W4RNL Antennas Made of Wires Vol 3

Antennas
Made of Wires
Volume 3
Simple & Effective
A Collection from the Works

of L.B. Cebik, W4RNL
Antennas
Made of Wires
Volume 3
Published by
antenneX Online Magazine
http://www.antennex.com/
POB 271229
Corpus Christi, Texas 78427-1229 USA
Copyright © 2010 by Publisher antenneX Online Magazine. All rights reserved. No

part of this book may be reproduced or transmitted in any form, by any means
(electronic, photocopying, recording, or otherwise) without the prior written permis-
sion of the publisher.
ISBN: 1-877992-87-9
Antennas Made of Wire – Volume 3 4
About the Author
L. B. Cebik, W4RNL, passed away in April 2008. He had written extensively

about antennas and antenna modeling (as well as
other electronics subjects) in most of the U.S. ham
journals, including QST, CQ, Communications
Quarterly, QEX, Ham Radio, 73, QRP Quarterly,
Radio-Electronics, and QRPp. Besides the continuing
series of antenna modeling columns he does for
antenneX (continues through 2010), he also wrote a
column for 10-10 News (An-Ten-Ten-nas) and another
for Low Down (Antennas from the Ground Up). A life
member of ARRL, he served as both Technical and
Educational Advisor. Several years ago, LB joined the
position as Technical Editor for antenneX.
L. B. has published over two dozen books, with works on antennas for both the
beginner and the advanced student. Among his books are a basic and
intermediate tutorial in the use of NEC antenna modeling software and
compilations of his many shorter pieces. Some 30 of these books have been
published by antenneX and listed in the BookShelf at our website.
He was a ham since 1954 and also a life member of QCWA and of 10-10
International. He also maintained a web site ( http://www.cebik.com ) on which he
has placed a large collection of entries from his notebooks and publications
sponsored by antenneX. A PhD and a teacher for over 30 years, he retired as
professor emeritus of philosophy at the University of Tennessee, Knoxville.
antenneX is/was very fortunate, indeed, to have had LB as a member of its
writing team and Tech Editor for some 12 years.
I for one, lament daily at the tragic loss of one of my closest friends. I think of him
often to this day. — November 2010
— Jack L. Stone, Publisher
About the Author

PREFACE
“it’s not just wires anymore, it’s an antenna!”
W
hile numerous articles and books have described various wire antenna
designs, but here is a series of new books from the works of antenna
master, L.B. Cebik, W4RNL (SK). He is known the world over for his
unique ideas about new ways to "bend wires" to get the most out of them. With
LB’s guidance, your success is practically guaranteed. It would be a rare
occasion indeed that any design recommended by this author will not work as
described. One can proceed with that confidence in mind.
This book is dedicated to the design, construction and use of antennas of various
types of wire. The reader can save a lot of time and effort by reading these
books. Then, experiment to your heart's content with an aim toward the goal of
achieving the best signal for your unique environment.
With wire, antennas are very simple and easy to build at a very lowest of cost to
achieve one’s goal. This book will demonstrate a number of designs from
conventional antenna wisdom. How satisfying is it to twist and bend wires
together and make connections only to suddenly discover, it’s not just wires
anymore, it’s an antenna!
One book is not enough to describe all of the best-known and LB’s unique
designs, but we continue with this third Volume picking up where Volume 1 and 2
left off and progress toward the more complex designs.
Along with some recommended wires, a pair of gloves and simple hand tools,
wonders will sprout from your efforts quickly. And, with wires, such designs can
be made to fit within the closest of environments. Many tips are suggested about
how to make cramped spaces an asset rather than a liability—and keep your
neighbors friendly as well.
We know the reader, newbie or advanced, will enjoy this book, Volume 3 of a 3-
book series, by one of the masters and have fun in the process!
Preface
Table of Contents
BROADBAND COVERAGE OF 80/75-METERS WITH AWG #12 WIRE

Chapter 51: Coverage of the 80/75-Meter Band with AWG #12 Copper Wire-----------------7
Chapter 52: Fine-Tune Broadband Antennas for 80/75 Meters----------------------------------38
SOME LONG WIRE
Chapter 53: Center- & End-Fed Unterminated Long-Wire-----------------------------------------60
Chapter 54: Terminated End-Fed Long-Wire Directional Antennas-----------------------------91
Chapter 55: V Arrays and Beams-----------------------------------------------------------------------116
Chapter 56: Rhombic Arrays and Beams-------------------------------------------------------------146
Chapter 57: Multi-Band, Multi-Wire & Multi-Element Rhombics--------------------------------174
THE RHOMBOIDS
Chapter 58: The Dual Rhomboid for 1296 MHz-----------------------------------------------------204
Chapter 59: The Dual Rhomboid, a True Laport Version-----------------------------------------222
Chapter 60: The Dual Rhomboid, Some Comparison Standards------------------------------237
MORE ON WIRE BEAMS-
Chapter 61: Folded X, Hex, Square & Moxon Rectangle Beams------------------------------254
Chapter 62: The EDZ Beams----------------------------------------------------------------------------283
Chapter 63: Feeding the EDZ---------------------------------------------------------------------------300
NVIS
Chapter 64: NVIS: Some Background-----------------------------------------------------------------307
Chapter 65: NVIS: Some Basic Antennas Used----------------------------------------------------330
Chapter 66: NVIS: Antennas with Reflectors--------------------------------------------------------385
Chapter 67: NVIS Dipoles, Inverted-Vs, 1-λ Loops & Doublets---------------------------------434
Chapter 68: Fixed 3-Band NVIS Antennas-----------------------------------------------------------477
Chapter 69: NVIS Antennas for Special Needs-----------------------------------------------------505
WIRE LOOPS
Chapter 70: All-Band Horizontal-Plane Loops-------------------------------------------------------553
Chapter 71: A 40-Meter Star-Shape Loop------------------------------------------------------------563
Chapter 72: Horizontally Oriented & Polarized Big Wire Loops---------------------------------576
Chapter 73: Configuring Horizontal Wire Loops----------------------------------------------------653
Chapter 74: Closed & Interrupted Loops for 40 Meters-------------------------------------------676
Chapter 75: The IL-ZX Loop for 40 Meters-----------------------------------------------------------686
OTHERS
Chapter 76: Experimental Omni-Directional Antennas for 6M----------------------------------704
Chapter 77: Modeling the T2FD------------------------------------------------------------------------741
Chapter 78: Wire Linear-Resonator Dipoles --------------------------------------------------------759
Other Publications------------------------------------------------------------------------------------------789
Chapter 51: Coverage of the 80/75-Meter Band

with AWG #12 Copper Wire
he chapter in The ARRL Antenna Book (9 in the 20th edition) is an
T excellent introduction to techniques for obtain full coverage of the

3.5-4.0-MHz amateur band, a 13% bandwidth as such things are
reckoned. It is also a tribute to long years of work, analysis, and
measurement by Frank Witt, AI1H, the chapter’s author. Nevertheless,
the subject is not completely closed.
The premise for these notes is that we have an endless supply of

