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UNIT I ELECTRICAL CIRCUITS

and MEASUREMENTS
DC Circuits and Ohm’s Law

The DC Circuits and Ohm’s Law, Electro-magnetic force(E.M.F), Voltage
Potential Difference Electromagnetism Applications of Electromagnetism
DC Circuits
A DC circuit (Direct Current circuit) is an electrical circuit that consists of any
combination of constant voltage sources, constant current sources, and resistors.
In this case, the circuit voltages and currents are constant, i.e., independent of
time.
More technically, a DC circuit has no memory.
That is, a particular circuit voltage or current does not depend on the past value
of any circuit voltage or current.
This implies that the system of equations that represent a DC circuit do not
involve integrals or derivatives.
Introduction:
In electronics, it is common to refer to a circuit that is powered by a DC voltage
source such as a battery or the output of a DC power supply as a DC circuit
even though what is meant is that the circuit is DC powered.
If a capacitor and/or inductor is added to a DC circuit, the resulting circuit is

not, strictly speaking, a DC circuit. However, most such circuits have a DC
solution.
This solution gives the circuit voltages and currents when the circuit is in DC
steady state.
More technically, such a circuit is represented by a system of differential

equations.
The solution to these equations usually contains a time varying or transient part
as well as constant or steady state part.
It is this steady state part that is the DC solution.
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There are some circuits that do not have a DC solution.
Two simple examples are a constant current source connected to a capacitor and
a constant voltage source connected to an inductor.
Electro-magnetic force(E.M.F):
Electromotive Force is, the voltage produced by an electric battery or generator
in an electrical circuit or, more precisely, the energy supplied by a source of
electric power in driving a unit charge around the circuit.
The unit is the volt. A difference in charge between two points in a material can
be created by an external energy source such as a battery.
This causes electrons to move so that there is an excess of electrons at one point
and a deficiency of electrons at a second point.
This difference in charge is stored as electrical potential energy known as emf.
It is the emf that causes a current to flow through a circuit.
Voltage:
Voltage is electric potential energy per unit charge, measured in joules per
coulomb.
It is often referred to as “electric potential”, which then must be distinguished

from electric potential energy by noting that the “potential” is a “per-unit-
charge” quantity.
Like mechanical potential energy, the zero of potential can be chosen at any
point, so the difference in voltage is the quantity which is physically
meaningful.
The difference in voltage measured when moving from point A to point B is

equal to the work which would have to be done, per unit charge, against the
electric field to move the charge from A to B.
Potential Difference:
A quantity related to the amount of energy needed to move an object from one
place to another against various types of forces.
The term is most often used as an abbreviation of “electrical potential

difference”, but it also occurs in many other branches of physics.
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Only changes in potential or potential energy (not the absolute values) can be
measured.
Electrical potential difference is the voltage between two points, or the voltage
drop transversely over an impedance (from one extremity to another).
It is related to the energy needed to move a unit of electrical charge from one
point to the other against the electrostatic field that is present.
The unit of electrical potential difference is the volt (joule per coulomb).
Gravitational potential difference between two points on Earth is related to the

energy needed to move a unit mass from one point to the other against the
Earth’s gravitational field.
The unit of gravitational potential differences is joules per kilogram.
Electromagnetism:
When current passes through a conductor, magnetic field will be generated
around the conductor and the conductor become a magnet.
This phenomenon is called electromagnetism.
Since the magnet is produced electric current, it is called the electromagnet.
An electromagnet is a type of magnet in which the magnetic field is produced

by a flow of electric current.
The magnetic field disappears when the current ceases.
In short, when current flow through a conductor, magnetic field will be

generated. When the current ceases, the magnetic field disappear.
Applications of Electromagnetism:
Electromagnetism has numerous applications in today’s world of science and
physics.
The very basic application of electromagnetism is in the use of motors.
The motor has a switch that continuously switches the polarity of the outside of
motor.
An electromagnet does the same thing. We can change the direction by simply
reversing the current.
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The inside of the motor has an electromagnet, but the current is controlled in
such a way that the outside magnet repels it.
Another very useful application of electromagnetism is the “CAT scan

machine.”
This machine is usually used in hospitals to diagnose a disease.
As we know that current is present in our body and the stronger the current, the
strong is the magnetic field.
This scanning technology is able to pick up the magnetic fields, and it can be
easily identified where there is a great amount of electrical activity inside the
body
The work of the human brain is based on electromagnetism. Electrical impulses

cause the operations inside the brain and it has some magnetic field.
When two magnetic fields cross each other inside the brain, interference occurs
which is not healthy for the brain.
Ohm’s Law
Ohm’s law states that the current through a conductor between two points is
directly proportional to the potential difference or voltage across the two points,
and inversely proportional to the resistance between them.
The mathematical equation that describes this relationship is:
I = V/R
where I is the current through the resistance in units of amperes,
V is the potential difference measured across the resistance in units of volts, and
R is the resistance of the conductor in units of ohms.
More specifically, Ohm’s law states that the R in this relation is constant,
independent of the current.
AC Circuits
An alternating current (AC) is an electrical current, where the magnitude of the
current varies in a cyclical form, as opposed to direct current, where the polarity
of the current stays constant.
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The usual waveform of an AC circuit is generally that of a sine wave, as this

results in the most efficient transmission of energy.
However in certain applications different waveforms are used, such as

triangular or square waves
Introduction:
Used generically, AC refers to the form in which electricity is delivered to
businesses and residences.
However, audio and radio signals carried on electrical wire are also examples of
alternating current.
In these applications, an important goal is often the recovery of information

encoded (or modulated) onto the AC signal.
Kirchhoff’s law:
There are Kirchhoff’s Current Law and Kirchhoff’s Voltage Law.
Kirchhoff’s Current Law:

First law (Current law or Point law): Statement:
The sum of the currents flowing towards any junction in an electric circuit equal
to the sum of currents flowing away from the junction.
Kirchhoff’s Current law can be stated in words as the sum of all currents
flowing into a node is zero.
Conversely, the sum of all currents leaving a node must be zero. As the image
below demonstrates, the sum of currents Ib, Ic, and Id, must equal the total
current in Ia.
Current flows through wires much like water flows through pipes.
If you have a definite amount of water entering a closed pipe system, the
amount of water that enters the system must equal the amount of water that
exists the system.
The number of branching pipes does not change the net volume of water (or
current in our case) in the system.
Kirchhoff’s Voltage Law:

Second law (voltage law or Mesh law): Statement:
In any closed circuit or mesh, the algebraic sum of all the electromotive forces
and the voltage drops is equal to zero.
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Kirchhoff’s voltage law can be stated in words as the sum of all voltage drops
and rises in a closed loop equals zero.
As the image below demonstrates, loop 1 and loop 2 are both closed loops
within the circuit.
The sum of all voltage drops and rises around loop 1 equals zero, and the sum
of all voltage drops and rises in loop 2 must also equal zero.
A closed loop can be defined as any path in which the originating point in the
loop is also the ending point for the loop.
No matter how the loop is defined or drawn, the sum of the voltages in the loop
must be zero.
Steady State Solution of DC Circuits:

Resistance in series connection:
The resistors R1, R2, R3 are connected in series across the supply voltage “V”.
The total current flowing through the circuit is denoted as “I”. The voltage
across the resistor R1, R2 and R3 is V1, V2, and V3 respectively.
V1 = I*R1 (as per ohms law)
V2= I*R2
V3 = I*R3
V = V1+V2+V3
= IR1+IR2+IR3
= (R1+R2+R3) I IR = (R1+R2+R3) I
R = R1+R2+R3
Resistance in parallel connection:
The resistors R1, R2, R3 are connected in parallel across the supply voltage “V”.
The total current flowing through the circuit is denoted as “I”. The current
flowing through the resistor
R1, R2 and R3 is I1, I2, and I3 respectively.
I = V / R (as per ohms law)
I 1 = V1 / R 1
I2 = V2 / R2
I3 = V3 / R3
V1 = V 2 = V 3 = V
From the above diagram
I = I1+I2+I3
= V1 / R1 + V2 / R2 + V3 / R3
= V / R1+ V/R2 +V/R3
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I = V (1/R1 +1/R2 +1/R3)

V / R = V (1/R1 +1/R2 +1/R3)
1/R = 1/R1 +1/R2 +1/R3
Below are problems based on ohm’s law
Problems based on ohm’s law
1. A current of 0.5 A is flowing through the resistance of 10Ω.Find the potential
difference between its ends.
Given data:
Current I= 0.5A.
Resistance R=1Ω
Tofind
Potential difference V = ?
Formula used:
V = IR
Solution:
V = 0.5 × 10 = 5V.
Result :
The potential difference between its ends = 5 V

2. A supply voltage of 220V is applied to a 100 Ω resistor. Find the current
flowing through it.
Given data
Voltage V = 220V
Resistance R = 100Ω
To find:
Current I = ?
Formula used:
Current I = V / R
Solution:
Current I = 220/100
= 2.2 A
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Result:
The current flowing through the resistor = 2.2 A

3. Calculate the resistance of the conductor if a current of 2A flows through it
when the potential difference across its ends is 6V.
Given data
Current I = 2A
Voltage V = 6V
To find:
Resistance R = ?
Formula used:
Resistance R = V / I
Solution:
Resistance R = 6 / 2
=3Ω
Result:
The value of resistance R = 3Ω

4. Calculate the current and resistance of a 100 W, 200V electric bulb.
Given data:
Power P = 100W
Voltage V = 200V
To find:
Current I =?
Resistance R =?
Formula used:
Power P = V *I
Current I = P / V
Resistance R = V / I
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Solution:
Current I = P / V
= 100 / 200
= 0.5 A Resistance R = V / I
= 200 / 0.2
= 400 Ω
Result:
The value of the current I = 0.5 A
The value of the Resistance R = 400 Ω

5. A circuit is made of 0.4 Ω wire, a 150Ω bulb and a 120Ω rheostat connected
in series. Determine the total resistance of the circuit.
Given data:
Resistance of the wire = 0.4Ω
Resistance of bulb =150Ω
Resistance of rheostat = 120Ω
To find:
The total resistance of the circuit R T =?
Formula used:
The total resistance of the circuit R T = R1+R2+R3
Solution:
Total resistance ,R = 0.4 + 150 +120
= 270.4Ω
Result:
The total resistance of the circuit R T = 270.4 Ω
6. Three resistances of values 2Ω, 3Ω and 5Ω are connected in series across 20
V, D.C supply
.Calculate (a) equivalent resistance of the circuit (b) the total current of the
circuit (c) the voltage drop across each resistor and (d) the power dissipated in
each resistor.
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Given data:
R1 = 2Ω
R2 = 3Ω
R3 = 5Ω
V = 20V
To find:
R T =?
I T =?
V1, V2, V3 =?
P1, P2, P3 =?
Formula used:
RT = R1+R2+R3 (series connection)
IT = VT / RT
V1 = R1*I1
V2= R2*I2
V3 = R3*I3
P1=V1*I1
P2=V2*I2
P3=V3*I3
Solution:
RT = R1+R2+R3 = 2+3+5
RT = 10Ω
IT = VT / RT = 20 / 10
IT = 2 A
In series connection I1 = I2 = I3 = IT = 2A
V1 = I1*R1 = 2*2
V1 = 4 V
V2 = I2*R2 = 2*3
V2 = 6 V
V3 = I3*R3 = 5*2
V3 = 10V
P1 = V1*I1
= 4*2
P1 = 8W
P2 = V2*I2
= 6*2
P2 = 12W
P3 = V3*I3 = 10*2
P3 = 20W
Result:
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(a). Equivalent resistance of the circuit RT = 10Ω

(b). The total current of the circuit IT = 2A
(c). Voltage drop across each resistor V1 = 4 V, V2 = 6 V, V3 = 10V
(d). The power dissipated in each resistor P1 = 8W, P2 = 12W, P3 = 20W
AC Instantaneous Value and RMS Value:
AC Instantaneous Value and RMS Value
Instantaneous Value:
The Instantaneous value of an alternating voltage or current is the value of
voltage or current at one particular instant.
The value may be zero if the particular instant is the time in the cycle at which
the polarity of the voltage is changing.
It may also be the same as the peak value, if the selected instant is the time in
the cycle at which the voltage or current stops increasing and starts decreasing.
There are actually an infinite number of instantaneous values between zero and
the peak value.
RMS Value:
The average value of an AC waveform is NOT the same value as that for a DC
waveforms average value.
This is because the AC waveform is constantly changing with time and the
heating effect given by the formula ( P = I 2.R ), will also be changing
producing a positive power consumption.
The equivalent average value for an alternating current system that provides the
same power to the load as a DC equivalent circuit is called the “effective
value”.
This effective power in an alternating current system is therefore equal to: (

I2.R. Average).
As power is proportional to current squared, the effective current, I will be
equal to √ I 2 Ave.
Therefore, the effective current in an AC system is called the Root Mean

Squared or RMS.
Pure Resistive circuit:

Resistors are “passive” devices that are they do not produce or consume any
electrical energy, but convert electrical energy into heat.
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In DC circuits the linear ratio of voltage to current in a resistor is called its

resistance.
However, in AC circuits this ratio of voltage to current depends upon the

frequency and phase difference or phase angle ( φ ) of the supply.
So when using resistors in AC circuits the term Impedance, symbol Z is the

generally used and we can say that DC resistance = AC impedance, R = Z.
It is important to note, that when used in AC circuits, a resistor will always have
the same resistive value no matter what the supply frequency from DC to very
high frequencies, unlike capacitor and inductors.
For resistors in AC circuits the direction of the current flowing through them
has no effect on the behaviour of the resistor so will rise and fall as the voltage
rises and falls.
The current and voltage reach maximum, fall through zero and reach minimum
at exactly the same time.
i.e, they rise and fall simultaneously and are said to be “in-phase” as shown
below.
We can see that at any point along the horizontal axis that the instantaneous
voltage and current are in-phase because the current and the voltage reach their
maximum values at the same time, that is their phase angle θ is 0 o.
Then these instantaneous values of voltage and current can be compared to give
the ohmic value of the resistance simply by using ohms law.
Consider below the circuit consisting of an AC source and a resistor.
The instantaneous voltage across the resistor, V R is equal to the supply voltage,
Vt and is given as:
VR = Vmax sinωt
The instantaneous current flowing in the resistor will therefore be:
IR = VR / R
= Vmax sinωt / R
= I max sinωt
In purely resistive series AC circuits, all the voltage drops across the resistors
can be added together to find the total circuit voltage as all the voltages are in-
phase with each other.
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Likewise, in a purely resistive parallel AC circuit, all the individual branch

currents can be added together to find the total circuit current because all the
branch currents are in-phase with each other.
Since for resistors in AC circuits the phase angle φ between the voltage and the
current is zero, then the power factor of the circuit is given as cos 0 o = 1.0.
The power in the circuit at any instant in time can be found by multiplying the
voltage and current at that instant.
Then the power (P), consumed by the circuit is given as P = Vrms Ι cos Φ in
watt’s. But since cos Φ = 1 in a purely resistive circuit, the power consumed is
simply given as, P = Vrms Ι the same as for Ohm’s Law.
This then gives us the “Power” waveform and which is shown below as a series
of positive pulses because when the voltage and current are both in their
positive half of the cycle the resultant power is positive.
When the voltage and current are both negative, the product of the two negative
values gives a positive power pulse.
Then the power dissipated in a purely resistive load fed from an AC rms supply
is the same as that for a resistor connected to a DC supply and is given as:
P = V rms * I rms
= I 2 rms * R
= V 2 rms / R
Pure Inductive circuits:

This simple circuit above consists of a pure inductance of L Henries ( H ),
connected across a sinusoidal voltage given by the expression: V(t) = V max sin
ωt.
When the switch is closed this sinusoidal voltage will cause a current to flow
and rise from zero to its maximum value.
This rise or change in the current will induce a magnetic field within the coil
which in turn will oppose or restrict this change in the current.
But before the current has had time to reach its maximum value as it would in a
DC circuit, the voltage changes polarity causing the current to change direction.
This change in the other direction once again being delayed by the self-induced
back emf in the coil, and in a circuit containing a pure inductance only, the
current is delayed by 90o.
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The applied voltage reaches its maximum positive value a quarter ( 1/4ƒ ) of a
cycle earlier than the current reaches its maximum positive value, in other
words, a voltage applied to a purely inductive circuit “LEADS” the current by a
quarter of a cycle or 90o as shown below.
The instantaneous voltage across the resistor, V R is equal to the supply voltage,
Vt and is given as:
VL = Vmax sin (ωt + 90)
IL = V / XL
XL = 2πfL
Pure Capacitive circuits:
When the switch is closed in the circuit above, a high current will start to flow
into the capacitor as there is no charge on the plates at t = 0.
The sinusoidal supply voltage, V is increasing in a positive direction at its
maximum rate as it crosses the zero reference axis at an instant in time given as
0o.
Since the rate of change of the potential difference across the plates is now at its
maximum value, the flow of current into the capacitor will also be at its
maximum rate as the maximum amount of electrons are moving from one plate
to the other.
As the sinusoidal supply voltage reaches its 90o point on the waveform it begins
to slow down and for a very brief instant in time the potential difference across
the plates is neither increasing nor decreasing therefore the current decreases to
zero as there is no rate of voltage change.
At this 90opoint the potential difference across the capacitor is at its maximum (
Vmax ), no current flows into the capacitor as the capacitor is now fully charged
and its plates saturated with electrons.
At the end of this instant in time the supply voltage begins to decrease in a
negative direction down towards the zero reference line at 180 o.
Although the supply voltage is still positive in nature the capacitor starts to
discharge some of its excess electrons on its plates in an effort to maintain a
constant voltage.
These results in the capacitor current flowing in the opposite or negative

direction.
When the supply voltage waveform crosses the zero reference axis point at
instant 180o, the rate of change or slope of the sinusoidal supply voltage is at its
maximum but in a negative direction, consequently the current flowing into the
capacitor is also at its maximum rate at that instant.
Also at this 180o point the potential difference across the plates is zero as the
amount of charge is equally distributed between the two plates.
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Then during this first half cycle 0o to 180o, the applied voltage reaches its
maximum positive value a quarter (1/4ƒ) of a cycle after the current reaches its
maximum positive value, in other words, a voltage applied to a purely
capacitive circuit “LAGS” the current by a quarter of a cycle or 90 o as shown
below.
IC = Imax sin (ωt + 90)
IL = V / XC
XC = 1 / 2πfC
RL Series circuit:
In other words, an Inductor in an electrical circuit opposes the flow of current, (
i ) through it.
While this is perfectly correct, we made the assumption in the tutorial that it
was an ideal inductor which had no resistance or capacitance associated with its
coil windings.
However, in the real world “ALL” coils whether they are chokes, solenoids,
relays or any wound component will always have a certain amount of resistance
no matter how small associated with the coils turns of wire being used to make
it as the copper wire will have a resistive value.
Then for real world purposes we can consider our simple coil as being an
“Inductance”, L in series with a “Resistance”, R.
LR Series Circuit
A LR Series Circuit consists basically of an inductor of inductance L
connected in series with a resistor of resistance R.
The resistance R is the DC resistive value of the wire turns or loops that goes
into making up the inductors coil
The above LR series circuit is connected across a constant voltage source, (the
battery) and a switch.
Assume that the switch, S is open until it is closed at a time t = 0, and then
remains permanently closed producing a “step response” type voltage input.
The current, i begins to flow through the circuit but does not rise rapidly to its
maximum value of Imax as determined by the ratio of V / R(Ohms Law).
This limiting factor is due to the presence of the self induced emf within the
inductor as a result of the growth of magnetic flux, (Lenz’s Law).
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After a time the voltage source neutralizes the effect of the self induced emf, the
current flow becomes constant and the induced current and field are reduced to
zero.
We can use Kirchoffs Voltage Law, ( Kirchoffs Voltage Law, (KVL) to define
the individual voltage drops that exist around the circuit and then hopefully use
it to give us an expression for the flow of current.
Vt = VR + VL
VR = I*R
VL = i dL / dt
V(t) = I*R + i dL / dt
Since the voltage drop across the resistor, VR is equal to IxR (Ohms Law), it
will have the same exponential growth and shape as the current.
However, the voltage drop across the inductor, VL will have a value equal to:
Ve(-Rt/L).
Then the voltage across the inductor, VL will have an initial value equal to the
battery voltage at time t = 0 or when the switch is first closed and then decays
exponentially to zero as represented in the above curves.
The time required for the current flowing in the LR series circuit to reach its
maximum steady state value is equivalent to about 5 time constants or 5τ.
This time constant τ, is measured by τ = L/R, in seconds, were R is the value of
the resistor in ohms and L is the value of the inductor in Henries.
This then forms the basis of an RL charging circuit were 5τ can also be thought
of as “5 x L/R” or thetransient time of the circuit.
The transient time of any inductive circuit is determined by the relationship
between the inductance and the resistance.
For example, for a fixed value resistance the larger the inductance the slower
will be the transient time and therefore a longer time constant for the LR series
circuit.
Likewise, for a fixed value inductance the smaller the resistance value the
longer the transient time.
However, for a fixed value inductance, by increasing the resistance value the
transient time and therefore the time constant of the circuit becomes shorter.
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This is because as the resistance increases the circuit becomes more and more
resistive as the value of the inductance becomes negligible compared to the
resistance.
If the value of the resistance is increased sufficiently large compared to the

inductance the transient time would effectively be reduced to almost zero.
RC Series circuit:
The fundamental passive linear circuit elements are the resistor (R), capacitor
(C) and inductor (L).
These circuit elements can be combined to form an electrical circuit in four

distinct ways: the RC circuit, the RL circuit, the LC circuit and the RLC circuit
with the abbreviations indicating which components are used.
These circuits exhibit important types of behaviour that are fundamental to

analogue electronics. In particular, they are able to act as passive filters.
This article considers the RL circuit in both series and parallel as shown in the
diagrams.
In practice, however, capacitors (and RC circuits) are usually preferred to

inductors since they can be more easily manufactured and are generally
physically smaller, particularly for higher values of components.
Both RC and RL circuits form a single-pole filter.
Depending on whether the reactive element (C or L) is in series with the load, or

parallel with the load will dictate whether the filter is low-pass or high-pass.
Frequently RL circuits are used for DC power supplies to RF amplifiers, where

the inductor is used to pass DC bias current and block the RF getting back into
the power supply.
RLC Series Circuit:

Difference between AC AND DC:
Current that flows continuously in one direction is called direct current .
Alternating current (A.C) is the current that flows in one direction for a brief
time then reverses and flows in opposite direction for a similar time.
The source for alternating current is called AC generator or alternator.
Cycle:
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One complete set of positive and negative values of an alternating quantity is

called cycle.
Frequency:
The number of cycles made by an alternating quantity per second is called
frequency. The unit of frequency is Hertz(Hz)
Amplitude or Peak value

The maximum positive or negative value of an alternating quantity is called
amplitude or peak value.
Average value:
This is the average of instantaneous values of an alternating quantity over one
complete cycle of the wave.
Time period:
The time taken to complete one complete cycle.
Star Delta transformation:

Star Delta Transformations allow us to convert impedances connected
together from one type of connection to another.
We can now solve simple series, parallel or bridge type resistive networks using
Kirchhoff´s Circuit Laws, mesh current analysis or nodal voltage analysis
techniques but in a balanced 3-phase circuit
we can use different mathematical techniques to simplify the analysis of the

circuit and thereby reduce the amount of math’s involved which in itself is a
good thing.
Standard 3-phase circuits or networks take on two major forms with names that
represent the way in which the resistances are connected, a Star connected
network which has the symbol of the letter, Υ (wye) and a Delta connected
network which has the symbol of a triangle, (delta).
If a 3-phase, 3-wire supply or even a 3-phase load is connected in one type of
configuration, it can be easily transformed or changed it into an equivalent
configuration of the other type by using either the Star Delta
Transformation or Delta Star Transformation process.
A resistive network consisting of three impedances can be connected together to
form a T or “Tee” configuration but the network can also be redrawn to form a
Star or Υ type network as shown below.
As we have already seen, we can redraw the T resistor network to produce an

equivalent Star or Υ type network.
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But we can also convert a Pi or π type resistor network into an equivalent Delta
or type network as shown below.
Pi-connected and Equivalent Delta Network
Having now defined exactly what is a Star and Delta connected
network it is possible to transform the Υ into an equivalent circuit and also to
convert a into an equivalent Υ circuit using a the transformation process.
This process allows us to produce a mathematical relationship between the
various resistors giving us a Star Delta Transformation as well as a Delta
Star Transformation.
These Circuit Transformations allow us to change the three connected
resistances (or impedances) by their equivalents measured between the
terminals 1-2, 1-3 or 2-3 for either a star or delta connected circuit.
However, the resulting networks are only equivalent for voltages and currents
external to the star or delta networks, as internally the voltages and currents are
different but each network will consume the same amount of power and have
the same power factor to each other.
The value of the resistor on any one side of the delta, network is the sum of all
the two-product combinations of resistors in the star network divide by the star
resistor located “directly opposite” the delta resistor being found.
For example, resistor A is given as:

A= (PQ + QR + RP) / R with respect to terminal 3 and resistor B is given as:
B = (PQ + QR + RP) / Q with respect to terminal 2 and resistor C given as:
B = (PQ + QR + RP) / R with respect to terminal 1.
By dividing out each equation by the value of the denominator we end up with
three separate transformation formulas that can be used to convert any Delta
resistive network into an equivalent star network as given below.
Star Delta Transformation allows us to convert one type of circuit connection

into another type in order for us to easily analyze the circuit and star delta
transformation techniques can be used for either resistances or impedance’s.
One final point about converting a star resistive network to an equivalent delta
network.
If all the resistors in the star network are all equal in value then the resultant
resistors in the equivalent delta network will be three times the value of the star
resistors and equal, giving: RDELTA = 3RSTAR
Delta to Star Transformation
Compare the resistances between terminals 1 and 2.
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P+Q= A in parallel with (B+C)
P+Q = A(B+C) / A+B+C… ................... (1)
Resistance between the terminals 2 and 3.
Q+R = C in parallel with (A+B)
Q+R=C(A+B) / A+B+C… .................... (2)
Resistance between the terminals 1 and 3.
P+R = B in parallel with (A+C)
P+R = B(A+C) / A+B+C… .................. (3)
This now gives us three equations and taking equation 3 from equation 2 gives:
P+R-Q-R = (B(A+C)) –( C(A+B) ) / A+B+C
P-Q =(BA + BC – CA – BC) / A+B+C P-Q = BA – CA /

