This
would require a B battery of twice the voltage required if there was no
IR drop in the external plate circuit and will give a voltage amplification
of 2/3 of mo (in the above case, 4).
As regards the first repeating resistance R it may be shown that it
should be very high as compared with the resistance in series with it; the
latter may be the plate-filament resistance of another tube or the resist
ance of a telephone line, etc.
The repeating resistances used are made up in units of small dimen
sions, approximately \ inch in diameter and 2 to 3 inches in length. There
are three general types in use: Type 1 consists of a tube of insulating
material wound with high resistance wire and coated with enamel; it
is made up in units up to about 5000 ohms. Type 2 consists of a tube
of insulating material wound with a few turns of carbon filament contain
ing a large percentage of clay and thus having a very high resistance; it
is made up in units up to 50,000 ohms. Type 3 consists of an evacuated
glass tube upon the inside walls of which there is " sputtered " a film of
tungsten which is very thin and therefore of very high resistance; it is
made up in units up to 2,000,000 ohms.
In every case it must be kept in mind that no matter what type of
resistance is used for repeating purposes it must have a current-carrying
capacity such as will enable it to carry the average current flowing in the
plate circuit of the tube wherein it is to be connected without overheating.
Thus,rin the case of a tube whose average plate current is 4 milliamperes
a repeating resistance of 50,000 ohms should be able to dissipate 0.8 watt
without overheating.
The repeating resistance should have negligible distributed capacity,
for, this would lower the value of its impedance and cause a reduction
in the amplification.
Another important point regarding the resistances used for repeating
comes up in connection with internal noises in an amplifier. It seems
that some of the high resistance units are " microphonic," that is, their
resistance continually varies by a very small amount. It will be at once
evident that such a resistance will give rise to noises in the amplifier,
especially if the microphonic resistance is in one of the first stages of the
amplifier. In general the higher the resistance the more likely is it to
be microphonic
Suitable Value of Grid Condenser.—The grid condenser must have a
small reactance as compared with the circuit from grid to filament, which
854 AMPLIFIERS [Chap. XI
circuit consists of the leak resistance and the capacity and resistance of
grid to filament; the point to keep in rnind is that the variation of poten
tial difference existing between the points k and o (see Fig. 19) should
be made to suffer but a negligible drop over the reactance of the grid
condenser, so that it may be applied very nearly in its entirety to the
grid-filament circuit. For audio-frequencies the reactance of the capacity
of the grid to filament is very high, i.e., one to two million ohms and does
not appreciably affect the impedance between the grid and filament,
which is almost entirely made up of the leak resistance and the internal
grid to filament resistance in multiple, which make up a resistance of the
order of 200,000 ohms. In this case the grid condenser may be allowed
to have a reactance of 50,000 ohms without seriously affecting the grid
voltage, or, in other words, for, say, 1000 cycles per sec. the capacity
of the grid condenser may be about gQ ooo**^® or' rou6my> 3000 wif.
If, however, the amplifier is used for high frequencies,1 say \=600
meters, then the impedance of grid to filament is made up almost wholly
of the grid-filament capacity reactance, which, for the amplifying tubes
generally used, is of the order of about 6000 ohms, hence the grid condenser
reactance should be of the order of about 1500 ohms or less; its capacity
may then be as low as 200 wxf without decreasing the value of E„ more
than 20 per cent. It is then apparent that smaller values of grid condenser
capacity may be used at high than at low frequencies. In any case it
is not advisable to use any larger capacity than just necessary, for in
doing so, the amplifier is too likely to block for longer periods of time than
necessary. If a pulse of e.m.f. is impressed on the amplifier all of these
repeating condensers will become charged and so cut the various plate
currents to probably zero. Before the amplifier can function the plate
currents must come back to normal value and this requires that all these
condensers (Ci, C2, C3, etc.) discharge themselves. The time required for
discharge is fixed by the time constants, RC, of these condensers. More
over if C3 and Ci discharge themselves before C\ does they will charge up
again when Ci discharges, due to this discharge sending another pulse of
e.m.f. through the amplifier. It is then evident that the time constant
RC should be only a small fraction of the time between two " dots " of a
signal, for example, if the blocking is not to interfere with reading the signal.
Hence RC must be made small and this must be accomplished by making
C as small as permissible because if the leak resistance R is made small it
would decrease the impedance of the grid-filament circuit so much that
too large a proportion of the voltage IpRi would be used up across the grid
1 It must be pointed out that the amplifier as ah-anged in Fig. 19 will not amplify
high-frequency spark signals; the condensers in series with the grids rectify the wave-
trains so that in the later stages of the amplifier, only low-frequency signals occur.
RESISTANCE AMPLIFIER FOR HIGH FREQUENCY 855
condenser, thus cutting down the voltage impressed on the grid. The
proper relative values of R and C to keep RC small must therefore be a
compromise.
Suitable Value of Leak Resistance.—The leak resistance should be
as high as possible without causing any of the tubes to " block." The
blocking would occur in case the grid became so negative as to make the
plate current zero; the signal would, then, not go through until some of
the electrons had escaped off the grid.
It is very difficult to lay down any exact rules or formulae as to the
best value of the leak resistance since some of the quantities which affect
it, such as the number of electrons collected on the grid are somewhat
indeterminate. It should be kept in mind, however, that a low leak
resistance reduces the total impedance between points k and o on Fig.
19 and hence makes the drop over the repeating resistance very small,
thus diminishing the amplification, and that a high leak resistance may
cause the tube to " block." In most amplifiers the leak resistance is in
the neighborhood of 1 to 5 million ohms.
The resistances commonly used for " leaks " are made up of a thin
strip of carboard, clamped between two terminals, over which there is
a coating of dried ink extending between the two terminals. The whole
is enclosed in a glass tube. India ink is a poor conductor, and such a
type of resistance as here described may be made up in units ranging
from i to 5 million ohms, depending upon the thickness and length of
the ink line. Of course the power capacity of such resistances is extremely
limited, and care should be taken not to overload them; they are meant
to be used on low-voltage tubes only.
Another type of resistance used for " leaks " is the glass tube with
the tungsten film deposited thereon already described on page 853.
As regards the connections of the low-frequency resistance-repeating
amplifier to the rectifying devices for damped or undamped waves they
are exactly similar to the connections for the low-frequency transformer-
repeating amplifier shown in Figs 13, 14, 15.
In every case the rectifying device, be it for damped or undamped
waves, is to be connected to the input points Q and S (Fig. 19) of the
resistance-repeating amplifier.
Resistance-repeating Amplifier for High Frequency.—The connec
tions of this type of amplifier for the purpose of receiving undamped
waves are shown in Fig. 21, where the last tube is an autodyne rectifying
tube. The input terminals of the amplifier are shown at QS and the out
put terminals at Qi»Si. The varying signal voltage existing across the
terminals of the receiving condenser C is applied to the grid of the first
tube and repeated from tube to tube, and it is finally made to affect the
grid of the rectifying or autodyne tube after several stages of amplifica
856 AMPLIFIERS [Chap. XI
tion. It will be noted that the grid-filament of the autodyne tube is con
nected not only across the output terminals of the amplifier but also across
ttHWr^h
the condenser Ci of the local oscillating circuit; hence it will have impressed
upon it both the local oscillations and the incoming antenna oscillations.
INDUCTANCE-REPEATING AMPLIFIER 857
In the case of the incoming waves being damped the same arrange
ment may be used as shown in Fig. 21, after reducing the coupling between
the grid and plate coils of the rectifying tubetothe point where no oscillations
are generated by it. The rectifying tube may, in the case of damped
waves, be connected in the simpler manner shown by Fig. 22. The high
frequency resistance-repeating amplifier is in no way different from the
low-frequency amplifier of the same type and the two may be used inter
changeably. The only point tha; must be noted in this respect is that
the grid condenser may be made much smaller for the high-frequency
than for the low-frequency amplifier, as already discussed on page 854,
and, furthermore, it is very important
that in the high-frequency amplifier To Points
the repeating-resistances be made
with the least amount of distributed
capacity, otherwise their impedance
will be lowered and the amplification
diminished.
As in the case of the transformer-
repeating high-frequency amplifier
the resistance-repeating amplifier suf Fig. 22.—In case the resistance-repeating
fers from the fact that at high radio amplifier is used to amplify spark signals
frequencies the condensive reactance it will be found unnecessary to use a
of the grid-filament circuit becomes rectifying tube with condenser in series
so low as practically to short-circuit with grid for detector; the high-frequen
cy signal will be changed to radio-fre
the repeating resistance, and con quency before going through the ampli
sequently reduces the amplifying fier very far.
action. Thus a resistance-repeating
amplifier which operates very successfully at audio-frequency may fail
to amplify at all at radio frequency, not because of any fault of the
amplifier, but because of the capacity of the grid to filament of each
tube.
Inductance-repeating Amplifiers.—This type is similar to the resist
ance-repeating amplifier, except that instead of a resistance in the plate
circuit of each amplifying tube an inductance is used whose reactance at
the frequency for which the amplifier is designed, is high. The theory
upon which the repeating action from tube to tube is based is exactly
the same as for the resistance-repeating amplifier and will not be gone
into here again. This method of repeating has an advantage over resist
ance repeating in so far as the repeating inductance offers but little
opposition to the flow of the direct current through the plate circuit and
hence the B battery may be of lower voltage than if resistance repeating
is used. For this reason the inductance-repeating amplifier is to be pre
ferred to the resistance repeater for low frequencies; but for high fre-
858 AMPLIFIERS [Chap. XI
/
/
Ucpeating reactance la Thousand Ohms
Fio. 23.—Amplifying characteristics of a tube using an inductance in the plate circuit;
the amplification obtainable is much greater than with the same number of ohms of
resistance.
other so-called " static interferences," which are always more or less
seriously affecting the reception of signals, produce audio-frequency currents,
which are amplified but little, or not at all by the radio-frequency ampli
fier; therefore, in this case, the final effect upon the telephone receivers,
or any other device used for detecting the signals, is due more to the ampli
fied radio-frequency signal currents than to the unamplified low-frequency
interfering currents. On the other hand, in the case of the audio-fre
quency amplifier, this will amplify not only the rectified radio-frequency
signal currents, but the atmospheric disturbances as well, so that the
telephone receivers will be subjected to both the signal and the inter
fering currents which have been equally well amplified. It would seem,
then, as if the radio-frequency amplifier would have the field entirely to
itself, but, unfortunately, the radio-frequency amplifier is, as has already
been pointed out, very difficult of construction for low, or even moderate,
wave-lengths, on account of the effect of the grid-filament capacity of
the tubes upon amplification. Tubes have been built where the grid-
filament capacity has been reduced to a very low value and they have
been employed with some success in the construction of high-frequency
amplifiers, but they are still in the experimental stage. An amplifier
quite extensively used during the war had three high-frequency air core,
transformer-repeating stages feeding into a detecting tube which in turn
fed into a three-stage low-frequency amplifier. (The advantage of
amplifying the high-frequency signal as much as possible before putting
it into the detector tube will be realized at once when it is remembered
that the detecting efficiency of a three-electrode tube increases with the
square of the signal voltage.) The overall voltage amplification of this
set was probably of the order of 10,000.
With the tubes at present available a good amplifier may be con
structed for frequencies of the order of 50,000 cycles per second, and since
this frequency is very much higher than that of most atmospheric dis
turbances, the latter will not be amplified, as much as the signal currents
of 50,000 cycles will be. In an amplifier originated by E. H. Armstrong
the difficulty of amplifying a high-frequency signal has been ingeniously
overcome; in it the incoming high-frequency currents are first reduced
by the heterodyne or autodyne method to about 50,000 cycles per second,
then amplified through a number of stages and finally reduced again by
another and last autodyne process to audio-frequency and transferred to
the receivers. The arrangement is shown in a simple form in the schematic
diagram of Fig. 24. It might seem that such an arrangement is very
complicated to handle, but, as a matter of fact, it is no more so than the
ordinary single tube autodyne set for receiving undamped waves. For,
it will be noted that the inductances and capacities in the second autodyne
tube are fixed, and their values are originally adjusted so that, when
Fio.