AWG #12 copper wire. As well, we can support an 80-75-meter dipole at
90’ above average ground. Besides a little preliminary modeling in free
space, we shall use these values as constants. Our goal is to create a
dipole antenna that covers the entire band with an SWR of less than 2:1,
using a reference impedance value that is appropriate for each situation
that we examine. We shall look at ribbons, cages, parasitic drivers, and
transmission lines. We shall omit the various broadband antennas that
involve using coaxial sections as part of the construction simply because
we cannot effectively model coaxially arranged wires. As we proceed, we
shall recall a pair of matching techniques that employ combinations of
transmission lines, including the system that Witt calls the transmission-
line resonator or TLR. Toward the end, we shall do something that
seems to have eluded authors to this point: we shall combine techniques
for improved radiation and SWR performance. But first, we shall wrap
ourselves in wire.
Some Ribbon and Cage Basics
We may create virtual fat wires by combining thinner wires in

certain arrangements. The most popular forms are the ribbon and the
Chapter 51
cage. Fig. 1 outlines some of the basic shapes and some of the critical
dimensions. We shall consider ribbons with 2 and 4 wires. As well, we
shall look at cages consisting of 4 and 6 wires. Our first task will be to
see what dimensions for each shape coincide with which single-wire
diameters. We may do this within the boundaries of NEC modeling if we
observe a few precautions.
The ends of ribbons and cages often come to a point at both the
center feedpoint gap and at the outer ends to which we normally attach
support ropes. Both angular geometries tend to yield AGT values that are
not ideal (1.000 in free space), and these variations can distort
comparisons. We can avoid the variable AGT values by two simple
modeling techniques. At the outer ends of cages and ribbons, we can
use a simple set of perimeter wires to join longitudinal ends. At the
feedpoint, we may run the wires in straight parallel lines. To create a
common feedpoint, we next select one wire as the source wire. We then
connect from this wire to each other wire in the group a near-zero length
of lossless transmission line. The characteristic impedance is not critical,
since the length is almost zero (1e10-5 or shorter) and virtually no
impedance transformation can occur. These models tend to yield more
accurate results relative to physical ribbon and cage antennas than do
models that try to replicate the details of the many angular junctions. For
example, the current values along wire that are directly fed and fed via
the lengthless lines are identical. As well, the scheme yields rather
precise feedpoint impedance values that coincide with physical antennas.
Chapter 51
Preliminary modeling consisted of checking the correlation

between multi-wire dipole ribbons and cages with roughly equivalent
round-wire dipoles. The test begins with a simple 1-wire dipole. Then it
proceeds to various multi-wire dipoles. In each case, the maximum
dimension is 1’ (12”). So for ribbon elements, the outer wires are 1’ apart.
There is a 2-wire ribbon and also a 4-wire ribbon with the wires 0.3333’
Chapter 51
(4”) apart. The 4-wire cage is 0.707’ per side for a diagonal dimension of
1’. The 6-wire cage has wires 0.5’ apart for a diagonal of 1’.
In each case, I adjusted the length of the dipole to resonance +/-j1-Ω

reactance at 3.6 MHz in free space. The resistive component in each
case is 72 Ohms +/-1 Ω. For each resonant length, I then created a
single-wire dipole of the same length and adjusted the wire diameter for
resonance. A comparison of the “fat” single wire dipole gain values with
the gain for ribbon or cage dipole elements gives a comparative measure
to the relative losses of equally resonant structures. All models showed
an AGT score of 1.000, eliminating the need for any gain value
adjustments. No intermediate current-equalizing shorting wires are used,
although they are common in actual practice.
Table 1 provides the results of the initial runs for a resonant frequency
of 3.6 MHz. From the data, we may draw a few initial conclusions.
1. The minor drop in gain for each multi-wire element relative to

its associated fat-single-wire element shows the small but numerically
noticeable difference in losses. In each case, the fat-wire element also
has a slightly wider 2:1 72-Ω SWR span than the associated multi-wire
element.
Chapter 51
Table 1. Multi-wire dipoles and the equivalent single fat-wire dipoles

Antenna Length Gain dBi 72-Ohm SWR Span
Single wire 133.07 2.04 3.50 to 3.71 MHz
2-wire ribbon 130.90 2.09 3.45 to 3.76

Fat 2.5” wire 130.90 2.13 3.40 to 3.78
4-wire ribbon 130.30 2.11 3.43 to 3.79

Fat 4” wire 130.30 2.13 3.43 to 3.80
4-wire cage 129.40 2.11 3.43 to 3.80

Fat 7” wire 129.40 2.13 3.41 to 3.80
6-wire cage 129.10 2.12 3.42 to 3.80

Fat 8” wire 129.10 2.13 3.41 to 3.83
2. The added two wires in the 4-wire ribbon element are inside the
outer wires that are 1’ apart. The current levels on the inner wires are
about 0.75 the values on the outer wires: lower but still very significant, as
indicated by the shorter resonant length of the 4-wire ribbon relative to the
2-wire ribbon.
3. The differences across the range of multi-wire models are too

small to be operationally noticeable. Even the SWR variation is only 0.07
MHz.
The slight differences in losses between each multi-wire dipole

and its single fat-wire equivalent is not as important a result as the
progression of increases in equivalent single-wire diameters as we
increase the complexity of the multi-wire dipole. If we wish to obtain less
than 2:1 SWR ac5ross the entire 3.5-4.0-MHz span, we can expect to use
much wider wire spacing. However, as we move from simple wire
ribbons to cages, we can also expect a decrease in spacing between
wires. At this stage in our efforts, we may expect some spacing values
Chapter 51
that would place the dipole structure outside the range of practicality.
Nevertheless, we shall explore almost all of the initial options. The one
exception is the 2-wire ribbon. This structure did not achieve the desired
goal even with a spacing of 9’, so I eliminated it from the list of samples.
Table 2 lists the remaining candidates for full-band 80-75-meter

coverage, beginning with a 16”-diameter single-wire dipole. All antennas
are 90’ above average ground, and the multi-wire structures are
composed of AWG #12 copper wire. The antenna specifications list the
wire spacing and the total or the diagonal spacing, as appropriate. See
Fig. 1 to identify the indicated dimensions relative to the structure. The
new table also replaces the data on the SWR span (which is at least 3.5
to 4.0 MHz) with the resonant frequency and the impedance at
resonance. Because these values are all about 72 Ω, the SWR values
are referenced to that value.
The table has a few minor surprises. Although the spacing

between wires shows the progression established in the preliminary tests,
the antenna lengths do not all grow shorter as we increase the complexity
of the structure. The 6-wire cage is somewhat longer than the 4-wire
cage. The table also omits gain values for the 90’-high dipoles, since we
shall address the question of gain across the band once we add a few
other broadband AWG #12 wire antennas to our collection.
Chapter 51
Table 2. Multi-wire dipoles for full coverage of 3.5-4.0 MHz
Antenna Length Res. Fq. Impedance
Single wire 123.6’ 3.72 MHz 71.6 – j0.4 Ω (free space)

16” diameter 89.1 – j4.8 Ω (90’)
4-wire ribbon 123.4’ 3.72 MHz 72.4 + j0.4 Ω (free space)

Wire spacing 2’ 89.3 – j4.1 Ω (90’)
Total width 6’
4-wire cage 121.8’ 3.71 MHz 72.1 – j0.5 Ω (free space)

Wire spacing 3’ 88.3 – j6.0 Ω (90’)
Diagonal 4.24’