(A+B+C)… ................ (4)
Then, re-writing Equation 1 will give us:
P+Q = (AB+AC) / A+B+C ................................ (5)
Equ (4) + Equ (5)
P+Q+ P-Q = (AB+AC) / A+B+C + (BA – CA) / A+B+C 2P = (AB+AC+BA-

CA) / A+B+C
2P = 2AB / A+B+C P = AB / A+B+C
Then to summarize a little about the above maths, we can now say that resistor
P in a Star network can be found as Equation 1 plus (Equation 3 minus Equation
2) or Eq1 + (Eq3 – Eq2).
Similarly, to find resistor Q in a star network, is equation 2 plus the result of

equation 1 minus equation 3 or Eq2 + (Eq1 – Eq3) and this gives us the
transformation of Q as:
Q = AC / A+B+C
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and again, to find resistor R in a Star network, is equation 3 plus the result of
equation 2 minus equation 1 or Eq3 + (Eq2 – Eq1) and this gives us the
transformation of R as:
R = BC / A+B+C
When converting a delta network into a star network the denominators of all of
the transformation formulas are the same:
A + B + C, and which is the sum of ALL the delta resistances.
Then to convert any delta connected network to an equivalent star network
If the three resistors in the delta network are all equal in value then the resultant
resistors in the equivalent star network will be equal to one third the value of the
delta resistors, giving each branch in the star network as: R STAR = 1/3RDELTA
Electrical Measuring Instruments
Classification of instruments
(i). Depending on the quality measured
(ii). Depending on the different principles used for their working
(iii). Depending on how the quantity is measured
Electrical Measuring Instruments classification Depending on the quality

measured
 Voltmeter
 Ammeter
 Energy meter
 Ohm meter
Electrical Measuring Instruments classification Depending on the different
principles used for their working
 Moving Iron type
 Moving coil type
 Dynamometer type
 Induction type
Electrical Measuring Instruments classification Depending on how the
quantity is measured
 Deflecting type
 Integrating type
 Recording type
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Deflecting Torque
The deflecting torque moves the moving system and the pointer from the zero
position.
The deflecting torque can be obtained through magnetic, thermal,

electromagnetic or electro dynamic effects
Controlling torque
The controlling torque acts in a direction opposite to that of deflecting torque.
When the controlling torque (TC) and the deflecting torque (TD) are
numerically equal the pointer takes a definite position.
In the absence of TC the pointer would deflect to maximum position

irrespective of the quantity to be measured.
Moreover TC also helps in bringing the moving system to zero position when
the instrument is disconnected from the circuit.
The controlling torque is obtained through spring control and gravity control
Spring Control:
The arrangement for spring control consists of two phosphor bronze spiral hair
springs attached to a moving system.
The springs are made of materials which
(i). are not affected by fatigue.
(ii). Have low temp-coefficient of resistance
(iii). Have low specific resistance
(iv). Are non-magnetic
As the pointer deflects the springs get twisted in the opposite direction.
The combined twist produces the necessary controlling torque which is

proportional to angle of deflection of moving system θ.
If we consider a permanent magnet moving coil meter with spring control

system the deflecting torque will be proportional to the current passing through
it and the controlling torque will be proportional to the angle of deflection
Thus TD α I
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TC α θ
Since TD = TC
We have θ α I
Thus the spring controlled instruments having uniform scale
Eddy current damping

Eddy current damping is the most efficient form of damping.
The essential components in this type of damping are a permanent magnet; and
a light conducting disc usually of alumninum.
When a sheet of conducting material moves in a magnetic field so as to cut

through lines of force, eddy currents are set up in it and a force exists between
these currents and the magnetic field, which is always in the direction opposing
the motion.
This force is proportional to the magnitude of the current, and to the strength of
field.
The former is proportional to the velocity of movement of the conductor, and

thus, if the magnetic field is constant, the damping force is proportional to the
velocity of the moving system and is zero when there is no movement of the
system.
Gravity control
In gravity control – gravity controlled instruments, as shown.
A small adjustable weight is attached to the spindle of the moving system such
that the deflecting torque produced by the instrument has to act against the
action of gravity.
Thus a controlling torque is obtained.
This weight is called the control weight.
Another adjustable weight is also attached is the moving system for zero
adjustment and balancing purpose.
This weight is called Balance weight.
When the control weight is in vertical position as shown
(a) , the controlling torque is zero and hence the pointer must read zero.
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However, if the deflecting torque lifts the controlling weight from position A to
B as shown
(b) such that the spindle rotates by an angle θ, then due to gravity a restoring (or
controlling) torque is exterted on the moving system.
The controlling (or restoring) torque, Tc , is given by
Tc = Wl sin θ = k g sin θ where W is the control weight;
l is the distance of the control weight from the axis of rotation of the moving
system; and k g is the gravity constant.
Equation shows the controlling torque can be varied quite simply by adjustment
of the position of the control weight upon the arm which carries it.
Again, if the deflecting torque is directly proportional to the current,
i.e., Td = kI
We have at the equilibrium position Td = Tc
kI = k g sin θ
I = g k sin θ / k
This relation shows that current I is proportional to sin θ and not θ.
Hence in gravity controlled instruments the scale is not uniform.
It is cramped for the lower readings, instead of being uniformly divided, for the
deflecting torque assumed to be directly proportional to the quantity being
measured.
Advantanges of Gravity Control

3. It is cheap and not affected by temperature variations.
4. It does not deteriorate with time.
5. It is not subject to fatigue.
Disadvantages of Gravity Control
3. Since the controlling torque is proportional to the sine of the angle of
deflection, the scale is not uniformly divided but cramped at its lower end.
4. It is not suitable for use in portable instruments (in which spring control is
always preferred).
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5. Gravity control instruments must be used in vertical position so that the

control weight may operate and also must be leveled otherwise they will give
zero error.
6. In view of these reasons, gravity control is not used for indicating
instruments in general and portable instruments in particular.
Damping Torque
Damping Torque : We have already seen that the moving system of the
instrument will tend to move under the action of the deflecting torque.
But on account of the control torque, it will try to occupy a position of rest
when the two torques are equal and opposite.
However, due to inertia of the moving system, the pointer will not come to rest
immediately but oscillate about its final deflected position as shown in Fig and
takes appreciable time to come to steady state.
To overcome this difficulty a damping torque is to be developed by using a

damping device attached to the moving system.
The damping torque is proportional to the speed of rotation of the moving

system, that is Tv = kv d dt θ
where kv = damping torque constant
d dt θ = speed of rotation of the moving system
Depending upon the degree of damping introduced in the moving system, the
instrument may have any one of the following conditions as depicted in Fig.
3. Under damped condition: The response is oscillatory

4. Over damped condition: The response is sluggish and it rises very slowly
from its zero position to final position.
5. Critically damped condition: When the response settles quickly without any
oscillation, the system is said to be critically damped.
In practice, the best response is slightly obtained when the damping is below the
critical value i.e., the instrument is slightly under damped.
The damping torque is produced by the following methods: Air Friction

Damping & Fluid friction damping
Air Friction Damping
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In this type of damping a light vane or vanes having considerable area is

attached to the moving system to develop a frictional force opposing the motion
by reason of the air they displace.
Two methods of damping by air friction are depicted
The arrangement of a light aluminum vane which moves in a quadrant (sector)

shaped air chamber.
The chamber also carries a cover plate at the top.
The vane is mounted on the spindle of the moving system.
The aluminum vane should not touch the air-chamber walls otherwise a serious
error in the deflection of the instrument will be introduced.
Now, with the motion, the vane displaces air and thereby a damping force is
created on the vane that produces a torque (damping) on the spindle.
When the movement is quicker the damping force is greater; when the spindle is
at rest, the damping force is zero.
The arrangement of consists of a light aluminum piston which is attached to the

moving system.
This piston moves in a fixed chamber which is closed at one end. Either circular
or rectangular chamber may be used.
The clearance (or gap) between the piston and chamber walls should be uniform
throughout and as small as possible.
When the piston moves rapidly into the chamber the air in the closed space is
compressed and the pressure of air thus developed opposes the motion of the
piston and thereby the whole moving system.
If the piston is moving out of the chamber, rapidly, the pressure in the closed
space falls and the pressure on the open side of the piston is greater than that on
the opposite side.
Motion is thus again opposed.
With this damping system care must be taken to ensure that the arm carrying the
piston should not touch the sides of the chamber during its movement.
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The friction which otherwise would occur may introduce a serious error in the
deflection.
The air friction damping is very simple and cheap.
But care must be taken to ensure that the piston is not bent or twisted.
This method is used in moving iron and hot wire instruments.
Fluid Friction Damping

This form is damping is similar to air friction damping.
The action is the same as in the air friction damping.
Mineral oil is used in place of air and as the viscosity of oil is greater, the
damping force is also much greater.
The vane attached to the spindle is arranged to move in the damping oil.
It is rarely used in commercial type instruments.
The oil used must fulfill the following requirements.
It should not evaporate quickly.
It should not have any corrosive effect on metals.
Its viscosity should not change appreciably with temperature.
It should be good insulator.
Advantages of Fluid Friction Damping

4. The oil used for damping can also be used for insulation purpose in some
forms of instruments which are submerged in oil.
5. The clearance between the vanes and oil chamber is not as critical as with the
air friction clamping system.
6. This method is suitable for use with instruments such as electrostatic type
where the movement is suspended rather than pivoted.
7. Due to the up thrust of oil, the loads on bearings or suspension system is
reduced thereby the reducing the frictional errors.
Disadvantages of Fluid Friction Damping
1. The instruments with this type of damping must be kept always in a vertical
position.
2. It is difficult to keep the instrument clean due to leakage of oil.
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3. It is not suitable for portable instruments.

4. The fluid friction damping can be used for laboratory type electrostatic
instruments.
Permanent Magnet Moving Coil Instruments

The permanent magnet moving coil instrument or PMMC type instrument uses
two permanent magnets in order to create stationary magnetic field.
These types of instruments are only used for measuring the dc quantities as if
we apply ac current to these type of instruments the direction of current will be
reversed during negative half cycle and hence the direction of torque will also
be reversed which gives average value of torque zero.
The pointer will not deflect due to high frequency from its mean position
showing zero reading.
However it can measure the direct current very accurately.
Construction of permanent magnet moving coil instruments:

We will see the construction of these types of instruments in four parts and they
are described below:
Stationary part or magnet system:

In the present time we use magnets of high field intensities, high coercive force
instead of using U shaped permanent magnet having soft iron pole pieces.
The magnets which we are using nowadays are made up of materials like
alcomax and alnico which provide high field strength.
Moving coil:
The moving coil can freely moves between the two permanent magnets as
shown in the figure given below.
The coil is wound with many turns of copper wire and is placed on rectangular
aluminum which is pivoted on jeweled bearings.
Control system:
The spring generally acts as control system for PMMC instruments.
The spring also serves another important function by providing the path to lead
current in and out of the coil.
Damping system:
The damping force hence torque is provided by movement of aluminium former
in the magnetic field created by the permanent magnets.
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Meter:
Meter of these instruments consists of light weight pointer to have free
movement and scale which is linear or uniform and varies with angle
Deflecting torque Equation:
Let us derive a general expression for torque in permanent magnet moving coil
instruments or PMMC instruments.
We know that in moving coil instruments the deflecting torque is given by the
expression:
Td = N B l dI
where N is number of turns,
B is magnetic flux density in air gap, l is the length of moving coil,
d is the width of the moving coil, And I is the electric current.
Now for a moving coil instruments deflecting torque should be proportional to

current, mathematically we can write Td = GI.
Thus on comparing we say G = NBIdl.
At steady state we have both the controlling and deflecting torques are equal.
Tc is controlling torque, on equating controlling torque with deflection torque

we have GI = K.x where x is deflection thus current is given by
I=K/Gx
Since the deflection is directly proportional to the current therefore we need a
uniform scale on the meter for measurement of current.
Now we are going to discuss about the basic circuit diagram of the ammeter.
Let us consider a circuit as shown below:
The current I is shown which breaks into two components at the point A.
The two components are Is and Im.
Before I comment on the magnitude values of these currents, let us know more
about the construction of shunt resistance.
The basic properties of shuntresistance are written below,
The electrical resistance of these shunts should not differ at higher temperature,
it they should posses very low value of temperature coefficient.
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Also the resistance should be time independent. Last and the most important
property they should posses is that they should be able to carry high value of
current without much rise in temperature.
Usually manganin is used for making dc resistance.
Thus we can say that the value of Is much greater than the value of Im as
resistance of shunt is low.
From the we have, Is .Rs = ImRm
Where Rs is resistance of shunt and Rm is the electrical resistance of the coil. Is

= I – Im
M= I / Im = 1+ (Rm + Rs)
Where m is the magnifying power of the shunt.
Errors in Permanent Magnet Moving Coil Instruments

There are three main types of errors
(a) Errors due to permanent magnets:

Due to temperature effects and aging of the magnets the magnet may lose their
magnetism to some extent.
The magnets are generally aged by the heat and vibration treatment.
(b) Error may appear in PMMC Instrument due to the aging of the spring:
However the error caused by the aging of the spring and the errors caused due
to permanent magnet are opposite to each other, hence both the errors are
compensated with each other.
(c) Change in the resistance of the moving coil with the temperature:
Generally the temperature coefficients of the value of coefficient of copper wire
in moving coil is 0.04 per degree Celsius rise in temperature.
Due to lower value of temperature coefficient the temperature rises at faster rate
and hence the resistance increases.
Due to this significant amount of error is caused.
Advantages of Permanent Magnet Moving Coil Instruments

(1) The scale is uniformly divided as the current is directly proportional to
deflection of the pointer.
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Hence it is very easy to measure quantities from these instruments.
(2)Power consumption is also very low in these types of instruments.
(3)Higher value of torque is to weight ratio.
(4)These are having multiple advantages, a single instrument can be used for
measuring various quantities by using different values of shunts and multipliers.
Disadvantages of Permanent Magnet Moving Coil Instruments

(1) These instruments cannot measure ac quantities.
(2) Cost of these instruments is high as compared to moving iron instruments.
Moving Iron instruments

Moving iron instruments are generally used to measure alternating voltages and
currents.
In moving-iron instruments the movable system consists of one or more pieces

of specially-shaped soft iron, which are so pivoted as to be acted upon by the
magnetic field produced by the current in coil.
There are two general types of moving iron instruments namely:
1. Repulsion (or double iron) type (figure 1)

2. Attraction (or single-iron) type (figure 2)
The brief description of different components of a moving-iron instrument is
given below:
Moving element:
A small piece of soft iron in the form of a vane or rod.
Coil:
To produce the magnetic field due to current flowing through it and also to
magnetize the iron pieces.
Repulsion type
In repulsion type, a fixed vane or rod is also used and magnetized with the
same polarity. Control torque is provided by spring or weight (gravity).
Damping torque is normally pneumatic, the damping device consisting of an
air chamber and a moving vane attached to the instrument spindle.
Deflecting torque produces a movement on an aluminum pointer over a
graduated scale.
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The deflecting torque in any moving-iron instrument is due to forces on a small

piece of magnetically ‘soft’ iron that is magnetized by a coil carrying
theoperating current.
In repulsion type moving–iron instrument consists of two cylindrical soft iron

vanes mounted within a fixed current-carrying coil.
One iron vane is held fixed to the coil frame and other is free to rotate, carrying
with it the pointer shaft.
Two irons lie in the magnetic field produced by the coil that consists of only
few turns if the instrument is an ammeter or of many turns if the instrument is a
voltmeter.
Current in the coil induces both vanes to become magnetized and repulsion
between the similarly magnetized vanes produces a proportional rotation.
The deflecting torque is proportional to the square of the current in the coil,
making the instrument reading is a true
‘RMS’ quantity Rotation is opposed by a hairspring that produces the restoring

torque .
Only the fixed coil carries load current, and it is constructed so as to withstand
high transient current.
Moving iron instruments having scales that are nonlinear and somewhat
crowded in the lower range of calibration.
Measurement of Electric Voltage and Current

Moving iron instruments are used as Voltmeter and Ammeter only.
Both can work on AC as well as on DC.
Ammeter
Instrument used to measure current in the circuit.
Always connected in series with the circuit and carries the current to be
measured. This current flowing through the coil produces the desired deflecting
torque.
It should have low resistance as it is to be connected in series.
Voltmeter
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Instrument used to measure voltage between two points in a circuit.
Always connected in parallel.
Current flowing through the operating coil of the meter produces deflecting
torque.
It should have high resistance. Thus a high resistance of order of kilo ohms is
connected in series with the coil of the instrument.
Ranges of Ammeter and Voltmeter

For a given moving-iron instrument the ampere-turns necessary to produce full-
scale deflection are constant.
One can alter the range of ammeters by providing a shunt coil with the moving
coil.
Voltmeter range may be altered connecting a resistance in series with the coil.
Hence the same coil winding specification may be employed for a number of
ranges.
Advantages
1. The instruments are suitable for use in AC and DC circuits.
2. The instruments are robust, owing to the simple construction of the moving
parts.
3. The stationary parts of the instruments are also simple.
4. Instrument is low cost compared to moving coil instrument.
5. Torque/weight ratio is high, thus less frictional error.
Errors
(i). Error due to variation in temperature.
(ii). Error due to friction is quite small as torque-weight ratio is high in moving
coil instruments.
(iii). Stray fields cause relatively low values of magnetizing force produced by
the coil. Efficient magnetic screening is essential to reduce this effect.
(iv). Error due to variation of frequency causes change of reactance of the coil
and also changes the eddy currents induced in neighbouring metal.
(v). Deflecting torque is not exactly proportional to the square of the current due
to non -linear characteristics of iron material.
Attraction type
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The basic construction of attraction type moving iron instrument is illustrated

bellow A thin disc of soft iron is eccentrically pivoted in front of a coil.
This iron tends to move inward that is from weaker magnetic field to stronger
magnetic field whencurrent flowing through the coil.
In attraction moving instrument gravity control was used previously but now
gravity control method is replaced by spring control in relatively modern
instrument.
By adjusting balance weight null deflection of the pointer is achieved.
The required damping force is provided in this instrument by air friction.
The figure shows a typical type of damping system provided in the instrument,
where damping is achieved by a moving piston in an air syringe.
Theory of Attraction Type Moving Iron Instrument

Suppose when there is no current through the coil, the pointer is at zero, the
angle made by the axis of the iron disc with the line perpendicular to the field is
φ.
Now due current I and corresponding magnetic field strength, the iron piece is
deflected to an angle θ.
Now component of H in the direction of defected iron disc axis is Hcos{90 – (θ

+ φ) or Hsin(θ + φ).
Now force F acting on the disc inward to the coil is thus proportional to H2sin(θ
+ φ) hence the force is also proportional to I2sin(θ + φ) for constant
permeability.
If this force is acting on the disc at a distance l from the pivot, then deflection
torque,
Td = Fl cos (θ+Φ)
Thus Td = I2 sin (θ+Φ) cos (θ+Φ)

Td = kI2 sin 2(θ+Φ)
Where k is constant.
Now, as the instrument is gravity controlled, controlling torque will be
Tc = k’ sin θ
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Where k ‘is constant
Electrodynamometer Type Wattmeter

Electrodynamometer Type Wattmeter in general, a watt meter is used to
measure the electric power of a circuit, or sometime it also measures the rate of
energy transferred from one circuit to another circuit.
When a moving coil (that is free to rotate) is kept under the influence of a
current carrying conductor, then automatically a mechanical force will be
applied to the moving coil, and this force will make a little deflection of the
moving coil.
If a pointer is connected with the moving coil, which will move of a scale, then
the deflection can be easily measured by connecting the moving coil with that
pointer.
This is the principle of operation of all dynamo meter type instruments, and
this principle is equally applicable for dynamo meter type watt meter also.
This type of watt meter consists of two types of coil, more specifically current
coil and voltage coil.
There are two current coils which are kept at constant position and the
measurable current will flow through those current coils.
A voltage coil is placed inside those two current coils, and this voltage coil is
totally free to rotate.
The current coils are arranged such a way, that they are connected with the
circuit in series.
And the voltage coil is connected in parallel with the circuit.
As simple as other voltmeter and ammeter connection.
In fact, a watt meter is a package of an ammeter and a voltmeter, because the

product of voltage and current is the power, which is the measurable quantity of
a watt meter
When current flows through the current coils, then automatically a magnetic
field is developed around those coils.
Under the influence of the electromagnetic field, voltage coil also carries some
amount of current as it is connected with the circuit in parallel.
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In this way, the deflection of the pointer will proportional to both current and
voltage of the circuit. In this way, Watt = Current × Voltage equation is satisfied
and the deflection shows the value of power inside the circuit.
A dynamo meter type watt meter is used in various applications where the
power or energy transfer has to be measured.
Construction and Working Principle of Electrodynamometer Type

Wattmeter
Now let us look at constructional details of Electrodynamometer Type
Wattmeter.
It consists of following parts There are two types of coils present in the
electrodynamometer.
They are :
(a) Moving coil :

Moving coil moves the pointer with the help of spring control instrument.
A limited amount of current flows through the moving coil so as to avoid

heating.
So in order to limit the current we have connect the high value resistor in series
with the moving coil.
The moving is air cored and is mounted on a pivoted spindle and can moves
freely. In electrodynamometer type wattmeter, moving coil works as pressure
coil.
Hence moving coil is connected across the voltage and thus the current flowing
through this coil is always proportional to the voltage.
(b) Fixed coil:

The fixed coil is divided into two equal parts and these are connected in series
with the load, therefore the load current will flow through these coils.
Now the reason is very obvious of using two fixed coils instead of one, so that it
can be constructed to carry considerable amount of electric current.
These coils are called the current coils of electrodynamometer type wattmeter.
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Earlier these fixed coils are designed to carry the current of about 100 amperes
but now the modern wattmeter are designed to carry current of about 20
amperes in order to save power.
(c) Control system:

Out of two controlling systems i.e.
(1). Gravity control
(2) Spring control, only spring controlled systems are used in these types of
wattmeter.
Gravity controlled system cannot be employed because they will appreciable

amount of errors.
(d) Damping system:

Air friction damping is used, as eddy current damping will distort the weak
operating magnetic field and thus it may leads to error.
(e) Scale:
There is uniform scale is used in these types of instrument as moving coil
moves linearly over a range of 40 degrees to 50 degrees on either sides.
Now let us derive the expressions for the controlling torque and deflecting
torques. In order to derive these expressions let us consider the circuit diagram
given below:
We know that instantaneous torque in electro dynamic type instruments is

directly proportional to product of instantaneous values of currents flowing
through both the coils and the rate of change of flux linked with the circuit.
Let I1 and I2 be the instantaneous values of currents in pressure and current coils
respectively. So the expression for the torque can be written as:
T = I1*I2*(dM / dx)
Where x is the angle
Now let the applied value of voltage across the pressure coil be V= – V sin ωt
Assuming the electrical resistance of the pressure coil be very high hence we
can neglect reactance with respect to its resistance.
In this the impedance is equal to its electrical resistance therefore it is purely

resistive
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The expression for instantaneous current can be written as I 2 = v / Rp where Rp

is the resistance of pressure coil.
I2 = V sin ωt / Rp
If there is phase difference between voltage and electric current, then expression
for instantaneous current through current coil can be written as
I1 = I(t) = – I sin (ωt – Φ)

As current through the pressure coil in very very small compare to current
through current coil hence current through the current coil can be considered as
equal to total load current.
Hence the instantaneous value of torque can be written as – V sin ωt / Rp * – I

sin (ωt – Φ) * (dM / dx)
Average value of deflecting torque can be obtained by integrating the

instantaneous torque from limit 0 to T where T is the time period of the cycle
Td = deflecting torque = VI cosΦ /Rp *(dM / dx)
Controlling torque is given by Tc = Kx where K is spring constant and x is final

steady state value of deflection.
Advantages of Electrodynamometer Type Wattmeter

Following are the advantages of electrodynamometer type wattmeters and they
are written as follows:
(a). Scale is uniform up to certain limit
(b). They can be used for both to measure AC as well as DC quantities as scale
is calibrated for both
Errors in Electrodynamometer Type Wattmeter

Following are the errors in the electrodynamometer type watt meters:
(a) Errors in the pressure coil inductance.
(b) Errors may be due to pressure coil capacitance.
(c) Errors may be due to mutual inductance effects.
(d) Errors may be due connections.
(i.e. pressure coil is connected after current coil )
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(e) Error due to Eddy currents.
(f) Errors caused by vibration of moving system.
(g) Temperature error.
(h) Errors due to stray magnetic field.
Single phase Energy meter

Single phase Energy meter single phase induction type energy meter is also
popularly known as watt-hour meter.
This name is given to it.
This article is only focused about its constructional features and its working.
Induction type energy meter essentially consists of following components:

1. Driving system
2. Moving system
3. Braking system and
4. Registering system
Driving system
It consists of two electromagnets, called “shunt” magnet and “series” magnet, of
laminated construction.
A coil having large number of turns of fine wire is wound on the middle limb of
the shunt magnet.
This coil is known as “pressure or voltage” coil and is connected across the
supply mains.
This voltage coil has many turns and is arranged to be as highly inductive as
possible.
In other words, the voltage coil produces a high ratio of inductance to

resistance.
This causes the current and therefore the flux, to lag the supply voltage by
nearly 90 degree
Adjustable copper shading rings are provided on the central limb of the shunt
magnet to make the phase angle displacement between magnetic field set up by
shunt magnet and supply voltage is approximately 90 degree.
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The copper shading bands are also called the power factor compensator or
compensating loop.
The series electromagnet is energized by a coil, known as “current” coil which

is connected in series with the load so that it carry the load current.
The flux produced by this magnet is proportional to, and in phase with the load
current.
Moving system
The moving system essentially consists of a light rotating aluminium disk
mounted on a vertical spindle or shaft.
The shaft that supports the aluminium disk is connected by a gear arrangement
to the clock mechanism on the front of the meter to provide information that
consumed energy by the load.
The time varying (sinusoidal) fluxes produced by shunt and series magnet
induce eddy currents in the aluminium disc
The interaction between these two magnetic fields and eddy currents set up a
driving torque in the disc.
The number of rotations of the disk is therefore proportional to the energy

consumed by the load in a certain time interval and is commonly measured in
kilowatt-hours (Kwh).
Braking system
Damping of the disk is provided by a small permanent magnet, located
diametrically opposite to the a.c magnets.
The disk passes between the magnet gaps.
The movement of rotating disc through the magnetic field crossing the air gap
sets up eddy currents in the disc that reacts with the magnetic field and exerts a
braking torque.
By changing the position of the brake magnet or diverting some of the flux there
form, the speed of the rotating disc can be controlled.
Registering or counting system