24. ecmrngupcdharerl-setufo—iprcfmentiqouednsorg,ncy cation)
first
beat
r(by
and
this
In
due
iAato
hthe about
cycles
aand
the
of
made
is
50,000
fsecond
this
then
to
at
output
act
mrpone;
per
lqiufeinecdry
A8-Stage
mplifier c50,000
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for
dasproduce
to
euitandgeioncbdtaloyerns.e
I\
862 AMPLIFIERS [Chap. XI
Frequency Frequency
Fia. 25.—Characteristics of different types of filters a and 6 having either resistance
and capacity or resistance and inductance while c and d must have resistance,
inductance, and capacity properly combined.
their structure, while the other two have inductance, resistance and
capacity.
A filter is generally applied to high-frequency amplifiers and may be
constructed to serve either one or both of two different purposes, i.e. :
(1) To prevent signals from all transmitting stations, except one,
from being amplified, and hence to keep interfering signals from reaching
the operator's ear.
(2) To prevent currents due to " strays," " static," etc., from being
amplified as much as they would otherwise be and hence to keep static
interference from reaching the operator's ear.
These two purposes of the filter might be carried out as shown in
Fig. 26. This figure represents a high-frequency resistance-repeating
amplifier. It will be noted that all incoming currents which go past the
timed receiving circuit (a), will produce varying voltages across the grid-
filament of the first tube and be thereby amplified into the plate circuit
of this tube. Across the points Y and 0 there is connected the circuit
Cz-H\—Ky-0] the circuit from Hi to Ki consists of L\-Ci in multiple
with the grid condenser d, the leak resistance n and the grid-filament
of the second tube. For the sake of convenience this part of the amplifier
circuit is reproduced in Fig. 27. The condenser C3 serves the purpose
of keeping the battery B\ from sending any direct current into the circuit
from Hi to 0, and may be made quite large, so as to have a low reactance
at as low a frequency as 1000 cycles per second or less. The circuit Li~C\
is one that is tuned to the frequency which it is desired to amplify, and,
of course, at this frequency it has a very high impedance, while at all
other frequencies, higher or lower, it offers a lower impedance.
The characteristic of this filter is given by curve (c) of Fig. 25. The
result is that the circuit of C3, Hi, Li-C\, K\ will practically short-circuit
the resistance from Y to 0 at all frequencies except the one to which L\
and Ci are tuned, and, therefore, the repeating resistance Ri will repeat
but poorly all frequencies except the desired one. Of course the fre
quencies nearest the desired one will be repeated, though not strongly,
into the second tube and these frequencies are still further weakened
in the process of repeating from the second into the third tube, so that,
finally, the output currents will contain the component of the original
input currents of the desired frequency strongly amplified and components
of other frequencies very much weakened or totally suppressed.
It will be noted that this type of filter acts as a barrier not only to high-
frequency interfering currents, but also to low-frequency static inter
ference. It has the objection of requiring the filtering circuits L1-C1,
L2-C2, etc., to be tuned to the incoming signal frequency, and, if this is
a variable one, the tuning complicates the operation of receiving. The
steady state impedance from Hi to Ki of the parallel circuit L\-Ci, is
866 AMPLIFIERS [Chap. XI
about as shown in curve c of Fig. 28, where fo is the frequency of the signal
which it is desired to amplify. The exact expression from which tk
curve can be plotted is given on the bottom of p. 71. It must be noted
that this impedance curve holds only for the steady state, and hence
gives no idea as to how the circuit will react to pulses or highly dampei
signals. In fact just because of the behavior of this circuit to pulses v.
is really a very poor filter to use with an amplifier for reasons now to
be given.
FILTERS 867
It was shown on pages 268 et seq. that when a damped wave of e.m.f.
is used for exciting a tuned circuit two distinct effects are produced. A
forced current, of the same fre
Tube 1 Tube 2
quency as the impressed e.m.f.,
flows in the circuit, and another
current of the same frequency
as the natural frequency of the
circuit is also set up. The rela
tive amplitudes of these two
currents are discussed in Chap
ter IV, page 270. It is there
fore evident that any impulsive
e.m.f. will start the circuit L\-C\
oscillating at its natural fre
quency which is practically the
same frequency as that for
which the amplifier is best
Fio. 27.—Circuit detail to show action of filter;
adjusted; this pulse of e.m.f. the circuit between Hl and K\ practically short
(atmospheric disturbance) will circuits any frequency except that for which it
therefore be sent through tube is tuned.
1 of the amplifier as a pulse
but after passing the filter Li-Ci it will be propagated through the rest
of the amplifier as a damped wave-signal of practically the same fre
quency as that for which
the amplifier is adjusted,
the damping of this spuri
ous signal being fixed by
the damping constant of
circuit L\-Ci.
This is an effect which
must be carefully guarded
against in the design of
amplifiers. With suitable
filtering circuits the pulse
A, Fig. 29, can be so
affected that it comes
Fia. 28.—The impedance between Hi and Ki varies with through the amplifier with
impressed frequency as shown here; the lower the
resistance in the Li-C\ circuit the sharper is this much less amplification
resonance curve. than the signal B. But
if tuned filter circuits are
used it may be that the pulse will be changed to a damped signal and be
amplified to practically the same extent as the signal B.
This tuned type of filter is excellent for differentiating between two
868 AMPLIFIERS [Chap. XI
measured it will be found to have somewhat the form of the curve (a)
of Fig. 26.
While no definite design of such a filter can be given here (it depend
ing upon the tubes used, etc.) it has proved satisfactory to make the react
ance of C3 and C4 for the signal frequency about one-fifth of the resist
ance R'i- In addition to this consideration the reactance of C3 and C4 in
870 AMPLIFIERS [Chap. XI
series must be small compared to the impedance between points M-N, and,
furthermore, the impedance of the network C^-R'^-C^-ri, etc., as measured
between the points Y-0 must be high compared to the resistance Ri;
and this resistance Ri should be about equal to the resistance of the plate
circuit of the tube. With this design of filter and amplifier circuit the
voltage amplification per stage is about /io/3.
As an example of how a filter of this kind differentiates between signals
of different frequencies a case has been worked out in Fig. 31. Points
O-Y on the figure would normally connect across the plate circuit resist-
c=boo fip./ ance °^ one tube, and points M-AT
r =6o,ooo ohms. would connect to the input circuit
-|| 1 1| iM of the next tube of the amplifier.
Power from Generators for
Amplifiers.—By using a suitable
filter it is possible to use a small
generator for lighting, the fila
ments or for furnishing the plate
current of an amplifier. Such an
wv«»«m«««oboy = i arrangement is indicated in Fig.
voita»« acron mn at 50,000 Cycles/Sec. =0.83 32. The amount of filter required
" " " " SiOOO " " =0.11
_ will depend upon the quality of
Fio. 31.—A section of a resistance capacity ... ... ,
C1. ., . , . , -nnnn . .
filter, through which 50,000 cycles is propa commutation of the machine. As
gated with but little attenuation, whereas the ordinary commutation fre-
6000 cycles is cut down to one-tenth of its quency is about 1000 per second
incoming amplitude. the reactance of each condenser
used in shunting the line should
be small, at this frequency, compared to the inductive reactance of the
coils (perhaps one-tenth as much). Iron core coils may be used, the
dimensions of L\, L\, etc., being necessarily much larger than L®, In,
etc., because of the greater current they have to carry.
Stability of Amplifiers—" Squealing."—An amplifier, especially if of
the inductance or transformer-repeating type, is very likely to produce
in the telephone receivers audio-frequency sustained notes which are
entirely independent of the incoming signals; this action is known as
" squealing," and is extremely objectionable and very difficult to over
come. The squealing of an amplifier is generally due to the fact that
the circuits of the various tubes are capable of oscillating, and may oscil
late if the conditions are favorable; this applies to both high-frequency
and low-frequency amplifiers. Thus assume, for the sake of clearness,
that a single tube is connected by itself as it would be connected were
it used in the low-frequency transformer-repeating amplifier of Fig. 13,
page 842, and let Fig. 33 represent it. The coils of the repeating trans
formers Ti and T2 have a large amount of distributed capacity, and hence
STABILITY OF AMPLIFIERS 871
luce a change in plate current; the latter will cause a variation of plate
lotential to take place, in view of the impedance of L2-C2 being connected
a series with the plate battery, and finally the variation of plate pot«n-
ial may, through the capacity of plate to filament and grid to filament,
eact back upon the grid, and may impress a higher voltage across the
ircuit L1-C1 than at first existed. Such a condition would, of course,
872 AMPLIFIERS [Chap. XI
The tube may also oscillate at the natural frequency of L2-C2 ; whether
it oscillates at the frequency of L1-C1 or of L2-C2 depends entirely upon
which of these frequencies gives correct phases of e.m.f.'s and the smaller
losses in the entire circuit.
If the frequency at which
Secondary the tube oscillates is audible,
o£ repeating
Transformer the currents produced there
by will be heard in the tele
phones connected in the plate
circuit of the last tube of
the amplifier, and will urn-
produce squealing. If the
Fig. 33.—Circuit detail of a transformer repeating frequency is inaudible the
amplifier; it may well be that, due to internal telephone will give no indi-
capacities of the coils (giving the circuit a natural ,. ... ,
,. ■between
period) and the coupling . , . and, grid cation of the rpresence ot sum.
plate
circuit inside the tube, self-sustained oscillations currents, but they will sen-
are set up in the circuit. ously interfere with the am
plifying action of the tubes.
In the case of a high-frequency transformer-repeating amplifier the tube
circuits may also oscillate, but they will do so at radio frequencies and wiE
not be heard, but the efficiency of the amplifier as a whole may be seriously
impaired by the presence of these interfering currents.
On the other hand inductance repeating high-frequency amplifiers,
oscillating at radio frequency, sometimes produce an audible tone in the
telephones due to the fact that the
grid condensers may, as a result of
the oscillations, become so highly nega
tive as to cause the plate current to
become zero and thus stop the oscil
lations; after a time the electrons
collected on the grid will leak off and
the plate current will start flowing;
but the oscillations will again start
Fig. 34.—The transformer coils of Fx
in and again make the plate current 33, with their internal capacities pr;
zero, etc. This starting and stopping a circuit as shown here.
of the oscillations, with consequent
pulsations in plate current, may take place at audio-frequency, in whict
jase the amplifier will " squeal." This phenomenon is similar to the
one fully discussed on page 523 in connection with oscillating receivim;
tubes equipped with grid condensers.
In the discussion given above we have, for the sake of simplidrj
STABILITY OF AMPLIFIERS 873
considered the action taking place in each individual tube, which may
be caused to oscillate due to the varying currents in the plate circuit of
that one tube reacting back upon the oscillating circuit to which the grid
and filament of the same tube are connected. Of course each tube may
be caused to oscillate in the same manner at the same or a slightly different
frequency from every other. What does happen, however, is that all
tubes are subjected to one single frequency and the value of this frequency
is the one at which it is " easiest " for the entire amplifier to oscillate,
that is, the one frequency at which the losses in the whole amplifier (for
a given strength of oscillation) are a minimum; of course if these losses
are greater than can be supplied by the plate battery through the reactions
of each plate upon each grid circuit the amplifier will fail to oscillate at
that frequency or at any other frequency for which this condition prevails.
It may happen, however, that the output circuit of the amplifier is
coupled, either magnetically or electrostatically, or both, to the input
circuit, in which case the amplifier may oscillate, even if it would not
otherwise do so. Thus, consider the three-stage transformer-repeating
amplifier of Fig. 6, which is similar to that of Fig. 13. Assume that oscil
latory currents start in the secondary of transformer T; these currents
will be repeated and amplified from tube to tube ; if now the plate circuit
of the last tube is so related to the grid circuit of the first that the varying
currents in the former can produce varying voltages in the latter, which
are sufficiently large and in the right phase to increase and sustain the
currents started in the secondary of transformer T, then the amplifier
will oscillate. It will be easily understood that if there is coupling between
the output and input circuit it is not a necessary condition, in order for
the amplifier to oscillate, that the oscillations shall start in the grid cir
cuit of the first tube, for, they may start in the grid circuit or even the
plate circuit of any one of the tubes, including the last, and, in every case,
the amplifying action of the apparatus may make it likely that oscillations
be sustained, even if the coupling between the output and input circuits
is feeble.