Wire spacing 1.5’ 88.6 – j5.9 Ω (90’)
Diagonal 3’
4-wire ribbon structures are subject to some overgeneralization to

the effect that most of the current lies in the outer wires (with the
presumption that little current is along the two inner wires. As shown in
Fig. 2¸ the differential is only about 15%. (Since the antenna view is in
the plane of the wires, only two current curves appear, with overlapping
outer-wire and overlapping inner-wire values.) The ratio of maximum
current on the inner wires to the maximum current on the outer wires
increases as the spacing between wires increases. The ratio for the 4-
wire ribbon with a wire-to-wire spacing pf 0.333’ is about 75% in contrast
to the 85% value for the widely space wires of the full-band 80-75-meter
4-wire ribbon element.
Chapter 51
The models used in developing the data in Table 2 initially used a

free-space environment. The goal in each case was to achieve a 72-Ω
SWR curve. When placed at 90’ above average ground, the values
change, as shown in the table for the free-space resonant frequencies.
However, 72-Ω SWR curve actually becomes shallower, as shown by Fig.
3. One desirable consequence is the fact that there is enough “play” to
allow for variations in ground quality and potential interactions with other
objects in the near field of the antenna with minimal need for field
adjustment of the antenna. In addition, the use of a coaxial cable feedline
of any length will further increase the SWR bandwidth, but with the usual
losses associated with coaxial cables.
The SWR curves in Fig. 2 are based upon the impedance values
at the actual antenna feedpoint. Before we close these notes, we shall
have occasion to add a feedline to the system. However, it will not be the
sort of single-cable installation that we usually think of in connection with
dipole antennas.
Chapter 51
Except for the 16”-diameter single-wire dipole, all of the antennas

modeled are feasible constructs for a serious 80-75-meter installation.
The 4- and 6-wire cages may be the most compact in terms of the cross
section, but require special attention to the set of wire spacers along the
length of the antenna. The 6’ total width of the 4-wire boon version
requires, in contrast, only linear spacing bars at periodic positions along
the element. In all cases, the construction of both the element and the
necessary supports represents a serious antenna installation project.
Parasitic Driver Basics
The cage and ribbon elements share some common features. All
have very significant cross section dimensions. As well, all show a typical
single-element dipole SWR curve with a single minimum at a frequency
just below the arithmetic mid-band point. If we can give up the shape of
the SWR curve, we may achieve full-band 80-75-meter coverage with
Chapter 51
other antenna designs, some of which are more compact with respect to
the cross section dimensions.
The use of open-sleeve or coupled resonator dipoles (and

monopoles) has been around for a considerable length of time. Chapter
7 of The ARRL Antenna Book contains a good introduction to the
practice, although mostly in a multi-band context. The principle is simple
to state, but more difficult to implement, either in models or in physical
antennas. Essentially, we directly feed an element for the lowest desired
frequency in a set of frequencies. By selecting proper spacing and length
values, we may add a series of parasitically coupled elements and
achieve resonance on one or more higher frequencies as determined by
the measured impedance at the feedpoint of the fed element. The goal is
not simply to achieve any resonant condition whatever, but to show an
impedance similar to that of the fed element along. This condition allows
us to use a single transmission-line characteristic impedance to provide a
matched impedance system for all frequencies covered by the multi-
element antenna.
The most common applications of the use of coupled resonators

include collections of monopoles with a common radial system and Yagi-
type directional antennas. In most cases, the goal is to cover 2 or more
amateur bands with a single directly fed element. However, we may also
apply the same technique to expand the SWR coverage of a single
antenna with multiple horizontal wires to cover a very wide band, such as
3.5-4.0 MHz. Slaved or secondary driver elements tend to have a
narrower SWR bandwidth than the directly fed driver. Hence, a single
parasitic element will not normally suffice to spread the coverage of an
AWG #12 copper wire to handle the entire band. We may need more
than one slaved element.
Chapter 51
Fig. 4 shows one version of a 3-wire broadband dipole array for

80 and 75 meters. The elements are AWG #12 copper wire, and the
dimensions apply to that diameter element. Only the longest element has
a direct connection to the feedline, although all three elements contribute
to the ability of the antenna to provide satisfactory SWR coverage from
3.5 to 4.0 MHz. The elements shown are arrayed below the fed element
running from the longest to the shortest. Equally possible is a version of
the antenna with one parasitic element on each side of the directly fed
element, although such an arrangement might well require adjustments to
the length and spacing values used. In the version shown, note that the
spacing between the two slaved elements is less than the spacing
between the fed element and the first parasitic element.
The 3-wire system shown requires a cross-section width of only

1.25’, considerably less than required by any of the multi-wire dipoles
shown in the previous section of these notes. Moreover, the SWR pattern
shown at the driven element feedpoint does not have a single minimum
Chapter 51
value with slowly rising values above and below the resonant frequency.
Instead, as shown in Fig. 5, the SWR show multiple minimums. The
values are well below 2:1 across the band, but often higher than 1.5:1, a
value at which some high-power amplifiers for amateur service set their
fold-back circuit cut-off points. However, like the ribbon and the cage
dipoles, the SWR curve for the 3-wire parasitic system does not include
the losses of reasonable lengths of coaxial cables in the 70-75-Ω range.
The design shown, although generated just for these notes, is not
unlike coupled resonator antennas that have appeared in amateur
journals, such as QST. Construction may be simpler than for any of the
other antennas examined so far, and it does not require any further
matching relative to current equipment input/output impedance standards.
An alternative method of achieving a similar goal is to use a folded

dipole structure in which we place a linear parasitic element in the center.
Lou Rummel, KE4UYP, developed such a design for AWG #12 copper
Chapter 51
wire, and the outline and dimensions appear in Fig. 6. The wire
arrangement is one possibility within a continuum of dimensions that yield
a multi-minimum SWR pattern.
The width of the folded structure is less than 5’. This width is in a
frontier zone between the folded structure acting like a folded dipole and
the structure acting like simply a highly elongated loop. The loop alone is
resonant at about 3.52 MHz, with the linear element having a self-
resonant point at about 4.05 MHz if it were not subject to very high
interaction with the loop. In turn, the parasitic linear element raises the
self-resonant point of the loop to produce the 300-Ω SWR curve in Fig. 7.
The curve for 450 Ω shows that the antenna would be equally at home
with a higher-impedance parallel line, such as common window line. The
latter has about half the loss per unit length as even transmitting versions
of 300-Ω ribbon or tubular line.
Chapter 51
The folded-dipole-linear-parasitic element version of the coupled-

resonator 80-75-meter antenna is the logical counterpart of the 3-wire
version for those who prefer to feed antennas with parallel transmission
line. Since advantages or disadvantages would lie mainly in the preferred
feeding system, we may bypass them for this discussion.
Transmission-Line Broad-Banding
Back in 1997, Dave Leeson, W6NL, brought to my attention an

interesting technique for achieving wide-band operation on the lower HF
bands, especially the 80/75-meter band. The technique derived from
mentions in texts and from references in ARRL publications by Frank
Witt, AI1H, a noted experimenter and evaluator of low-HF broad-banding
methods.
The broad-banding method begins by selecting the geometric mean

between the two desired frequencies (that is, the square root of the
product of the two frequencies). Suppose that we cut a dipole to be
Chapter 51
resonant at this frequency. Next, for the dipoles design frequency, we

should cut a length of 50-Ω coax that is a multiple of a half wavelength so
that its length is perhaps from 0.5-λ to 2.0 λ. Of course, the physical
length will be the line's velocity factor times the electrical wavelength at
the design frequency. To the shack or source end of this line, we connect
a 1/4-λ 75-Ω transformer line section, again multiplying the electrical
length by the line's velocity factor to arrive at a physical length. The result
is a well-established broadening of the operating SWR-bandwidth.
Chapter 51
Fig. 8 shows the general outline of one recommended system