The registering or counting system essentially consists of gear train, driven
either by worm or pinion gear on the disc shaft, which turns pointers that
indicate on dials the number of times the disc has turned.
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The energy meter thus determines and adds together or integrates all
the instantaneous power values so that total energy used over a period is thus
known.
Therefore, this type of meter is also called an“integrating” meter.
Working of Single phase induction type Energy Meter
The basic working of Single phase induction type Energy Meter is only focused
on two mechanisms:
2. Mechanism of rotation of an aluminum disc which is made to rotate at a

speed proportional to the power.
3. The mechanism of counting and displaying the amount of energy transferred.
Mechanism of rotation of an aluminum disc
The metallic disc is acted upon by two coils.
One coil is connected or arranged in such a way that it produces a magnetic flux
in proportion to the voltage and the other produces a magnetic flux in
proportion to the current.
The field of the voltage coil is delayed by 90 degrees using a lag coil.
This produces eddy currents in the disc and the effect is such that a force is
exerted on the disc in proportion to the product of the instantaneous current and
voltage.
A permanent magnet exerts an opposing force proportional to the speed of

rotation of the disc
– this acts as a brake which causes the disc to stop spinning when power stops
being drawn rather than allowing it to spin faster and faster.
This causes the disc to rotate at a speed proportional to the power being used.
Mechanism of displaying the amount of energy transferred

The aluminum disc is supported by a spindle which has a worm gear which
drives the register.
The register is a series of dials which record the amount of energy used.
The dials may be of the cyclometer type, an odometer-like display that is easy
to read where for each dial a single digit is shown through a window in the face
of the meter, or of the pointer type where a pointer indicates each digit.
It should be noted that with the dial pointer type, adjacent pointers generally
rotate in opposite directions due to the gearing mechanism.
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UNIT II ELECTRICAL MACHINES

Construction of DC GENERATOR
An electrical generator is a device that converts mechanical energy to
electrical energy, generally using electromagnetic induction.
The source of mechanical energy may be a reciprocating or turbine steam
engine, water falling through a turbine or waterwheel, an internal combustion
engine, a wind turbine, a hand crank, or any other source of mechanical energy.
The Dynamo was the first electrical generator capable of delivering power for
industry.
The dynamo uses electromagnetic principles to convert mechanical rotation into

an alternating electric current.
A dynamo machine consists of a stationary structure which generates a strong

magnetic field, and a set of rotating winding’s which turn within that field.
On small machines the magnetic field may be provided by a permanent magnet;

larger machines have the magnetic field created by electromagnets.
The energy conversion in generator is based on the principle of the production

of dynamically induced e.m.f. whenever a conductor cuts magnetic flux,
dynamically induced e.m.f is produced in it according to Faraday’s Laws of
Electromagnetic induction.
This e.m.f causes a current to flow if the conductor circuit is closed.
CONSTRUCTION OF DC MACHINES
A D.C. machine consists mainly of two part the stationary part called stator and
the rotating part called rotor.
The stator consists of main poles used to produce magnetic flux ,commutating
poles or interpoles in between the main poles to avoid sparking at the
commutator but in the case of small machines sometimes the inter poles are
avoided and finally the frame or yoke which forms the supporting structure of
the machine.
The rotor consist of an armature a cylindrical metallic body or core with slots in
it to place armature winding’s or bars,a commutator and brush gears The
magnetic flux path in a motor or generator is show below and it is called the
magnetic structure of generator or motor.
The major parts in the Construction of DC GENERATOR can be

identified as
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5. Frame
6. Poles
7. Armature
8. Field winding
9. Commutator
10.Brush
11.Other mechanical parts
Frame
Frame is the stationary part of a machine on which the main poles and
commutator poles are bolted and it forms the supporting structure by connecting
the frame to the bed plate.
The ring shaped body portion of the frame which makes the magnetic path for
the magnetic fluxes from the main poles and inter poles is called Yoke.
Why we use cast steel instead of cast iron for the construction of Yoke?
In early days Yoke was made up of cast iron but now it is replaced by cast steel.
This is because cast iron is saturated by a flux density of 0.8 Wb/sq.m where as
saturation with cast iron steel is about 1.5 Wb/sq.m.
So for the same magnetic flux density the cross section area needed for cast
steel is less than cast iron hence the weight of the machine too.
If we use cast iron there may be chances of blow holes in it while casting.
So now rolled steels are developed and these have consistent magnetic and
mechanical properties.
poles:
Solid poles of fabricated steel with separate/integral pole shoes are fastened to
the frame by means of bolts.
Pole shoes are generally laminated.
Sometimes pole body and pole shoe are formed from the same laminations.
The pole shoes are shaped so as to have a slightly increased air gap at the tips.
Inter-poles are small additional poles located in between the main poles.
These can be solid, or laminated just as the main poles.
These are also fastened to the yoke by bolts.
Sometimes the yoke may be slotted to receive these poles.
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The inter poles could be of tapered section or of uniform cross section. These
are also called as commutating poles or com poles.
The width of the tip of the com pole can be about a rotor slot pitch.
Armature
The armature is where the moving conductors are located.
The armature is constructed by stacking laminated sheets of silicon steel.
Thickness of these lamination is kept low to reduce eddy current losses.
As the laminations carry alternating flux the choice of suitable material,

insulation coating on the laminations, stacking it etc are to be done more
carefully.
The core is divided into packets to facilitate ventilation.
The winding cannot be placed on the surface of the rotor due to the mechanical
forces coming on the same.
Open parallel sided equally spaced slots are normally punched in the rotor
laminations.
These slots house the armature winding.
Large sized machines employ a spider on which the laminations are stacked in
segments.
End plates are suitably shaped so as to serve as ’Winding supporters’.
Armature construction process must ensure provision of sufficient axial and

radial ducts to facilitate easy removal of heat from the armature winding.
Field windings:
In the case of wound field machines (as against permanent magnet excited
machines) the field winding takes the form of a concentric coil wound around
the main poles.
These carry the excitation current and produce the main field in the machine.
Thus the poles are created electromagnetically.
Two types of windings are generally employed.
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In shunt winding large number of turns of small section copper conductor is

used.
The resistance of such winding would be an order of magnitude larger than the
armature winding resistance.
In the case of series winding a few turns of heavy cross section conductor is
used.
The resistance of such windings is low and is comparable to armature

resistance.
Some machines may have both the windings on the poles.
The total ampere turns required to establish the necessary flux under the poles is
calculated from the magnetic circuit calculations.
The total mmf required is divided equally between north and south poles as the
poles are produced in pairs.
The mmf required to be shared between shunt and series windings are
apportioned as per the design requirements.
As these work on the same magnetic system they are in the form of concentric
coils. Mmf ’per pole’ is normally used in these calculations.
Armature winding As mentioned earlier, if the armature coils are wound on the
surface of the armature, such construction becomes mechanically weak.
The conductors may fly away when the armature starts rotating.
Hence the armature windings are in general pre-formed, taped and lowered into
the open slots on the armature.
In the case of small machines, they can be hand wound.
The coils are prevented from flying out due to the centrifugal forces by means
of bands of steel wire on the surface of the rotor in small groves cut into it.
In the case of large machines slot wedges are additionally used to restrain the
coils from flying away.
The end portion of the windings are taped at the free end and bound to the
winding carrier ring of the armature at the commutator end.
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The armature must be dynamically balanced to reduce the centrifugal forces at

the operating speeds.
Compensating winding One may find a bar winding housed in the slots on the
pole shoes.
This is mostly found in d.c. machines of very large rating.
Such winding is called compensating winding.
In smaller machines, they may be absent.
Commutator:
Commutator is the key element which made the d.c. machine of the present day
possible.
It consists of copper segments tightly fastened together with mica/micanite

insulating separators on an insulated base.
The whole commutator forms a rigid and solid assembly of insulated copper
strips and can rotate at high speeds.
Each commutator segment is provided with a ’riser’ where the ends of the
armature coils get connected.
The surface of the commutator is machined and surface is made concentric with
the shaft and the current collecting brushes rest on the same.
Under-cutting the mica insulators that are between these commutator segments
has to be done periodically to avoid fouling of the surface of the commutator by
mica when the commutator gets worn out.
Some details of the construction of the commutator are seen in Fig
Brush and brush holders:

Brushes rest on the surface of the commutator.
Normally electro-graphite is used as brush material.
The actual composition of the brush depends on the peripheral speed of the
commutator and the working voltage.
The hardness of the graphite brush is selected to be lower than that of the
commutator.
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When the brush wears out the graphite works as a solid lubricant reducing
frictional coefficient.
More number of relatively smaller width brushes are preferred in place of large
broad brushes.
The brush holders provide slots for the brushes to be placed.
The connection Brush holder with a Brush and Positioning of the brush on the
commutator from the brush is taken out by means of flexible pigtail.
The brushes are kept pressed on the commutator with the help of springs.
This is to ensure proper contact between the brushes and the commutator even
under high speeds of operation.
Jumping of brushes must be avoided to ensure arc free current collection and to
keep the brush contact drop low.
Other mechanical parts End covers, fan and shaft bearings form other important
mechanical parts.
End covers are completely solid or have opening for ventilation.
They support the bearings which are on the shaft.
Proper machining is to be ensured for easy assembly.
Fans can be external or internal.
In most machines the fan is on the non-commutator end sucking the air from the
commutator end and throwing the same out.
Adequate quantity of hot air removal has to be ensured.
Bearings Small machines employ ball bearings at both ends.
For larger machines roller bearings are used especially at the driving end.
The bearings are mounted press-fit on the shaft.
They are housed inside the end shield in such a manner that it is not necessary
to remove the bearings from the shaft for dismantling.
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End Shields or Bearings

If the armature diameter does not exceed 35 to 45 cm then in addition to poles
end shields or frame head with bearing are attached to the frame.
If the armature diameter is greater than 1m pedestral type bearings are

mounted on the machine bed plate outside the frame.
These bearings could be ball or roller type but generally plain pedestral bearings
are employed.
If the diameter of the armature is large a brush holder yoke is generally fixed
to the frame.
PRINCIPLE OF OPERATION
DC generator converts mechanical energy into electrical energy. when a

conductor move in a magnetic field in such a way conductors cuts across a
magnetic flux of lines and emf produces in a generator and it is defined by
faradays law of electromagnetic induction emf causes current to flow if the
conductor circuit is closed.
The pole pieces (marked N and S) provide the magnetic field. The pole pieces are
shaped and positioned as shown to concentrate the magnetic field as close as
possible to the wire loop. The loop of wire that rotates through the field is called
the ARMATURE. The ends of the armature loop are connected to rings called
SLIP RINGS. They rotate with the armature. The brushes, usually made of
carbon, with wires attached to them, ride against the rings. The generated voltage
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appears across these brushes. The elementary generator produces a voltage in the
following manner (fig. 1-3). The armature loop is rotated in a clockwise direction.
The initial or starting point is shown at position A. (This will be considered the
zero-degree position.) At 0º_ the armature loop is perpendicular to the magnetic
field. The black and white conductors of the loop are moving parallel to the field.
The instant the conductors are moving parallel to the magnetic field, they do not
cut any lines of flux. Therefore, no emf is induced in the conductors, and the
meter at position A indicates zero. This position is called the NEUTRAL PLANE.
As the armature loop rotates from position A (0º) to position B (90º), the
conductors cut through more and more lines of flux, at a continually increasing
angle. At 90º they are cutting through a maximum number of lines of flux and at
maximum angle. The result is that between 0º and 90º , the induced emf in the
conductors builds up from zero to a maximum value. Observe that from 0º_ to
90º_, the black conductor cuts DOWN through the field. At the same time the
white conductor cuts UP through the field.
The induced emfs in the conductors are series-adding. This means the resultant
voltage across the brushes (the terminal voltage) is the sum of the two induced
voltages. The meter at position B reads maximum value. As the armature loop
continues rotating from 90º_ (position B) to 180º_ (position C), the conductors
which were cutting through a maximum number of lines of flux at position B now
cut through fewer lines. They are again moving parallel to the magnetic field at
position C. They no longer cut through any lines of flux. As the armature rotates
from 90º_ to 180º_, the induced voltage will decrease to zero in the same manner
that it increased during the rotation from 0º_ to 90º_. The meter again reads zero.
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From 0º_ to 180º_ the conductors of the armature loop have been moving in the
same direction through the magnetic field. Therefore, the polarity of the induced
voltage has remained the same. This is shown by points A through C on the graph.
As the loop rotates beyond 180º_ (position C), through 270º_ (position D), and
back to the initial or starting point (position A), the direction of the cutting action
of the conductors through the magnetic field reverses. Now the black conductor
cuts UP through the field while the white conductor cuts DOWN through the
field. As a result, the polarity of the induced voltage reverses. Following the
sequence shown by graph points C, D, and back to A, the voltage will be in the
direction opposite to that shown from points A, B, and C. The terminal voltage
will be the same as it was from A to C except that the polarity is reversed (as
shown by the meter deflection at position D). The voltage output waveform for
the complete revolution of the loop is shown on the graph in figure
DC GENERATOR E.M.F EQUATION

Let
Φ = flux/pole in weber
Z = total number of armture conductors = No.of slots x No.of conductors/slot

P = No.of generator poles
A = No.of parallel paths in armature
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N = armature rotation in revolutions per minute (r.p.m) E = e.m.f induced in any

parallel path in armature
Generated e.m.f Eg = e.m.f generated in any one of the parallel paths i.e E.
Average e.m.f geneated /conductor = dΦ/dt volt (n=1)
Now, flux cut/conductor in one revolution dΦ = ΦP Wb No.of revolutions/second

= N/60
Time for one revolution, dt = 60/N second

Hence, according to Faraday's Laws of Electroagnetic Induction,
E.M.F generated/conductor is
For a simplex wave-wound generator

No.of parallel paths = 2
No.of conductors (in series) in one path = Z/2

E.M.F. generated/path is
For a simplex lap-wound generator

No.of parallel paths = P
No.of conductors (in series) in one path = Z/P

E.M.F.generated/path
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In general generated e.m.f
where A = 2 for simplex wave-winding A = P for simplex lap-winding
PRINCIPLE OF OPERATION
DC generator converts mechanical energy into electrical energy. when a

conductor move in a magnetic field in such a way conductors cuts across a
magnetic flux of lines and emf produces in a generator and it is defined by
faradays law of electromagnetic induction emf causes current to flow if the
conductor circuit is closed.
TYPES OF D.C. GENERATORS
The magnetic field in a d.c. generator is normally produced by

electromagnets rather than permanent magnets. Generators are generally
classified according to their methods of field excitation. On this basis, d.c.
generators are divided into the following two classes:
(i) Separately excited d.c. generators

(ii) Self-excited d.c. generators
The behaviour of a d.c. generator on load depends upon the method of field
excitation adopted.
(i) Separately Excited D.C. Generators
A d.c. generator whose field magnet winding is supplied from an independent

external d.c. source (e.g., a battery etc.) is called a separately excited generator.
Fig shows the connections of a separately excited generator. The voltage output
depends upon the speed of rotation of armature and the field current (Eg =PfØ
ZN/60 A). The greater the speed and field current, greater is the generated e.m.f.
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It may be noted that separately excited d.c. generators are rarely used in practice.
The d.c. generators are normally of self-excited type.
Armature current, Ia = IL
Terminal voltage, V = Eg - IaRa
Electric power developed = EgIa
Power delivered to load = EgIa - Ia2Ra
(ii) Self-Excited D.C. Generators
A d.c. generator whose field magnet winding is supplied current from the
output of the generator itself is called a self-excited generator. There are three
types of self-excited generators depending upon the manner in which the field
winding isconnected to the armature, namely;
(a) Series generator;

(b) Shunt generator;
(c) Compound generator
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(a) Series generator
In a series wound generator, the field winding is connected in series with armature
winding so that whole armature current flows through the field winding as well
as the load. Fig. shows the connections of a series wound generator. Since the
field winding carries the whole of load current, it has a few turns of thick wire
having low resistance. Series generators are rarely used except for special
purposes e.g., as boosters.
Armature current, Ia = Ise = IL = I(say)

Terminal voltage, V = EG - I(Ra + Rse)
Power developed in armature = EgIa
Power delivered to load
(b) Shunt generator
In a shunt generator, the field winding is connected in parallel with the armature
winding so that terminal voltage of the generator is applied across it. The shunt
field winding has many turns of fine wire having high resistance. Therefore, only
a part of armature current flows through shunt field winding and the rest flows
through the load. Fig. shows the connections of a shunt-wound generator.
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Shunt field current, Ish = V/Rsh

Armature current, Ia = IL + Ish
Terminal voltage, V = Eg - IaRa
Power developed in armature = EgIa
Power delivered to load = VIL
(c) Compound generator
In a compound-wound generator, there are two sets of field windings on each

pole—one is in series and the other in parallel with the armature. A compound
wound generator may be: Short Shunt in which only shunt field winding is in
parallel with the armature winding.Long Shunt in which shunt field winding is in
parallel with both series field and armature winding
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DC GENERATOR CHARACTERISTICS:
The three most important characteristics or curves of a d.c generator are
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1. OpenCircuitCharacteristic (O.C.C.)
This curve shows the relation between the generated e.m.f. at no-load (E0)
and the field current (If) at constant speed. It is also known as magnetic
characteristic or no-load saturation curve. Its shape is practically the same for all
generators whether separately or self-excited. The data for O.C.C. curve are
obtained experimentally by operating the generator at no load and constant speed
and recording the change in terminal voltage as the field current is varied.
2. Internal or Total characteristic (E/Ia)
This curve shows the relation between the generated e.m.f. on load (E) and
the armature current (Ia). The e.m.f. E is less than E0 due to the demagnetizing
effect of armature reaction. Therefore, this curve will lie below the open circuit
characteristic (O.C.C.). The internal characteristic is of interest chiefly to the
designer. It cannot be obtained directly by experiment. It is because a voltmeter
cannot read the e.m.f. generated on load due to the voltage drop in armature
resistance. The internal characteristic can be obtained from external characteristic
if winding resistances are known because armature reaction effect is included in
both characteristics
3. External characteristic (V/IL)
This curve shows the relation between the terminal voltage (V) and load
current (IL). The terminal voltage V will be less than E due to voltage drop in the
armature circuit. Therefore, this curve will lie below the internal characteristic.
This characteristic is very important in determining the suitability of a generator
for a given purpose. It can be obtained by making simultaneous
1 characteristics Series of DC generator:
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Fig. shows the connections of a series wound generator. Since there is only one
current (that which flows through the whole machine), the load currentis the same
as the exciting current.
(i) O.C.C.
Curve 1 shows the open circuit characteristic (O.C.C.) of a series generator.

It can be obtainedexperimentally by disconnecting the field winding from the
machine and exciting it from aseparate d.c. source
(ii) Internal characteristic
Curve 2 shows the total or internal characteristic of a series generator. It

gives the relation between the generated e.m.f. E. on load and armature current.
Due to armature reaction, the flux in the machine will be less than the flux at no
load. Hence, e.m.f. E generated under load conditions will be less than the e.m.f.
EO generated under no load conditions. Consequently, internal characteristic
curve generated under no load conditions. Consequently, internal characteristic
curve lies below the O.C.C. curve; the difference between them representing the
effect of armature reaction
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(iii) Externalcharacteristic
Curve 3 shows the external characteristic of a series generator. It gives the
relation between terminal voltage and load current IL.
V= E-Ia(Ra+Rse)
Therefore, external characteristic curve will lie below internal characteristic

curve by an amount equal to ohmic drop[i.e., Ia(Ra+Rse)] in the machine. The
internal and external characteristics of a d.c. series generator can be plotted from
one another as shown in Fig. Suppose we are given the internal characteristic of
the generator. Let the line OC represent the resistance of the whole machine i.e.
Ra+Rse.If the load current is OB, drop in the machine is AB i.e.
AB = Ohmic drop in the machine = OB(Ra+Rse)
Now raise a perpendicular from point B and mark a point b on this line such that
ab = AB. Then point b will lie on the external characteristic of the generator.
Following similar procedure, other points of external characteristic can be
located. It is easy to see that we can also plot internal characteristic from the
external characteristic.
Characteristics Shunt DC generator:
Fig shows the connections of a shunt wound generator. The armature current Ia
splits up into two parts; a small fraction Ish flowing through shunt field winding
while the major part IL goes to the external load.
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(i) O.C.C.
The O.C.C. of a shunt generator is similar in shape to that of a series

generator as shown in Fig. The line OA represents the shunt field circuit
resistance. When the generator is run at normal speed, it will build up a voltage
OM. At no-load, the terminal voltage of the generator will be constant (= OM)
represented by the horizontal dotted line MC.
(ii) Internal characteristic
When the generator is loaded, flux per pole is reduced due to armature
reaction. Therefore, e.m.f. E generated on load is less than the e.m.f. generated at
no load.As a result, the internal characteristic (E/Ia) drops down slightly as shown
in Fig.
(iii)External characteristic
Curve 2 shows the external characteristic of a shunt generator. It gives the

relation between terminal voltage V and load current IL.
V = E – IaRa = E -(IL +Ish)Ra
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Therefore, external characteristic curve will lie below the internal characteristic
curve by an amount equal to drop in the armature circuit [i.e., (IL +Ish)Ra ] as
shown in Fig
Critical External Resistance for Shunt Generator
If the load resistance across the terminals of a shunt generator is decreased,

then load current increase? However, there is a limit to the increase in load current
with the decrease of load resistance. Any decrease of load resistance beyond this
point, instead of increasing the current, ultimately results in reduced current.
Consequently, the external characteristic turns back (dottedcurve) as shown in
Fig. The tangent OA to the curve represents the minimum external resistance
required to excite the shunt generator on load and is called critical external
resistance. If the resistance of the external circuit is less than the critical external
resistance (represented by tangent OA in Fig, the machine will refuse to excite or
will de-excite if already running This means that external resistance is so low as
virtually to short circuit the machine and so doing away with its excitation.
There are two critical resistances for a shunt generator viz.,

(i) critical field resistance
(ii) critical external resistance. For the shunt generator to build up voltage,
the former should not be exceeded and the latter must not be gone below
Characteristics compound generator:
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In a compound generator, both series and shunt excitation are combined as

shown in Fig. The shunt winding can be connected either across the armature only
(short-shunt connection S) or across armature plus series field (long-shunt
connection G). The compound generator can be cumulatively compounded or
differentially compounded generator. The latter is rarely used in practice.
Therefore, we shall discuss the characteristics of cumulatively compounded
generator. It may be noted that external characteristics of long and short shunt
compound generators are almost identical.
External characteristic
Fig. shows the external characteristics of a cumulatively compounded generator.

The series excitation aids the shunt excitation. The degree of compounding
depends upon the increase in series excitation with the increase in load current.
(i) If series winding turns are so adjusted that with the increase in load current
the terminal voltage increases, it is called over-compounded generator. In such a
case, as the load current increases, the series field m.m.f. increases and tends to
increase the flux and hence the generated voltage. The increase in generated
voltage is greater than the IaRa drop so that instead of decreasing, the terminal
voltage increases as shown by curve A in Fig.
(ii) If series winding turns are so adjusted that with the increase in load current,
the terminal voltage substantially remains constant, it is called flat-compounded
generator. The series winding of such a machine has lesser number of turns than
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the one in over-compounded machine and, therefore, does not increase the flux
as much for a given load current. Consequently, the full-load voltage is nearly
equal to the no-load voltage as indicated by curve B in Fig
(iii) If series field winding has lesser number of turns than for a flat compounded
machine, the terminal voltage falls with increase in load current as indicated by
curve C m Fig. Such a machine is called under-compounded generator.
APPLICATIONS OF DC GENERATOR
DC Separately Exited Generator:
As a supply source to DC Motors, whose speed is to be controlled for

certain applications. Where a wide range of voltage is required for the testing
purposes.
DC Shunt Generator
The terminal voltage of DC shunt generator is more or less constant from no

load to full load .Therefore these generators are used where constant voltage is
required.
For electro plating
Battery charging
For excitation of Alternators.

DC Series Generator
The terminal voltage of series generator increases with load current from no
load to full load .Therefore these generators are,
Used as Boosters
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Used for supply to arc Lamps
DC Compound Generator:
Differential Compound generators are used to supply dc welding machines.

Level compound generators are used to supply power for offices, hostels and
Lodges etc. Over compound generators are used to compensate the voltage drop
in Feeders.
An electrical generator is a device that converts mechanical energy to

electrical energy, generally using electromagnetic induction. The source of
mechanical energy may be a reciprocating or turbine steam engine, water falling
through a turbine or waterwheel, an internal combustion engine, a wind turbine,
a hand crank, or any other source of mechanical energy.
DC MOTOR - INTRODUCTION
A machine that converts dc power into mechanical energy is known as dc

motor. Its operation is based on the principle that when a current carrying
conductor is placed in a magnetic field, the conductor experiences a mechanical
force. The direction of the force is given by
Fleming’s left hand rule.
How DC motors work?
There are different kinds of D.C. motors, but they all work on the same
principles.When a permanent magnet is positioned around a loop of wire that is
hooked up to a D.C. power source, we have the basics of a D.C. motor. In order
to make the loop of wire spin, we have to connect a battery or DC power supply
between its ends, and support it so it can spin about its axis. To allow the rotor to
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turn without twisting the wires, the ends of the wire loop are connected to a set
of contacts called the commutator, which rubs against a set of conductors called
the brushes. The brushes make electrical contact with the commutator as it spins,
and are connected to the positive and negative leads of the power source, allowing
electricity to flow through the loop. The electricity flowing through the loop
creates a magnetic field that interacts with the magnetic field of the permanent
magnet to make the loop spin.
PRINCIPLES OF OPERATION
It is based on the principle that when a current-carrying conductor is placed

in a magnetic field, it experiences a mechanical force whose direction is given by
Fleming's Left-hand rule and whose magnitude is given by
Force, F = B I l newton
Where B is the magnetic field in weber/m2. I is the current in amperes and
l is the length of the coil in meter.