Again, while in the preceding paragraphs we have assumed that the
plate circuit of the last tube is coupled to the grid circuit of the first tube
the amplifier may oscillate even if the plate circuit of an intermediate
iube is coupled to the grid circuit of the first tube or, in general, it may
>scillate if the plate circuit of any one tube is coupled to the grid circuit
>f any of the preceding tubes. For, as long as any currents started in
he oscillatory circuit of any one tube are sustained by the reactions of
he other tubes the amplifier as a whole may oscillate.
Remedies for Amplifier Squealing.—It must be stated at the outset
hat the more an amplifier amplifies the more likely it is to squeal; in
►ther words, a silent amplifier is not necessarily better than one which
874 AMPLIFIERS [Chap. XI
gives loud " sputtering " noises in the telephones, even when the input
circuit is short-circuited. This may be due to a " bad " tube somewhere
in the amplifier (to be discussed in the next section) or it may be due
to either the A or B batteries. A storage battery is practically always
used for filament heating, so it is evident that this battery has a low
resistance, but it will be found that if a good amplifier (high amplification)
is used with an A battery nearly discharged (say lower than 1.8 volts
for a lead cell) all sorts of odd noises may be heard in the amplifier,
whereas if a normally charged A battery is substituted the amplifier is
quiet.
The same remark holds true regarding the B battery to an even
greater degree; the small dry cells generally used for the plate battery
develop a very high variable resistance towards the end of their life, and
if there is one such " worn-out " cell in the battery it will result in very
bad noises in the amplifier. A test of the cells with a low resistance volt
meter will at once show of the defective cell.
Tube Noises.—Another feature which causes considerable difficulty
in the operation of an amplifier is the " noise " produced by the tubes.
The reader will realize that any slight change in the currents flowing in
the plate or filament circuit of an amplifier tube, especially if it be one
of the first tubes, may be so amplified as to finally produce a very large
change in the plate current of the last tube, and hence a loud click in the
phones. Sometimes these clicks are frequent and almost deafening as
compared with the signals, hence very objectionable. As a matter of
fact these noises form one of the limitations of amplifiers in so far as the
number of stages is concerned, since it is almost impossible to prevent j
minute changes of currents in the first tubes, which, if repeated and
amplified through a large number of stages, may finally " swamp " the
legitimate signals. These minute changes of current in the tube circuits
may take place due to several causes, the most common of which are :
(1) Sudden slight changes in the electromotive forces of the vari
ous batteries (discussed in previous section).
(2) Mechanical vibration of the elements of the tubes.
(3) A slight amount of gas causing ionization, or, what is more
difficult to overcome, actual irregularities in the rate of emis
sion of electrons from the filaments. This is probably due
to surface impurities of the hot filament.
It is evident that mechanical vibrations of the tube elements will
vary the distance between the grid and filament and, of course, the plate
current will change accordingly; the same is true of any changes in the
distance between plate and filament and plate and grid. Hence the
elements should be firmly supported. Of course, no matter how firmly
876 AMPLIFIERS [Chap. XI
a common rheostat; the battery used in the plate circuit (the same battery
serves all tubes) should be about 40 volts. An over-all voltage ampli
fication of about 3000 is obtained, but there is generally an audible tube
noise present, making it useless for reading very weak signals.
In Figs. 36 and 37 is shown a very carefully designed amplifier having
its best performance for a signal of 6000 meters wave-length. Induc
tance repeating is used, the coils being toroids with iron-dust cores; they
have a reactance of about 50,000 ohms. The tubes used have fio equal
to 35 and use a plate potential of 130 volts. The total voltage ampli-
fication possible, without squealing, is about 50,000, but its useful ampli
fication for very weak signals, is only about 5000.
This question of useful amplification is seldom mentioned in texts,
but is really very important. It may be that two amplifiers are com
pared in the laboratory and it is found that one gives a voltage ampli
fication ten times as much as the other. It may be that this comparative
figure checks when different tests are made so that there is no doubt
regarding its accuracy. It might be then assumed that if a signal giving
a certain current in the antenna is just readable with amplifier A (the
878 AMPLIFIERS [Chap. XI
poorer one) that when amplifier B is used the signal would be readable
if the antenna current were decreased to one-tenth its former value. It
will probably be found, however, that when amplifier B is used an antenna
current about one-half that used with amplifier A is the least audible
signal, instead of one-tenth, as is naturally assumed. The reason for this
is the " background " of noise (from tubes and other sources) present
to a greater extent with B than with A. And the presence of the noisy
background requires a much stronger signal in the phones when using
amplifier B than is required when A is used.
CHAPTER XII
EXPERIMENT NO. 1
Object
To investigate the phenomena of resonance in a simple series circuit
and in two circuits coupled together by mutual inductance. To find the
effect of coupling upon the form of the resonance curve and to study
the effect of mistuning the secondary circuit.
Apparatus1
Two fixed condensers Ci and C2. (These should be of suitable value
and may be equal in value, although not necessarily so.)
Two fixed inductances Li and Li. (These inductances should have
such value that, when combined with C\ and d respectively, the oscil
lation frequencies are at the middle of the range of frequencies obtain
able with the alternator available.)
1 In this experiment, as well as those which follow, suitable values of apparatus
constants have been suggested wherever considered desirable, and in the specific direc
tions for each test, such suggested apparatus has been considered as available.
880
RESONANCE CURVES 881
Operation
Fig. 1. Fig. 2.
Curves
Plot resonance curves for each of the six runs specified above. Illustra
tive curves are shown in Chapter I, Figs. 53, 54 and 95. For tests Nos.
2 and 3, calculate «' and to", using formula; (101), (102), (103) and (104),
Chapter I. It is suggested that the student review that part of Chapter
I dealing with coupled circuits before attempting to carry out the fore
going tests.
EXPERIMENT NO. 2
Object
Use of a buzzer-wave generator; setting up and adjusting a receiving
circuit using a crystal detector; characteristic curves of a crystal rectifier
by continuous current test; operation of a crystal rectifier on alternating
current.
Apparatus
Two dry cells.
Fixed inductance U (about 150 microhenries).
Fixed capacity C (about .005 microfarad).
Buzzer rheostat.
Buzzer.
Variable inductance L (O-5000 microhenries).
Variable capacity C (0-.0010 microfarad).
Phones.
Crystal rectifier.
Micro-ammeter (0-1000 micro-amperes).
Potentiometer.
Low-reading d.c. voltmeter.
Source of low potential alternating current. (May be conveniently
obtained from an alternator operated with its field circuit open.)
Low-reading a.c. voltmeter.
CHARACTERISTICS OF CRYSTAL RECTIFIERS 883
Operation
Test 1.—Connect the buzzer wave-generator in accordance with
Fig. 3. Vary the buzzer adjustment and series resistance until a pure
musical note is obtained.
Test 2.—Connect the receiver circuit in accordance with Fig. 4.
Couple this circuit closely to the buzzer generator, and adjust the recti
fying crystal until a loud signal is heard in the phones. Jar the crystal
and note how easily its adjustment is spoiled. Note how easy or difficult
it is to find another good rectifying point on the crystal. ■ ,
Test 3.—With tight coupling, and holding the inductance constant,
vary the capacity until resonance is obtained (maximum signal in phones).
Note the range of condenser adjustment oyer which the signal is heard.
This is a measure of the selectivity. (See Note.) Repeat this test with
various values of coupling, and note the relation between selectivity and
coupling.
i T^wva
I sWi
Fig. 3. Fig. 4.
Note: A circuit is said to be selective when it is necessary (in order
to get a maximum strength of signal) to adjust closely the value of induc
tance or capacity being used for tuning the circuit. If the signal is of
about the same strength for widely different values of the tuning con
denser or inductance, the circuit is said to be non-selective; or it may
be said that the tuning is broad for such a circuit, while a selective circuit
is said to have sharp tuning. A circuit which has no natural period is
said to be " aperiodic."
Test 4.—With loose coupling make the inductance as low as possible,
obtain resonance by varying the condenser, and note the strength of
signals and selectivity. Repeat, using a very high inductance. Com
pare the strength of signals and selectivity in the two cases.
Test 5.—Obtain the continuous current characteristic of the rectifier
(in this case a crystal), making the connections as indicated in Fig. 5.
Vary the voltage impressed on the crystal from plus one volt to minus
one volt. Get a reading of the current for each 0.1 volt between the
limits named. The above test should be made for a point on the crystal
which shows good rectification in the receiving circuit of Fig. 4. Obtain
another curve for a second point on the crystal which shows poor detection
884 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
when tried with the buzzer. Make a note of which side of the detector
is positive when the larger current flows.
Test 6.—Replace the battery shown in Fig. 5 by a low potential alter
nating current source and connect the a.c. volt
meter directly across this source. Starting with a
potentiometer setting which gives the lowest volt
age, get a series of readings of the micro-ammeter
and of the impressed voltage, and note how the
rectification varies with the impressed voltage.
The voltage impressed across the crystal and
galvanometer is to be calculated from the meas
ured voltage of the a.c. generator and the position
of the potentiometer contact; the resistance used in the potentiometer
must, of course, be low compared to that of the crystal.
Questions
1. If in a buzzer circuit L = 100 microhenries and C = .0004 micro
farad, what is the wave-length? If C = .0002 microfarad, what value
must L have to generate a wave-length of 600 meters?
2. Judging from your experimental results is tight coupling or loose
coupling generally desirable under actual field conditions where much
interference is likely to occur?
3. A circuit is tuned for an incoming signal with certain values of
L and C. If L is increased four times what change must be made in C
to maintain the tuning?
4. What three characteristics should a good crystal rectifier possess?
EXPERIMENT NO. 3
Object
Study of the wave-meter; use of the meter for measuring the wave
length of low- and high-powered circuits, i.e., receiving and transmitting
circuits; measurement of inductance and capacity by means of the wave-
meter, using the meter as a detecting circuit or as a calibrated wave-
generator.
Apparatus
Two dry cells.
Coil A—standard fixed inductance (about 50 microhenries).
Coil B—unknown fixed inductance (one designed for low voltage
service).
Coil C—unknown fixed inductance (antenna loading coil or one coil
of an oscillation transformer).
CONSTRUCTION AND USE OF WAVE-METER 885
Operation
Test 1. Inspection of Wave-meter.—Open and inspect in detail
whatever wave-meter may be available. Draw a diagram of the con
nections, and study carefully the various parts. Note how the unilateral
connection of the detector and phones may be obtained.
Test 2. Measurement of Capacity.—Set up a buzzer-excited circuit
as indicated in Fig. 6 and consisting of A and D. (See Note.) Measure
by means of the wave-meter, the wave
length of the oscillations generated, using H^aw
no tighter coupling than necessary (weak I
coupling is necessary if an accurate J_
setting of the wave-meter is to be "T-
obtained). From the measured wave- fffl/*1
length and the known value of the
inductance calculate the capacity of the FlG- 6-
condenser.
Note: In this and in subsequent tests make connections with short
leads. Use particularly short leads in the oscillating circuits. The
capacity of the leads connecting the condenser to the inductance or to
the detector circuit or to the buzzer acts as part of the capacity of the
oscillating circuit, thus making the capacity of the circuit greater than
that of the condenser and giving an error proportional to the capacity
of the leads. The error depends upon the value of the capacity of the
condenser; for large condensers the effect is small, but for condensers
of 100 micro-microfarads or less an error of 25 per cent may easily be made.
886 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
A similar error occurs due to the inductance of the leads in the oscillating
circuit.
Test 3. Measurement of Capacity.—Repeat Test 2, substituting
condenser E for condenser D.
Test 4. Measurement of Capacity; Computation of Capacity from
Dimensions.—Repeat Test 2, substituting condenser F (set for maximum
capacity) for condenser D. Before performing this test take apart con
denser F, obtain the dimensions and number of plates, and compute
capacity. Compare the computed with the measured capacity.
Test 5. Measurement of Inductance; Computation of Inductance
from Dimensions.—Calculate the value of inductance of Coil B from
its dimensions, and then measure it, using for a standard capacity such
a combination of condensers D, E, and F as will produce a wave-length
within the range of the wave-meter. This value of wave-length is to be
calculated from the known values of the capacities and the computed
value of the inductance.
Test 6. Wave-length of an Oscillating Circuit Excited by a Buzzer.—
Measure the wave-length produced by the combination of Coil C and
condenser E, using a buzzer circuit
as in previous tests.