consisting of a 0.5-λ length of 50-Ω cable, followed by a 0.25-λ section of
75-Ω cable. Essentially, the 50-Ohm cable replicates the antenna
feedpoint impedance at resonance, but off resonance, the line is no
longer ½-λ and the impedance is either capacitively or inductively
reactive, according to whether we move below or above the resonant
frequency. Once we further transform these initially transformed
impedance values with the 75-Ω matching section, we obtain a usable 50-
Ω impedance across the band.
The results of the technique can be modeled in a misleading way

if we only use the lossless transmission lines available within NEC.
However, recent implementations of the NEC have introduced methods of
including line losses and arriving at a more accurate picture of the results.
To provide a clearer view of how well the system works, I used the
following lines to model the matching system with the dipole at 90’ above
average ground: 50 Ω: RG-213, VF 0.66, loss 0.6 dB/100' @ 10 MHz; 75
Ω: RG-216, VF 0.66, loss 0.7 dB/100' @ 10 MHz. These cables easily
handle the upper limits of amateur power levels. The sum of the two
lines, accounting for the velocity factors involved, is 129.83’ of cable that
is both part of the matching system and part of the main feed system,
since the elements are in series. (This line length will become significant
shortly.) The total line length is not unreasonable as nearly a minimum
value for a dipole that is 90’ above ground and somewhat offset from the
station equipment.
Chapter 51
Fig. 9 shows the 72-Ω SWR curve for the dipole without the
matching system in place and the 50-Ω curve at the junction of the
matching section and the main feedline. The system easily covers the
entire band, although the SWR values exceed 1.5:1 near the ends of the
band. Theoretically, we can use any multiple of ½-λ for the 50-Ω section
of the line. Longer lines will show the double-dip SWR curve that is not
fully visible with a single half-wavelength section. However, for real lines
with losses, the band-edge SWR performance will deteriorate.
In 1995, Frank Witt, AI1H, presented an alternative to the 50-75-Ω

transmission-line broadband matching system. He called the system the
Transmission-Line Resonator (TLR). It consisted of three lengths of 50-Ω
cable. We shall continue to use RG-213 with a velocity factor of 0.66 and
a loss factor of 0.6 dB/100' as our implementation, which coincides with
Witt's own version. A length of cable connects the antenna terminals to
the source, which can be the station equipment or a further length of 50-Ω
cable that reaches the equipment. At the antenna terminals, he connects
Chapter 51
an open stub across the terminals, effectively adding a shunt capacitance

(more correctly, a capacitive reactance) to the antenna terminal
impedance. At the source end of what Witt calls the "link" line, he adds a
shorted stub across the line, effectively adding a shunt inductance (or
inductive reactance). With the proper proportions, shown for the 80/75-
meter band in Fig. 10, the combination yields a broadband 50-Ω match
for the dipole. The dimensions used in the model vary slightly from Witt’s
original, but fit the dipole length and cables used in the model. Any
implementation of the matching system would require a bit of field
adjustment to arrive at the final lengths of the two stubs and the linking
line. (For detailed information on and calculations for the TLR matching
system see chapter 9 of the current (20th) edition of The ARRL Antenna
Book and Witt’s original article.
Chapter 51
We can view the Witt system as a version of the “match line and
stub” matching system, after suitable adjustment of the feedpoint
impedance values with the top open stub. The calculated values required
for each of the three lines provides for broad-band service by opposing
the natural trends in impedance transformation at key points in the
system. The result is the double-dip 50-Ω SWR curve shown in Fig. 11.
Of the systems that we have examined, only the two transmission-

line matching systems and the 3-wire coupled resonator array arrived at
50-Ω impedances. The ribbon and cage systems use 72-Ω reference
impedances to achieve full band coverage, while the folded-dipole and
linear parasitic element array uses a high impedance value suited to
parallel transmission lines. 50-Ω coaxial cable remains the preferred
feedline based on the nearly universal standard of a 50-Ω input and
output impedance value of current amateur equipment.
Chapter 51
Efficiency
When we combine any antenna with a transmission line in

broadband service, we incur losses at one or both ends of the band
relative to potential performance of the dipole alone. None of our
systems is immune to this condition. Even a system that is well matched
at the resonant frequency is subject to increased feedline losses as we
move away from the resonant frequency and add the SWR multiplier to
basic matched line losses.
Arriving at a reasonably fair comparison of system losses is

difficult at best when we consider that two of the systems require certain
lengths of coaxial cable as part of the matching system. The maximum
line length involved in matching for our 80-75-meter samples is 129.83’.
Therefore, to equalize the playing field, I added to each sample antenna a
cable of this length, using RG-213 for the 50-Ω runs and RG-216 for the
75-Ω lines. The ribbon and cage antennas required a single cable, while
the TLR system requires the addition of a short section of 50-Ω cable to
arrive at the total cable length. Rather than calculating losses in dB, I
simply obtained gain values for each entire system, including antenna
wire and cable losses. The resulting pattern of gain values will reveal—
by comparison with an uncabled AWG #12 copper dipole—not only the
level of loss, but as well the pattern of where in the band those losses are
likely to occur. Table 3 summarizes the loss picture with sample gain
values at 3.5, 3.75, and 4.0 MHz.
Chapter 51
Table 3. Comparative gain values of broadband 80-75-meter antennas and

matching systems at 90’ above average ground with 129.83’ of feedline
Antenna Gain in dBi at 3.5 MHz 3.75 MHz 4.0 MHz

Bare antenna with no feedline 6.10 6.24 6.44
“W6NL” ½ -λ + ¼-λ matching system 5.07 5.68 5.36
AI1H TLR matching system 5.07 5.68 5.36
16” dia reference dipole /75-Ω line 5.52 5.75 5.86
4-wire cage dipole /75-Ω line 5.51 5.76 5.88
3-wire coupled-resonator/75-Ω line 5.58 5.74 5.69
Except at mid-band, the two matching systems show about 0.5-dB

lower gain than the wire antenna samples. Besides showing a higher
band-edge gain, the addition of 129.83’ of 75-Ω transmission line provides
improved SWR bandwidth at the source end of the line by forming a 3/4 –
λ transformer. Fig. 12 exemplifies the altered SWR curve by showing 50-
Ω and 75-Ω curves for the 4-wire cage. All of the ribbon and cage dipoles
would show similar curves.
The SWR curves are satisfactory for virtually al applications.