The force, current and the magnetic field are all in different directions.
If an Electric current flows through two copper wires that are between the poles
of a magnet, an upward force will move one wire up and a downward force will
move the other wire down.
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BACK OR COUNTER EMF
When the armature of a d.c. motor rotates under the influence of the driving
torque, the armature conductors move through the magnetic field and hence an
e.m.f. is induced in them. The induced e.m.f. acts in opposite direction to the
applied voltage V(Lenz’s law) and is known as back orcounter e.m.f. Eb.
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SIGNIFICANCE OF BACK E.M.F
The presence of back e.m.f. makes the d.c. motor a self-regulating machine
i.e., it makes the motor to draw as much armature current as is just sufficient to
develop the torque required by the load. Back e.m.f. in a d.c. motor regulates the
flow of armature current i.e., it automatically changes the armature current to
meet the load requirement.
CLASSIFICATION OF DC MOTOR
DC motors are more common than we may think. A car may have as many as 20
DC motors to drive fans, seats, and windows. They come in three different types,
classified according to the electrical circuit used. In the shunt motor, the armature
and field windings are connected in parallel, and so the currents through each are
relatively independent. The current through the field winding can be controlled
with a field rheostat (variable resistor), thus allowing a wide variation in the motor
speed over a large range of load conditions. This type of motor is used for driving
machine tools or fans, which require a wide range of speeds.
In the series motor, the field winding is connected in series with the
armature winding, resulting in a very high starting torque since both the armature
current and field strength run at their maximum. However, once the armature
starts to rotate, the counter EMF reduces the current in the circuit, thus reducing
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the field strength. The series motor is used where a large starting torque is
required, such as in automobile starter motors, cranes, and hoists.
The compound motor is a combination of the series and shunt motors, having
parallel and series field windings. This type of motor has a high starting torque
and the ability to vary the speed and is used in situations requiring both these
properties such as punch presses, conveyors and elevators.
DC MOTOR TYPES
1. Shunt Wound
2. Series Wound
3. Compound wound
1. Shunt Motor
In shunt wound motor the field winding is connected in parallel with armature.
The current through the shunt field winding is not the same as the armature
current. Shunt field windings are designed to produce the necessary m.m.f. by
means of a relatively large number of turns of wire having high resistance.
Therefore, shunt field current is relatively small compared with the armature
current
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2. Series Motor
In series wound motor the field winding is connected in series with the armature.
Therefore, series field winding carries the armature current. Since the current
passing through a series field winding is the same as the armature current, series
field windings must be designed with much fewer turns than shunt field windings
for the same mmf.Therefore, a series field winding has a relatively small number
of turns of thick wire and, therefore, will possess a low resistance.
3. Compound Wound Motor
Compound wound motor has two field windings; one connected in parallel
with the armature and the other in series with it. There are two types of compound
motor connections
1) Short-shunt connection
2) Long shunt connection
When the shunt field winding is directly connected across the armature terminals
it is called short-shunt connection.
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When the shunt winding is so connected that it shunts the series combination of
armature and series field it is called long-shunt connection.
VOLTAGE EQUATION OF MOTORS

Let in a d.c. motor
V = applied voltage
Eb = back e.m.f.
Ra = armature resistance
Ia = armature current
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Since back e.m.f. Eb acts in opposition to the applied voltage V, the net voltage
across the armature circuit is V-Eb.
The armature current Ia is given by
APPLICATIONS OF DC MOTORS:
1. D.C Shunt Motors:
It is a constant speed motor.Where the speed is required to remain almost

constant from noload to full load.Where the load has to be driven at a number of
speeds and any one of which is nearly constant.
Industrial use:
Lathes
Drills
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Boring mills
Shapers
Spinning and Weaving machines.
2. D.CSeries motor:
It is a variable speed motor.The speed is low at high torque.At light or no load

,the motor speed attains dangerously high speed.The motor has a high starting
torque.(elevators,electric traction)
Industrial Uses:
Electric traction
Cranes
Elevators
Air compressor
3. D.C Compound motor:
Differential compound motors are rarely used because of its poor torque
characteristics. Industrial uses:
PressesShears
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Reciprocating machine.
CLASSIFICATION OF DC MOTOR
DC motors are more common than we may think. A car may have as many as 20
DC motors to drive fans, seats, and windows. They come in three different types,
classified according to the electrical circuit used. In the shunt motor, the armature
and field windings are connected in parallel, and so the currents through each are
relatively independent. The current through the field winding can be controlled
with a field rheostat (variable resistor), thus allowing a wide variation in the motor
speed over a large range of load conditions. This type of motor is used for driving
machine tools or fans, which require a wide range of speeds.
TRANSFORMER
INTRODUCTION
A TRANSFORMER is a device that transfers electrical energy from one

circuit to another by electromagnetic induction (transformer action). The
electrical energy is always transferred without a change in frequency, but may
involve changes in magnitudes of voltage and current. Because a transformer
works on the principle of electromagnetic induction, it must be used with an input
source voltage that varies in amplitude. There are many types of power that fit
this description; for ease of explanation and understanding, transformer action
will be explained using an ac voltage as the input source.
BASIC OPERATION OF A TRANSFORMER
In its most basic form a transformer consists of: A primary coil or winding.
A secondary coil or winding.
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A core that supports the coils or windings.
Refer to the transformer circuit in figure as you read the following explanation:
The primary winding is connected to a 60 hertz ac voltage source. The magnetic
field (flux) builds up (expands) and collapses (contracts) about the primary
winding. The expanding and contracting magnetic field around the primary
winding cuts the secondary winding and induces an alternating voltage into the
winding. This voltage causes alternating current to flow through the load. The
voltage may be stepped up or down depending on the design of the primary and
secondary windings.
AN IDEAL TRANSFORMER
An ideal transformer is shown in the adjacent figure. Current passing

through the primary coil creates a magnetic field. The primary and secondary
coils are wrapped around a core of very high magnetic permeability, such as iron,
so that most of the magnetic flux passes through both the primary and secondary
coils.
BASIC WORKING PRINCIPLE OF TRANSFORMER
A transformer can be defined as a static device which helps in the

transformation of electric power in one circuit to electric power of the same
frequency in another circuit. The voltage can be raised or lowered in a circuit, but
with a proportional increase or decrease in the current ratings.
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The main principle of operation of a transformer is mutual inductance between

two circuits which is linked by a common magnetic flux. A basic transformer
consists of two coils that are electrically separate and inductive, but are
magnetically linked through a path of reluctance. The working principle of the
transformer can be understood from the figure below.
As shown above the transformer has primary and secondary windings. The
core laminations are joined in the form of strips in between the strips you can see
that there are some narrow gaps right through the cross-section of the core. These
staggered joints are said to be
‘imbricated’. Both the coils have high mutual inductance. A mutual electro-
motive force is induced in the transformer from the alternating flux that is set up
in the laminated core, due to the coil that is connected to a source of alternating
voltage. Most of the alternating flux developed by this coil is linked with the other
coil and thus produces the mutual induced electro-motive force. The so produced
electro-motive force can be explained with the help of Faraday’s laws of
Electromagnetic Induction as
e=M*dI/dt
If the second coil circuit is closed, a current flows in it and thus electrical energy
is transferred magnetically from the first to the second coil.
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The alternating current supply is given to the first coil and hence it can be
called as the primary winding. The energy is drawn out from the second
coil and thus can be called as the secondary winding.
In short, a transformer carries the operations shown below:
Transfer of electric power from one circuit to another.
Transfer of electric power without any change in frequency.
Transfer with the principle of electromagnetic induction.
The two electrical circuits are linked by mutual induction
TRANSFORMER CONSTRUCTION
Two coils of wire (called windings) are wound on some type of core
material. In some cases the coils of wire are wound on a cylindrical or
rectangular cardboard form. In effect, the core material is air and the
transformer is called an AIR-CORE TRANSFORMER. Transformers used
at low frequencies, such as 60 hertz and 400 hertz, require a core of low-
reluctance magnetic material, usually iron. This type of transformer is
called an IRON-CORE TRANSFORMER. Most power transformers are
of the iron-core type.
The principle parts of a transformer and their functions are:

The CORE, which provides a path for the magnetic lines of flux.
The PRIMARY WINDING, which receives energy from the ac source.
The SECONDARY WINDING, which receives energy from the primary

winding and delivers it to the load.
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The ENCLOSURE, which protects the above components from dirt,

moisture, and mechanical damage.
(i) CORE
There are two main shapes of cores used in laminated-steel-core

transformers. One is the HOLLOWCORE, so named because the core is
shaped with a hollow square through the center. This shape of core. Notice
that the core is made up of many laminations of steel it shows how the
transformer windings are wrapped around both sides of the core.
(ii) WINDINGS
As stated above, the transformer consists of two coils called

WINDINGS which are wrapped around a core. The transformer operates
when a source of ac voltage is connected to one of the windings and a load
device is connected to the other. The winding that is connected to the
source is called the PRIMARY WINDING. The winding that is connected
to the load is called the SECONDARY WINDING. The primary is wound
in layers directly on a rectangular cardboard form.
EMF Equation of Transformer:
Let the applied voltage V1 applied to the primary of a transformer,

with secondary open-circuited, be sinusoidal (or sine wave). Then the
current I1, due to applied voltage V1, will also be a sine wave. The mmf
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N1 I1 and core flux Ø will follow the variations of I1 closely. That is the
flux is in time phase with the current I1 and varies sinusoidally.
Let,
NA = Number of turns in primary
NB = Number of turns in secondary
Ømax = Maximum flux in the core in webers = Bmax X A f =

Frequency of alternating current input in hertz (HZ)
As shown in figure above, the core flux increases from its zero value to
maximum value Ømax in one quarter of the cycle , that is in ¼ frequency
second.
Therefore, average rate of change of flux = Ømax/ ¼ f = 4f ØmaxWb/s
Now, rate of change of flux per turn means induced electro motive force in
volts. Therefore,
average electro-motive force induced/turn = 4f Ømaxvolt
If flux Ø varies sinusoidally, then r.m.s value of induced e.m.f is obtained

by multiplying the average value with form factor.
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Form Factor = r.m.s. value/average value = 1.11 Therefore, r.m.s

value of e.m.f/turn = 1.11 X 4f Ømax = 4.44f ØmaxNow, r.m.s value of
induced e.m.f in the whole of primary winding
= (induced e.m.f./turn) X Number of primary turns
Therefore,
EA = 4.44f NAØmax = 4.44fNABmA

Similarly, r.m.s value of induced e.m.f in secondary is
EB = 4.44f NB Ømax = 4.44fNBBmA

In an ideal transformer on no load, VA = EA and VB = EB , where
VB is the terminal voltage
Voltage Transformation Ratio.
The ratio of secondary voltage to primary voltage is known as the

voltage transformation ratio and is designated by letter K. i.e.
Voltage transformation ratio, K = V2/V1 = E2/E1 = N2/N1
Current Ratio.
The ratio of secondary current to primary current is known as current

ratio and is reciprocal of voltage transformation ratio in an ideal
transformer.
Transformer on No Load.
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When the primary of a transformer is connected to the source of an ac supply and

the secondary is open circuited, the transformer is said to be on no load. The
Transformer on No Load alternating applied voltage will cause flow of an
alternating current I0 in the primary
winding, which will create alternating flux Ø. No-load current I0, also known as
excitation or exciting current, has two components the magnetizing component
Im and the energy component Ie. Im is used to create the flux in the core and Ie
is used to overcome the hysteresis and eddy current losses occurring in the core
in addition to small amount of copper losses occurring in the primary only (no
copper loss occurs in the secondary, because it carries no current, being open
circuited.)
From vector diagram shown in above it is obvious that
1. Induced emfs in primary and secondary windings, E1 and E2 lag the

main flux Ø by and are in phase with each other.
2. Applied voltage to primary V1 and leads the main flux Ø by and is in

phase opposition to E1.
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3. Secondary voltage V2 is in phase and equal to E2 since there is no

voltage drop in secondary.
4. Im is in phase with Ø and so lags V1 by

5. Ie is in phase with the applied voltage V1.
6. Input power on no load = V1Ie = V1I0 cos Ø0 where Ø0 = tan-1
Transformer on Load:
The transformer is said to be loaded, when its secondary circuit is

completed through an impedance or load. The magnitude and phase of secondary
current (i.e. current flowing through secondary) I2 with respect to secondary
terminals depends upon the characteristic of the load i.e. current I2 will be in
phase, lag behind and lead the terminal voltage V+2+ respectively when the load
is non-inductive, inductive and capacitive. The net flux passing through the core
remains almost constant from no-load to full load irrespective of load conditions
and so core losses remain almost constant from no-load to full load. Vector
diagram for an ideal transformer supplying inductive load is shown
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Resistance and Leakage Reactance In actual practice, both of the primary and
secondary windings have got some ohmic resistance causing voltage drops and
copper losses in the windings. In actual practice, the total flux created does not
link both of the primary and secondary windings but is divided into three
components namely the main or mutual flux Ø linking both of the primary and
secondary windings, primary leakage flux ØL1 linking with primary winding only
and secondary leakage flux ØL2linking with secondary winding only. The
primary leakage flux ØL1 is produced by primary ampere-turns and is
proportional to primary current, number of primary turns being fixed. The
primary leakage flux ØL1 is in phase with I1 and produces self induced emf ØL1 is
in phase with I1 and produces self induced emf EL1 given as 2f L1 I1 in the primary
winding.
The self induced emf divided by the primary current gives the reactance of
primary and is denoted by X1.
X1 = EL1/I1 = 2πfL1I1/I1 = 2FL1,

Similarly leakage reactance of secondary X2 = EL2/E2 = 2fπL2I2/I2 = 2πfL2
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Equivalent Resistance and Reactance. The equivalent resistances and reactance’s

of transformer windings referred to primary and secondary sides are given as
below Referred to primary side Equivalent resistance,
Equivalent resistance, = X'1 = Referred to secondary side Equivalent resistance,
Equivalent resistance, = X2 + K2X1 Where K is the transformation ratio.
EQUIVALENT CIRCUIT OF TRANSFORMER
Equivalent impedance of transformer is essential to be calculated because the

electrical power transformer is an electrical power system equipment for
estimating different parameters of electrical power system which may be required
to calculate total internal impedance of an electrical power transformer, viewing
from primary side or secondary side as per requirement. This calculation requires
equivalent circuit of transformer referred to primary or equivalent circuit of
transformer referred to secondary sides respectively. Percentage impedance is
also very essential parameter of transformer. Special attention is to be given to
this parameter during installing a transformer in an existing electrical power
system. Percentage impedance of different power transformers should be
properly matched during parallel operation of power transformers. The
percentage impedance can be derived from equivalent impedance of transformer
so, it can be said that equivalent circuit of transformer is also required during
calculation of % impedance.
Equivalent Circuit of Transformer Referred to Primary
For drawing equivalent circuit of transformer referred to primary, first we

have to establish general equivalent circuit of transformer then, we will modify
it for referring from primary side. For doing this, first we need to recall the
complete vector diagram of a transformer which is shown in the figure below.
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Let us consider the transformation ratio be,
In the figure right, the applied voltage to the primary is V1 and voltage across the
primary winding is E1. Total current supplied to primary is I1. So
the voltage V1 applied to the primary is partly dropped by I1Z1 or I1R1 +
j.I1X1 before it appears across primary winding. The voltage appeared across
winding is countered by primary induced emf E1.
The equivalent circuit for that equation can be drawn as below,
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From the vector diagram above, it is found that the total primary current I1 has
two components, one is no - load component Ioand the other is load component
I2′. As this primary current has two a component or branches, so there must be a
parallel path with primary winding of transformer. This parallel path of current is
known as excitation branch of equivalent circuit of transformer. The resistive and
reactive branches of the excitation circuit can be represented as
The load component I2′ flows through the primary winding of transformer
and induced voltage across the winding is E1as shown in the figure right. This
induced voltage E1transforms to secondary and it is E2 and load component of
primary current I2′ is transformed to secondary as secondary current I2. Current
of secondary is I 2. So the voltage E2 across secondary winding is partly dropped
by I2Z2 or I2R2 + j.I2X2 before it appears across load. The load voltage is V2.
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From above equation, secondary impedance of transformer referred to primary

is,
So, the complete equivalent circuit of transformer referred to primary is shown in

the figure below,
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Approximate Equivalent Circuit of Transformer
Since Io is very small compared to I1, it is less than 5% of full load primary
current, Iochanges the voltage drop insignificantly. Hence, it is good
approximation to ignore the excitation circuit in approximate equivalent circuit
of transformer. The winding resistanceand reactance being in series can now be
combined into equivalent resistance and reactance of transformer, referred to any
particular side. In this case it is side 1 or primary side.
Equivalent Circuit of Transformer Referred to Secondary
In similar way, approximate equivalent circuit of transformer referred to

secondary can be drawn. Where equivalent impedance of transformer referred to
secondary, can be derived as
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VOLTAGE REGULATION
The voltage regulation is the percentage of voltage difference between no load

and full load voltages of a transformer with respect to its full load voltage.
Explanation of Voltage Regulation of Transformer
Say an electrical power transformer is open circuited, means load is not connected
with secondary terminals. In this situation, the secondary terminalvoltage of the
transformer will be its secondary induced emf E2. Whenever full load is
connected to the secondary terminals of the transformer, ratedcurrent I2 flows
through the secondary circuit and voltage drop comes into picture. At this
situation, primary winding will also draw equivalent full load current from
source. The voltagedrop in the secondary is I2Z2 where Z2 is the secondary
impedance of transformer. Now if at this loading condition, any one measures the
voltage between secondary terminals, he or she will getvoltage V 2 across load
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terminals which is obviously less than no load secondary voltage E2 and this is
because of I2Z2 voltage drop in the transformer.
Expression of Voltage Regulation of Transformer, represented in percentage, is
Transformer on No Load.
When the primary of a transformer is connected to the source of an ac supply and

the secondary is open circuited, the transformer is said to be on no load. The
Transformer on No Load alternating applied voltage will cause flow of an
alternating current I0 in the primary
winding, which will create alternating flux Ø. No-load current I0, also known as
excitation or exciting current, has two components the magnetizing component
Im and the energy component Ie. Im is used to create the flux in the core and Ie
is used to overcome the hysteresis and eddy current losses occurring in the core
in addition to small amount of copper losses occurring in the primary only (no
copper loss occurs in the secondary, because it carries no current, being open
circuited.)
From vector diagram shown in above it is obvious that
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1. Induced emfs in primary and secondary windings, E1 and E2 lag the

main flux Ø by and are in phase with each other.
2. Applied voltage to primary V1 and leads the main flux Ø by and is in

phase opposition to E1.
3. Secondary voltage V2 is in phase and equal to E2 since there is no

voltage drop in secondary.
4. Im is in phase with Ø and so lags V1 by

5. Ie is in phase with the applied voltage V1.
6. Input power on no load = V1Ie = V1I0 cos Ø0 where Ø0 = tan-1
Transformer on Load:
The transformer is said to be loaded, when its secondary circuit is

completed through an impedance or load. The magnitude and phase of secondary
current (i.e. current flowing through secondary) I2 with respect to secondary
terminals depends upon the characteristic of the load i.e. current I2 will be in
phase, lag behind and lead the terminal voltage V+2+ respectively when the load
is non-inductive, inductive and capacitive. The net flux passing through the core
remains almost constant from no-load to full load irrespective of load conditions
and so core losses remain almost constant from no-load to full load. Vector
diagram for an ideal transformer supplying inductive load is shown
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Resistance and Leakage Reactance In actual practice, both of the primary and
secondary windings have got some ohmic resistance causing voltage drops and
copper losses in the windings. In actual practice, the total flux created does not
link both of the primary and secondary windings but is divided into three
components namely the main or mutual flux Ø linking both of the primary and
secondary windings, primary leakage flux ØL1 linking with primary winding
only and secondary leakage flux ØL2 linking with secondary winding only. The
primary leakage flux ØL1 is produced by primary ampere-turns and is
proportional to primary current, number of primary turns being fixed. The
primary leakage flux ØL1 is in phase with I1 and produces self induced emf
ØL1 is in phase with I1 and produces self induced emf EL1 given as 2f L1 I1 in
the primary winding.
The self induced emf divided by the primary current gives the reactance of
primary and is denoted by X1.
X1 = EL1/I1 = 2πfL1I1/I1 = 2FL1,

Similarly leakage reactance of secondary X 2 = EL2/E2 = 2fπL2I2/I2 = 2πfL2
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Equivalent Resistance and Reactance. The equivalent resistances and reactance’s

of transformer windings referred to primary and secondary sides are given as
below Referred to primary side Equivalent resistance,
Equivalent resistance, = X'1 = Referred to secondary side Equivalent resistance,
Equivalent resistance, = X2 + K2X1 Where K is the transformation ratio.

EQUIVALENT CIRCUIT OF TRANSFORMER

Equivalent Circuit of Transformer Referred to Primary
For drawing equivalent circuit of transformer referred to primary, first we

have to establish general equivalent circuit of transformer then, we will modify
it for referring from primary side. For doing this, first we need to recall the
complete vector diagram of a transformer which is shown in the figure below.
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Let us consider the transformation ratio be,
In the figure right, the applied voltage to the primary is V1 and voltage across the
primary winding is E1. Total current supplied to primary is I1. So
the voltage V1 applied to the primary is partly dropped by I1Z1 or I1R1 +
j.I1X1 before it appears across primary winding. The voltage appeared across
winding is countered by primary induced emf E1.
The equivalent circuit for that equation can be drawn as below,
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From the vector diagram above, it is found that the total primary current I1 has
two components, one is no - load component Io and the other is load component
I2′. As this primary current has two a component or branches, so there must be a
parallel path with primary winding of transformer. This parallel path of current is
known as excitation branch of equivalent circuit of transformer. The resistive and
reactive branches of the excitation circuit can be represented as
The load component I2′ flows through the primary winding of transformer
and induced voltage across the winding is E1 as shown in the figure right. This
induced voltage E1transforms to secondary and it is E2 and load component of
primary current I2′ is transformed to secondary as secondary current I2. Current
of secondary is I 2. So the voltage E2 across secondary winding is partly dropped
by I2Z2 or I2R2 + j.I2X2 before it appears across load. The load voltage is V2.
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From above equation, secondary impedance of transformer referred to primary

is,
So, the complete equivalent circuit of transformer referred to primary is shown in

the figure below,
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Approximate Equivalent Circuit of Transformer
Since Io is very small compared to I1, it is less than 5% of full load primary
current, Iochanges the voltage drop insignificantly. Hence, it is good
approximation to ignore the excitation circuit in approximate equivalent circuit
of transformer. The winding resistanceand reactance being in series can now be
combined into equivalent resistance and reactance of transformer, referred to any
particular side. In this case it is side 1 or primary side.
Equivalent Circuit of Transformer Referred to Secondary
In similar way, approximate equivalent circuit of transformer referred to

secondary can be drawn. Where equivalent impedance of transformer referred to
secondary, can be derived
as
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VOLTAGE REGULATION
The voltage regulation is the percentage of voltage difference between no load

and full load voltages of a transformer with respect to its full load voltage.
Explanation of Voltage Regulation of Transformer
Say an electrical power transformer is open circuited, means load is not connected
with secondary terminals. In this situation, the secondary terminalvoltage of the
transformer will be its secondary induced emf E2. Whenever full load is
connected to the secondary terminals of the transformer, ratedcurrent I2 flows
through the secondary circuit and voltage drop comes into picture. At this
situation, primary winding will also draw equivalent full load current from
source. The voltagedrop in the secondary is I2Z2 where Z2 is the secondary
impedance of transformer. Now if at this loading condition, any one measures the
voltage between secondary terminals, he or she will getvoltage V2 across load
terminals which is obviously less than no load secondary voltage E2 and this is
because of I2Z2 voltage drop in the transformer.
Expression of Voltage Regulation of Transformer, represented in percentage, is
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SINGLE PHASE INDUCTION MOTOR
INTRODUCTION
The single-phase induction machine is the most frequently used motor for
refrigerators, washing machines, clocks, drills, compressors, pumps, and so forth.
• The single-phase motor stator has a laminated iron core with two
windings arranged perpendicularly.
• One is the main and

• The other is the auxiliary winding or starting winding
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• This “single-phase” motors are truly two phase machines.