Test 7. Wave-length of an Os
cillating Circuit Excited by a Power-
set.—Transfer C and E to the high-
power circuit shown in Fig. 7, and
again measure the wave-length. It
Fig. 7. should be found that the wave-length
for tests 6 and 7 is the same.
Test 8. The Wave-meter as a Wave-generator.—Connect the wave-
meter as a wave-generator as indicated in Fig. 8 and couple to it the oscil
lating circuit consisting of coil A and condenser D, with detector and
phones as shown in the fig
ure. Vary the wave-length —T^w>-
X
generated by the wave-meter
until the test circuit indi
cates resonance; the wave
length of the test circuit is
then read from the wave- Fig. 8.
meter. From this and the
known inductance compute the capacity. It should be found that the
capacity thus obtained agrees with that found in Test 2, when the wave-
meter was used as the detecting circuit. What small difference occurs
is due to the capacity and inductance of leads, personal error, etc.
ADJUSTMENT OP TRANSMITTING SET 887
Questions
1. If the wave-length of a circuit is to be increased from 600 meters
to 2500 meters how much must the L of the circuit be increased, the C
of the circuit remaining the same?
2. The maximum capacity of the condenser of a certain wave-meter
is 5500 micro-micro-farads. Its maximum wave-length is 6200 meters.
What is the inductance of the coil used? If the range of the meter is
to be increased to 12,000 meters how much inductance must be added
to that of the meter?
3. A solenoidal coil has a winding 5 inches long, 25 turns to the inch,
and is 4 inches in diameter. What is L in cm. and in microhenries and
in millihenries?
4. A sliding plate condenser has eleven fixed plates and ten movable
plates. The plates are 3 inches by 4^ inches and the separation of adjacent
plates is inch. What is the capacity in cm. and in microfarads?
EXPERIMENT NO. 4
Object
To set up and adjust a transmitting set, using inductive coupling;
to investigate the effect on antenna current of tuning the antenna circuit
to the closed circuit; effect of coupling on the amount of antenna current
and wave-lengths radiated; energy distribution curve; determination
of the decrement of the set; conductive coupling.
Apparatus
Source of alternating current supply (500~ or 60~) and step-up
power transformer designed for radio service (about 1 kw. rating). Spark
gap (plain open gap). Oscillation transformer (the inductances used
may be of the flat spiral type, should be insulated for high voltages, and
have a maximum inductance of about 40-50 microhenries).
High-voltage condensers for primary and secondary circuits. (These
may conveniently consist of Leyden jars, properly connected. The
amount of capacity will depend on the wave-length for which it is decided
to adjust the set, but will probably not exceed .005 to .010 microfarad
for either circuit.)
Hot-wire ammeter for antenna circuit.
Wave-meter.
Loading inductance (may or may not be needed, depending on relative
values of closed and open circuit inductance and capacity).
888 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
Fiq. 9.
adjust the turns included in this circuit until the antenna ammeter gives
a maximum indication. With this adjustment take an energy distribu
tion curve by means of the wave-meter.
Test 8. Adjustment of the Spark Gap.—Carry out the following
tests on spark gap adjustment with the antenna circuit open. Place a
suitable hot-wire ammeter in the primary of the oscillation transformer.
Set the gap to ^ inch, and note current and character of sparking; repeat
the gap settings of J, j, f^, f inch. It will be noted that if the gap
is made too short for the voltage the set is generating the spark will
change from a white snappy spark to a more or less transparent arc.
This is especially true if the gap surfaces are rough and dirty.
The arcing type of spark makes a transmitting set practically inopera
tive because of the very small amount of high-frequency power generated
with such a spark. If the gap of a set acts in this manner it should first
be cleaned thoroughly and then the voltage of the set reduced or the length
of the gap increased. It will be noted in support of this statement that
when the gap has the arcing character the reading of the hot-wire ammeter,
showing the amount of high-frequency current, is small compared to the
reading when the spark has the snappy, noisy, and white appearance.
ANTENNA MEASUREMENTS 891
Questions
1. A spark gap is set to break down at 5000 volts; the closed circuit
condenser has a capacity of .0009 microfarad; there are 350 sparks per
second. How many watts of high-frequency power are generated in the
closed circuit? If 60 per cent of this power is transferred to the antenna
circuit and the effective resistance of the antenna is 8 ohms, what will
the antenna ammeter read?
2. An open spark set is tuned for 410 meters; the coupling is 30 per
cent. What wave-lengths are radiated? If the coupling is decreased
to 8 per cent what two waves would be radiated? Would they appear
as two waves with an ordinary receiving set?
3. Calculate the decrement of your transmitting set for one of the
adjustments for which an energy distribution curve was obtained, using
that curve showing the purest radiation. Assume the wave-meter decre
ment is .03, if it is not known.
4. From the energy distribution curve for the tighest coupling used
in your experiment calculate the percent coupling for that adjustment?
EXPERIMENT NO. 5
Object
To measure the natural wave-length, inductance and capacity of an
antenna and its variation with loading, etc. If time permits, to measure
antenna resistance.
Apparatus
Large and small antenna, variable known inductance of about 4000
microhenries. Receiving coupler, phones, and detectors to set up aperi
odic detecting circuit, wave-meter for wave-generator. Variable known
condenser from about .001 microforad to zero.
Operation
Test 1. To measure the natural wave-length of an antenna we use two
other circuits coupled loosely to the antenna and so arranged that no energy
can get directly from one into the other.
The wave-meter, used as a wave-generator, is coupled to the antenna,
using only one or two small turns in the antenna for the coupling. The
detecting circuit made up of one or two turns of the primary of a coupler
in the antenna and all of the secondary coil, used with crystal detector
and phone, forms the detecting circuit.
892 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
In case a quenched gap is used in the exciting circuit, the value of resist
ance obtained should be increased by about 20 per cent.
Another method for getting the resistance is by getting the decrement
of the antenna at various wave-lengths, using quenched spark excitation.
The resistance is then obtained by the relation
5=wRVC/L
If C and L are not known the decrement may be obtained after a small
non-inductive resistance has been added in the base of the antenna. This
combined with the decrement obtained before the addition of resistance,
will give the antenna resistance even if L and C are not known.
The tests outlined above are for damped wave excitation; the results
of the test should be checked by measurements with continuous wave
excitation after Ex. 11 has been carried out.
Questions
1. Why is it necessary to use few turns in the coupling coils, when
measuring natural wave-length? How could you tell (approximately)
the natural wave-length of a ship's antenna? About how much is the
capacity of a ship's antenna?
2. How many microhenries of inductance would you add in the base
of such an antenna to increase the wave-length to 1000 meters? to 2500
meters?
• 3. Using the same width spreader, how much might the capacity of
a 4-wire aerial be increased by increasing the number of wires to eight?
Explain.
4. Would the capacity of a ship's aerial change as coal is taken on
board? Why? How much? How much would such a change, alter the
natural length of the aerial?
5. Why are aerials always operated at a wave-length greater than
the natural wave-length?
6. Of what two general components is the total resistance of antenna
composed?
7. How do these vary with the wave-length radiated from the antenna? •
8. Explain the difference between the shape of resistance curves of
a land station and a ship station?
9. If a land station shows a high ground resistance, how would you
attempt to remedy it? Why is a high ground resistance objectionable?
10. Show by sketches the distribution of current and voltage in an
antenna for the three cases, first, antenna, by itself ; second, antenna with
loading coil in base; third, antenna with series condenser in base.
894 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
11. Explain how the series condenser cuts down the natural wave
length of an antenna.
12. What is the effect on the antenna resistance of adding loading
coil in base of antenna and also of adding series condenser?
13. How will the decrement of an antenna vary as the amount of
loading inductance is increased?
14. What is likely to happen to a series condenser in the base of ap
antenna? Why? How may it be prevented?
15. In what part of a ship's antenna is the current a maximum?
EXPERIMENT NO. 6
Object
To determine the continuous current characteristics of a three-electrode
tube, using a tube suitable for receiving and amplifying radio signals.
Free grid potential. Effect of low plate voltage or low filament current
on the characteristics of the tube. Effect of reversed plate battery or
reversed filament battery.
Apparatus
One vacuum tube (receiving type, as for instance, the Western Electric
Co.'s VT-1, or General Electric Co.'s .VT-11).
Vacuum tube receptacle.
Two dry cells (to be used for grid potential).
Ammeter (for filament current).
Milliameter (for plate current).
Micro-ammeter (for grid current).
Potentiometer (should be of high resistance).
Voltmeter (for reading plate voltage).
Low range voltmeter. (For reading grid voltage. If voltmeter for
measuring plate voltage is equipped with low-range scale, this instrument
will not be required.)
Rheostat for filament circuit.
Dry battery for plate circuit (about 40 volts).
Storage battery (for filament circuit).
Operation
Test L Tube Characteristic under Normal Conditions of Plate
Voltage and Filament Current.—Grid voltage vs. plate current and Grid
voltage vs. Grid current curves should be plotted for each of the tests
indicated, plotting current on the Y axis.
THE THREE-ELECTRODE VACUUM TUBE 895
Connect the tube in accordance with Fig. 11 with the negative side
of the filament as the common junction. With plate voltage about 20
volts, filament current = 1.1 ampere,
vary grid potential from +2 to —2
volts in steps of 0.2 volt, and read
plate current and grid current for
each adjustment of grid voltage.
Test 2. Free Grid Potential
under Normal Conditions of Plate
Current.—Determine the free grid
potential by reading the plate cur
rent with grid entirely disconnected from the rest of the circuit. From
this reading of the plate current and the tube characteristic curve
obtained in Test 1, the free grid potential may be obtained.
Test 3. Tube Characteristic with Reduced Plate Voltage.—Repeat
Tests 1 and 2, using about half plate voltage, filament current = 1.1 ampere.
Test 4. Tube Characteristic with Reduced Filament Current.—
Repeat Tests 1 and 2, using normal plate voltage, filament current =0.8
ampere.
Test 5. Tube Characteristic under Normal Conditions of Plate Volt
age and Filament Current with Plate Battery Reversed.—Repeat Tests
1 and 2 with plate battery reversed.
Test 6. Tube Characteristic under Normal Conditions of Plate Voltage
and Filament Current with Filament Battery Reversed.—Repeat Tests
1 and 2 with filament battery reversed, the positive side of filament now
being the common junction.
Questions
1. What is the normal resistance of the plate circuit of the type of tube
used in this experiment?
2. What is meant by the space charge in a vacuum tube and what
is the effect of the grid potential upon its action?
3. What effect does a low plate voltage have upon the characteristic
curves of a tube? What effect does a low filament current have?
4. What is the effect upon the characteristic curves of a tube of using as
the common junction the positive side of the filament instead of the negative?
EXPERIMENT NO. 7
Object
Study of the connections and xise of the three-electrode vacuum tube as
a detector of high-frequency damped waves with and without suitable
grid condenser. Effect of the grid condenser leak. Effect of using too
896 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
large or too small a grid condenser. Effect of filament current and plate
voltage upon the detector action of the tube. Effect of reversed plate
battery or reversed filament battery. Comparison of the vacuum tube
and rectifying crystal as detectors.
Apparatus
Vacuum tube (similar to that used in Experiment No. 6).
Vacuum tube receptacle.
Storage battery for filament circuit.
Dry battery for plate circuit (about 40 volts).
Two dry cells for buzzer circuit.
Ammeter for filament circuit.
Voltmeter for measuring plate voltage.
Phones.
Buzzer and rheostat.
Two fixed inductances (about 50 and 150 microhenries).
One fixed condenser for buzzer circuit (about .002 microfarad).
One fixed condenser for shunting phones (about .005 microfarad).
Three fixed condensers for grid circuit (about .005, .0001 and 1 micro
farad).
Three leak resistances for grid circuit (about 2 megohms, 50,000 ohms
and 10,000 ohms).
One variable condenser (about .001 microfarad maximum capacity).
One crystal rectifier.
One filament circuit rheostat.
Two D. P. D. T. switches (one to be a reversing switch).
One S. P. S. T. switch.
Operation
Caution.—In making the tests indicated below, it is important that
the receiving circuit be excited only by the high-frequency oscillations gen
erated by the buzzer-wave generator. If the receiving circuit is placed
near to the buzzer leads, which are carrying pulsating current of audible
frequency, current of this frequency will be induced directly into the
receiving circuit, and so heard in the phones. The signal thus received
cannot be tuned out and may result in wrong conclusions. It is, there
fore, important that the buzzer leads be short and kept remote from the
receiving circuit.