Perhaps only users of high power amplifiers with very sensitive fold-back
Chapter 51
circuits might find a shortcoming: the 72-Ω SWR exceeds 1.5:1 at the
band edges, although the 50-Ω curves is quite well tamed. A similar
concern might strike the user of a 3-wire coupled resonator system with
an equal length of 75-Ω cable, as shown in Fig. 13.
The final question is whether we can further tame the SWR curves
without adversely harming dipole efficiency.
Combining Techniques
A simple AWG #12 copper wire dipole responds to either the

W6NL or the AI1H transmission-line based matching systems with an
SWR curve that yields a 50-Ω SWR less than 2:1 across the 80-75-meter
band. Equipping the ribbon and the cage dipoles with a 75-Ω cable of the
specified length (129.83’) produces even lower SWR values using a 50-Ω
reference. The final question, applicable only to those who use
Chapter 51
equipment sensitive to 50-Ω SWR values above 1.5:1, is whether we can

lower the SWR curve even further. To a limited extent, we can.
Although I am aware of no actual attempt to do so, there is no rule

against combining a wide-band dipole with the W6NL matching system.
Like the thin-wire dipole, all of the cages and ribbons have resonant
impedances close to 72 Ω. Therefore the mid-band SWR values for the
original design and when applied to a ribbon or cage will be quite similar.
The differences will appear as we move away from the resonant
frequency. The thin-wire dipole shows a rising SWR based on a slow
change in the resistive component and a faster change in the reactance.
The 3-wire coupled resonator system shows a relatively flat SWR

relative to 72 Ω across the band. At the band edges, we find no
significant increase in the reactance, but instead a small fluctuation. As a
consequence, the band-edge values should not depart radically from the
mid-band SWR value.
In fact, as revealed by the SWR curves in Fig. 14, we do obtain a

small amount of improvement, but it applies in the main to the 72-Ω SWR
curve. The 50-Ω curve average value is not quite as good as when we
use a simple run of 75-Ω cable, but the value at 4.0 MHz is marginally
better. (In either case, we might shorten the second parasitic driver
slightly and stretch the SWR curve to give us a vale of less than 1.5:1.)
Modeling simplifies the calculation of both the antenna impedance and
the line losses at each frequency in the 3.5-4.0-MHz span so that we can
obtain a relatively reliable assessment of our design options.
Chapter 51
We can apply the same technique to any one of the wide-band

ribbon or cage dipoles and assess its performance against the use of a
75-Ω cable alone. Fig. 15 provides the 50-Ω and 72-Ω SWR curves for
the 4-wire cage version. Once more, the improvement accrues to the 72-
Ω curve rather than to the 50-Ω curve.
Chapter 51
Perhaps the best application of combined broad-banding methods

involves dipole designs that do not quite reach the desired goal of an
SWR curve with maximum values of less than 2:1, but that are
improvements upon the simple thin wire (AWG #12) dipole. Early on, we
rejected the use of a 2-wire ribbon dipole for this very reason. Suppose
that we construct such a dipole with a 5’ wire spacing. The 72-Ω SWR
curve in Fig. 16 shows why we omitted the design. The SWR rises above
2:1 well before we arrive at either band edge, although the curve is
certainly an improvement upon the thin-wire dipole shown as one of the
curves in Fig. 9.
If we add our standard 129.83’ length of 75-Ω cable, we obtain a

50-Ω curve with a maximum SWR value of about 1.6:1. However, if we
instead employ a ½-λ 50-Ω cable plus a ¼-λ 75-Ω matching section, we
obtain a curve with a maximum 50-Ω SWR of about 1.3:1. This final
curve would satisfy the requirements of even the most sensitive fold-back
Chapter 51
circuit. Similar results would emerge with undersized versions of most of

the ribbon and cage dipoles.
Whether we lose anything by using the matching system rather

than the simple cable run appears in Table 4. The data compares
antenna-only gain values with values that emerge from the use of a
simple 75-Ω cable and from the more complex matching system.
Table 3. Comparative gain values of a 2-wire ribbon dipole for 80-75-
meter at 90’ above average ground alone, with 129.83’ of feedline, and
with a 129.83’ matching system
Antenna Gain in dBi at 3.5 MHz 3.75 MHz 4.0 MHz

2-wire ribbon ant with no feedline 6.13 6.26 6.45
2-wire ribbon/75-Ω line 5.33 5.70 5.77
2-wire ribbon/ “W6NL” match 5.36 5.70 5.73
Chapter 51
As we might expect, the 2-wire ribbon dipole with either feedline

shows better gain values than a thin-wire dipole equipped with either the
AI1H TLR match or what we have labeled for convenience as the W6NL
match. The similarity of gain values between the single-cable feedline
and the matching system shows that there is essentially no difference in
feedline efficiencies, since the SWR values at the antenna feedpoint do
not rise to very high values but instead only to inconveniently high values.
One way to minimize losses from a matching system and to arrive at a
more nearly perfect SWR curve is to begin with a reasonably wide-band
dipole design (even if not perfect) and to apply the matching system to it
rather than to a thin-wire dipole.
Conclusion
We have examined numerous, but by no means all, of the broad-

banding techniques. We progressed from complex wire dipoles to multi-
wire coupled resonator arrays and finally to transmission-line-based
matching systems. We required no lumped components or coaxial
antenna sections to achieve exceptionally broadband results. Our only
presumption was that we would need a feedline about 1.4 times the
height of the antenna above ground for the 90’ height used in the
samples.
The best results occurred with broadband dipoles and either 75-Ω
cable or one of the transmission-line-based matching systems. Although
the samples used the W6NL system, the AI1H system would have
returned equivalent results. Each case showed that if we opt for a coaxial
cable feedline, a certain reduction in gain is a cost of the option, however
we arrange the cable. However, the broader the bandwidths of the initial
dipoles, the lower were the losses at the band edges. Moreover, by
combining physical methods of creating broadband dipoles with
Chapter 51
appropriate matching methods, we could reduce the required structural

size of the dipole and still obtain a 50-Ω SWR curve that never reach a
value of 1.5:1. Hence, the initial broadband ribbon and cage dipoles can
have smaller cross sections and still arrive at a very desirable SWR curve
without further sacrificing gain at either band edge.
Appendix: The UR0GT Broadband 80-75-Meter Dipole
Recently, I uncovered an interesting dual-wire broadband antenna for

80 and 75 meters from Russia, a design by UR0GT. In metric terms, it
consists of two 2-mm diameter copper wires, each 37.88 m long.
However, as shown in Fig. 17, the wires are offset relative to the center
point. The shorter wire is (in my NEC-4 model) 17.3 m long, while the
longer wire is 20.58 m. The spacing is 1.48 m, although this dimension is
not critical within several centimeters, but it does set the mid-band relative
phase angles of the element currents. At the center point, between the
two wires, we run a single wire and feed it in the middle.
Chapter 51
The 50-Ω SWR curves show distinct higher and lower frequency
resonance points. To move each resonant frequency, one may adjust the
length of either the longer wire or the shorter wire. Although the
frequencies of the resonant points are relatively independent, their
positions determine both the band-edge and the mid-band SWR values.
Note from the SWR curves that, like all broadband 80/75-meter antennas,
the SWR curves will be somewhat height-sensitive, since on average,
antennas for the band are less than ½-λ above ground. Therefore,
anyone who wishes to replicate the antenna—and it is worthy of
Chapter 51
replication—should model the exact dimensions for the planned

installation height.
The offset wires of the antenna produce some patterns—at the

band edges—that are also offset from a true broadside to the wires. Fig.
18 provides 3 E-plane free-space patterns to show the effect. In general,
the pattern offset is only about 3° relative to a true broadside in the
extreme cases. Therefore, with a beamwidth approaching 80°, an
operator could not detect the pattern offset during use, even when
switching from the low end of the CW band to the top end of the phone
allocation.
One key to the operation of the UR0GT wide-band antenna is the fact
that on each side of center, the two wires are 90° apart in current phase
angle at 3.75 MHz. The relative current magnitudes on the short and the
long sections vary with frequency within the overall passband, yielding a
low 50-Ω SWR across the entire band. Note in Fig. 19 the dominance of
either the long wire or the short wire at the lower and upper band edges.
(The last line in the data in the figure shows the ratio of higher to lower
Chapter 51
current and also the phase-angle difference [Δ] between the wires at each
sampled frequency.)
The relative simplicity of the UR0GT antenna recommends it for