• The motor uses a squirrel cage rotor, which has a laminated iron core
with slots.
• Aluminum bars are molded on the slots and short-circuited at both ends
with a ring.
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The single-phase induction motor operation can be described by two

methods:
• Double revolving field theory; and
• Cross-field theory.
Double revolving theory is perhaps the easier of the two explanations to
understand
Double revolving field theory
• A single-phase ac current supplies the main winding that produces a

pulsating magnetic field.
• Mathematically, the pulsating field could be divided into two fields,

which are rotating in opposite directions.
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• The interaction between the fields and the current induced in the rotor
bars generates opposing torque
STARTING METHODS
The single-phase IM has no starting torque, but has resultant torque, when it
rotates at any other speed, except synchronous speed. It is also known that, in a
balanced two-phase IM having two windings, each having equal number of turns
and placed at a space angle of 90 0(electrical), and are fed from a balanced two-
phase supply, with two voltages equal in magnitude, at an angle of 900, the
rotating magnetic fields are produced, as in a three-phase IM. The torque-speed
characteristic is same as that of a three-phase one, having both starting and also
running torque as shown earlier. So, in a single-phase IM, if an auxiliary winding
is introduced in the stator, in addition to the main winding, but placed at a space
angle of 900 (electrical), starting torque is produced. The currents in the two (main
and auxiliary) stator windings also must be at an angle of 900 , to produce
maximum starting torque, as shown in a balanced two-phase stator. Thus, rotating
magnetic field is produced in such motor, giving rise to starting torque. The
various starting methods used in a single-phase IM are described here.
1. RESISTANCE SPLIT-PHASE MOTOR
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The schematic (circuit) diagram of this motor is given in Fig. As detailed earlier,
another (auxiliary) winding with a high resistance in series is to be added along
with the main winding in the stator. This winding has higher resistance to
reactance () ratio as compared to that in the main winding, and is placed at a space
angle of from the main winding as given earlier. The phasor diagram of the
currents in two windings and the input voltage is shown in Fig.The current () in
the auxiliary winding lags the voltage (V) by an angle, aaXR/°90aIaφ, which is
small, whereas the current () in the main winding lags the voltage (V) by an
angle, mImφ, which is nearly . The phase angle between the two currents is
(°90aφ−°90), which should be at least . This results in a small amount of starting
torque. The switch, S (centrifugal switch) is in series with the auxiliary winding.
It automatically cuts out the auxiliary or starting winding, when the motor attains
a speed close to full load speed. The motor has a starting torque of 100−200% of
full load torque, with the starting current as 5-7 times the full load current. The
torque-speed characteristics of the motor with/without auxiliary winding are
shown in Fig.The change over occurs, when the auxiliary winding is switched off
as given earlier. The direction of rotation is reversed by reversing the terminals
of any one of two windings, but not both, before connecting the motor to the
supply terminals. This motor is used in applications, such as fan, saw, small lathe,
centrifugal pump, blower, office equipment, washing machine, etc.
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2. CAPACITOR-START MOTOR
The schematic (circuit) diagram of this motor is given in Fig. It may be

observed that a capacitor along with a centrifugal switch is connected in series
with the auxiliary winding, which is being used here as a starting winding. The
capacitor may be rated only for intermittent duty, the cost of which decreases, as
it is used only at the time of starting. The function of the centrifugal switch has
been described earlier. The phasor diagram of two currents as described earlier,
and the torque-speed characteristics of the motor with/without auxiliary winding,
are shown in Fig. This motor is used in applications, such as compressor,
conveyor, machine tool drive, refrigeration and air-conditioning equipment, etc.
3. Capacitor-start and Capacitor-run Motor

In this motor two capacitors − Csfor starting, and Cr for running, are used. The
first capacitor is rated for intermittent duty, as described earlier, being used only
for starting. A centrifugal switch is also needed here. The second one is to be
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rated for continuous duty, as it is used for running. The phasor diagram of two
currents in both cases, and the torque-speed characteristics with two windings
having different values of capacitors, are shown in respectively. The phase
difference between the two currents is (φ m+φa>900) in the first case (starting),
while it is900 for second case (running). In the second case, the motor is a
balanced two phase one, the two windings having same number of turns and other
conditions as given earlier, are also satisfied. So, only the forward rotating field
is present, and the no backward rotating field exists. The efficiency of the motor
under this condition is higher. Hence, using two capacitors, the performance of
the motor improves both at the time of starting and then running. This motor is
used in applications, such as compressor, refrigerator, etc.
Beside the above two types of motors, a Permanent Capacitor Motor with
the same capacitor being utilised for both starting and running, is also used. The
power factor of this motor, when it is operating (running), is high. The operation
is also quiet and smooth. This motor is used in applications, such as ceiling fans,
air circulator, blower, etc.
4. Shaded-pole Motor
A typical shaded-pole motor with a cage rotor is shown in Fig. 34.8a. This
is a single-phase induction motor, with main winding in the stator. A small
portion of each pole is covered with a short-circuited, single-turn copper coil
called the shading coil. The sinusoidally varying flux created by ac (single-phase)
excitation of the main winding induces emf in the shading coil. As a result,
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induced currents flow in the shading coil producing their own flux in the shaded
portion of the pole.
Let the main winding flux be φm=φmaxsinwt
The reversal of the direction of rotation, where desired, can be achieved by

providing two shading coils, one on each end of every pole, and by open-
circuiting one set of shading coils and by short-circuiting the other set.
The fact that the shaded-pole motor is single-winding (no auxiliary

winding) self-starting one, makes it less costly and results in rugged construction.
The motor has low efficiency and is usually available in a range of 1/300 to 1/20
kW. It is used for domestic fans, record players and tape recorders, humidifiers,
slide projectors, small business machines, etc. The shaded-pole principle is used
in starting electric clocks and other single-phase synchronous timing motors.
no starting torque is produced in the single-phase induction motor with only one
(main) stator winding, as the flux produced is a pulsating one, with the winding
being fed from single phase supply. Using double revolving field theory, the
torque-speed characteristics of this type of motor are described, and it is also
shown that, if the motor is initially given some torque in either direction, the
motor accelerates in that direction, and also the torque is produced in that
direction. Then, the various types of single phase induction motors, along with
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the starting methods used in each one are presented. Two stator windings − main
and auxiliary, are needed to produce the starting torque. The merits and demerits
of each type, along with their application area, are presented. The process of
production of starting torque in shade-pole motor is also described in brief. In the
next module consisting of seven lessons, the construction and also operation of
dc machines, both as generator and motor, will be discussed.
STARTING METHODS
The single-phase IM has no starting torque, but has resultant torque, when it
rotates at any other speed, except synchronous speed. It is also known that, in a
balanced two-phase IM having two windings, each having equal number of turns
and placed at a space angle of 900(electrical), and are fed from a balanced two-
phase supply, with two voltages equal in magnitude, at an angle of 900, the
rotating magnetic fields are produced, as in a three-phase IM. The torque-speed
characteristic is same as that of a three-phase one, having both starting and also
running torque as shown earlier. So, in a single-phase IM, if an auxiliary winding
is introduced in the stator, in addition to the main winding, but placed at a space
angle of 900 (electrical), starting torque is produced. The currents in the two
(main and auxiliary) stator windings also must be at an angle of 900 , to produce
maximum starting torque, as shown in a balanced two-phase stator. Thus, rotating
magnetic field is produced in such motor, giving rise to starting torque. The
various starting methods used in a single-phase IM are described here.
1. RESISTANCE SPLIT-PHASE MOTOR
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The schematic (circuit) diagram of this motor is given in Fig. As detailed earlier,
another (auxiliary) winding with a high resistance in series is to be added along
with the main winding in the stator. This winding has higher resistance to
reactance () ratio as compared to that in the main winding, and is placed at a space
angle of from the main winding as given earlier. The phasor diagram of the
currents in two windings and the input voltage is shown in Fig.The current () in
the auxiliary winding lags the voltage (V) by an angle, aaXR/°90aIaφ, which is
small, whereas the current () in the main winding lags the voltage (V) by an
angle, mImφ, which is nearly . The phase angle between the two currents is
(°90aφ−°90), which should be at least . This results in a small amount of starting
torque. The switch, S (centrifugal switch) is in series with the auxiliary winding.
It automatically cuts out the auxiliary or starting winding, when the motor attains
a speed close to full load speed. The motor has a starting torque of 100−200% of
full load torque, with the starting current as 5-7 times the full load current. The
torque-speed characteristics of the motor with/without auxiliary winding are
shown in Fig.The change over occurs, when the auxiliary winding is switched off
as given earlier. The direction of rotation is reversed by reversing the terminals
of any one of two windings, but not both, before connecting the motor to the
supply terminals. This motor is used in applications, such as fan, saw, small lathe,
centrifugal pump, blower, office equipment, washing machine, etc.
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2. CAPACITOR-START MOTOR
The schematic (circuit) diagram of this motor is given in Fig. It may be

observed that a capacitor along with a centrifugal switch is connected in series
with the auxiliary winding, which is being used here as a starting winding. The
capacitor may be rated only for intermittent duty, the cost of which decreases, as
it is used only at the time of starting. The function of the centrifugal switch has
been described earlier. The phasor diagram of two currents as described earlier,
and the torque-speed characteristics of the motor with/without auxiliary winding,
are shown in Fig. This motor is used in applications, such as compressor,
conveyor, machine tool drive, refrigeration and air-conditioning equipment, etc.
3. Capacitor-start and Capacitor-run Motor

In this motor two capacitors − Csfor starting, and Cr for running, are used. The
first capacitor is rated for intermittent duty, as described earlier, being used only
for starting. A centrifugal switch is also needed here. The second one is to be
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rated for continuous duty, as it is used for running. The phasor diagram of two
currents in both cases, and the torque-speed characteristics with two windings
having different values of capacitors, are shown in respectively. The phase
difference between the two currents is (φm+φa>900) in the first case (starting),
while it is900 for second case (running). In the second case, the motor is a
balanced two phase one, the two windings having same number of turns and other
conditions as given earlier, are also satisfied. So, only the forward rotating field
is present, and the no backward rotating field exists. The efficiency of the motor
under this condition is higher. Hence, using two capacitors, the performance of
the motor improves both at the time of starting and then running. This motor is
used in applications, such as compressor, refrigerator, etc.
Beside the above two types of motors, a Permanent Capacitor Motor with
the same capacitor being utilised for both starting and running, is also used. The
power factor of this motor, when it is operating (running), is high. The operation
is also quiet and smooth. This motor is used in applications, such as ceiling fans,
air circulator, blower, etc.
4. Shaded-pole Motor
A typical shaded-pole motor with a cage rotor is shown in Fig. 34.8a. This
is a single-phase induction motor, with main winding in the stator. A small
portion of each pole is covered with a short-circuited, single-turn copper coil
called the shading coil. The sinusoidally varying flux created by ac (single-phase)
excitation of the main winding induces emf in the shading coil. As a result,
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induced currents flow in the shading coil producing their own flux in the shaded
portion of the pole.
Let the main winding flux be φm=φmaxsinwt
The reversal of the direction of rotation, where desired, can be achieved by

providing two shading coils, one on each end of every pole, and by open-
circuiting one set of shading coils and by short-circuiting the other set.
The fact that the shaded-pole motor is single-winding (no auxiliary

winding) self-starting one, makes it less costly and results in rugged construction.
The motor has low efficiency and is usually available in a range of 1/300 to 1/20
kW. It is used for domestic fans, record players and tape recorders, humidifiers,
slide projectors, small business machines, etc. The shaded-pole principle is used
in starting electric clocks and other single-phase synchronous timing motors.
no starting torque is produced in the single-phase induction motor with only one
(main) stator winding, as the flux produced is a pulsating one, with the winding
being fed from single phase supply. Using double revolving field theory, the
torque-speed characteristics of this type of motor are described, and it is also
shown that, if the motor is initially given some torque in either direction, the
motor accelerates in that direction, and also the torque is produced in that
direction. Then, the various types of single phase induction motors, along with
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the starting methods used in each one are presented. Two stator windings − main
and auxiliary, are needed to produce the starting torque. The merits and demerits
of each type, along with their application area, are presented. The process of
production of starting torque in shade-pole motor is also described in brief. In the
next module consisting of seven lessons, the construction and also operation of
dc machines, both as generator and motor, will be discussed.
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UNIT III SEMICONDUCTOR DEVICES AND APPLICATIONS

SEMICONDUCTOR DEVICES AND APPLICATIONS
Prerequisites
The semiconductor device i.e., solid state device is capable of amplifying

the weak signal. The devices are solid rather than hollow like the vaccum tube.
These semiconductor devices are smaller in size, more rugged and less power
consumption than vaccum tubes. The various semiconductor devices include
semiconductor diode, Zener diode, transistor, JFET, MOSFET, UJT, SCR, DIAC
and TRIAC etc. The semiconductor devices have very wide range of applications
in various fields such as communication systems, medical electronics,
microprocessor based systems, instrumentation, process control, aerospace,
consumer electronics, etc.
INTRODUCTION
Basic Definitions
Valence electrons
The electrons present in the outer most orbit that are loosely bound to the
nucleus are called valence electrons.
Conduction electrons
When an electric field is applied, the valence electrons get detached

themselves from the nucleus, constituting the flow of current. These electrons are
called conduction electrons.
Energy band
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The (range of) energy possessed by the electrons in an atom is called

energy band.
Conduction band
The (range of) energy possessed by the conduction electrons is called

conduction band.
Valence electrons
The (range of) energy possessed by the valence electrons is called valence
band.
Forbidden energy gap
The gap between the valence band and the conduction band is called
forbidden energy gap.
CLASSIFICATION OF MATERIALS
The materials are classified based on their conducting property. Energy

band theory can be used to explain the classification of materials.
1 Conductors
Conductor is materials that easily conducts or pass the current. There are
plenty of free electrons available for electric conduction. In terms of energy band
theory, the conductors have overlapping of valence band and conductive band.
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Example: Copper, Aluminum, iron, etc
Properties: 1. It is rigid, non directional and crystalline in nature.
2. Conductivity is good.
3. Low melting and boiling temperatures.
2 Semiconductors
Semiconductor is a material with partially filled conduction band and

valence band. The current in the semiconductor is due to the movement of
electrons and holes. As the temperature increases the conduction increases.
Example: Silicon, Germanium, etc.
Properties: 1. It is rigid, directional and crystalline in nature.
2. Conductivity can be increased if proper doping material is

added.
3. Low melting and boiling temperatures.
2 Insulators
In the case of insulators, the valence electrons are very tightly bound to their
parent atom. The valence band and conduction band are separated by a large
forbidden energy gap. The insulators have full valence band and an empty
conduction band.
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Example: Paper, Mica. Sodium chloride, etc.
Properties: 1. It is rigid, Unidirectional and crystalline in nature.
2. Conductivity is poor in the solid form.
3. High melting and boiling temperatures.
Energy band structure
Comparison of Conductors,Semiconductors and Insulators
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Classification of Semiconductor
Intrinsic Semiconductor
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An intrinsic semiconductor also called an undoped semiconductor or i- type

semiconductor.
It is a pure semiconductor without any significant dopant species present.
The number of charge carriers determined by the properties of the m aterial itself
instead of the amount of impurities.
In intrinsic semiconductors the number of excited electrons and the number of

holes are equal: n = p.
Conductivity of Intrinsic semiconductor

 The electrical conductivity of intrinsic semiconductors can be due to crystal
defects or to thermal excitation.
 Both electrons and holes contribute to current flow in an intrinsic
semiconductor.
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 The current which will flow in an intrinsic semiconductor consists of both

electron and hole current.
 That is, the electrons which have been freed from their lattice positions into
the conduction band can move through the material.
 In addition, other electrons can hop between lattice positions to fill the
vacancies left by the freed electrons.
 This additional mechanism is called hole conduction because it is as if
the holes are migrating across the material in the direction opposite to the free
electron movement.
 The current flow in an intrinsic semiconductor is influenced by the density of
energy states which in turn influences the electron density in the conduction band.
 This current is highly temperature dependent.
Thermal excitation:
 In an intrinsic semiconductor like silicon at temperatures above absolute

zero, there will be some electrons which are excited across the band gap into the
conduction band and which can produce current.
 When the electron in pure silicon crosses the gap, it leaves behind an
electron vacancy or "hole" in the regular silicon lattice.
 Under the influence of an external voltage, both the electron and the hole
can move across the material.
 In n-type semiconductor:
The dopant contributes extra electrons, dramatically increasing the conductivity
 In p-type semiconductor:
The dopant produces extra vacancies or holes, which likewise increase the
conductivity.
Extrinsic Semiconductor
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 The electrical conductivity of a pure semiconductor is very small.

 To increase the conductivity, impurities are added.
 The impurity added semiconductor is called extrinsic semiconductor.
 The process of adding impurity is called doping.
 The added impurity is called dopant.
 Usually one or two atoms of impurity is added per 106 atoms of a
semiconductor.
 There are two types (i) p-type and (ii) n-type semiconductors.
 When an impurity, from V group elements like arsenic (As), antimony having
5 valence electrons is added to Ge (or Si), the impurity atom donates one electron
to Ge (or Si).
 The 4 electrons of the impurity atom is engaged in covalent bonding with
Si atom.
 The fifth electron is free. This increases the conductivity.
 The impurities are called donors.
 The impurity added semiconductor is called n-type semiconductor, because
their increased conductivity is due to the presence of the negatively charged
electrons, which are called the majority carriers.
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 The energy band of the electrons donated by the impurity atoms is just
below the conduction band.
 The electrons absorb thermal energy and occupy the conduction band.
 Due to the breaking of covalent bond, there will be a few holes in the valence
band at this temperature.
 These holes in n-type are called minority carriers.
 If a III group element, like indium (In), boron (B), aluminium (AI) etc., having
three valence electrons, is added to a semiconductor say Si, the three electrons
form covalent bond.
 There is a deficiency of one electron to complete the 4th covalent bond and is
called a hole.The presence of the hole increases the conductivity because these
holes move to the nearby atom, at the same time the electrons move in the
opposite direction.
 The impurities added semiconductor is called p-type semiconductor.
 The impurities are called acceptors as they accept electrons from the
semiconductor
 Holes are the majority carriers and the electrons produced by the breaking of
bonds are the minority carriers.
PN JUNCTION DIODE
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
A p–n junction is formed by joining P-type and N-type semiconductors
together in very close contact.

The term junction refers to the boundary interface where the two regions of
the semiconductor meet.

Diode is a two-terminal electronic component that conducts electric current
in only one direction.

The crystal conducts conventional current in a direction from the p-type side
(called the anode) to the n-type side (called the cathode), but not in the
opposite direction.
Symbol of PN junction diode
1Biasing
“Biasing” is providing minimum external voltage and current to activate

the device to study its characteristics.
There are two operating regions and two "biasing" conditions for the standard
Junction Diode and they are:

Zero Bias:
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When a diode is Zero Biased no external energy source is applied and a

natural Potential Barrier is developed across a depletion layer.
(i) Forward Bias:

When the positive terminal of a battery is connected to P-type
semiconductor and negative terminal to N-type is known asforward
bias of PN junction.



The applied forward potential establishes an electric field opposite to the
potential barrier. Therefore the potential barrier is reduced at the junction.
As the potential barrier is very small (0.3V for Ge and 0.7V for Si),a small
forward voltage is sufficient to completely eliminate the barrier potential,
thus the junction resistance becomes zero.
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


In otherwords, the applied positive potential repels the holes in the ‘P’
region so that the holes moves towards the junction and applied negative
potential repels the electrons in the ‘N’ region towards the junction results
in depletion region starts decreasing. When the applied potential is more
than the internal barrier potential then the depletion region completely
disappear, thus the junction resistance becomes zero.



Once the potential barrier is eliminated by a forward voltage, j unction
establishes the low resistance path for the entire circuit, thus a current flows
in the circuit, it is called as forward current.
(ii) Reverse Bias:

For reverse bias, the negative terminal is connected to P-type semiconductor
and positive terminal to N type semiconductor.



When reverse bias voltage is applied to the junction, all the majority carriers
of ‘P’ region are attracted towards the negative terminal of the battery and
the majority carriers of the N region attracted towards the positive terminal
of the battery, hence the depletion region increases.



The applied reverse voltage establishes an electric field which acts in the
same direction of the potential barrier. Therefore, the resultant field at the
junction is strengthened and the barrier width is increased. This increased
potential barrier prevents the flow of charge carriers across the junction,
results in a high resistance path.

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
This process cannot continue indefinitely because after certain extent the
junction break down occurs. As a result a small amount of current flows
through it due to minority carriers. This current is known as “reverse
saturation current”.


V-I characteristics of PN junction diode
Forward Bias:

The application of a forward biasing voltage on the junction diode results
in the depletion layer becoming very thin and narrow which represents a
low impedance path through the junction thereby allowing high currents
to flow.



The point at which this sudden increase in current takes place is represented
on the static I-V characteristics curve above as the "knee" point.
Reverse Bias:

In Reverse biasing voltage a high resistance value to the PN junction and
practically zero current flows through the junction diode with an increase
in bias voltage.



However, a very small leakage current does flow through the junction which
can be measured in microamperes, (μA).



One final point, if the reverse bias voltage Vr applied to the diode is
increased to a
sufficiently high enough value, it will cause the PN junction to overheat

and fail due to
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the avalanche effect around the junction.

This may cause the diode to become shorted and will result in the flow of
maximum circuit current, and this shown as a step downward slope in the
reverse static characteristics curve below.
ZENER EFFECT

In a general purpose PN diode the doping is light; as a result of this the
breakdown voltage is high. If a P and N region are heavily doped then the
breakdown voltage can be reduced.



When the doping is heavy, even the reverse voltage is low, the electric field
at barrier will be so strong thus the electrons in the covalent bonds can
break away from the bonds. This effect is known as Zener effect.


ZENER DIODE
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
A diode which exhibits the zener effect is called a Zener Diode. Hence it is
defined as a reverse biased heavily doped PN junction diode which
operates in breakdown region. The zener diodes have been designed to
operate at voltages ranging from a few volts to several hundred volts.



Zener Breakdown occurs in junctions which is heavily doped and have
narrow depletion layers. The breakdown voltage sets up a very strong
electric field. This field is so strong enough to break or rupture the covalent
bonds thereby generating electron hole pairs.

Even a small reverse voltage is capable of producing large number of current
carrier. When a zener diode is operated in the breakdown region care must
be taken to see that the power dissipation across the junction is within the
power rating of the diode otherwise heavy current flowing through the
diode may destroy it.
V-I characteristics of Zener diode
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
The illustration above shows this phenomenon in a current vs voltage graph
with a zener diode connected in the forward direction .It behaves exactly
as a standard diode.



In the reverse direction however there is a very small leakage curre
nt between 0v
and the zener voltage –i.e. just a tiny amount of current is able to flow.

Then, when the voltage reaches the breakdown voltage (vz),suddenly
current can flow freely through it.


Application of Zener diode
a) as voltage regulator
b) as peak clippers
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c) for reshaping waveforms

RECTIFIERS
The “rectifier” is a circuit that converts AC voltages and currents into

pulsating DC voltages and currents. It consists of DC components and the
unwanted ac ripple or harmonic components which can be removed by using filter
circuit. Thus the output obtained will be steady DC voltage and magnitude of DC
voltage can be varied by varying the magnitude of AC voltage.
Filters: A circuit that removes ripples (unwanted ac components) present

in the pulsating dc voltage.
Regulator: A circuit that maintains the terminal voltage as constant even

if the input voltage or load current varying.
Types of rectifiers:
Rectifiers are grouped into two categories depending on the period of

conduction.
(a) Half wave rectifier (b) Full wave rectifier
Half wave Rectifier:
Principle
It is a circuit that converts alternating voltage or current into pulsating

voltage or current for half the period of input cycle hence it is named as “half
wave rectifier”.
Construction
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
It consists of step-down transformer, semiconductor diode and the load
resistance.



The step-down transformer – reduce the available ac voltage into required
level of smaller ac voltage.



The diode can be used to convert the ac into pulsating dc.
Operation

During the positive half cycle of input, the diode D is forward biased, it
offers very small resistance and it acts as closed switch and hence conducts
the current through the load resistor.



During the negative half cycle of the input diode D is heavily reverse biased,
it offers very high resistance and it acts as open switch hence it does not
conduct any current. The rectified output voltage will be in phase with AC
input voltage for completely resistive load.
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Full wave Rectifier:
Principle
A circuit that converts the ac voltage or current into pulsating voltage or

current during both half cycle of input is known as “full wave rectifier”.
Operation
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
During positive half cycle of ac input, diode D1 becomes forward
biased, provides very small resistance and acts as closed switch,
resulting in the flow of current.

During negative half cycle, diode D1 reverse biased, offers high
resistance and it acts as open circuit.
Voltage Regulation:
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Ratio of Difference of secondary voltage to Primary voltage

to secondary voltage.
BIPOLAR JUNCTION TRANSISTOR

A bipolar junction transistor is a three terminal semiconductor device in
which the operation depends on the interaction of majority and minority
carriers.



Transistor refers to Transfer Resistor i.e., signals are transferred from low
resistance circuit into high resistance circuit.



BJT consists of silicon crystal in which a layer of ‘N’ type silicon is
sandwiched between two layers of ‘P’ type silicon. The semiconductor
sandwiched is extremely smaller in size.



In other words, it consists of two back to back PN junction joined together
to form single piece of semiconductor crystal. These two junctions gives
three region called Emitter, Base and Collector.



There are two types of transistors such as PNP and NPN. The arrow on the
emitter specifies whether the transistor is PNP or NPN type and also
determines the direction of flow of current, when the emitter base junction
is forward biased.
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Emitter: It is more heavily doped than any of the other region because its main
function is to supply majority charge carriers to the base.
Base: It forms the middle section of the transistor. It is very thin as compared to
either the emitter or collector and is very lightly doped.
Collector: Its main function is to collect the majority charge carriers coming from
the emitter and passing through the base. In most transistors, collector region is
made physically larger than the emitter because it has to dissipate much greater
power.
Operation of Transistor
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
The basic operation will be described using the pnp transistor. The operation
of the pnp transistor is exactly the same if the roles played by the electron
and hole are interchanged.



One p-n junction of a transistor is reverse-biased, whereas the other is
forward-biased.



Both biasing potentials have been applied to a pnp transistor and resulting
majority and minority carrier flows indicated.
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
Majority carriers (+) will diffuse across the forward-biased p-n junction into
the n-type material.



A very small number of carriers (+) will through n-type material to the base
terminal. Resulting IB is typically in order of microamperes.



The large number of majority carriers will diffuse across the reverse-biased
junction into the p-type material connected to the collector terminal.



Majority carriers can cross the reverse-biased junction because the injected
majority carriers will appear as minority carriers in the n-type material.

Applying KCL to the transistor :
IE = IC + IB

The comprises of two components – the majority and minority carriers
IC = ICmajority + ICOminority

ICO – IC current with emitter terminal open and is called leakage current.
Common Base configuration


Common-base terminology is derived from the fact that the :


- base is common to both input and output of the configuration.
- base is usually the terminal closest to or at ground potential.

All current directions will refer to conventional (hole) flow and the arrows
in all electronic symbols have a direction defined by this convention.

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
Note that the applied biasing (voltage sources) are such as to establish
current in the direction indicated for each branch.

To describe the behavior of common-base amplifiers requires two set of
characteristics: o Input or driving point characteristics.


o Output or collector characteristics

The output characteristics has 3 basic regions:
o Active region –defined by the biasing arrangements
o Cutoff region – region where the collector current is 0A

o Saturation region- region of the characteristics to the left of V CB = 0V
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
The curves (output characteristics) clearly indicate that a first approximation
to the relationship between IE and IC in the active region is given by
IC ≈IE

Once a transistor is in the ‘on’ state, the base-emitter voltage will be
assumed to be
VBE = 0.7V

In the dc mode the level of IC and IE due to the majority carriers are related
by a quantity called alpha
α = IC / IE
IC = α IE + ICBO

It can then be summarize to IC = αIE (ignore ICBO due to small value)

For ac situations where the point of operation moves on the characteristics
curve, an ac alpha defined by
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
Alpha a common base current gain factor that shows the efficiency by
calculating the current percent from current flow from emitter to collector.
The value of is typical from
0.9 ~ 0.998.
Common Emitter configuration

It is called common-emitter configuration since :
o emitter is common or reference to both input and output terminals.
o emitter is usually the terminal closest to or at ground potential.

Almost amplifier design is using connection of CE due to the high gain for
current and voltage.



Two set of characteristics are necessary to describe the behavior for CE;
input (base terminal) and output (collector terminal) parameters.
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Input characteristics for CE configuration

IB in microamperes compared to milliamperes of IC.



IB will flow when VBE > 0.7V for silicon and 0.3V for germanium



Before this value IB is very small and no IB.



Base-emitter junction is forward bias

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
Increasing VCE will reduce IB for different values.
Output characteristics for CE configuration


For small VCE (VCE < VCESAT, IC increase linearly with increasing of VCE



VCE > VCESAT IC not totally depends on VCE -- > constant IC



IB(uA) is very small compare to IC (mA). Small increase in IB cause big
increase in IC



IB=0 A -- > ICEO occur.



Noticing the value when IC=0A. There is still some value of current flows.
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Common Collector configuration


Also called emitter-follower (EF).



It is called common-emitter configuration since both the
o signal source and the load share the collector terminal as a common
connection point.

The output voltage is obtained at emitter terminal.

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
The input characteristic of common-collector configuration is similar with
common-emitter. configuration.