If an audibility meter is available it may be used in connection with the
phones, and its indications may be used instead of varying the coupling
between receiving circuit and buzzer generator. The audibility meter
must be of the constant impedance type.
VACUUM TUBE AS DETECTOR 897
r generator mounted
Fig. 12.
Questions
1. When no grid condenser is used, why is it difficult to find a good
rectifying adjustment of the tube?
2. Why would the tube detect poorly when a grid condenser is used
without a leak resistance, assuming no leak in the tube?
3. Why does a grid condenser with suitable leak make the rectifying
action of the tube certain for a wide range of values of plate voltage and
filament current?
4. A certain tube with grid condenser and leak rectifies well when the
group frequency of the incoming waves is 120; it rectifies very poorly
when the group frequency is 1000? Explain.
EXPERIMENT NO. 8
Object
To determine (a) the geometric amplifying factor (juo) of the tube and
its variation with filament current and plate voltage; (6) the amplifying
factor (ji), which represents the true amplification obtained when the
output circuit of the tube is loaded, and its variation with external resist
ance in the plate circuit; (c) the internal plate circuit resistance of
a three-electrode vacuum tube and its variation with filament current
and plate voltage.
Apparatus
Vacuum tube (similar to that suggested for experiment No. 6).
Vacuum tube receptacle.
Storage battery for filament.
Source of high-frequency current. (About 1000~. Source should
be ungrounded. An oscillating tube generator may be conveniently
used or a small alternator.)
Plate battery (40-volt dry battery).
Phones.
DETERMINATION OF TUBE CONSTANTS 899
Operation
Throughout the following tests (with exception of test No. 1 (d))
the grid voltage should be
adjusted to a certain value
and held constant at this
value. This value may be
arbitrarily chosen, although
it is desirable to make Ec
of that value which has
been found to give the best
performance with the tube,
e.g., for reception or ampli
fication.
Test 1.—Determination
of juo.
(a) With normal fila
ment current and plate voltage, open switch S, close switch S', and adjust
rj, and r2 until no sound is heard in the phones. Under these conditions:
XT2 T2
no= —
ir\ =—.
ri
Test 2.—Determination of n.
(a) With switch S closed and S' open and R set at the value at which
fi is to be measured, vary r% or T\ until when <S' is closed no note is heard
in the phones. Under this condition the alternating voltage drop across
R is equal to the alternating voltage drop across r2
or
ipR =t>2 =m17*i,
and
(i>) Repeat test (a) with various values of R and plot results obtained.
Note: As R is increased E& must be increased to keep Ev at its rated
value (Ep represents the voltage impressed between plate and filament).
To do this, note what plate current flows when R is made equal to 0 and
Ed is at rated value for the tube. Then keep Ip at this value by increasing
Ed as R is increased.
Eg must be kept small and should not exceed 0. 1 volt. To make sure
of this, the milliammeter A is connected in series with the potentio
meter. From its indications and the known value of ri, the value of E,
( =jVi) is readily obtained.
Test 3.—Determination of the internal resistance (Rp) of the tube.
(a) With normal values of filament current and plate voltage close
switches S and <S'. Adjust potentiometer resistance so that n =r2 and
vary R until no note is heard in the phones. Under this condition
Rp = (w-l)R
where no is known from the results obtained in Test 1.
(b) Repeat test (a) using various values of plate voltage, holding the
filament current constant at normal value.
(c) Repeat test (a) using various values of filament current, holding
the plate voltage constant at normal value.
In case it is not feasible to get a balance with ri=r2 then a suitable
ratio of n— r2 may be chosen, in which case we have:
EXPERIMENT NO. 9
Object
To measure the power output of an oscillating tube generator (with
separate excitation) and its variation with plate voltage, filament current,
excitation and plate circuit external resistance.
TRIODE AS CONVERTER 901
Apparatus
Operation
In all of the tests outlined below care must be exercised that the
amount of power expended on the plate or grid is not greater than the
safe rating for the tube used.
Part I.—The action of the tube will first be investigated with the plate
circuit untuned since this is the easier circuit to manipulate. The large
value of inductance should be inserted in the plate circuit during the
following tests.
Test 1.—With suitable values of Es, Ec1 and R, and with Ev normal,
note the output of the tube and its variation as the filament current is
varied, plotting your results in the form of a curve. A proper value for
R makes it equal to the normal value of Rv.
Test 2. Repeat Test 1, varying the plate voltage instead of the fila
ment current.
Test 3.—Repeat Test 1, varying E, instead of the filament current.
(In this test Ec must be varied so as to get maximum output at each
setting of E„, without, however, exceeding the safe rating of the
tube.)
Test 4.—With all conditions' normal, determine the variation in out
put of the tube, as the resistance (R) in the output circuit is varied.
In all of the foregoing tests the high-frequency power in the output
circuit is given by
P=v*R
where i is the current measured by the ammeter A'. Due to the high
impedance of L to high-frequency currents, it may be reasonable
assumed that practically no high-frequency current passes through this
branch.
Part II.—The characteristics of the generator when using a tuned-
plate circuit will next be investigated. The high inductance should there
fore be replaced by the low inductance to permit tuning the parallel cir
cuit LC to radio frequencies. A suitable low inductance, such that the
capacity used in parallel with it will permit tuning (parallel resonance)
to the frequency used for grid excitation.
Test 1.—With all conditions normal, e.g., Ev, Ir, Ee of proper value,
and Eg held fixed at a certain value, find the effect on the output, of the
tube of tuning or of not tuning the output circuit to the input frequency,
using a low value of R.
1 Ec should be held constant at some value which has previously been found to be
most suitable for the tube when acting as a generator with all conditions normal. This
will generally be about 80 per cent of the maximum value of the excitation voltage.
SELF-EXCITING POWER TUBE 903
Test 2.—With the plate circuit tuned and all conditions normal,
determine the variation in output with variation in R', calculating for
each value of R' the load circuit resistance as follows :
EXPERIMENT NO. 10
Object
Study of the power tube as applied to a typical oscillating circuit,1
such as might be applicable to a radio telephone set. Effect of the plate
inductance, the condenser in series with the antenna, the resistance in
the oscillating circuit, the degree of coupling of the plate to the oscillating
circuit, the plate voltage, the filament current, the grid condenser, the grid
leak, and the grid potential.
Apparatus
Vacuum tube (similar to that used in Experiment No. 9).
Vacuum-tube receptacle.
Ammeter for filament circuit.
Rheostat for filament circuit.
Plate battery or d.c. generator (about 300 volte).
Ammeter for plate circuit.
Condenser for shunting plate battery and ammeter (about 1 micro
farad).
Hot-wire ammeter for antenna circuit (may conveniently be a galvanom
eter and thermo-couple with a maximum range of about 0.5 ampere).
Wave-meter of suitable range.
Dummy antenna. (The constants of this antenna are arbitrarily
chosen. A representative one would be:
L =40 microhenries
C =400 micro-microfarads (mica)
R =8 ohms.)
1 The circuit which is investigated in this experiment is discussed on page 561 et seq.
and the student should thoroughly review the theory and principles of operation as
given there, before attempting to perform the tests specified.
904 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
Operation
Test 1. Adjustment of Plate Inductance.—Make connections as in
Fig. 15, place the coupling contact M at D and the wave-length contact
about 12 steps
Fig. 15.
H at the third step away from D, use C„ =500 ntf, R„ = 12,000 ohms,
Ci = 1200 (inf. Vary the plate inductance Lp, from its minimum to its
maximum value and read A and Ap for each point on the inductance L,.
Note that the circuit can be made to oscillate for a limited range of values
of Lp, and that when it starts to oscillate the plate current decreases.
Note the value of Lv, giving maximum current in the oscillating circuit,
and use it in the following tests.
Test 2. Effect of the Condenser in Series with the Antenna.—With
all other adjustments as in Test 1 vary the capacity Ci in series with the
antenna from 50 wf to 3200 nnf in the following steps: 50, 100, 200,
SELF-EXCITING POWER TUBE 905
400, 800, 1200, 1600, 2000, 2400, 2800, 3200, and read A, also measure
the wave-length. Do not increase Ci beyond the point where the circuit
refuses to oscillate. Note that the circuit cannot be made to oscillate
for certain values of Ci, also that the value of C\ affects the wave-length.
Note the value of C\ which gives the maximum current in the oscillating
circuit and use it in the following tests.
Test 3. Effect of High Resistance in the Oscillating Circuit.—With
all other adjustments as in Test 2 introduce a resistance of 50 ohms in
the oscillating circuit and note A. Compare this reading of A with that
obtained in Test 2 for best adjustment of &.
Test 4. Effect of Shifting the Wave-length Contact H—With all
other adjustments as in Test 2 shift the wave-length contact H from
point D towards K in steps, and note the step number, the reading of A,
and also measure the wave-length. Note that, although this is primarily
a wave-length adjustment, yet the coupling of the plate circuit to the
oscillating circuit is also varied and hence the current in the oscillating
circuit is varied.
Test 5. Effect of Shifting the Coupling Contact M —With all other
adjustments as in Test 2 shift the coupling contact M from D towards
K in steps and note the step number, the reading of A and also the wave
length. Note that when the coupling contact is moved about half way
down, the tube stops oscillating. The adjustment for this test is primarily
a coupling adjustment, and should only affect the current in the oscillating
circuit, the wave-length being but slightly affected.
Test 6. Effect of Plate Voltage.—With all other adjustments as in
Test 2 vary the plate voltage from its normal value both up and down
and note A. Be careful not to exceed the safe plate voltage and watts.
Test 7. Effect of Filament Current.—With all other adjustments
as in Test 2 decrease the filament current in steps from its normal value
to 1.0 ampere and note A. Note that A decreases with decreasing fila
ment current.
Test 8. Effect of Value of Grid Condenser.—With all other adjust
ments as in Test 2 make the grid condenser C„ 100 wif, 500 puf, 5000
nnf, 1.0 nf, and note A and Av. Note the best value of C„.
Test 9. Effect of Value of Leak Resistance.—With all other adjust
ments as in Test 2 make the value of the leak resistance R„ infinite (open
circuit), 2 megohms, 50,000 ohms, 10,000 ohms, and zero and read A and
Af. Note the best value of Re.
Test 10. Effect of Holding the Grid at Different Negative Potential —
With all other adjustments as in Test 2 vary the e.m.f. in series with the
leak resistance from zero to 30 volts in several steps and read A and A p.
Note that as this e.m.f. is increased the reading of A may decrease some
what, but the reading of Av decreases much more.
DUG EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
EXPERIMENT NO. 11
Object
To measure the high-frequency resistance of a simple radio circuit
and to determine the variation of this resistance with change in frequency.1
Apparatus .
Standard inductance whose inductance is practically independent
of frequency (about 500 microhenries).
Standard variable condenser whose capacity is practically independ
ent of frequency (about 0— .005 microfarad). (An oil-filled condenser
is most desirable due to the large capacities obtainable and decreased
losses.)
Hot-wire ammeter, of low range.
Known resistance R, which does not vary with frequency; radio
cable of German silver strands is most suitable for this.
Source of undamped high-frequency current whose frequency may
be varied from perhaps 50,000 to 300,000 cycles per second. (The oscil
lating tube circuit considered in Experiment No. 10, or ite equivalent,
may be conveniently used for this purpose.)
Wave-meter.
Operation
Note: When making the following tests, it is important to have
sufficient power generated by the tube and transferred to the test circuit
so that the currents will be reasonably large and easily read on the hot
wire ammeter. This will aid in minimizing the errors involved in the
measurement, the accuracy of which depends largely on the precision
with which the current is measured. It is also necessary to keep E,
the e.m.f. induced in the test circuit, constant in value throughout the
measurements.
1 The student is referred to Bulletin No. 74, published by the Bureau of Standards,
pages 180-187, for a complete treatment and discussion of these measurements.
RESISTANCE MEASUREMENT AT HIGH FREQUENCY 907
(The reading of A\, and relative positions of L and L\ must be the same
as when making the previous measurement.)