consideration among the array of broadband options for the 80/75-meter
band. With the usually lengths of coaxial cable necessary to connect the
antenna to the station, the SWR curves at the equipment end of the line
should be even flatter than those shown. However, as with all antenna
designs, successful replication lies in the details of the installation.
Chapter 51
Chapter 52: Fine-Tune Broadband Antennas for 80-75 Meters
I
n Chapter 51: “Coverage of the 80/75-Meter Band with AWG #12
Copper Wire”, I explored some of the methods for obtaining full
coverage across the 3.5 to 4.0 MHz span with a single antenna. I re-
examined some further options in a QEX column that opened some
additional possibilities offered by combining broadbanding techniques.
Some of the methods of matching via combinations of transmission line
proved robust enough to allow the use of ribbon or cage constructs with
relative small proportions, instead of the very large dimensions required
for direct full coverage by the antenna alone. In fact, we were able to
obtain 50-Ω SWR curves with values less the 1.5:1, thus meeting the
most rigorous requirements of amateur amplifiers having the most
sensitive fold-back circuits.
Near the end of the QEX piece, I cautioned that the dimensions
shown in the samples applied only to antennas in the 70’ to 100’ height
range over average ground. Outside that range, the antenna builder will
have to make a considerable number of experimental adjustments to
assure performance, and at some heights, the arrangement may not work
at all. Because most amateurs under-appreciate the effects of height on
the resonant frequency and feedpoint impedance of dipoles less than 1 λ
above ground, we might well re-visit the question. Along the way, we
shall discover why certain matching schemes have application only at
certain heights for 80-75-meter antennas. As well, we can investigate
how we might tailor the dipole length and the lengths of cables forming
the matching system to optimize performance at heights within the usable
range.
Chapter 52
Some Fundamentals
The restrictions and the goals for our project remain unchanged
relative to earlier investigations. The antenna material is AWG #12
copper wire. I use the following transmission lines to model the matching
system with the dipole at 90’ above average ground: 50 Ω: RG-213, VF
0.66, loss 0.6 dB/100' @ 10 MHz; 75 Ω: RG-216, VF 0.66, loss 0.7
dB/100' @ 10 MHz. These lines easily handle amateur power limits on 80
and 75 meters. The goal is to achieve with reasonable efficiency a 50-Ω
SWR curve from 3.5 to 4.0 MHz with no SWR value exceeding 1.5:1.
Fig. 1 reviews the most common options for obtain wide-band

performance directly from the antenna structure. A single wire that is 16”
in diameter will just cover the band with a 72-Ω SWR of 2:1 or less. Such
a wire is impractical in amateur (or any other) service, so we tend to
create simulations composed of several wires (AWG #12 by our
specification). One popular choice is a ribbon element composed of 2 or
more wires in a common plane. An alternative is the 4-wire or 6-wire
cage of wires.
Models of these structures use end structures similar to those

shown in the sketches rather than creating junctions of wires forming a
point. At the center feedpoint, the models use linear wires and create a
parallel feedpoint by running near-zero length transmission lines from the
designated source wire to the center segment of each other wire. These
measures result in uniformly ideal average gain test values that facilitate
comparisons. In these notes, we shall be interested almost solely in
matters relating to the feedpoint impedance and the SWR curves across
the 3.5-4.0-MHz band.
Chapter 52
Table 1 provides the required dimensions for full-size dipoles

using each type of structure displayed in Fig. 1. The 2-wire ribbon
antenna is missing because there is no practical size that will cover the
entire band.
Chapter 52
Table 1. Dimensions of dipoles with virtually identical full-band

coverage of 80-75 meters with less than a 2:1 72-Ω SWR value
Antenna Length Res. Frequency Impedance
Single wire 123.6’ 3.72 MHz 71.6 – j0.4 Ω (free space)

16” diameter 89.1 – j4.8 Ω (90’)
4-wire ribbon 123.4’ 3.72 MHz 72.4 + j0.4 Ω (free space)

Wire spacing 2’ 89.3 – j4.1 Ω (90’)
Total width 6’

Wire spacing 3’ 88.3 – j6.0 Ω (90’)
Diagonal 4.24’

Wire spacing 1.5’ 88.6 – j5.9 Ω (90’)
Diagonal 3’
Since our goal is to combine the simulated fat dipole with a

second broadbanding technique, we do not need to achieve full band
coverage. Instead, we may opt for more reasonable cross-section
dimensions for the multi-wire dipoles. Table 2 provides very usable
dimensions of dipoles having virtually identical properties. Note that the
band-edge 72-Ω SWR values are just about the same in each case. The
cross section dimensions fall within the shop capabilities of most serious
80-75-meter antenna users. Despite the smaller dimensions, the ribbons
and cages achieve a fair amount on initial broadbanding when compared
to the reference single AWG #12 wire dipole at the bottom of the list.
Chapter 52
Table 2. Dimensions of dipoles at 90’ above average ground with virtually

identical coverage of 80-75 meters
72-Ω SWR at
Antenna Length 3.5 MHz 4.0 MHz
2-wire ribbon 122.4’ 2.42 2.17

Wire spacing 5’ (60”)
4-wire ribbon 125.3’ 2.41 2.15

Wire spacing 0.3’ (3.6”)
Total width 0.9’ (10.8”)
4-wire cage 125.2’ 2.41 2.16

Diagonal 0.57’ (6.79”)
6-wire cage 125.4’ 2.39 2.16

Diagonal 0.4’ (4.8”)
Single #12 wire (reference) 128.8’ 3.54 3.78
We do not need to use a 2:1 limiting value of SWR because the

transmission-line matching systems we shall employ are capable of
achieving that value with a single AWG #12 wire dipole. Instead, we
need sufficient broadbanding from the antenna structure alone so that
when we apply the transmission-line matching schemes, the maximum
50-Ω SWR value will be less than 1.5:1.
There are two general matching methods in use, and both appear
in Fig. 2. The two-line system uses a ½-λ section of 50-Ω cable followed
by a ¼-λ section of 75-Ω cable. At 90’, the dipole impedance is close to
90 Ω at resonance. If we cut the ½-λ section of 50-Ω cable for the
geometric mean frequency of the passband (about 3.742 MHz), the
feedpoint impedance will repeat itself at that frequency. On either side of
this frequency, the cable length will no longer be precisely ½-λ. Hence,
Chapter 52
the impedance at the source end will be a transformed value. When we

pass the range of transformed impedance values through a ¼-λ 75-Ω
matching section, the new impedance values will be very close to 50 Ω
across the entire band. Adjusting the cables for the 0.66 velocity factor
that applies to both lines, we obtain a combination of 86.55’ and 43.28’ for
a total length close to 130’. For an antenna that is 90’ above ground and
offset from the operating position, the line length is reasonable as a
minimum needed to reach from the equipment to the antenna. Any
additional cable length would use 50-Ω cable.
Chapter 52
The right side of Fig. 2 shows the three-line system developed by