Common-collector circuit configuration is provided with the load resistor
connected from emitter to ground.

It is used primarily for impedance-matching purpose since it has high input
impedance and low output impedance.

For the common-collector configuration, the output characteristics
are a plot of IE vs VCE for a range of values of IB.
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Small Signal Amplifier
When the input signal is so weak as to produce small fluctuations in the

collector current compared to its quiescent value, the amplifier is known as Small
Signal Amplifier.
In other words, as the name indicates, the input applied to the circuit is V in <<
Vth. It has only one amplifying device.
Α = IC / IE
IC = α IE + ICBO
Voltage and current equation for hybrid parameters:
V1 = h11i1 + h12V2
I2 = h21i1 + h22V2
The values of h-parameters:
h11 = V1/ i1
h12 = V1 / V2
h21 = i2 / i1
h22 = i2 / V2
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UNIT IV DIGITAL ELECTRONICS

BINARY NUMBER SYSTEM
Introduction
The number system that you are familiar with, that you use every day,
is the decimal number system, also commonly referred to as the base-10
system. When you perform computations such as 3 + 2 = 5, or 21 – 7 = 14,
you are using the decimal number system. This system, which you likely
learned in first or second grade, is ingrained into your subconscious; it’s the
natural way that you think about numbers. Evidence exists that Egyptians were
using a decimal number system five thousand years ago. The Roman numeral
system, predominant for hundreds of years, was also a decimal number system
(though organized differently from the Arabic base-10 number system that we
are most familiar with). Indeed, base-10 systems, in one form or another, have
been the most widely used number systems ever since civilization started
counting.
In dealing with the inner workings of a computer, though, you are going
to have to learn to think in a different number system, the binary number
system, also referred to as the base-2 system.
Consider a child counting a pile of pennies. He would begin: “One, two,

three, …, eight, nine.” Upon reaching nine, the next penny counted makes the
total one single group of ten pennies. He then keeps counting: “One group of
ten pennies… two groups of ten pennies… three groups of ten pennies … eight
groups of ten pennies … nine groups of ten pennies…” Upon reaching nine
groups of ten pennies plus nine additional pennies, the next penny counted
makes the total thus far: one single group of one hundred pennies. Upon
completing the task, the child might find that he has three groups of one
hundred pennies, five groups of ten pennies, and two pennies left over: 352
pennies.
More formally, the base-10 system is a positional system, where the

rightmost digit is the ones position (the number of ones), the next digit to the
left is the tens position (the number of groups of 10), the next digit to the left
is the hundreds position (the number of groups of 100), and so forth. The base-
10 number system has 10 distinct symbols, or digits (0, 1, 2, 3,…8, 9). In
decimal notation, we write a number as a string of symbols, where each
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symbol is one of these ten digits, and to interpret a decimal number, we

multiply each digit by the power of 10 associated with that digit’s position.
For example, consider the decimal number: 6349. This number is:
Consider: Computers are built from transistors, and an individual transistor

can only be ON or OFF (two options). Similarly, data storage devices can be
optical or magnetic. Optical storage devices store data in a specific location by
controlling whether light is reflected off that location or is not reflected off that
location (two options). Likewise, magnetic storage devices store data in a specific
location by magnetizing the particles in that location with a specific orientation.
We can have the north magnetic pole pointing in one direction, or the opposite
direction (two options).
Computers can most readily use two symbols, and therefore a base-2
system, or binary number system, is most appropriate. The base-10 number
system has 10 distinct symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The base-2 system
has exactly two symbols: 0 and 1. The base-10 symbols are termed digits. The
base-2 symbols are termed binary digits, or bits for short. All base-10 numbers
are built as strings of digits (such as 6349). All binary numbers are built as strings
of bits (such as 1101). Just as we would say that the decimal number 12890 has
five digits, we would say that the binary number 11001 is a five-bit number.
2 The Binary Number System

Consider again the example of a child counting a pile of pennies, but this
time in binary.
He would begin with the first penny: “1.” The next penny counted makes the total
one single group of two pennies. What number is this?
When the base-10 child reached nine (the highest symbol in his scheme),
the next penny gave him “one group of ten”, denoted as 10, where the “1”
indicated one collection of ten.
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Similarly, when the base-2 child reaches one (the highest symbol in his scheme),
the next penny gives him “one group of two”, denoted as 10, where the “1”
indicates one collection of two.
Back to the base-2 child: The next penny makes one group of two pennies
and one additional penny: “11.” The next penny added makes two groups of two,
which is one group of 4: “100.” The “1” here indicates a collection of two groups
of two, just as the “1” in the base-10 number 100 indicates ten groups of ten.
Upon completing the counting task, base -2 child might find that he has
one group of four pennies, no groups of two pennies, and one penny left over:
101 pennies. The child counting the same pile of pennies in base-10 would
conclude that there were 5 pennies. So, 5 in base-10 is equivalent to101 in base-
2. To avoid confusion when the base in use if not clear from the context, or when
using multiple bases in a single expression, we append a subscript to the number
to indicate the base, and write:
510 =1012
Just as with decimal notation, we write a binary number as a string of
symbols, but now each symbol is a 0 or a 1. To interpret a binary number, we
multiply each digit by the power of 2 associated with that digit’s position.
For example, consider the binary number 1101. This number is:
Since binary numbers can only contain the two symbols 0 and 1, numbers
such as 25 and 1114000 cannot be binary numbers.
We say that all data in a computer is stored in binary—that is, as 1’s and
0’s. It is important to keep in mind that values of 0 and 1 are logical values, not
the values of a physical quantity, such as a voltage. The actual physical binary
values used to store data internally within a computer might be, for instance, 5
volts and 0 volts, or perhaps 3.3 volts and 0.3 volts or perhaps reflection and no
reflection. The two values that are used to physically store data can differ within
different portions of the same computer. All that really matters is that there are
two different symbols, so we will always refer to them as 0 and 1.
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A string of eight bits (such as 11000110) is termed a byte. A collection of

four bits (such as 1011) is smaller than a byte, and is hence termed a nibble. (This
is the sort of nerd-humor for which engineers are famous.)
The idea of describing numbers using a positional system, as we have illustrated

for base-10 and base-2, can be extended to any base. For example, the base-4
number 231 is:
3 Converting Between Binary Numbers and Decimal

Numbers
We humans about numbers using the decimal number system, whereas computers
use the binary number system. We need to be able to readily shift between the
binary and decimal number representations.
Converting a Binary Number to a Decimal Number
To convert a binary number to a decimal number, we simply write the binary

number as a sum of powers of 2. For example, to convert the binary
number 1011 to a decimal number, we note that the rightmost position is the
ones position and the bit value in this position is a 1. So, this rightmost bit has
the decimal value of 1⋅20 . The next position to the left is the twos position, and
the bit value in this position is also a 1. So, this next bit has the decimal value of
1⋅ 21 . The next position to the left is the fours position, and the bit value in this
position is a 0. The leftmost position is the eights position, and the bit value in
this position is a 1. So, this leftmost bit has the decimal value of 1⋅23 . Thus:
1. The binary number 110110 as a decimal number. Solution:

For example, to convert the binary number 10101 to decimal, we annotate
the position values below the bit values:
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Then we add the position values for those positions that have a bit value of
1: 16 + 4 + 1 = 21. Thus
101012 = 2110
You should “memorize” the binary representations of the decimal digits 0 through
15 shown below.
You may be wondering about the leading zeros in the table above. For
example, the decimal number 5 is represented in the table as the binary number
0101. We could have represented the binary equivalent of 5 as 101, 00101,
0000000101, or with any other number of leading zeros. All answers are correct.
Sometimes, though, you will be given the size of a storage location. When you
are given the size of the storage location, include the leading zeros to show all
bits in the storage location. For example, if told to represent decimal 5 as an 8-bit
binary number, your answer should be 00000101.
Converting a Decimal Number to a Binary Number: Method 2
The second method of converting a decimal number to a binary number

entails repeatedly dividing the decimal number by 2, keeping track of the
remainder at each step. To convert the decimal number x to binary:
Step 1. Divide x by 2 to obtain a quotient and remainder. The remainder will

be 0 or 1.
Step 2. If the quotient is zero, you are finished: Proceed to Step 3. Otherwise,
go back to Step 1, assigning x to be the value of the most-recent
quotient from Step 1.
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Step 3. The sequence of remainders forms the binary representation of the

number.
4 Hexadecimal Numbers
In addition to binary, another number base that is commonly used in digital
systems is base 16. This number system is called hexadecimal, and each digit
position represents a power of 16. For any number base greater than ten, a
problem occurs because there are more than ten symbols needed to represent the
numerals for that number base. It is customary in these cases to use the ten
decimal numerals followed by the letters of the alphabet beginning with A to
provide the needed numerals. Since the hexadecimal system is base 16, there are
sixteen numerals required. The following are the hexadecimal numerals:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
The following are some examples of hexadecimal numbers:
1016 4716 3FA16 A03F16
The reason for the common use of hexadecimal numbers is the relationship
between the numbers 2 and 16. Sixteen is a power of 2 (16 = 2 4). Because of this
relationship, four digits in a binary number can be represented with a single
hexadecimal digit. This makes conversion between binary and hexadecimal
numbers very easy, and hexadecimal can be used to write large binary numbers
with much fewer digits. When working with large digital systems, such as
computers, it is common to find binary numbers with 8, 16 and even 32 digits.
Writing a 16 or 32 bit binary number would be quite tedious and error prone. By
using hexadecimal, the numbers can be written with fewer digits and much less
likelihood of error.
To convert a binary number to hexadecimal, divide it into groups of four digits

starting with the rightmost digit. If the number of digits isn’t a multiple of 4,
prefix the number with 0’s so that each group contains 4 digits. For each four
digit group, convert the 4 bit binary number into an equivalent hexadecimal digit.
(See the Binary, BCD, and Hexadecimal Number Tables at the end of this
document for the correspondence between 4 bit binary patterns and hexadecimal
digits)
2. Convert the binary number 10110101 to a hexadecimal number
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To convert a hexadecimal number to a binary number, convert each

hexadecimal digit into a group of 4 binary digits.
4. Convert the hex number 374F into binary
There are several ways in common use to specify that a given number is in
hexadecimal representation rather than some other radix. In cases where the
context makes it absolutely clear that numbers are represented in hexadecimal,
no indicator is used. In much written material where the context doesn’t make it
clear what the radix is, the numeric subscript 16 following the hexadecimal
number is used. In most programming languages, this method isn’t really feasible,
so there are several conventions used depending on the language. In the C and
C++ languages, hexadecimal constants are represented with a ‘0x’ preceding the
number, as in: 0x317F, or 0x1234, or 0xAF. In assembler programming
languages that follow the Intel style, a hexadecimal constant begins with a
numeric character (so that the assembler can distinguish it from a variable name),
a leading ‘0’ being used if necessary. The letter ‘h’ is then suffixed onto the
number to inform the assembler that it is a hexadecimal constant. In Intel style
assembler format: 371Fh and
0FABCh are valid hexadecimal constants. Note that: A37h isn’t a valid
hexadecimal constant. It doesn’t begin with a numeric character, and so will be
taken by the assembler as a variable name. In assembler programming languages
that follow the Motorola style, hexadecimal constants begin with a ‘$’ character.
So in this case: $371F or $FABC or $01 are valid hexadecimal constants.
5 Binary Coded Decimal Numbers
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Another number system that is encountered occasionally is Binary Coded

Decimal. In this system, numbers are represented in a decimal form, however
each decimal digit is encoded using a four bit binary number.
The decimal number 136 would be represented in BCD as follows: 136 = 0001
0011 0110
1 3 6
Conversion of numbers between decimal and BCD is quite simple. To

convert from decimal to BCD, simply write down the four bit binary pattern for
each decimal digit. To convert from BCD to decimal, divide the number into
groups of 4 bits and write down the corresponding decimal digit for each 4 bit
group.
There are a couple of variations on the BCD representation, namely packed

and unpacked. An unpacked BCD number has only a single decimal digit stored
in each data byte. In this case, the decimal digit will be in the low four bits and
the upper 4 bits of the byte will be 0. In the packed BCD representation, two
decimal digits are placed in each byte. Generally, the high order bits of the data
byte contain the more significant decimal digit.
6. The following is a 16 bit number encoded in packed BCD format:
01010110 10010011
This is converted to a decimal number as follows: 0101 0110 1001 0011
5 6 9 3 The value is 5693 decimal
7. The same number in unpacked BCD (requires 32 bits)
00000101 00000110 00001001 00000011
5 6 9 3
The use of BCD to represent numbers isn’t as common as binary in most

computer systems, as it is not as space efficient. In packed BCD, only 10 of the
16 possible bit patterns in each 4 bit unit are used. In unpacked BCD, only 10 of
the 256 possible bit patterns in each byte are used. A 16 bit quantity can represent
the range 0-65535 in binary, 0-9999 in packed BCD and only 0-99 in unpacked
BCD.
Fixed Precision and Overflow
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we haven’t considered the maximum size of the number. We have assumed

that as many bits are available as needed to represent the number. In most
computer systems, this isn’t the case. Numbers in computers are typically
represented using a fixed number of bits. These sizes are typically 8 bits, 16 bits,
32 bits, 64 bits and 80 bits. These sizes are generally a multiple of 8, as most
computer memories are organized on an 8 bit byte basis. Numbers in which a
specific number of bits are used to represent the value are called fixed precision
numbers. When a specific number of bits are used to represent a number, that
determines the range of possible values that can be represented. For example,
there are 256 possible combinations of 8 bits, therefore an 8 bit number can
represent 256 distinct numeric values and the range is typically considered to be
0-255. Any number larger than 255 can’t be represented using 8 bits. Similarly,
16 bits allows a range of 0-65535.
When fixed precision numbers are used, (as they are in virtually all computer
calculations) the concept of overflow must be considered. An overflow occurs
when the result of a calculation can’t be represented with the number of bits
available. For example when adding the two eight bit quantities: 150 + 170, the
result is 320. This is outside the range 0-255, and so the result can’t be represented
using 8 bits. The result has overflowed the available range. When overflow
occurs, the low order bits of the result will remain valid, but the high order bits
will be lost. This results in a value that is significantly smaller than the correct
result.
When doing fixed precision arithmetic (which all computer arithmetic

involves) it is necessary to be conscious of the possibility of overflow in the
calculations.
Signed and Unsigned Numbers.
we have only considered positive values for binary numbers. When a fixed
precision binary number is used to hold only positive values, it is said to be
unsigned. In this case, the range of positive values that can be represented is 0 --
2n-1, where n is the number of bits used. It is also possible to represent signed
(negative as well as positive) numbers in binary. In this case, part of the total
range of values is used to represent positive values, and the rest of the range is
used to represent negative values.
There are several ways that signed numbers can be represented in binary,
but the most common representation used today is called two’s complement. The
term two’s complement is somewhat ambiguous, in that it is used in two different
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ways. First, as a representation, two’s complement is a way of interpreting and

assigning meaning to a bit pattern contained in a fixed precision binary quantity.
Second, the term two’s complement is also used to refer to an operation that can
be performed on the bits of a binary quantity. As an operation, the two’s
complement of a number is formed by inverting all of the bits and adding 1. In a
binary number being interpreted using the two’s complement representation, the
high order bit of the number indicates the sign. If the sign bit is 0, the number is
positive, and if the sign bit is 1, the number is negative. For positive numbers, the
rest of the bits hold the true magnitude of the number. For negative numbers, the
lower order bits hold the complement (or bitwise inverse) of the magnitude of the
number. It is important to note that two’s complement representation can only be
applied to fixed precision quantities, that is, quantities where there are a set
number of bits.
Two’s complement representation is used because it reduces the

complexity of the hardware in the arithmetic-logic unit of a computer’s CPU.
Using a two’s complement representation, all of the arithmetic operations can be
performed by the same hardware whether the numbers are considered to be
unsigned or signed. The bit operations performed are identical, the difference
comes from the interpretation of the bits. The interpretation of the value will be
different depending on whether the value is considered to be unsigned or signed.
8. Find the 2’s complement of the following 8 bit number
The 2’s complement of 00101001 is 11010111

9. Find the 2’s complement of the following 8 bit number 10110101
The 2’s complement of 10110101 is 01001011
The counting sequence for an eight bit binary value using 2’s complement
representation appears as follows:
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Counting up from 0, when 127 is reached, the next binary pattern in the
sequence corresponds to -128. The values jump from the greatest positive number
to the greatest negative number, but that the sequence is as expected after that.
(i.e. adding 1 to –128 yields –127, and so on.). When the count has progressed to
0FFh (or the largest unsigned magnitude possible) the count wraps around to 0.
(i.e. adding 1 to –1 yields 0).
ASCII Character Encoding
The name ASCII is an acronym for: American Standard Code for Information
Interchange. It is a character encoding standard developed several decades ago to
provide a standard way for digital machines to encode characters. The ASCII
code provides a mechanism for encoding alphabetic characters, numeric digits,
and punctuation marks for use in representing text and numbers written using the
Roman alphabet. As originally designed, it was a seven bit code. The seven bits
allow the representation of 128 unique characters. All of the alphabet, numeric
digits and standard English punctuation marks are encoded. The ASCII standard
was later extended to an eight bit code (which allows 256 unique code patterns)
and various additional symbols were added, including characters with diacritical
marks (such as accents) used in European languages, which don’t appear in
English. There are also numerous non-standard extensions to ASCII giving
different encoding for the upper 128 character codes than the standard. For
example, The character set encoded into the display card for the original IBM PC
had a non-standard encoding for the upper character set. This is a non-standard
extension that is in very wide spread use, and could be considered a standard in
itself.
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Some important things to points about ASCII code:
The numeric digits, 0-9, are encoded in sequence starting at 30h The
upper case alphabetic characters are sequential beginning at 41h The
lower case alphabetic characters are sequential beginning at 61h
The first 32 characters (codes 0-1Fh) and 7Fh are control characters.
They do not have a standard symbol (glyph) associated with them. They
are used for carriage control, and protocol purposes. They include 0Dh
(CR or carriage return), 0Ah (LF or line feed), 0Ch (FF or form feed),
08h (BS or backspace).
Most keyboards generate the control characters by holding down a

control key (CTRL) and simultaneously pressing an alphabetic
character key. The control code will have the same value as the lower
five bits of the alphabetic key pressed. So, for example, the control
character 0Dh is carriage return. It can be generated by pressing CTRL-
M. To get the full 32 control characters a few at the upper end of the
range are generated by pressing CTRL and a punctuation key in
combination. For example, the ESC (escape) character is generated by
pressing CTRL-[ (left square bracket).
Conversions Between Upper and Lower Case ASCII Letters.
ASCII code chart that the uppercase letters start at 41h and that the lower
case letters begin at 61h. In each case, the rest of the letters are consecutive and
in alphabetic order. The difference between 41h and 61h is 20h. Therefore the
conversion between upper and lower case involves either adding or subtracting
20h to the character code. To convert a lower case letter to upper case, subtract
20h, and conversely to convert upper case to lower case, add 20h. It is important
to note that you need to first ensure that you do in fact have an alphabetic
character before performing the addition or subtraction. Ordinarily, a check
should be made that the character is in the range 41h–5Ah for upper case or 61h-
7Ah for lower case.
Conversion Between ASCII and BCD
ASCII code chart that the numeric characters are in the range 30h-39h.
Conversion between an ASCII encoded digit and an unpacked BCD digit can be
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accomplished by adding or subtracting 30h. Subtract 30h from an ASCII digit to

get BCD, or add 30h to a BCD digit to get ASCII. Again, as with upper and lower
case conversion for alphabetic characters, it is necessary to ensure that the
character is in fact a numeric digit before performing the subtraction. The digit
characters are in the range 30h-39h.
Converting Between Binary Numbers and Decimal

Numbers
We humans about numbers using the decimal number system, whereas computers
use the binary number system. We need to be able to readily shift between the
binary and decimal number representations.
Converting a Binary Number to a Decimal Number
To convert a binary number to a decimal number, we simply write the binary

number as a sum of powers of 2. For example, to convert the binary
number 1011 to a decimal number, we note that the rightmost position is the
ones position and the bit value in this position is a 1. So, this rightmost bit has
the decimal value of 1⋅20 . The next position to the left is the twos position, and
the bit value in this position is also a 1. So, this next bit has the decimal value of
1⋅ 21 . The next position to the left is the fours position, and the bit value in this
position is a 0. The leftmost position is the eights position, and the bit value in
this position is a 1. So, this leftmost bit has the decimal value of 1⋅23 . Thus:
1. The binary number 110110 as a decimal number. Solution:

For example, to convert the binary number 10101 to decimal, we annotate
the position values below the bit values:
Then we add the position values for those positions that have a bit value of
1: 16 + 4 + 1 = 21. Thus
101012 = 2110
You should “memorize” the binary representations of the decimal digits 0 through
15 shown below.
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You may be wondering about the leading zeros in the table above. For
example, the decimal number 5 is represented in the table as the binary number
0101. We could have represented the binary equivalent of 5 as 101, 00101,
0000000101, or with any other number of leading zeros. All answers are correct.
Sometimes, though, you will be given the size of a storage location. When you
are given the size of the storage location, include the leading zeros to show all
bits in the storage location. For example, if told to represent decimal 5 as an 8-bit
binary number, your answer should be 00000101.
Converting a Decimal Number to a Binary Number: Method 2
The second method of converting a decimal number to a binary number

entails repeatedly dividing the decimal number by 2, keeping track of the
remainder at each step. To convert the decimal number x to binary:
Step 1. Divide x by 2 to obtain a quotient and remainder. The remainder will

be 0 or 1.
Step 2. If the quotient is zero, you are finished: Proceed to Step 3. Otherwise,
go back to Step 1, assigning x to be the value of the most-recent
quotient from Step 1.
Step 3. The sequence of remainders forms the binary representation of the

number.
LOGIC GATES
All digital systems are made from a few basic digital circuits that we call
logic gates. These circuits perform the basic logic functions that we will describe
in this session. The physical realization of these logic gates has changed over the
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years from mechanical relays to electronic vacuum tubes to transistors to

integrated circuits containing thousands of transistors.
In this appendix you will learn:

Definitions of the basic gates in terms of truth tables and logic equations
DeMorgan's Theorem
How gates defined in terms of positive and negative logic are related To
use multiple-input gates
How to perform a sum of products and a product of sums design from a

truth table specification
1 The Three Basic Logic Gates

Much of a computer’s hardware is comprised of digital logic circuits. Digital
logic circuits are built from just a handful of primitive elements, called logic
gates, combined in various ways.
In a digital logic circuit, only two values may be present. The values may be
−5 and + 5 volts. Or the values may be 0.5 and 3.5 volts. Or the values may be…
you get the picture. To allow consideration of all of these possibilities, we will
say that digital logic circuits allow the presence of two logical values: 0 and 1.
So, signals in a digital logic circuit take on the values of 0 or 1. Logic gates
are devices which compute functions of these binary signals.
The AND Gate
Consider the circuit below which consists of a battery, a light, and two switches
in series:
When will the light turn on? It should be clear that the light will turn on only
if both switch S1 and switch S2 are shut.
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It is quite likely that you encounter the and operation in some shape or form
hundreds of times each day. Consider the simple action of withdrawing funds
from your checking account at an ATM. You will only be able to complete the
transaction if you have a checking account and you have money in it. The ATM
will only permit the transaction if you have your ATM card and you enter your
correct 4-digit PIN. To enter the correct PIN, you have to enter the first digit
correctly and enter the second digit correctly and enter the third digit correctly
and enter the fourth digit correctly.
Returning to the circuit above, we can represent the light's operation using a table:
The switch is a binary device: it can be open or closed. Let’s represent these two
states as 0 and 1. Likewise, the light is a binary device with two states: off and
on, which we will represent as 0 and 1. Rewriting the table above with this
notation, we have:
This table, which displays the output for all possible combinations of the input,
is termed the truth table for the AND operation. In a computer, this and
functionality is implemented with a circuit called an AND gate. The simplest
AND gate has two inputs and one output and is represented pictorially by the
symbol:
where the inputs have been labeled a and b, and the output has been
labeled c. If both inputs are 1 then the output is 1. Otherwise, the output is 0.
We represent the and operation by using either the multiplication symbol

(i.e., “ ∙ “) or by writing the inputs together. Thus, for the AND gate shown above,
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we would write the output c as c = a b or as c = ab. This would be pronounced:

“c = a and b.”
The truth table for the AND gate is shown below. The output c = ab is equal
to 1 if and only if (iff) a is 1 and b is 1. Otherwise, the output is 0.
AND gates can have more than one input (however, an AND gate always has just
a single output). Let’s consider a three-input AND gate:
The OR Gate
Now consider the circuit shown below, that has 2 switches in parallel.
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It is evident that the light will turn on when either switch S 1 is shut
or switch S2 is shut or both are shut.
It is quite likely that you encounter the or operation in some shape or form
hundreds of times each day. Consider the simple action of sitting on your couch
at home at two in the morning studying for your Digital Logic class. Your phone
will ring if you get a call from Alice or from Bob. Your home’s security alarm
will go off if the front door opens or the back door opens. You will drink a cup
of coffee if you are drowsy or you are thirsty.
We can represent the light's operation using a table
Changing the words open and off to 0 and the words shut and on to 1 and the table
becomes:
This is the truth table for the OR operation. This or functionality is implemented
with a circuit called an OR gate. The simplest OR gate has two inputs and one
output and is represented pictorially by the symbol:
If either or both inputs are 1, the output is 1. Otherwise, the output is 0.
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We represent the or operation by using the addition symbol. Thus, for the
OR gate above, we would write the output c as c = a + b. This would be
pronounced: “c = a or b.”
The truth table for the OR gate is shown below. The output is 1 if a is
1 or b is 1; otherwise, the output is 0.
The NOT Gate
The last of our basic logic gates is the NOT gate. The NOT gate always has
one input and one output. If the input is 1, the output is 0. If the input is 0, the
output is 1. This operation— chaging the value of the binary input—is called
complementation, negation or inversion. The mathematical symbol for negation
is an apostrophe. If the input to a NOT gate is P, the output, termed the
complement, is denoted as P’.
The pictorial symbol for a NOT gate is intended to depict an amplifier

followed by a bubble, shown below. Sometimes the NOT operation is represented
by just the bubble, without the amplifier.
The truth table for the NOT gate is shown below:
Three New Gates
Three new gates, NAND, NOR, and Exclusive-OR, can be formed from our three
basic gates: NOT, AND, and OR.
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NAND Gate
The logic symbol for a NAND gate is like an AND gate with a small circle (or
bubble) on the output.we see that the output of a NAND gate is 0 (low) only if
both inputs are 1 (high) . The NAND gate is equivalent to an AND gate followed
by an inverter (NOT-AND).
NOR Gate
The logic symbol for a NOR gate is like an OR gate with a small circle (or bubble)
on the output. From the truth table .we see that the output of a NOR gate is 1
(high) only if both inputs are 0 (low). The NOR gate is equivalent to an OR gate
followed by an inverter (NOT-OR), as shown by the two truth tables.
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Exclusive-OR Gate.
The XOR gate logic symbol is like an OR gate symbol with an extra curved
vertical line on the input. From the truth table .we see that the output Z of an XOR
gate is 1 (true or high) if either input, X or Y, is 1 (true or high), but not both. The
output Z will be zero if both X and Y are the same (either both 1 or both 0).
The equation for the XOR gate is given as Z = X ^ Y. In this book we will use
the symbol ^ as the XOR operator. Sometimes the symbol or the dollar sign $ is
used to denote Exclusive-OR. We will use the symbol ^ because that is the symbol
recognized by the Verilog software used to program a CPLD.
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BOOLEAN ALGEBRA
Boolean algebra is an algebraic structure defined by a set of elements, B, together
with two binary operators, + and., provider that the following postulates are
satisfied.
T1: Commutative Law