Combining this expression with Eq. (1) we obtain the value of cir
cuit resistance (Rx) as:
R
Rx-
—1
place. (Be sure that the current through the primary exciting coil is
not changed during this adjustment; if it does vary, as indicated by a
hot-wire ammeter in the tube circuit, the proper adjustment should be
made to hold it constant.)
Under the new condition:
E2
h2=W+x? (3)
In this case:
EXPERIMENT NO. 12
Object
Study of the oscillating tube receiving circuit; methods of detecting
when a tube circuit is oscillating by indication of the plate current ammeter
and by phone indication; effect of the degree of coupling, the oscillating
circuit capacity, the oscillating circuit resistance, the plate voltage and
filament current, upon the oscillations; periodic phone clicks produced
in the oscillating tube circuit with grid condenser with improper adjust
ments; use of the oscillating tube circuit for the reception of continuous-
wave signals; use of the regenerative action of the tickler coil for the
amplification of damped-wave signals.
Apparatus
Vacuum tube (similar to that used in Experiment No. 6).
Vacuum-tube receptacle.
OSCILLATING TUBE AS RECEIVER 909
Operation
Test L—Effect of the beginning of oscillations upon the plate current
and upon the phones when no grid condenser is used.
Make connections as in Fig. 17. Make the plate voltage and filament
current normal. Set for the weakest coupling possible between the tickler
and the oscillating-circuit induct-
ance. This is done by using very j Tickler
few turns for the tickler coil and
having the two coils of the coupler
as far apart as possible. In case
one of the coils of the coupler re
volves, weakest coupling is had
when the two coils are at right
angles. Set the condenser in the
oscillating circuit at 10 per cent of
its maximum value; now increase 17.
the coupling by bringing the
movable coil more and more within the field of the fixed coil, and '
note any change in the plate current and noise in the phones. When
the coupling reaches a certain critical value, oscillations will start,
910 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
providing the two coils of the coupler have the proper relative polari
ties. The starting of the oscillations produces a sudden change in
the plate current and a resultant noise in the phones; this noise has
a peculiar quality, something like the plucking of a rubber band, and is
sometimes difficult to detect.
In case no indication of oscillation occurs, even when the coils of the
coupler are close together, increase the number of turns in the tickler
coil. If the circuit still refuses to oscillate, it is almost certain that the
relative polarity of the two coils of the coupler is incorrect, in which case
reverse the connections to either coil and repeat the test, noting the phone
click at the beginning of the oscillations, also the plate current before
and after the oscillations have started.
Repeat the test with normal plate voltage and a filament current of
about 75 per cent of normal, and again with normal filament current
and a plate voltage of about 75 per cent normal.
Test 2.—'Effect of the beginning of oscillations upon the plate current
and upon the phones when a grid condenser and suitable leak resistance
are used.
In the circuit of Fig. 17 introduce a grid condenser of 100 puf and
a grid leak resistance of 2 megohms and repeat Test 1 with normal plate
voltage and filament current; also with normal plate voltage and reduced
filament current, and with reduced plate voltage and normal filament
current.
Test 3.—Oscillating condition as indicated by the " finger test " when
no grid condenser is used.
With all adjustments as in Test 1 increase the coupling until oscil
lations start. After the oscillating condition has been reached the phones
are quiet; they do not indicate the presence of the oscillations. The
oscillating condition may, however, be tested for as follows: With the
thumb on the common junction of filament and grid circuits touch the gric
with one finger; this should give a click in the phones. Take the finger
off from the grid, and the phones should give a click. Now reverse the
connections to the tickler so that the circuit does not oscillate, and try
the " finger test " as before; it will be noted that no click is heard in the
phones either when the finger is placed on the grid or when removed
from it.
Test 4.—Oscillating condition as indicated by the " finger test " when
a grid condenser and leak are used.
Repeat Test 3 after introducing a grid condenser of 100 nfif and leak
resistance of 2 megohms. Note that when the circuit is oscillating a click
is heard in the phones both when the finger is placed on the grid and when
removed therefrom.
On the other hand, when the circuit is not oscillating, although a
OSCILLATING TUBE AS RECEIVER 911
click is heard when the finger touches the grid, it will.be found that there
is little or no click when the finger is removed; this, however, may not
always be the case, and the finger test in this case is not reliable.
Repeat the " finger test " both with and without grid condenser suf
ficiently to become convinced of the following summary of facts:
Check up the points listed in the above table which are borne out
by experiment.
Test 5.—Effect of a high resistance in the oscillating circuit upon the
coupling necessary to produce oscillations.
With all other conditions as in Test 1, find the position of the movable
coil of the coupler necessary to start oscillations and note it. Introduce
50 ohms in the oscillating circuit and repeat the test.
Test 6.—Effect of the value of the capacity in the oscillating circuit
upon the coupling necessary to produce oscillations.
With all other adjustments as in Test 1, note and record the position
of the movable coil of the coupler necessary to start oscillations with
oscillating circuit condenser set at 100 per cent, 60 per cent, and 10 per
cent of its maximum value. Note that the smaller the capacity of the
oscillating circuit the easier it is to start oscillations as indicated by the
weaker coupling needed.
Test 7.—Effect of low plate voltage or low filament current upon the
coupling necessary to produce oscillations.
With all other adjustments as in Test 1, note and record the position
of the movable coil of the coupler necessary to start oscillations for the
following conditions:
Plate voltage =normal value. Filament current = normal value.
Plate voltage = normal value. Filament current =75% normal value.
Plate voltage =75% normal value. Filament current = normal value.
Test 8. Periodic Phone Clicks when Grid Condenser is Used.—With
normal plate voltage and filament current, grid condenser = 100 nnf,
leak resistance =2 megohms and tight coupling, start with the condenser
in the oscillating circuit set at its maximum value, decrease it slowly, and
note the reading of condenser when periodic clicks start. If the periodic
ity of the clicks is high enough, a musical note results and gives what is
known as " squealing " or " singing " of the tube. Without changing
912 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
the leak resistance, -determine the setting of the oscillating circuit con
denser necessary to start periodic clicks with tight coupling for the follow
ing values of grid condenser: V/, 5,000 nnf, 100 nnf. Also note the
frequency of the clicks. Repeat the test with constant grid condenser
of 100 nftf and grid leak resistance of: infinity (open circuit), 2 megohms,
50,000 ohms, 10,000 ohms and zero.
Test 9. Reception of Undamped Wave-telegraphy by Means of the
Oscillating Tube.—Set the circuit oscillating with conditions as in Test 1
and receive the undamped wave-signal sent out by an oscillating tube
generator set up as in Experiment 10. (A small antenna should be con
nected to the point H on the transmitter and on the receiving circuit
as shown to increase the energy received.) This is done by adjusting
the oscillating circuit condenser until nearly in tune with the transmitter,
when a " whistle " will be heard in the phones.
By interrupting the oscillations of the transmitter, signals may easily
be transmitted.
Test 10. Regenerative Action of the Tickler Coil.—Reception of
Damped Waves.—With all other adjustments as in Test 9, make the
coupling much below that which will start oscillations, and tune by means
of the condenser to receive the damped wave-signals sent out by the source
of damped high-frequency oscillations. Note that the reception takes
place when the tube is not oscillating. Gradually increase the coupling,
continually retuning the receiving circuit for the incoming signal and
note the great increase in the signal strength due to the regenerative
action of the tickler coil as the coupling is increased. Too great a coupling
results in oscillations and the musical quality of the signal is spoiled; it is
therefore best to receive with the circuit just out of the oscillating con
dition, when the regenerative action of the tickler in amplifying the
received signals will be a maximum.
Note: If poor signals are received due to the poor rectification of the
tube, introduce normal grid condenser and grid leak.
Questions
1. From the results of Tests 1 and 2 what may the plate current do
when oscillations start if no grid condenser is used, and if a grid condenser
is used?
2. From the results of your tests what is the effect upon the strength
of oscillations of: loose coupling, large resistance and large capacity in
oscillating circuit, low plate voltage, and low filament current?
3. What is the reason for the singing of the tube when a grid con
denser is used, and how may it be avoided?
4. An incoming undamped wave signal of a wave-length of 1000
LOW-FREQUENCY AMPLIFIER 913
EXPERIMENT NO. 13
Object
(a) Study of the low-frequency amplifier equipped with inductance
"repeater." Investigation of the effect of the value of the inductance
in the plate circuit upon amplifying power; effect of the value of grid
condenser and grid leak resistance upon amplifying power: and effect of
plate voltage and filament current.
(6) Study of the low-frequency amplifier equipped with transformer
" repeater."
Apparatus
Two vacuum tubes (similar to the tube investigated in Experiment
No. 6).
Two vacuum-tube receptacles.
Storage battery, ammeters and rheostat for filament circuit.
Dry battery for plate circuit (about 40 volts).
Voltmeter for measuring plate voltage.
Phones.
Buzzer wave generator. (This is exactly similar to the equipment
described in Experiment No. 7, to be mounted on a small board to permit
the whole circuit to be readily moved.)
Variable tuning condenser C (about .001 microfarad maximum value).
Fixed inductance L (about 150 microhenries).
Fixed inductance for Test 4. (Secondary of receiving coupler having
about 4 millihenries inductance would be suitable.)
Grid condensers (Test 6). (.0001, .0005, .005 and 1.0 microfarad
would be suitable. These condensers have already been used in previous
experiments.)
Grid leak resistances (Test 7). (50,000 ohms and 2 megohms resist
ances may be used.)
D. P. D. T. switch.
Crystal detector (for use in Tests 9 and 10).
Shunting condenser for plate circuit (about .01 microfarad).
Grid condenser and leak resistance for receiving tube grid circuit (to
be normal value for the tube: .0001 microfarad and 2 megohms would
probably be satisfactory).
Grid condenser and leak resistance for amplifying tube grid circuit
(.0005 microfarad and 1 megohm respectively).
914 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
Operation
Fia. 18.
note and record the distance between the two inductances. This dis
tance is, to a certain degree, a measure of the sensitiveness of the tube.
Test 3. Sensitiveness of the Two Tubes with Normal Repeating
Inductance.—Place phones into the plate circuit of the second tube.
Use for G, K and M (see Fig. 18) the values specified in Test 1. With
all other conditions normal, measure the distance P-S necessary to make
the signal just audible.
Test 4. Sensitiveness of the Two Tubes with Low Repeating Induc
tance.—Use for G the low air core inductance, and repeat Test 3 with all
other conditions the same as in Test 3.
Test 6. Sensitiveness of the Two Tubes with Resistance Repeater.—
Use for G a 50,000-obm resistance and repeat Test 3 with all other con
ditions the same as in Test 3.
Test 6. Effect of the Grid Condenser of the Second Tube upon
Amplification.—With all other conditions as in Test 3, measure the sen
sitiveness of the two tubes for values of the capacity in the grid of the
second tube of 100 mm/, 500 mm/, 5000 mm/, and 1.0 m/.
Test 7. Effect of the Grid Leak Resistance of the Second Tube on
Amplification.—With all other conditions as in Test 3, measure the sen
sitiveness of the two tubes for values of the leak resistance M (see Fig. 19)
of infinity, 2 megohms, 50,000 ohms, and zero.
Test 8. Effect of Low Plate Voltage or Low Filament Current upon
Amplification.—With all other conditions as in Test 3, measure the sen
sitiveness of the two tubes with plate voltage about 75 per cent of normal
and normal filament current; also with normal plate voltage and reduced
filament current.
Test 9. Connections of a Low-frequency Amplifier with Transformer
Repeater.—Make connections as in Fig. 19. Note that the rectifying
Fig. 19.
will, in this case, be done by the crystal and the amplifying by the
step-up transformers and by the tubes.
916 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
EXPERIMENT NO. 14
Object
Study of the radio-telephone transmitter and receiver, utilizing equip
ment giving a range of transmission of 20 to 30 miles. The apparatus is
small, of light weight, and readily portable, and has found a wide applica
tion for establishing communication in military aeronautics. Investi
gation of the effect of improper adjustment of the voltage of the grid
of the modulating tube and of the modulating inductance.
RADIO TELEPHONE SET 917
Apparatus
1. The Receiver.—The receiver consists of a detecting and amplifying
tube connected as shown in Fig. 20. This circuit is identical to that
illustrated in Fig. 18, Experiment 13, and the apparatus required is as
previously specified. The D. P. D. T. switch is omitted, or may be con
sidered permanently thrown to the right (for amplifying action) in Fig. 18.