Frank Witt, AI1H, in 1995. One can view the system equally as a single
line with the antenna tapped down from the open top and the main 50-Ω
feedline tapped upward from the shorted bottom. For full-band coverage
with a simple AWG #12 dipole, Witt discovered that the SWR bandwidth
improved if he moved the self-resonant dipole frequency downward from
the geometric mean frequency to the indicated value of 3.710 MHz.
Since we shall make comparisons and since the line length of this all-50-
Ω system between the antenna and the main feedline does not quite
equal 130’, I added 30’ of RG-213 between the shorted-stub junction and
the model source.
As the 50-Ω SWR sweeps in Fig. 3 show, both matching systems

are capable of matching a single-wire AWG #12 copper dipole to values
less than 2:1 across the entire 80/75-meter band. In the test model, the
total transmission-line length is 130’. Moreover, the antenna is at a fixed
90’ height above average ground. Our requirement is more severe: 50-Ω
Chapter 52
SWR values of less than 1.5:1 across the band. In pursuit of that goal,
we shall have to adopt a dipole with an initial SWR bandwidth that is
wider than the value we may obtain from a single #12 wire. Moreover, we
may wish to vary the antenna height and the soil quality. Each of these
variations from the original problem confronts us with limitations of the
matching systems.
Both matching systems rely on the fact that at about 90’ the dipole
impedance at resonance is approximately 90 Ω. An impedance value in
this vicinity provides the correct conditions for the main 50-Ω line in either
system to transform off-resonance impedance values within the passband
to values that, when further transformed by the ¼-λ series section or
compensated for by the open and shorted stubs, provide near-50-Ω
impedance values across the band. At other heights, the dipole resonant
impedance may not be optimal.
To sample what happens to a dipole with changes in antenna

height, let’s select one of the semi-fat multi-wire constructs. Since they all
have the same resonance impedance and SWR bandwidth, any of the
constructs will do the job. Therefore, I selected the 4-wire cage as our
representative from the group in Table 2. I then surveyed the results of
varying the height in 10’ increments from 30’ to 150’. Table 3 provides
data from this series.
Chapter 52
Table 3. The effects of antenna height above average ground on the

impedance properties of a semi-fat 4-wire cage dipole 0.4’ (4.8”) per
cross-section side dimension
Height Impedance (Ω) 72-Ω SWR Resonant

Feet λ at 3.745 MHz 3.5 MHz 4.0 MHz Frequency MHz
30 0.114 51.1 + j14.6 2.68 3.81 3.675
40 0.152 61.2 + j17.6 2.27 3.54 3.650
50 0.190 71.9 + j16.4 2.05 3.21 3.650
60 0.228 80.8 + j11.3 2.00 2.90 3.675
70 0.266 86.5 + j3.8 2.07 2.61 3.700
80 0.304 88.4 – j4.7 2.22 2.36 3.725
90 0.342 86.9 – j12.5 2.41 2.16 3.750
100 0.380 82.6 – j18.4 2.62 2.03 3.775
110 0.418 76.8 – j21.7 2.83 1.99 3.800
120 0.457 70.6 – j22.3 3.03 2.07 3.800
130 0.496 65.2 – j20.3 3.18 2.24 3.775
140 0.533 61.3 – j16.5 3.26 2.45 3.775
150 0.571 59.6 – j11.6 3.25 2.64 3.750
(Free Space 72.4 + j0.6 2.73 2.41 3.745)
Notes: 1. Dipole length: 125.2’. 2. Height in λ at 3.745 MHz.

3. Resonant frequency to nearest 0.025-MHz increment.
The table reveals that the impedance at the geometric mean

frequency of the 80-75-meter band varies both the resistive and reactive
components, but the cycles are offset from each other. There are two
significant consequences of the variation. First, the impedance value is
only optimal for broadband transformation in a fairly narrow range of
heights above ground, perhaps in the 70’ to 110’ range for the low
maximum value of permitted 50-Ω SWR. Second, the shifting reactive
component strongly suggests that the dipole length itself may become
one of the variables as we attempt to optimize the matching system for
different heights above ground.
Chapter 52
Adjusting the 2-Line Matching System with a 4-Wire Cage Dipole
As shown in Fig. 2 on the left, the 2-line matching system consists

of a ½-λ 50-Ω line that functions to pre-transform dipole feedpoint
impedance values in preparation for the final transformation in the ¼-λ
75-λ line section. The initial system used lines calculated for a height of
90’ above average ground and for the geometric mean frequency in the
passband. The SWR curve in Fig. 4 shows that the result meets the
initial specifications. The character of the curve differs somewhat from
the curve for the same matching system applied to the single-wire dipole.
Rather than having SWR peak values only at the band edges, we also
find a mid-band peak value. We shall use this peak value in conjunction
with the band edge values as we characterize the performance of the
system at various heights above ground.
Chapter 52

impedance properties of a semi-fat 4-wire cage dipole plus a 2-line
matching section

Feet λ at 3.745 MHz 3.5 MHz Mid-Band 4.0 MHz Frequency MHz
30 0.114 88.0 – j39.1 1.94 2.27 1.86 3.650
40 0.152 76.2 – j31.9 1.70 1.97 1.74 3.650
50 0.190 69.5 – j23.9 1.48 1.72 1.61 3.625
60 0.228 66.0 – j16.6 1.33 1.52 1.49 3.650
70 0.266 64.6 – j10.3 1.24 1.40 1.38 3.650
80 0.304 64.7 – j4.6 1.24 1.33 1.28 3.700
90 0.342 66.1 + j0.4 1.29 1.33 1.18 3.745
100 0.380 68.7 + j4.8 1.37 1.40 1.10 3.775
110 0.418 72.6 + j8.2 1.47 1.50 1.09 3.800
120 0.457 77.7 + j10.1 1.56 1.61 1.16 3.800
130 0.496 84.1 + j9.5 1.65 1.72 1.26 3.775
140 0.533 89.6 + j5.7 1.72 1.81 1.34 3.750
150 0.571 92.1 – j0.8 1.75 1.87 1.40 3.750

Table 4 provides data on what happens as we change the

antenna height with the standard matching system. The italicized entries
show the range of acceptable SWR curves to meet the stringent 1.5:1 50-
Ω SWR limit. As the changing difference in the band-edge SWR values
with different heights suggests, the mid-band peak value may vary its
frequency. In most instances, the mid-band peak SWR value is the
limiting factor in meeting specifications. Still, we may note that for all
heights except the lowest, the semi-fat cage plus the matching system
meets the usual 2:1 SWR limit that may apply to less critical systems.
There are no rules against adjusting the dipole and the

transmission line lengths to better optimize the system. The standard
calculation of the ½-λ 50-Ω line section yields a length of 86.5’, while the
75-Ω transformer section is half that length—when we adjust the lengths
for the velocity factor of 0.66. The standard calculation uses the
Chapter 52
geometric mean frequency of about 3.742 MHz. We may alter any one or
more of the three variables to seek a better curve. We may define a
better curve as one in which all peak SWR values are the lowest possible
with relatively equal values for all three peaks (band-edge and mid-band).
We shall eventually modify this definition slightly.
As samples of what the adjustment process may yield by way of

different lengths for the dipole and the two transmission lines, let’s
arbitrarily select dipole heights of 70’, 90’, and 110’. In this way, we can
compare the results with the initial table that used standard calculated
length for the transmission lines. In general, changing the dipole length
has no significant effect on the mid-band peak. However, it does allow
one to equalize as best possible the band-edge peak values of SWR.
Changing the line length affects the impedance transformations and may
raise or lower all three peaks. Table 5 provides the key dimensions and
SWR results from optimizing the system for each of the three heights.
Table 5. Optimized dimension and 50-Ω SWR results for 70’, 90’, and 110’
high 4-wire cages dipoles with a 2-line matching system
Dipole Dipole ½-λ Line ¼-λ Line 50-Ω SWR