(a)A+B = B+A
(b) A B = BA
T2: Associative Law

(a) (A+B) +C = A+ (B+C)
(b) (A B) C = A (B C)
T3: Distributive Law

(a) A (B +C) = A B + AC
(b) A + (B C) = (A +B) (A+C)
T4: Identity Law

(a) A+A =A
(b) A A =A
T5: Negative Law

(a) (A’) =A’
(b) (A’’) = A
T6: Redundant Law

(a) A+AB=A
(b) A (A +B) =A
T7: Null Law

(a)0 + A = A
(b) 1 A = A
(c) 1 + A = 1
(d) 0 A = 0
T8: Double Negation Law

(a) A’ +A=1
(b) A’ A=0
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T9: Absorption Law

(a) A+A’B =A+B
(b) A (A’ + B) =AB
T10: De Morgan's Theorem

(a) (A+B)’ = A’ B’
(b) (AB)’ = A’+B’
Example 1:
Using theorems,
A + A’ B = A l + A’ B
= A (l + B) + A’B
=A + AB + A’B
=A + B (A + A’)
=A+B
Using Truth Table
1 Verification Of De Morgan's Theorems:
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• De Morgan's First Theorem states:
The complement of a product of variables is equal to the sum of the

complements of the individual variables
• De Morgan's Second Theorem states:
The complement of sum of variables is equal to the product of the

complements of the dividable variables
ADDER
1 Half Adder
Half adder is a circuit that will add two bits & produce a sum & a carry bit. It
needs two input bits & two output bits.Fig.4.1 shows the block diagram of a half
adder.
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Ex-OR gate will only produce an output "1" when "EITHER" input is at logic
"1", so we need an additional output to produce a carry output, "1" when "BOTH"
inputs "A" and "B" are at logic "1" and a standard AND Gate fits the bill nicely.
By combining the Ex-OR gate with the AND gate results in a simple digital binary
adder circuit known commonly as the "Half Adder" circuit.
2 Full Adder
A half adder has only two inputs &there is no provision to add a carry coming
from the lower order bits when multi addition is performed. For this purpose, a
full adder is designed.
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The 1-bit Full Adder circuit is basically two half adders connected together and
consists of three Ex-OR gates, two AND gates and an OR gate, six logic gates in
total. The truth table for the full adder includes an additional column to take into
account the Carry-in input as well as the summed output and carry-output.
Figure: Logic diagram of a Full adder using two Half Adders

Table: Truth Table for Full Adder
FLIP FLOP
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1 RS Flip Flop
RS Flip Flop have two inputs, S and R. S is called set and R is called reset. The
S input is used to produce HIGH on Q ( i.e. store binary 1 in flip-flop). The R
input is used to produce LOW on Q (i.e. store binary 0 in flip-flop). Q' is Q
complementary output, so it always holds the opposite value of Q. The output of
the S-R Flip Flop depends on current as well as previous inputs or state, and its
state (value stored) can change as soon as its inputs change. The circuit and the
truth table of RS Flip Flop is shown below.
The operation has to be analyzed with the 4 inputs combinations together with
the 2 possible previous states.
When S = 0 and R = 0: If we assume Q = 1 and Q' = 0 as initial condition,

then output Q after input is applied would be Q = (R + Q')' = 1 and Q' = (S
+ Q)' = 0. Assuming Q = 0 and Q' = 1 as initial condition, then output Q
after the input applied would be Q = (R + Q')' = 0 and Q' = (S + Q)' = 1. So
it is clear that when both S and R inputs are LOW, the output is retained as
before the application of inputs. (i.e. there is no state change).
in simple words when S is HIGH and R is LOW, output Q is HIGH.
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in simple words when S is LOW and R is HIGH, output Q is LOW.
When S = 1 and R =1 : No matter what state Q and Q' are in, application
of 1 at input of NOR gate always results in 0 at output of NOR gate, which
results in both Q and Q' set to LOW (i.e. Q = Q'). LOW in both the outputs
basically is wrong, so this case is invalid.
It is possible to construct the RS Flip Flop using NAND gates (of course as
seen in Logic gates section). The only difference is that NAND is NOR gate dual
form (Did I say that in Logic gates section?). So in this case the R = 0 and S = 0
case becomes the invalid case. The circuit and Truth table of RS Flip Flop using
NAND is shown below.
If you look closely, there is no control signal, so this kind of Flip Flopes
or flip-flops are called asynchronous logic elements. Since all the sequential
circuits are built around the RS Flip Flop, we will concentrate on synchronous
circuits and not on asynchronous circuits.
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2 RS Flip Flop with Clock

We have seen this circuit earlier with two possible input configurations: one with
level sensitive input and one with edge sensitive input. The circuit below shows
the level sensitive RS Flip Flop. Control signal "Enable" E is used to gate the
input S and R to the RS Flip Flop. When Enable E is HIGH, both the AND gates
act as buffers and thus R and S appears at the RS Flip Flop input and it functions
like a normal RS Flip Flop. When Enable E is LOW, it drives LOW to both inputs
of RS Flip Flop. As we saw in previous page, when both inputs of a NOR Flip
Flop are low, values are retained (i.e. the output does not change).
Set up and Hold time
For synchronous flip-flops, we have special requirements for the inputs

with respect to clock signal input. They are
Setup Time: Minimum time period during which data must be stable
before the clock makes a valid transition. For example, for a posedge
triggered flip-flop, with a setup time of 2 ns, Input Data (i.e. R and S in the
case of RS flip-flop) should be stable for at least 2 ns before clock makes
transition from 0 to 1.
Hold Time: Minimum time period during which data must be stable after
the clock has made a valid transition. For example, for a posed triggered
flip-flop, with a hold time of 1 ns. Input Data (i.e. R and S in the case of
RS flip-flop) should be stable for at least 1 ns after clock has made
transition from 0 to 1.
If data makes transition within this setup window and before the hold window,
then the flip-flop output is not predictable, and flip-flop enters what is known as
meta stable state. In this state flip-flop output oscillates between 0 and 1. It takes
some time for the flip-flop to settle down. The whole process is called Meta
stability. You could refer to tidbits section to know more information on this
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topic. The waveform below shows input S (R is not shown), and CLK and output
Q (Q' is not shown) for a SR posed flip-flop.
Figure: Waveform for S-R and CLK
3 D Flip Flop
The RS Flip Flop seen earlier contains ambiguous state; to eliminate this
condition we can ensure that S and R are never equal. This is done by connecting
S and R together with an inverter. Thus we have D Flip Flop: the same as the RS
Flip Flop, with the only difference that there is only one input, instead of two (R
and S). This input is called D or Data input. D Flip Flop is called D transparent
Flip Flop for the reasons explained earlier. Delay flip-flop or delay latch is
another name used. Below is the truth table and circuit of D Flip Flop.
In real world designs (ASIC/FPGA Designs) only D latches/Flip-Flops are

used.
Figure 2.12: D Flip Flop with Edge Sensitive and Level sensitive
Table: Truth table for D Flip Flop
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Below is the D Flip Flop waveform, which is similar to the RS Flip Flop one, but
with R removed.
Figure: D Flip Flop waveform
5 JK Flip Flop
The ambiguous state output in the RS Flip Flop was eliminated in the D Flip Flop
by joining the inputs with an inverter. But the D Flip Flop has a single input. JK
Flip Flop is similar to RS Flip Flop in that it has 2 inputs J and K as shown Figurer
below. The ambiguous state has been eliminated here: when both inputs are high,
output toggles. The only difference we see here is output feedback to inputs,
which is not there in the RS Flip Flop.
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4 T Flip Flop
When the two inputs of JK Flip Flop are shorted, a T Flip Flop is formed. It is
called T Flip Flop as, when input is held HIGH, output toggles.
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6 JK Master Slave Flip-Flop

All sequential circuits that we have seen in the last few pages have a
problem (All level sensitive sequential circuits have this problem). Before the
enable input changes state from HIGH to LOW (assuming HIGH is ON and LOW
is OFF state), if inputs changes, then another state transition occurs for the same
enable pulse. This sort of multiple transition problem is called racing.
If we make the sequential element sensitive to edges, instead of levels, we

can overcome this problem, as input is evaluated only during enable/clock edges.
Figure: JK Master Slave Flip Flop
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In the Figure above there are two Flip Flop, the first Flip Flop on the left is called
master Flip Flop and the one on the right is called slave Flip Flop. Master Flip
Flop is positively clocked and slave Flip Flop is negatively clocked.
Figure : JK Master Slave Flip Flop
COUNTERS
• Counters are a specific type of sequential circuit.
• Like registers, the state, or the flip-flop values themselves, serves as the
“output.”
• The output value increases by one on each clock cycle.
• After the largest value, the output “wraps around” back to 0.
Benefits of counters
• Counters can act as simple clocks to keep track of “time.”
• You may need to record how many times something has happened.
– How many bits have been sent or received?
– How many steps have been performed in some computation?
• All processors contain a program counter, or PC.
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– Programs consist of a list of instructions that are to be executed one

after another (for the most part).
– The PC keeps track of the instruction currently being executed.

– The PC increments once on each clock cycle, and the next program
instruction is then executed.
Counter Types
Asynchronous Counter (Ripple or Serial Counter)
Each FF is triggered one at a time with output of one FF serving as clock

input of next FF in the chain.
Synchronous Counter (a.k.a. Parallel Counter)
All the FF‟ s in the counter are clocked at the same time.
Up Counter
Counter counts from zero to a maximum count.
Down Counter
Counter counts from a maximum count down to zero.
BCD Counter
Counter counts from 0000 to 1001 before it recycles.
Pre-settable Counter
Counter that can be preset to any starting count either synchronously or

asynchronously
Ring Counter
Shift register in which the output of the last FF is connected back to the
input of the first FF.
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Johnson Counter
Shift register in which the inverted output of the last FF is connected to the input
of the first FF.
1 Synchronous Counter
There is a problem with the ripple counter just discussed. The output stages
of the flip-flops further down the line (from the first clocked flip-flop) take time
to respond to changes that occur due to the initial clock signal. This is a result of
the internal propagation delay that occurs within a given flip-flop.
A standard TTL flip-flop may have an internal propagation delay of 30 ns.
If you join four flip-flops to create a MOD-16 counter, the accumulative
propagation delay at the highest-order output will be 120 ns. When used in high-
precision synchronous systems, such large delays can lead to timing problems.
To avoid large delays, you can create what is called a synchronous counter.
Synchronous counters, unlike ripple (asynchronous) counters, contain flip-flops
whose clock inputs are driven at the same time by a common clock line. This
means that output transitions for each flip-flop will occur at the same time. Now,
unlike the ripple counter, you must use some additional logic circuitry placed
between various flip-flop inputs and outputs to give the desired count waveform.
For example, to create a 4-bit MOD-16 synchronous counter requires

adding two additional AND gates, as shown below. The AND gates act to keep
a flip-flop in hold mode (if both input of the gate are low) or toggle mode (if
both inputs of the gate are high). So, during the 0–1 count, the first flip-flop is
in toggle mode (and always is); all the rest are held in hold mode. When it is
time for the 2–4 count, the first and second flip-flops are placed in toggle mode;
the last two are held in hold mode.
When it is time for the 4–8 count, the first AND gate is enabled, allowing
the third flip-flop to toggle. When it is time for the 8–15 count, the second AND
gate is enabled, allowing the last flip-flop to toggle
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Figure: Mod 16 Synchronous Counters and Cycle Diagram
The ripple (asynchronous) and synchronous counters discussed so far are

simple but hardly ever used. In practice, if you need a counter, be it ripple or
synchronous, you go out and purchase a counter IC. These ICs are often MOD-
16 or MOD-10 counters and usually come with many additional features. For
example, many ICs allow you to preset the count to a desired number via parallel
input lines.
Synchronous Up /Down Counter
The down counter counts in reverse from 1111 to 0000 and then goes to
1111. If we inspect the count cycle, we find that each flip-flop will complement
when the previous flip- flops are all 0 (this is the opposite of the up counter).
The down counter can be implemented similar to the up counter, except that the
AND gate input is taken from Q’ instead of Q. This is shown in the following
Figure of a 4-bit up-down counter using T flip-flops.
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Figure: Synchronous Up /Down Counter
2 Asynchronous Up /Down Counter:

In certain applications, a counter must be able to count both up and down.
The circuit below is a 3-bit up-down counter. It counts up or down depending on
the status of the control signals UP and DOWN. When the UP input is at 1 and
the DOWN input is at 0, the NAND network between FF0 and FF1 will gate the
non-inverted output (Q) of FF0 into the clock input of FF1. Similarly, Q of FF1
will be gated through the other NAND network into the clock input of FF2. Thus
the counter will count up.
Figure: Asynchronous Up /Down Counter
When the control input UP is at 0 and DOWN is at 1, the inverted outputs

of FF0 and FF1 are gated into the clock inputs of FF1 and FF2 respectively. If the
flip-flops are initially y reset to 0's, then the counter will go through the following
sequence as input pulses are applied
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Notice that an asynchronous up-down counter is slower than an up counter

or a down counter because of the additional propagation delay introduced by
the NAND networks.
Design of Synchronous Counters
This section begins our study of designing an important class of clocked

sequential logic circuits-synchronous fi ni t e -state machines. Like all sequential
circuits, a finite-state machine determines its outputs and its next state from its
current inputs and current state. A synchronous finite state machine changes state
only on the clocking event.
ANALOG TO DIGITAL CONVERSION

A comparator compares the unknown voltage with a known value of voltage and
then produces proportional output (i.e. it will produce either a 1 or a 0). This
principle is basically used in the above circuit. Here three comparators are used.
Each has two inputs. One input of each comparator is connected to analog input
voltage. The other input terminals are connected to fixed reference voltage like
+3/4V, +V/2 and +V/4. Now the circuit can convert analog voltage into
equivalent digital signal. Since the analog output voltage is connected in parallel
to all the comparators, the circuit is also called as parallel A/D converter.
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Working – Here each comparator is connected to a reference voltage of +3/4V,

+V/2 and +V/4 with their outputs as C C C respectively. Now suppose the analog
3 2 1
input voltage change from 0 – 4V, then the actual values of reference voltages
will be +3/4V = 3V, +V/2 =2V and +V/4 =1V. Now there will be following
conditions of outputs of the circuit
1) When input voltage is between 0 and 1V, the output will be C 3C2C1 = 000.
2) When input voltage > 1V £ 2V, the output will be C 3C2C1 = 001.
In this way, the circuit can convert the analog input voltage into its
equivalent or proportional binary number in digital style.
1 Successive Approximation Technique

The basic drawback of counter method (given above) is that it has longer
conversion time. Because it always starts from 0000 at every measurement, until
the analog voltage is matched. This drawback is removed in successive
approximation method. In the adjacent figure, the method of successive
approximation technique is shown. When unknown voltage (V a) is applied, the
circuit starts up from 0000, as shown above. The output of SAR advances with
each MSB. The output of SAR does not increase step–by–step in BCD bus
pattern, but individual bit becomes high–starting from MSB. Then by
comparison, the bit is fixed or removed. Thus, it sets first MSB (1000), then the
second MSB (0100) and so on. Every time, the output of SAR is converted to
equivalent analog voltage by binary ladder. It is then compared with applied
unknown voltage (Va). The comparison process goes on, in binary search style,
until the binary equivalent of analog voltage is obtained. In this way following
steps are carried out during conversion.
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Figure: Successive Approximation Technique
Now refer the following figure and the given steps -
1) The unknown analog voltage (V a) is applied.

2) Starts up from 0000 and sets up first MSB 1000.
3) If Va >= 1000, the first MSB is fixed.
4) If Va < 1000, the first MSB is removed and second MSB is set
5) The fixing and removing the MSBs continues up to last bit (LSB), until
equivalent binary output is obtained.
Figure 3.38 Equivalent Binary Output
2 Flash ADC
Also called the parallel A/D converter, this circuit is the simplest to understand.
It is formed of a series of comparators, each one comparing the input signal to a
unique reference voltage. The comparator outputs connect to the inputs of a
priority encoder circuit, which then produces a binary output.
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Figure: Flash ADC

The following illustration shows a 3-bit flash ADC circuit:
Vref is a stable reference voltage provided by a precision voltage regulator
as part of the converter circuit, not shown in the schematic. As the analog input
voltage exceeds the reference voltage at each comparator, the comparator outputs
will sequentially saturate to a high state. The priority encoder generates a binary
number based on the highest-order active input, ignoring all other active inputs.
When operated, the flash ADC produces an output that looks something like this
DIGITAL TO ANALOG CONVERTER(DAC)

The process of converting digital signal into equivalent analog signal is
called D/A conversion. The electronics circuit, which does this process, is called
D/A converter. The circuit has „n’ number of digital data inputs with only one
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output. Basically, there are two types of D/A converter circuits: Weighted
resistors D/A converter circuit and Binary ladder or R–2R ladder D/A converter
circuit.
1 Weighted resistors D/A converter

Here an OPAMP is used as summing amplifier. There are four resistors R, 2R,
4R and 8R at the input terminals of the OPAMP with R as feedback resistor. The
network of resistors at the input terminal of OPAMP is called as variable resistor
network. The four inputs of the circuit are D, C, B & A. Input D is at MSB and
A is at LSB. Here we shall connect 8V DC voltage as logic–1 level. So we shall
assume that 0 = 0V and 1 = 8V.
Figure: Weighted resistors D/A converter

Now the working of the circuit is as follows. Since the circuit is summing
amplifier, its output is given by the following equation
Working of the circuit
When input DCBA = 0000, then putting these value in above equation (1) we get
When digital input of the circuit DCBA = 0001, then putting these value in above
equation (1) we get
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When digital input of the circuit DCBA = 0010, then putting these value in above
equation (1) we get
…………… so on.
In this way, when digital input changes from 0000 to 1111 (in BCD style),
output voltage (Vo) changes proportionally. This is given in the conversion chart.
There are some main disadvantages of the circuit.
They are
1) Each resistor in the circuit has different value.

2) So error in value of each resistor adds up.
3) The value of resistor at MSB is the lowest. Hence, it draws more current.
4) Also, its heat & power dissipation is very high.
5) There is the problem of impedance matching due to different values of
resistors.
2 R–2R Ladder D/A Converter

It is modern type of resistor network. It has only two values of resistors the R and
2R. These values repeat throughout in the circuit. The OPAMP is used at output
for scaling the output voltage. The working of the circuit can be understood as
follows. For simplicity, we ignore the OPAMP in the above circuit (this is
because its gain is unity). Now consider the circuit, without OPAMP. Suppose
the digital input is DCBA = 1000. Then the circuit is reduced to a small circuit.
Its output is given by –
Reduced circuit of R-2R ladder, when we consider that all inputs=0
Now suppose digital input of the same circuit is changed to DCBA = 0100. Then
the output voltage will be V/4, when DCBA = 0010, output voltage will be V/8,
for DCBA = 0001, output voltage will be V/16 and so on. The general formula
for the above circuit of R–2R ladder, including the OPAMP also, will be –
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You can take (R) common from the above formula and simplify it. With the help
of this formula, we can calculate any combination of digital input into its
equivalent analog voltage at the output terminals.
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UNIT V FUNDAMENTALS OF COMMUNICATION ENGINEERING

Types of signal
Analog signal and digital signal

Definitions of Analog vs Digital signals
An Analog signal is any continuous signal for which the time varying feature
(variable) of the signal is a representation of some other time varying quantity,
i.e., analogous to another time varying signal. It differs from a digital signal in
terms of small fluctuations in the signal which are meaningful.
A digital signal uses discrete (discontinuous) values. By contrast, non-digital (or

analog) systems use a continuous range of values to represent information.
Although digital representations are discrete, the information represented can be
either discrete, such as numbers or letters, or continuous, such as sounds, images,
and other measurements of continuous systems.
Properties of Digital vs Analog signals
Digital information has certain properties that distinguish it from analog

communication methods. These include
Synchronization – digital communication uses specific synchronization

sequences for determining synchronization.
Language – digital communications requires a language which should be

possessed by both sender and receiver and should specify meaning of symbol
sequences.
Errors – disturbances in analog communication causes errors in actual intended

communication but disturbances in digital communication does not cause errors
enabling error free communication. Errors should be able to substitute, insert or
delete symbols to be expressed.
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Copying – analog communication copies are quality wise not as good as their
originals while due to error free digital communication, copies can be made
indefinitely.
Granularity – for a continuously variable analog value to be represented in

digital form there occur quantization error which is difference in actual analog
value and digital representation and this property of digital communication is
known as granularity.
Differences in Usage in Equipment
Many devices come with built in translation facilities from analog to digital.
Microphones and speaker are perfect examples of analog devices. Analog
technology is cheaper but there is a limitation of size of data that can be
transmitted at a given time.
Digital technology has revolutionized the way most of the equipments work.
Data is converted into binary code and then reassembled back into original form
at reception point. Since these can be easily manipulated, it offers a wider range
of options. Digital equipment is more expensive than analog equipment.
Comparison of Analog vs Digital Quality
Digital devices translate and reassemble data and in the process are more prone
to loss of quality as compared to analog devices. Computer advancement has
enabled use of error detection and error correction techniques to remove
disturbances artificially from digital signals and improve quality.
Differences in Applications
Digital technology has been most efficient in cellular phone industry. Analog
phones have become redundant even though sound clarity and quality was good.
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Analog technology comprises of natural signals like human speech. With digital
technology this human speech can be saved and stored in a computer. Thus digital
technology opens up the horizon for endless possible uses.
Comparison chart
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Principles of Amplitude modulation
mplitude Modulation (AM) plus frequency division multiplexing (FDM) is one

way of solving above problem. Each conversation is shifted to a different part of
the frequency spectrum by using a high-frequency waveform to "carry" each
individual speech signal. These high frequencies are called carrier frequencies .
Amplitude modulation is the process of varying the amplitude of the sinusoidal
carrier wave by the amplitude of the modulating signal, and is illustrated in Fig.
The unmodulated carrier wave has a constant peakvalueand a higher frequency

than the modulating signal , but, when the modulating signal is applied, the peak
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value of the carrier varies in accordance with the instantaneous value of the
modulating signal, and the outline wave shape or "envelope" of the modulated
wave's peak values is the same as the original modulating signal wave shape. The
modulating signal waveform has been superimposed on the carrier wave.
When a sinusoidal carrier wave of frequency fc Hz is amplitude - modulated by
a sinusoidal modulating signal of frequency fm Hz , then the modulated carrier
wave contains three frequencies .
1) fc Hz : Original carrier frequency
2) ( fc + fm ) Hz : The sum of carrier and modulating signal frequencies
3) ( fc - fm ) Hz : The difference between carrier and modulating signal
This is illustrated in Fig
It should be noted that two of these frequencies are new, being produced by the
amplitude-modulation process, and are called side-frequencies. The sum of
carrier and modulating signal frequencies is called the upper side-frequency. The
difference between carrier and modulating signal frequency is called the lower
side-frequency. This is illustrated in the frequency spectrum diagram of Fig.
The bandwidth of the modulated carrier wave is