The several capacities and grid leaks should have approximately the values
indicated in the diagram.
2. The Transmitter.—The oscillating tube generator and its associated
circuit is identical to that studied in Experiment 10, and much of the
equipment specified in that experiment may be utilized. For the modu
lator element the following additional apparatus is required and used
as indicated in Fig. 21.
Vacuum tube and receptacle (similar to the oscillator, as specified in
Experiment 10).
Ordinary telephone transmitter.
Dry cells for telephone transmitter local circuit (five No 6 dry cells
should give satisfactory results).
S. P. S. T. switch for transmitter circuit.
Step-up audio-frequency transformer for coupling transmitter circuit
to modulator grid circuit. (This transformer measures about 3X3X2J
inches and is of the closed iron core type. The inductance of the primary
and secondary windings would be about .04 and 160 henries respectively,
the resistance of the primary is 2 ohms while the turn ratio is approxi
mately 60.)
Grid battery for modulator tube (about 40 volts).
" Modulating " inductance. (This is a high inductance having between
1 and 2 henries. The coil is about 25 inches high and \\ inches in diam
eter, has an iron core and is assembled within a surrounding soft iron
shield. The d.c. resistance will be about 90 ohms.)
Low inductance. (The inductance may be any value which may be
available as long as it is considerably less than the preceding inductance
which represents the " normal " value.)
Antennae for transmitter and receiver. (These are easily made, each
consisting of 20 or 30 feet of wire well insulated and supported from the
ceiling of the laboratory, above the apparatus. The " lead in " wire may
consist simply of a voltmeter lead clipped onto this horizontal wire and
properly connected to the circuit beneath.)
Operation
Before proceeding with the tests indicated below, the student should
review thoroughly the theory of action of the above circuits, as described
in Chapters VIII and XI.
918 EXPERIMENTS WITH RADIO CIRCUITS [Chap. XII
Antenna
Fig. 20.
ment 10 and in addition a modulating-tube circuit. The receiving circuit
consists of a three-electrode tube detector and a single-stage amplifier
with inductance repeater.
Test 2. Transmission of Speech under Normal Conditions of Modu
lating Inductance and of Potential of the Modulating Tube Grid.—Use
I Antennu
Fig. 21.
for the modulating inductance an iron cored inductance of about 1.3
henries. Make the grid potential of the modulating tube about 22 volts
(negative) and adjust the filament current and plate voltage of all tubes
to the normal values. Start the oscillating circuit of the transmitter
working, and adjust the wave-length to a suitable value by adjustment
RADIO TELEPHONE SET 919
Questions
1. In the diagram of Fig. 21 what is the purpose of the iron-cored
inductance in series with the plate battery?
2. Why must the potential of the grid of the modulating tube be
adjusted to a certain value for correct transmission of speech?
3. What was the quality of the transmission in Test 3, and why?
4. What was the quality of the transmission in Test 4, and why?
INDEX
A
PAGE
Adjustment of oscillating detectors, peculiarities of 522
Aerial 694
Alexanderson alternator, construction and action of 594
Alexanderson's barrage receiver 688
scheme of modulation 669
Alternating current supply for the plate of a tube 529
effective value of 17
wave-shape of 17
Alternator, armature reaction of 291
high frequency for continuous-wave telegraphy 593
inductor type 289
internal impedance of 290
used for spark transmitter, action of 287
use of consequent poles in construction of 290
Amplification, distortionless, of a tube, conditions for 572
Amplifying factor of vacuum tube, experimental determination of 898
Ampere-turns 18
Amplifier, characteristics of three-electrode tube 570
classification of 824-829
connections of, for reception of damped and undamped waves 841
effect of R and L in plate circuit on action of 827-829
fields of use of radio and audio frequency types 859
inductance repeating 857
low-frequency, experimental study of 913
resistance repeating 849
stability of 870
test for quality of 577
transformer repeating 830
tube characteristics for different stages 863
tube noises in operation of 875
Amplifiers, arrangement of apparatus in 876
Amplifying power of a tube as affected by grid potential and plate circuit voltage. 575
average potential of grid 574
measurement of .' 417
Amplitude of vacuum tube oscillations in the steady state 495
Antenna, coil, as directional radiator 711
receiver 722
constants, experimental determination of 891
"loading" \ 760
921
922 INDEX
PAGE
Antenna, natural wave-length of 751
pulse excitation of an 780
radiation, law of 730
reactance 757
receiving, current in 738
resistance . . 140, 746
setting up steady state in 776
Antennae, comparative merits of different types of 743
distribution of current and voltage in 755, 760, 763
effective height of 716
for aeroplanes and airships 723
underwater 726
ground 729
simple, mechanism of radiation by means of 694
various types of 713
Arc generator or converter (Poulsen) construction of 589
Poulsen, theory and action of 580
resistance of 136
Armstrong, E. EL, type of high frequency amplifier due to 860
amplification measurements by 518
Attenuation of propagated waves 196
Audio circuit of spark transmitter, analysis of action of 301
Austin, L. W., formula for range of radio-signal transmission 357
Austin's formula, analysis of 200
for receiving antenna current 196
Autodyne method of reception of continuous-wave signals 483, 514, 635
wave-meter 795
B
"Balancing out" schemes for simultaneous transmission and reception 687
Baldwin receiver, construction and action of 342
Barrage receiver 688, 690
Battery, polarizing, function of, with crystal rectifiers 343
Beat frequency, control of, in reception of continuous wave signals, using hetero
dyne method 63S
in coupled circuits 246
receiver of continuous wave signals 634
Bellini and Tosi goniometer 767
Bridge for high-frequency measurements 428
Buzzer wave generator, use of 882
C
Capacity 29
electrostatic, general discussion of 161
of conducting, isolated sphere in air 162
two flat circular parallel plates in air 162
single vertical wire in space 162
horizontal wire, earth as other plate 162
INDEX 923
PAoa
Capacity of two horizontal overhead wires with respect to each other 164
wire antenna 164
a multi-plate condenser 165
internal, of a two-layer solenoid 171
multiple-layer coil 175
mutual, of two horizontal wires 163
required in closed circuit of spark transmitter, calculation of 299
specific inductive 31
Carrier frequency for radio-telephony 649
values of, for radio-telephony 653
Chaffee, E. L., quenched spark gap of 317
Charged body > 2
Charges, bound and free 6
induced 6, 7
positive and negative, difference between 8
Child's formula for plate current in a two-electrode vacuum tube 377
Circuits having resistance and iron-core inductance 53
with distributed capacity and inductance, characteristics of .•. 107
Coil antenna 714, 720, 725
as directional radiator and receiver 711, 722
for submarines 727
Condenser, bridging, application of 349
charge and discharge of 37
charging of 29
discharge, oscillatory, frequency of 212
through R and L, criterion for oscillations 211
effect of condenser Jeakage on 210
theory of 202
equivalent series or shunt resistance of 168
grid, in connection with use of vacuum tube in self-heterodyne circuit . 643
losses occurring in 166
phase difference of 171
special form of, for wave-meter 792
variable, forms of 165
Condensers, construction of, for use in spark transmitters 297
power, characteristics of 169
Conductor, constitution of 364
Conductors 11
Consequent poles, use of, in radio alternator 290
Continuous-wave generators, efficiency of 619
forms of 580
receivers, action of 631
chopper 631
Goldschmidt tone wheel 632
oscillating vacuum tube 634
rotating plate condenser -634
tikker 634
signals, reception of 629
telegraphy, advantages of 188, 578
use of radiophone transmitting set for 627
transmitters, methods of signaling with 620
924 r INDEX :
nam
C!ounterpoise 604, 745
Coupled circuits, amplitude relations in (Chaffee, E. L.) 230
analysis of oscillations in 226
determination of the two frequencies of oscillation 227
form of current in, if primary circuit is opened at the right time. . 247
formula for damping factors and decrements of current in 237
wave-length of oscillations 231
frequency of beats in 246
general case of three 229
oscillatory discharge in one circuit and non-oscillatory discharge
in the other -249
possibility of no beats without quenching gap 248
shape and frequency of actual current in 238
vector representation of current in 242
oscillatory circuits, mechanical analogue of 223
pendulums, analysis of motion of 225
Coupling, capacitive 80, 84, 279
. coefficient of 27, 79
conductive 279
direct 81
inductive 80
effect of variation of, in tuned circuits 103
of grid and plate circuits of an oscillating tube by capacity 503
a vacuum tube by capacity, critical value of,
for oscillations 506
input and output circuits of a vacuum tube, critical value of, for
oscillations 492
test for detecting oscillating condition of tubes 520, 522
various kinds of 79
Critical coupling of oscillating tube as affected by condenser in series with grid . . . 518
Crystal rectifiers, characteristics of 343
laboratory investigation of 882
Current, continuous and alternating 14
direction of flow of 11
distribution in conductor carrying high-frequency current 113
electric, nature of 8
in a circuit containing resistance and a condenser in series 57
inductance and capacity in series 58
with resistance only 32, 42
an inductive circuit 32, 45
a condenser 55
coil receiving antenna 740
parallel circuits 66
simple receiving antenna 738
vs. frequency in an inductive circuit 49
inductively-coupled circuits 89
Currents, decaying, effect of, on neighboring circuits 35
in a parallel resonant circuit, oscillogram of 75
INDEX 925
D
FAQE
Damped wave, current, voltage and energy in 215
train, effective value of current in 221
Damping coefficient, definition of 214
Decrement 62
effect of, on quality of received speech in radio-telephony 678
measurement of, with wavemeter 801
Decremeter, construction and uses of (Kolster) 809
Detecting efficiency of three-electrode tube, measurement of 465
tube requirements 465
Detection of damped waves by means of regenerative tube circuit 525, 526
radio signals, visual, audible 336
undamped waves by means of oscillating vacuum tube with no grid
condenser 483, 514
undamped waves by means of oscillating vacuum tube with grid con
denser 486
undamped waves by means of an oscillating tube, analysis of 514
Detector action of three-electrode tube with grid condenser, analysis of 455
illustrated by oscillo
grams 462
of three-electrode tube with grid condenser as affected by fre
quency and decrement of signal 461
vacuum tube type 350
Detectors, action of 338
Direction finders 766
elimination of "180° uncertainty" in 772
incomplete extinction of signals in 775
reliability of 775
Distance, transmission of radio telegraphic signals 357
Dynatron 534
E
Effect of high and low grid excitation upon the form of Ev and lv of a separately
excited power tube 541
high and low load resistance upon the form of Ep and Ip of a separately
excited power tube 543
the local oscillations of a tube detector of undamped waves upon strength
of signals 516
Efficiency, calculated, of a separately excited power tube for various forms of
plate current 552
calculated, of a separately excited power tube for various plate voltages. 552
measured, of a separately excited power tube 554
of a three-electrode tube as a detector, analysis of 446
Electric fields 3
represented by lines 4
Electricity, nature of 1
Electro-magnetic waves, discussion of 181, 702
Electro-motive force 10
induced 23
926 INDEX
F
Fan antenna 713, 718
Fence wire as receiving antenna 730
Field, electric, due to an antenna, intensity of 703, 707
electric, in motion 696
electric, open and closed 5, 699
magnetic 18
magnetic, due to an antenna, intensity of 703, 707
magnetic, in motion 696
magnetic, open and closed 698, 699
energy stored in 26
induction 182, 703
radiation 182, 704
radiated, at any distance from an antenna consisting of a vertical wire. . . . 705
a coil antenna 708
Fields, electric 3
represented by lines 4
Filament of a vacuum tube, unequal currents in 379, 403
resistance of 404
Filaments for vacuum tubes, tungsten and oxide coated 400
Filters, use of, in amplifiers 864
"Fleming" valve 372
Fluorescence in vacuum tubes with oxide coated filaments 392
"Freak" transmission 200
Frequency changers, application of rectifier elements to 616
types of ' 608
INDEX 927
PAGE
Frequency changers, types of, for tripling frequency (Joly) 608
(Taylor) 611
for doubling frequency (Epstein-Vallouri) 609
(Plohl) 610
losses of 613
audio 186
effect of upon input capacity and conductance of a tube 439
of oscillating tube current for capacity coupling of grid and plate circuits. 506
an oscillating tube, constancy of 514
radio : 186
transformation 607
tripling, use of wabbling neutral for obtaining 613
Finger test for detecting oscillating condition of tubes 520, 522
G
Gas in tungsten filament tubes, tendency of, to disappear 396
a vacuum tube, effect of 390
detection of 394
Generator, electric 16
Generators of high frequency, undamped waves, types of 580
use of, for power supply to amplifiers 870
Goldschmidt alternator, construction of 606
theory of action of 599
Goniometer, Bellini and Tosi . 767
Grid 381
action of, in three-electrode tubes 382
condenser for three-electrode tube when used as detector of damped waves . . 451
value of, for tubes used as detectors 455, 461
current in well-evacuated three-electrode vacuum tube 399
normal potential of . .- 454
potential of a three-electrode tube when acting as detector with grid condenser 464
free 402,410
Ground antennae 729
H
Harmonics, upper, effect of, in reception of continuous-wave signals, using hetero
dyne receiver 639
Harp antenna 713
Heating of the plate of a three-electrode tube 473
Heising's scheme of modulation 664, 665
Heterodyne reception of undamped waves 483, 517, 635
"Hysteresis" in vacuum tubes 397
I
Impedance, definition 47
of a branched circuit containing L and R in one branch and C and R
in the other 68
circuit containing L, R and C in series 68
928 INDEX
VAGI
Impulse excitation of a parallel resonant circuit 266
oscillating circuit 259
Inductance, in grid and plate circuits of an osculating tube, effect of, upon the
operation of tube 570
mutual, of two single turns, coaxial 156
coaxial, circular coils of rectangular cross-section .... 156
solenoids 157
of two overhead parallel wires, grounded, at same height from ground. 157
between two concentric coils, as one rotates 158
coaxial spirals 160
Belf-, discussion of 143
of a single straight vertical wire distant from all other conductors. 144
circular turn of round wire 145
-layer solenoid closely wound 145
flat spiral 147
flat square coil 151
toroidal coil of rectangular cross-section 149
circular cross-section 150
single-layer square coil 150
multi-layer coils of rectangular cross-section 152
two-wire antenna; 157
variable, design of 153
Induction coil, action of 282
Inductor alternator, action of 287
Input circuit of a tube 421
capacity and conductance of, vs. plate circuit resistance. . . 435
conductance of, vs. filament current 429
plate voltage 430
grid potential 431
effective capacity of 434
geometrical capacity of 432
negative conductance of 437
resistance of 428
used as a detector, equivalent of 454
Insulators 11
disruptive strength of 13
effect of temperature on disruptive strength of 13
Interference, discussion of 191, 193
Interrupter action, requirements of 282
'' hammer break "type 282
Interrupters for primary circuit of induction coils, types of 287
Ionization, danger of, to vacuum tubes 392
in vacuum tubes 390
Iron-core coils, resistance of 134
K
Kenotron 373
Kenotrons used for rectifying alternating current for supply to plate of a vacuum
tube 529
Kolster, F. A., decremeter, construction and uses 809
INDEX 929
L
PAGE
"L," inverted, type of antenna 713, 716, 718
Leak resistance for three-electrode tube when used as detector of damped waves. . . 451
value of, for tube used as a detector 455
Leyden jar, use of, in i-park transmitter 298, 299
Limitations of transmission formuke 744
"Loading" an antenna 760
Logarithmic decrement, definition of 214
formula for 214, 215
graphs for three-electrode tubes 421
Loop antenna for submarine. 727
M
Magnetic field 18
effect of iron in 19
Marconi, multi-gap generator of continuous waves 616
Mercury rectifier 372
Meters in alternating current circuits 44
Microphone, liquid 656
transmitter 655
Miller, J. M., method for measuring w of a tube 417
A.C. output resistance of a tube 426
Modulated current 649
wave, analysis of ' 674
Modulating frequency 649
Modulation, analysis of 657
percentage of 660
requirements for 656, 668
sch mes for 661
Motor, speed of, for driving radio alternator 334
types of, for driving radio alternator 290
Multiple-tuned antenna 714, 719
Multiplex radio-telephony 680
Mutual induction 26
N
Natural period of multi-layer coils 177
Neutralization schemes for simultaneous transmission and reception 687
Noises in oscillating tube detector circuit 523
O
Oscillating conditions of a tube, criterions for 520
power tube circuit, laboratory study of characteristics of 903
tubes in multiple 527
receiving set for radio-telephony 677
tube circuits of very high frequency 511
receiving circuit, laboratory investigation of 908
930 INDEX
PAO«
Oscillating tube under conditions of oscillating current comparable in value with
plate current 503
tube, use as a continuous wave generator 617
Oscillation transformer, construction of 318
experimental investigation of power output 900
with oscillating circuit in grid circuit 510
vacuum tube, adjustment for maximum output 501
as a detector of undamped waves 483
circuits, analysis of 487
conditions for maximum output of 471, 497
efficiency of 468,471
elementary analysis of 469
excitation of 469
output of 471
uses of " 468
current and power of, vs. exciting grid voltage. . . 480
conditions necessary for self-excitation 478
Oscillations of a vacuum tube, effect of, on grid and plate currents 500
tube, effect of, upon plate current 519
vacuum tube at other than desired frequency 502, 512
stability of 498
starting and stopping 499
types of (of arc generators) 586
Oscillograph 33
Oscillatory circuit, current and voltage relations in 213
excited by a damped sine wave, analysis of 268
being connected to a line of alternating e.m.f.,
theory of 252
continuous voltage, theory of 249
damped sine waves, resonance curve of 227
energy stored in inductance, theory of . 250
pulse, analysis of 259
condition of a vacuum tube, prediction of, by placing total resistance
equal to zero '. 492
currents of a spark transmitter, discussion of 321
discharge, frequency and damping of, as affected by neighboring cir
cuits 222
through a spark gap 218
Output circuit of a tube 421
impedance of a tube 423
resistance of a tube 423
A.C., measurement of 424
P
Phase 42
of the grid voltage of a self-excited tube, possibility of variation of 562
relation of electric and magnetic fields in electro-magnetic radiation .... 702, 705
relations, effect of, on the possible power output of vacuum tube generator.. 476
of voltages and current in a vacuum-tube generator 474, 493
Pliodynatron 534
INDEX 931
PAGE
Potential difference 11
, gradient between plate and filament of a two-electrode vacuum tube .... 377
Poulsen arc, theory and action of :. 580
Power, amount sent out and received 198
factor 48
in a circuit excited by pulsating current 40
continuous current circuit 38
an inductive circuit 47
a resistance circuit 43
transmitted and received 198
used in the plate of a three-electrode tube 473
Production of current in antenna, methods for 711
Protective equipment of spark transmitter 278
Pulse excitation of oscillating circuit 259
Q
Quality of speech received by radio-telephony as affected by decrement 678
Quenched gap, construction of 314
theory of action of 247
R
Radiation 182
mechanism of, by means of simple antenna 694
of light from a hot filament compared to radiation from an antenna .... 734
power from an antenna, law of 730
a coil antenna, law of 735
resistance 737
Radio-compass service or ships 771
Radiophone seta 684, 692
Radiophone transmitting set, use of, for undamped wave telegraphy 627
Radio-telephony, fundamental idea 189
Radio-telephone transmitter and receiver, experimental study of 916
Reactance, definition 47
Receiving circuits 190
adjustment of, for damped wave signals 350, 882
for damped wave signals 340
station, essential elements of a 189, 336
Reception of undamped waves by means of oscillating tubes 483, 514
Rectification by three-electrode tube without grid condenser, as shown by oscillo
grams 445
Rectifying detectors, action of 338
Resistance 14, 21, 111
and reactance of the primary of an inductively-coupled circuit as affected
by secondary 93
effective 40
high frequency, general concept of Ill
laboratory measurement of 906
of antenna 746
coils, effect of neighboring circuits on 133
932 INDEX
S
Saturation current 367, 373
Selectivity, general discussion of 191
Self-heterodyne method of reception of continuous-wave signals 635
Self-induction, coefficient of 25
of a coil as affected by presence of a short-circuited neighboring coil 28
Short-wave condenser, function of 278
Shunting condenser used with induction coil, action of 283
Signal, day and night variation in strength of 197
seasonal variation in strength of 198
selection of 350
Signaling with high frequency, continuous-wave generators, methods of 620
Simultaneous radiophone transmission and reception 686
sending and receiving, essential elements required for 192
Skid-fin antenna for aeroplanes 724
Skin effect, analysis of 117
discussion of 113
elimination of 122
in coils 125
Space charge in vacuum tubes 376, 380
Spark gap, care of 333
Chaffee type 317
classification of, for spark transmitter 309
non-synchronous type 313
open type, operating conditions of 309
quenched 247-314
synchronous rotating type, description and operation of 311
resistance of 136
telegraphy, definition of 187
transmitter, adjustment of 328
INDEX 933
i PAGE
Spark transmitter, capacity and inductance required in closed and open circuits 334
description of 275
experimental investigation of 887
Specific inductive capacity, table of values 167
Static 193
Steady state in an antenna, setting up of 776
Stone, J. S., equation for spark-gap resistance 219
Strays, classification of . 193
i elimination of 194
T
"T" antenna 713,716,725
Time constant of an inductive circuit 33
a condenser circuit 38
Telephone receivers, construction and action of 340
impedance of 839
Telephony, radio multiplex 680
current in transmitting antenna 648
receiver 652
receiving antenna 650
field of use 646
principle of operation of transmitter 647
I receiver 649
power required to cover distances 683
receiving system for 673
sources of power for 654
transmission of speech 651
Temp rature, max m m safe, for tungsten filaments 371
Transformer, "open core," description of 296
power for spark transmitter 292
Transformers, construction of, for low-frequency amplifiers 839
Transmission, distance of radio signal 357
formula;, limitations of 744
Transient conditions in a circuit consisting of L, R and C in series, analysis of ... . 252
current in an inductive circuit 49
a circuit consisting of resistance and a condenser in series. ... 58
on switching a resistance circuit to an A.C. line 45
phenomena in audio circuit of spark transmitter, analysis of 304
Transmitter for radio-telephony, best resistance for 660
Transmitters for radio-telephony 654
Tree as receiving antenna 730
Tube, three-electrode 381
as detector of damped waves 440
a source of alternating current 467
power converter, detailed study of, when self-excited . . 561
separately ex
cited 539
characteristics of, with positive common junction and with
negative common junction 459
two-electrode as voltage regulator for a variable >j»eed generator 373
characteristic curves of 373
934 INDEX
U
Umbrella antenna 713
Unequal currents in the filament of a vacuum tube 379, 403
Unilateral connection of wavemeter • 786
Unipotelitia emitting surface for a vacuum tube 379
Units of electrical quantities 20
V
Vacuum tube, experimental determination of amplifying factor and internal plate
circuit resistance 898
investigation of characteristic curves of 894
study of its characteristics when used as a detector of
damped waves 895
generator, measurement of power output of 900
transmitting sets, arrangement of apparatus in 645
use as a detector 350
Voltage amplification factor of a three-electrode tube 384, 417
determination of 417
W
Wattmeter 49
Wave-length 183
natural, of antenna 751
of electro-magnetic radiations 213
Wave-lengths, range of, for radio communication 187
used in spark telegraphy. 356
Wave-meter, autodyne type -. 795
devices and schemes for indicating resonance 783
condenser, special form of 792
crystal detector and phones 785
hot-wire ammeter 784
incandescent lamp 791
neon tube 790
crystal detector and galvanometer 790
thermo-couple and galvanometer 788
INDEX 936
PAGE
Wave-meter, experiment on uses of the 884
how to improvise a 821
principle and construction of 781
use of, to determine decrement 801
mutual inductance and coefficient of coupling. . . . 819
measure antenna constants 815
inductance and capacity 814
wave-length and energy distribution curves . . . 796-798
Wave motion, discussion of 179
propagation, equation for 183
velocity of 184
Waves, attentuation of 196
damped 186
electromagnetic, discussion of 181, 702
transmission of, in water 728
number of, in a tra'n, formula for 220
stationary, on antenna 756
undamped 186
various types of, used in radio communication 185
water 179
Wave-shape of alternating currents 16
Wave-trains 186
CABOT SCIENCE LIBRARY
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JUL 3 0 1997
LgOOKDUC
JUN 1 7 1999
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