( fc + fm ) - ( fc - fm ) = 2 fm
i.e. double the modulating signal frequency
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The complete amplitude-modulated wave band of lower sideband plus carrier

plus upper sideband shown in Fig. 8 takes up more frequency bandwidth than is
really necessary to transmit the information signal since all the information is
carried by either one of the sidebands alone . The carrier component is of constant
amplitude and frequency so does not carry any of the information signal at all . It
is possible by using special equipment to suppress both the carrier and one
sideband and to transmit just the other sideband with no loss of information. This
method of working is called single sideband working ( SSB ) . This method is not
used for domestic radio broadcasting , but it is used for some long-distance radio
telephony systems and for multi-channel carrier systems used in national
telephone networks.
Principle of frequency modulation
Frequency modulation uses the information signal, V m(t) to vary the carrier
frequency within some small range about its original value. Here are the three
signals in mathematical form:
Information: Vm(t)
Carrier: Vc(t) = Vco sin ( 2 p fc t + f )
FM: VFM (t) = Vco sin (2 p [fc + (Df/Vmo) Vm (t) ] t + f)
We have replaced the carrier frequency term, with a time-varying frequency. We

have also introduced a new term: Df, the peak frequency deviation. In this form,
you should be able to see that the carrier frequency term: fc + (Df/Vmo) Vm (t) now
varies between the extremes of fc - Df and fc + Df. The interpretation of Df
becomes clear: it is the farthest away from the original frequency that the FM
signal can be. Sometimes it is referred to as the "swing" in the frequency.
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We can also define a modulation index for FM, analogous to AM: b = Df/fm ,
where fm is the maximum modulating frequency used.
The simplest interpretation of the modulation index, b, is as a measure of the peak

frequency deviation, Df. In other words, b represents a way to express the peak
deviation frequency as a multiple of the maximum modulating frequency, fm, i.e.
Df = b fm.
Example: suppose in FM radio that the audio signal to be transmitted ranges from
20 to 15,000 Hz (it does). If the FM system used a maximum modulating index,
b, of 5.0, then the frequency would "swing" by a maximum of 5 x 15 kHz = 75
kHz above and below the carrier frequency.
Here is a simple FM signal:
Here, the carrier is at 30 Hz, and the modulating frequency is 5 Hz. The
modulation index is about 3, making the peak frequency deviation about 15 Hz.
That means the frequency will vary somewhere between 15 and 45 Hz. How fast
the cycle is completed is a function of the modulating frequency.
FM Spectrum
A spectrum represents the relative amounts of different frequency components in

any signal. Its like the display on the graphic-equalizer in your stereo which has
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leds showing the relative amounts of bass, midrange and treble. These correspond
directly to increasing frequencies (treble being the high frequency components).
It is a well-know fact of mathematics, that any function (signal) can be
decomposed into purely sinusoidal components (with a few pathological
exceptions) . In technical terms, the sines and cosines form a complete set of
functions, also known as a basis in the infinite-dimensional vector space of real-
valued functions (gag reflex). Given that any signal can be thought to be made up
of sinusoidal signals, the spectrum then represents the "recipe card" of how to
make the signal from sinusoids. Like: 1 part of 50 Hz and 2 parts of 200 Hz. Pure
sinusoids have the simplest spectrum of all, just one component:
In this example, the carrier has 8 Hz and so the spectrum has a single component
with value 1.0 at 8 Hz
The FM spectrum is considerably more complicated. The spectrum of a simple
FM signal looks like:
The carrier is now 65 Hz, the modulating signal is a pure 5 Hz tone, and the
modulation index is 2. What we see are multiple side-bands (spikes at other than
the carrier frequency) separated by the modulating frequency, 5 Hz. There are
roughly 3 side-bands on either side of the carrier. The shape of the spectrum may
be explained using a simple heterodyne argument: when you mix the three
frequencies (fc, fm and Df) together you get the sum and difference frequencies.
The largest combination is fc + fm + Df, and the smallest is fc - fm - Df. Since Df
= b fm, the frequency varies (b + 1) fm above and below the carrier.
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A more realistic example is to use an audio spectrum to provide the modulation:
In this example, the information signal varies between 1 and 11 Hz. The carrier
is at 65 Hz and the modulation index is 2. The individual side-band spikes are
replaced by a more-or-less continuous spectrum. However, the extent of the side-
bands is limited (approximately) to (b + 1) fm above and below. Here, that would
be 33 Hz above and below, making the bandwidth about 66 Hz. We see the side-
bands extend from 35 to 90 Hz, so out observed bandwidth is 65 Hz.
You may have wondered why we ignored the smooth humps at the extreme ends
of the spectrum. The truth is that they are in fact a by-product of frequency
modulation (there is no random noise in this example). However, they may be
safely ignored because they are have only a minute fraction of the total power. In
practice, the random noise would obscure them anyway.
Example: FM Radio
FM radio uses frequency modulation, of course. The frequency band for FM radio
is about 88 to 108 MHz. The information signal is music and voice which falls in
the audio spectrum. The full audio spectrum ranges form 20 to 20,000 Hz, but
FM radio limits the upper modulating requency to 15 kHz (cf. AM radio which
limits the upper frequency to 5 kHz). Although, some of the signal may be lost
above 15 kHz, most people can't hear it anyway, so there is little loss of fidelity.
FM radio maybe appropriately referred to as "high-fidelity."
If FM transmitters use a maximum modulation index of about 5.0, so the resulting

bandwidth is 180 kHz (roughly 0.2 MHz). The FCC assigns stations ) 0.2 MHz
apart to prevent overlapping signals (coincidence? I think not!). If you were to
fill up the FM band with stations, you could get 108 - 88 / .2 = 100 stations, about
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the same number as AM radio (107). This sounds convincing, but is actually more
complicated (agh!).
FM radio is broadcast in stereo, meaning two channels of information. In practice,

they generate three signals prior to applying the modulation:
the L + R (left + right) signal in the range of 50 to 15,000 Hz. a 19 kHz pilot
carrier.
the L-R signal centered on a 38 kHz pilot carrier (which is suppressed) that ranges
from 23 to 53 kHz .
So, the information signal actually has a maximum modulating frequency of 53

kHz, requiring a reduction in the modulation index to about 1.0 to keep the total
signal bandwidth about 200 kHz.
FM Performance
Bandwidth
As we have already shown, the bandwidth of a FM signal may be predicted using:
BW = 2 (b + 1 ) fm
where b is the modulation index and
fm is the maximum modulating frequency used.
FM radio has a significantly larger bandwidth than AM radio, but the FM radio
band is also larger. The combination keeps the number of available channels
about the same.
The bandwidth of an FM signal has a more complicated dependency than in the

AM case (recall, the bandwidth of AM signals depend only on the maximum
modulation frequency). In FM, both the modulation index and the modulating
frequency affect the bandwidth. As the information is made stronger, the
bandwidth also grows.
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Efficiency
The efficiency of a signal is the power in the side-bands as a fraction of the total.
In FM signals, because of the considerable side-bands produced, the efficiency is
generally high. Recall that conventional AM is limited to about 33 % efficiency
to prevent distortion in the receiver when the modulation index was greater than
1. FM has no analogous problem.
The side-band structure is fairly complicated, but it is safe to say that the
efficiency is generally improved by making the modulation index larger (as it
should be). But if you make the modulation index larger, so make the bandwidth
larger (unlike AM) which has its disadvantages. As is typical in engineering, a
compromise between efficiency and performance is struck. The modulation index
is normally limited to a value between 1 and 5, depending on the application.
Noise
FM systems are far better at rejecting noise than AM systems. Noise generally is
spread uniformly across the spectrum (the so-called white noise, meaning wide
spectrum). The amplitude of the noise varies randomly at these frequencies. The
change in amplitude can actually modulate the signal and be picked up in the AM
system. As a result, AM systems are very sensitive to random noise. An example
might be ignition system noise in your car. Special filters need to be installed to
keep the interference out of your car radio.
FM systems are inherently immune to random noise. In order for the noise to
interfere, it would have to modulate the frequency somehow. But the noise is
distributed uniformly in frequency and varies mostly in amplitude. As a result,
there is virtually no interference picked up in the FM receiver. FM is sometimes
called "static free, " referring to its superior immunity to random noise.
Block diagram of radio
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AM Transmitter
In order to better understand the way the radio transmitter works, block - diagram
of a simple AM (amplitude modulated) signal transmitter is shown on Pic. The
amplitude modulation is being performed in a stage called the modulator. Two
signals are entering it: high frequency signal called the carrier (or the signal
carrier), being created into the HF oscillator and amplified in the HF amplifier to
the required signal level, and the low frequency (modulating) signal coming from
the microphone or some other LF signal source (cassette player, record player,
CD player etc.), being amplified in the LF amplifier. On modulator's output the
amplitude modulated signal UAM is acquired. This signal is then amplified in the
power amplifier, and then led to the emission antenna.
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The shape and characteristics of the AM carrier, being taken from the HF
amplifier into the modulator, are shown on Pic. As you can see, it is a HF voltage
of constant amplitude US and frequency fS. On Pic. the LF signal that appears at
the input of the modulator at the moment t0 is shown. With this signal the
modulation of the carrier's amplitude is being performed, therefore it is being
called the modulating signal. The shape of the AM signal exiting the modulator
is shown on Pic. From the point t0 this voltage has the same shape as that on Pic.
From the moment t0 the amplitude of AM signal is being changed in accordance
with the current value of the modulating signal, in such a way that the signal
envelope (fictive line connecting the voltage peaks) has the same shape as the
modulating signal.
Let's take a look at a practical example. Let the LF signal on Pic. be, say, an
electrical image of the tone being created by some musical instrument, and that
the time gap between the points t0 and t2 is 1 ms. Suppose that carrier frequency
is fS=1 MHz (approximately the frequency of radio Kladovo, exact value is 999
kHz). In that case, in period from t0 till t2 signals us on Pic. and AM on should
make a thousand oscillations and not just eighteen, as shown in the picture. Then
It is clear that it isn't possible to draw a realistic picture, since all the lines would
connect into a dark spot. The true picture of AM signal from this example is given
on Pic. That is the picture that appears on screen of the oscilloscope, connected
on the output of the modulator: light coloured lines representing the AM signal
have interconnected, since they are thicker than the gap between them.
Block - diagram on Pic is a simplified schematic of an AM transmitter. In reality

there are some additional stages in professional transmitters that provide the
necessary work stability, transmitter power supply, cooling for certain stages etc.
For simple use, however, even simpler block diagrams exist, making the
completion of an ordinary AM transmitter possible with just a few electronic
components.
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FM Transmitter
Block diagram of an FM (frequency modulated) transmitter is given on Pic.2.4.

Information being transferred, i.e. the modulating signal, is a signal from some
LF source. it is being amplified in LF amplifier and then led into the HF oscillator,
where the carrier signal is being created. The carrier is a HF voltage of constant
amplitude, whose frequency is, in the absence of modulating signal, equal to the
transmitter's carrier frequency fS. In the oscillatory circuit of the HF oscillator a
varicap (capacitive) diode is located. It is a diode whose capacitance depends
upon the voltage between its ends, so when being exposed to LF voltage, its
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capacitance is changing in accordance with this voltage. Due to that frequency of

the oscillator is also changing, i.e. the frequency modulation is being obtained.
The FM signal from the HF oscillator is being proceeded to the power amplifier
that provides the necessary output power of the transmission signal. Voltage
shapes in FM transmitter are given on Pic.2.5. Pic.2.5-a shows the LF modulating
signal. The frequency modulation begins at moment t0 and the transmission
frequency begins to change, as shown on Pic.2.5-b: Whilst current value of the
LF signal is raising so is the trasmitter frequency, and when it is falling the
frequency is also falling. As seen on Pic.2.5-c, the information (LF signal) is
being implied in frequency change of the carrier.
The carrier frequencies of the radio difusion FM transmitters (that emmit the
program for "broad audience") are placed in the waveband from 88 MHz til 108
MHz, the maximum frequency shift of the transmitter (during the modulation)
being ±75 kHz. Because of that the FM signal should be drawn much "thicker",
but it would result in a black-square-shaped picture.
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AM radio broad cast transmitter
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AM broadcasting is the process of radio broadcasting using amplitude modulation

(AM). AM was the first method of impressing sound on a radio signal and is still
widely used today. Commercial and public AM broadcasting is authorized in the
medium wave band worldwide, and also in parts of the long wave and short wave
bands. Radio broadcasting was made possible by the invention of the amplifying
vacuum tube, the Audion(triode), by Lee de Forest in 1906, which led to the
development of inexpensive vacuum tube AM radio receivers and transmitters
during World War I. Commercial AM broadcasting developed from amateur
broadcasts around 1920, and was the only commercially important form of radio
broadcasting until FM broadcasting began after World War II. This period is
known as the "Golden Age of Radio". Today, AM competes with FM, as well as
with various digital radio broadcasting services distributed from terrestrial and
satellite transmitters. In many countries the higher levels of interference
experienced with AM transmission have caused AM broadcasters to specialize in
news, sports and talk radio, leaving transmission of music mainly to FM and
digital broadcasters.
AM radio technology is simpler than frequency modulated (FM) radio, Digital
Audio Broadcasting (DAB), satellite radio or HD (digital) radio. An AM receiver
detects amplitude variations in the radio waves at a particular frequency.
It then amplifies changes in the signal voltage to drive aloudspeaker or earphones.
The earliest crystal radio receivers used a crystal diode detector with no
amplification, and required no power source other than the radio signal itself.
In North American broadcasting practice, transmitter power input to the antenna
for commercial AM stations ranges from about 250 to 50,000watts. Experimental
licenses were issued for up to 500,000 watts radiated power, for stations intended
for wide-area communication during disasters. One such superstation was
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Cincinnati station WLW, which used such power on occasion before World War
II. WLW's superpower transmitter still exists at the station's suburban transmitter
site, but it was decommissioned in the early 1940s and no current commercial
broadcaster in the U.S. or Canada is authorized for such power levels. Some other
countries do authorize higher power operation (for example the Mexican station
XERF formerly operated at 250,000 watts). Antenna design must consider the
coverage desired and stations may be required, based on the terms of their license,
to directionalize their transmitted signal to avoid interfering with other stations
operating on the same frequency.
Radio receiver
In the early days of what is now known as early radio transmissions, say about
100 years ago, signals were generated by various means but only up to the L.F.
region.
Communication was by way of morse code much in the form that a short
transmission denoted a dot (dit) and a longer transmission was a dash (dah). This
was the only form of radio transmission until the 1920's and only of use to the
military, commercial telegraph companies and amateur experimenters.
Then it was discovered that if the amplitude (voltage levels - plus and minus about
zero) could be controlled or varied by a much lower frequency such as A.F. then
real intelligence could be conveyed e.g. speech and music. This process could be
easily reversed by simple means at the receiving end by using diode detectors.
This is called modulation and obviously in this case amplitude modulation or
A.M.
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This discovery spawned whole new industries and revolutionized the world of
communications. Industries grew up manufacturing radio parts, receiver
manufacturers, radio stations, news agencies, recording industries etc.
Disadvantages to A.M. radio
Firstly because of the modulation process we generate at least two copies of the
intelligence plus the carrier. For example consider a local radio station
transmitting on say 900 Khz. This frequency will be very stable and held to a tight
tolerance. To suit our discussion and keep it as simple as possible we will have
the transmission modulated by a 1000 Hz or 1Khz tone.
At the receiving end 3 frequencies will be available. 900 Khz, 901 Khz and 899
Khz i.e. the original 900 Khz (the carrier) plus and minus the modulating
frequency which are called side bands. For very simple receivers such as a
cheap transistor radio we only require the original plus either one of the side
bands. The other one is a total waste. For sophisticated receivers one side band
can be eliminated.
The net effect is A.M. radio stations are spaced 10 Khz apart (9 kHz in Australia)
e.g. 530 Khz...540 Khz...550 Khz. This spacing could be reduced and nearly twice
as many stations accommodated by deleting one side band. Unfortunately the
increased cost of receiver complexity forbids this but it certainly is feasible.
Block diagram of television transmitter
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The basic television Broadcast transmitter block diagram is shown in figure (a).
The block diagram can be broadly divided into two separate section, viz., one that
- Generates an electronic signal (called video signal) corresponding to the actual
picture and then uses this video signal to modulate an R-F carrier so as to be
applied to the transmitting antenna for transmission, other that generates an
electronic signal (called audio signal) containing sound information and then uses
this signal to modulate another RF carrier and then applied to the transmitting
antenna for transmission.
However only one antenna is used for transmission of the video as well as audio
signals. Thus these modulated signals have to be combined together in some
appropriate network. In addition there are other accessories also. For instance,
video as well as audio signals have to be amplified to the desired degree before
they modulate their respective RF carriers.
This function is performed by video and audio amplifiers. The block picture
signal transmitter and audio signal transmitter shown in figure (a) may consist of
modulators as the essential component; Video signal transmitter employs an AM
transmitter as amplitude-modulation is used for video signals whereas audio
signal transmitter employs FM modulator as frequency modulation is used for
sound information. Scanning circuits are used to mike the electron beam scan the
actual picture to produce the corresponding video signal. The scanning by
electron beam is in the receiver too. The beam scans the picture tube to reproduce
the original picture from the video signal and this scanning at the receiver must
be matched properly to the scanning at the transmitter. It is for this reason that
synchronizing Circuits are used at the transmitter as well as receiver.
Complete TV transmitter Block Diagram
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Figure (b) depicts the complete block diagram of a Television Broadcast

Transmitter. The important block have already been discussed individually in the
preceding sections. that makes understanding of the diagram shown here much
more simple. A brief explanation is given ahead. The block diagram can be
broadly divided into two -sections, viz., an amplitude modulated transmitter and
a frequency modulated transmitter. Former is used for video modulation whereas
latter is used for audio modulation.
Master oscillator in both generates an RF carrier frequency. Generally, a master

oscillator generates a sub multiple of carrier and then drives harmonic generators
(frequency multipliers) to achieve correct value carrier. Harmonic generators are
nothing but class C tuned amplifiers whose output tuned circuit is to tuned to
some harmonic of the input signal. In actual practice, master oscillator and
harmonic generator are s crated or isolated by a buffer stage to av214Joactrrig of
the harmonic generator on the oscillator output. The carrier is then fed to an
amplitude modulator in video transmitter and a frequency modulator in audio
transmitter. Into-the modulator, the modulation signal is also fed with proper
amplitude. Since low-level modulation is employed, the modulating signal is
amplified by linear amplifiers up-to the desired degree required for transmission.
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Video and audio signals on separate carriers are then combined together so as to
be fed to the transmitting antenna as on signal.
Block diagram of television receiver
Television Receiver
A radio receiver designed to amplify and convert the video and audio radio-
frequency signals of a television broadcast that have been picked up by a
television antenna; the receiver reproduces the visual image broadcast and the
accompanying sound. Television receivers are designed for color or black-and-
white operation; both non portable and portable models are produced. Those
manufactured in the USSR are capable of receiving signals from television
stations transmitting in specifically assigned portions of thevery-high-frequency
(VHF) band (48.5–100 megahertz and 174– 230 megahertz; 12 channels) and
ultra high-frequency (UHF) band (470– 638 megahertz; several tens of channels).
Television receivers must simultaneously amplify and convert video and audio
radio- frequency signals. They are usually designed with a super heterodyne
circuit, and versions differ in the methods used to extract and amplify the audio
signal. The principal components of a television receiver are shown in Figure1.
The tuner selects the signals of the desired channel and converts them to a lower
frequency within the inter mediate-frequency pass band. The signal-processing
circuits include an intermediate-frequency amplifier for the video signal, an
amplitude detector, a video amplifier for the brightness signal, and, incolor
receivers, a color- processing circuit for the chrominance signal. The processing
circuit produces a brightness signal and a color- difference signal, which are fed
to the control electrodes of a kinescope; an audio signal, which is fed to the audio
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channel; and horizontal and vertical synchronizing pulses (or a composite

television signal), which are fed to a scanning generator. In the color television
system used in the USSR , the color-processing circuit for the chrominance signal
consists of a band- pass amplifier, in which the chrominance signal is extracted,
channels for the direct and delayed signals, an electronic switching device, two
frequency detectors for the color- difference signals, a matrix circuit, and
amplifiers for the three color-difference signals. The color processing circuit has
provisions for the extraction and decoding of the chrominance signal and for line
selection, as well as chrominance disconnect circuits that operate when black-
and-white transmissions are received.
The scanning generators include horizontal and vertical scanning circuits that
produce sawtooth c urrentsin the horizontal and vertical scanning coils of the
deflection system.
The high voltage for feeding the second anode of the kinescope is derived from a
special high voltage winding of the line transformer or by rectifying pulses from
the transformer; the volt age for the focusing electrode is similarly derived.
The kinescope’s interface includes static and dynamic white balance controls,
switches for exting uishingthe electron guns, and regulators for focusing the
beams. The demagnetizing circuit for a color kinescopecreates a damped
alternating current in a demagnetizing loop that circles the kine scope screen. The
current demagnetizes the shadow mask and tube rim, which are made of steel.
The audio section consists of an amplifier for the difference frequency, which in
the USSR is 6.5 megahertz, a frequency detector for the audio signal, and a low-
frequency amplifier from which the audio signal is fed to a high- quality
acoustical system, usually composed of several loudspeakers. The power- supply
section converts mains voltage into the supply voltages for all components of the
television set, including the kinescope and vacuum tube heaters.
Microwave communication
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Microwave transmission refers to the technology of transmitting information or

energy by the use ofelectromagnetic waves whose wavelengths are conveniently
measured in small numbers of centimetre; these are called microwaves. This part
of the radio spectrum ranges across frequencies of roughly 1.0 gigahertz (GHz)
to 30 GHz. These correspond to wavelengths from 30 centimeters down to 1.0
cm.
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Microwaves are widely used for point-to-point communications because their

small wavelength allows conveniently-sized antennas to direct them in narrow
beams, which can be pointed directly at the receiving antenna. This allows nearby
microwave equipment to use the same frequencies without interfering with each
other, as lower frequency radio waves do. Another advantage is that the high
frequency of microwaves gives the microwave band a very large information-
carrying capacity; the microwave band has a bandwidth 30 times that of all the
rest of the radio spectrum below it. A disadvantage is that microwaves are limited
to line of sight propagation; they cannot pass around hills or mountains as lower
frequency radio waves can.
Microwave radio transmission is commonly used in point-to-point
communication systems on the surface of the Earth, in satellite communications,
and in deep space radio communications. Other parts of the microwave radio band
are used for radars, radio navigation systems, sensor systems, and radio
astronomy.
The next higher part of the radio electromagnetic spectrum, where the frequencies
are above 30 GHz and below 100 GHz, are called "millimeter waves" because
their wavelengths are conveniently measured in millimeters, and their
wavelengths range from 10 mm down to 3.0 mm. Radio waves in this band are
usually strongly attenuated by the Earthly atmosphere and particles contained in
it, especially during wet weather. Also, in wide band of frequencies around 60
GHz, the radio waves are strongly attenuated by molecular oxygen in the
atmosphere. The electronic technologies needed in the millimeter wave band are
also much more difficult to utilize than those of the microwave band.
Satellite communication
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A communications satellite or comsat is an artificial satellite sent to space for the

purpose oftelecommunications. Modern communications satellites use a variety
of orbits including geostationary orbits, Molniya orbits, elliptical orbits and low
(polar and non- polar) Earth orbits.
For fixed (point-to-point) services, communications satellites provide a

microwave radio relay technology complementary to that of communication
cables. They are also used for mobile applications such as communications to
ships, vehicles, planes and hand-held terminals, and for TV and radio
broadcasting.
Communications Satellites are usually composed of the following subsystems:

Communication Payload, normally composed of transponders, antenna, and
switching systems Engines used to bring the satellite to its desired orbit
Station Keeping Tracking and stabilization subsystem used to keep the satellite
in the right orbit, with its antennas pointed in the right direction, and its power
system pointed towards the sun Power subsystem, used to power the Satellite
systems, normally composed of solar cells, and batteries that maintain power
during solar eclipse
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Command and Control subsystem, which maintains communications with ground

control stations. The ground control earth stations monitor the satellite
performance and control its functionality during various phases of its life-cycle.
The bandwidth available from a satellite depends upon the number of

transponders provided by the satellite. Each service (TV, Voice, Internet, radio)
requires a different amount of bandwidth for transmission. This is typically
known as link budgeting and a network simulator can be used to arrive at the
exact value.
Optical fiber communication
Fiber-optic communication is a method of transmitting information from one

place to another by sending pulses of light through an optical fiber. The light
forms an electromagnetic carrier wave that ismodulated to carry information.
First developed in the 1970s, fiber- optic communication systems have
revolutionized the telecommunications industry and have played a major role in
the advent of theInformation Age. Because of its advantages over electrical
transmission, optical fibers have largely replaced copper wire communications in
core networks in the developed world. Optical fiber is used by many
telecommunications companies to transmit telephone signals, Internet
communication, and cable television signals. Researchers at Bell Labs have
reached internet speeds of over 100 petabits per second using fiber-optic
communication.
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The process of communicating using fiber-optics involves the following basic

steps: Creating the optical signal involving the use of a transmitter, relaying the
signal along the fiber, ensuring that the signal does not become too distorted or
weak, receiving the optical signal, and converting it into an electrical
signal.Optical fiber is used by many telecommunications companies to transmit
telephone signals, Internet communication, and cable television signals.
Due to much lower attenuation and interference, optical fiber has large
advantages over existing copper wire in long-distance and high-demand
applications. However, infrastructure development within cities was relatively
difficult and time-consuming, and fiber-optic systems were complex and
expensive to install and operate. Due to these difficulties, fiber-optic
communication systems have primarily been installed in long-distance
applications, where they can be used to their full transmission capacity, offsetting
the increased cost. Since 2000, the prices for fiber-optic communications have
dropped considerably. The price for rolling out fiber to the home has currently
become more cost-effective than that of rolling out a copper based network.
Prices have dropped to $850 per subscriber in the US and lower in countries like
The Netherlands, where digging costs are low and housing density is high.
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Click Here for Basic Electrical and Electronics Engineering full study material.

UNIT I ELECTRICAL CIRCUITS

DC Circuits and Ohm’s Law

More technically, a DC circuit has no memory.

If a capacitor and/or inductor is added to a DC circuit, the resulting circuit is

More technically, such a circuit is represented by a system of differential

It is this steady state part that is the DC solution.

There are some circuits that do not have a DC solution.

This difference in charge is stored as electrical potential energy known as emf.

It is the emf that causes a current to flow through a circuit.

It is often referred to as “electric potential”, which then must be distinguished

The difference in voltage measured when moving from point A to point B is

The term is most often used as an abbreviation of “electrical potential

Gravitational potential difference between two points on Earth is related to the

The unit of gravitational potential differences is joules per kilogram.

This phenomenon is called electromagnetism.

Since the magnet is produced electric current, it is called the electromagnet.

An electromagnet is a type of magnet in which the magnetic field is produced

The magnetic field disappears when the current ceases.

In short, when current flow through a conductor, magnetic field will be

The very basic application of electromagnetism is in the use of motors.

Another very useful application of electromagnetism is the “CAT scan

This machine is usually used in hospitals to diagnose a disease.

The work of the human brain is based on electromagnetism. Electrical impulses

The mathematical equation that describes this relationship is:

where I is the current through the resistance in units of amperes,

The usual waveform of an AC circuit is generally that of a sine wave, as this

However in certain applications different waveforms are used, such as

In these applications, an important goal is often the recovery of information

Kirchhoff’s Current Law:

Kirchhoff’s Voltage Law:

Steady State Solution of DC Circuits:

I = V (1/R1 +1/R2 +1/R3)

Problems based on ohm’s law

Problems based on ohm’s law

Problems based on ohm’s law

The value of the Resistance R = 400 Ω

Problems based on ohm’s law

Resistance of bulb =150Ω

Resistance of rheostat = 120Ω

(a). Equivalent resistance of the circuit RT = 10Ω

This effective power in an alternating current system is therefore equal to: (

Therefore, the effective current in an AC system is called the Root Mean

Pure Resistive circuit:

In DC circuits the linear ratio of voltage to current in a resistor is called its

However, in AC circuits this ratio of voltage to current depends upon the

So when using resistors in AC circuits the term Impedance, symbol Z is the

Consider below the circuit consisting of an AC source and a resistor.

Likewise, in a purely resistive parallel AC circuit, all the individual branch

Pure Inductive circuits:

These results in the capacitor current flowing in the opposite or negative

If the value of the resistance is increased sufficiently large compared to the

These circuit elements can be combined to form an electrical circuit in four

These circuits exhibit important types of behaviour that are fundamental to

In practice, however, capacitors (and RC circuits) are usually preferred to

Both RC and RL circuits form a single-pole filter.

Depending on whether the reactive element (C or L) is in series with the load, or

Frequently RL circuits are used for DC power supplies to RF amplifiers, where

RLC Series Circuit:

The source for alternating current is called AC generator or alternator.