Height Length Length Length 3.5 MHz Mid-band 4.0 MHz
70’ 124.4’ 85.5’ 43.75’ 1.23 1.39 1.30
90’ 125.2’ 86.0’ 41.25’ 1.22 1.32 1.19
110’ 126.0’ 85.5’ 42.25’ 1.33 1.44 1.24
The changes in line lengths for a 90’ dipole height are largely
cosmetic, compared to using the standard calculations. However, at both
70’ and 110’, the changes in all three variables yield superior SWR curves
compared to making no changes at all. The required dipole length
increases with height. However, for both new heights, the ½-λ 50-Ω line
is slightly shorter than for 90’. In contrast, in both cases, the ¼-λ 75-Ω
transformer section is longer. The precise changes are functions of the
Chapter 52
fact that as we change the antenna height, the resistive and reactive
components of the impedance do not change in step with each other.
Although we have altered the dimensions to improve the SWR

curves over average soil at the three test heights, we have yet to see how
the curves change as we change the soil quality. To test this aspect of
the broadbanding question, I created SWR curves for each variation of
the original system for three soil types: very good (cond. 0.0303 S/m,
perm. 20), average (cond. 0.005 S/m, perm. 13), and very poor (cond.
0.001 S/m, perm. 5). Fig. 5, 6, and 7 show the family of curves for each
antenna height. The results may provide us with clues as to further
refinements we might make to the adjustments.
Chapter 52
In conjunction with the data in Table 5, the three SWR plot

collections tell us a bit of a story. Over average ground, the dipole at 90’
Chapter 52
provides the best SWR pattern across the passband. We must note that
soil improvement also yields SWR improvement—however small it might
be—while soil degradation provides a less optimal plot. As we reduce the
antenna height, with a resulting change in the dipole length to keep the
curve centered, we find slightly lesser values over average ground than
we found at 90’, but the three curves for different soil types are more
tightly grouped with far less difference related to soil quality. In contrast,
the family of patterns at 110’ results in patterns with a higher set of mid-
band peak values. In fact, the SWR curve for very poor soil yields a mid-
band peak value just slightly above our 1.5:1 limit. The variations that we
see inform us of a basic system limitation.
The 2-line matching system limits the degree of variation that we

can put into the antenna and feedlines in terms of adjusting the
impedances that the lines transform. As a result, the basic curves for
heights that depart from the most optimal value (90’ in this example) are
less optimal (although quite acceptable). A superior matching system
would be one that would allow us to match at 70’ and at 110’ the basic
curves displayed at 90’. Such a system would not necessarily be able to
fully compensate for the antenna impedance changes for all mounting
heights, especially when the impedance approaches 50 Ω. However, it
would allow us to carry the compensation for height changes a good bit
further.
Adjusting the AI1H Matching System with a 4-Wire Cage Dipole
If we use the same 4-wire cage construction for our dipole and
then employ the AI1H matching system, as outlined on the right in Fig. 2,
we add a fourth variable to the adjustment list. We may change the
length of the dipole itself, which will be longer than the dipole for the 2-line
system. In addition, we can change the lengths of the main linking line,
Chapter 52
the open stub at the dipole end, and the shorted stub at the junction with
the main feedline. Before we explore these changes, let’s create a set of
data on the changes created by simple height changes with the standard
set-up relatively optimized for a height of 90’. Table 6 provides the
necessary information.
impedance properties of a semi-fat 4-wire cage dipole plus the AI1H
matching system

Feet λ at 3.745 MHz 3.5 MHz Mid-Band 4.0 MHz Frequencies MHz
30 0.114 103.4 – j27.4 1.28 2.26 1.79 3.650, 4.000
40 0.152 87.8 – j28.7 1.22 2.02 1.72 3.625, 4.000
50 0.190 76.5 – j25.0 1.21 1.79 1.64 3.525, 3.975
60 0.228 70.1 – j20.1 1.24 1.60 1.55 3.550, 3.950
70 0.266 65.9 – j15.0 1.28 1.46 1.47 3.575, 3.950
80 0.304 63.6 – j10.1 1.32 1.34 1.38 3.600, 3.925
90 0.342 62.6 – j5.4 1.36 1.28 1.29 3.650, 3.925
100 0.380 62.9 – j0.9 1.38 1.28 1.20 3.625, 3.950
110 0.418 64.4 + j3.4 1.40 1.35 1.12 3.600, 3.975
120 0.457 67.4 + j7.0 1.39 1.45 1.11 3.575, 4.000
130 0.496 71.9 + j9.4 1.38 1.56 1.18 3.550, 4.000
140 0.533 77.4 + j9.5 1.34 1.65 1.27 3.525, 4.000
150 0.571 82.6 + j6.6 1.29 1.72 1.35 3.525, 4.000

For reference, Fig. 8 shows the 50-Ω SWR sweep for the initial
system at 90’ above average ground. The curve is similar to the one for
the 2-line system (in Fig. 4) in having not only band-edge peak values,
but also a distinct mid-band peak SWR value. Essentially, when we place
an antenna analyzer at the junction of the main feedline and the matching
system, we shall find two near-resonant frequencies, as reflected in the
tabular data. We may note in passing that the two frequencies are
closest together at the height at which we obtain the most optimal results.
Chapter 52
As we move away from that height, either upward or downward, the two
frequencies grow father apart.
The height range for basically acceptable results extends from

about 70’ to 120’ over average ground, using the unmodified matching
system. In fact, performance tilts toward higher elevations using a 2:1
standard, with usable values all of the way to 150’ and beyond. However,
at lower height (30’ and 40’), the curves exceed even a 2:1 50-Ω SWR
limit.
Adjusting all four of the variables to optimize the curves for various
heights requires patience, and even so, there are other combinations that
can produce virtually the same results. Table 7 shows the results of
optimizing the 50-Ω SWR curves for 70’, 90’, and 110’ above average
ground. Once more, the dipole length increases as we increase the
antenna height over the span of the samples. However, the other length
values do not appear to follow a clearly regular pattern because the
Chapter 52
antenna feedpoint impedance value changes with both the height above
ground and the length of the dipole. Since the resonant points are widely
separated, resonating the dipole at a particular frequency does not
provide ready guidance.
Table 7. Optimized dimension and 50-Ω SWR results for 70’, 90’, and 110’
high 4-wire cages dipoles with a 2-line matching system
Dipole Dipole Open St. Shorted St. Link Line 50-Ω SWR
Height Length Length Length Length 3.5 MHz Mid-band 4.0 MHz
70’ 124.4’ 13.5’ 21.5’ 99.0’ 1.33 1.25 1.35
90’ 127.0’ 13.5’ 21.0’ 99.0’ 1.33 1.25 1.33
110’ 127.8’ 13.1’ 22.0’ 99.5’ 1.28 1.27 1.28
The goal of the optimizing exercise was to produce roughly equal

band-edge SWR values accompanied by the lowest possible mid-band
peak SWR value. The process does yield curves for each height that are
very close to coincident, unlike our results with the 2-line system. In none
of the curves does the SWR value exceed 1.35:1.
As we did for the 2-line system, we shall compare the SWR

curves with the optimized settings for very good, average, and very poor
soil. Fig. 9, 10, and 11 provide the visual comparisons among the soil
types for each of the 3 heights. Because the availability of 4 variables
allows the basic curves at each height to reach similarly low levels, none
of the soil variations pushes any curve close to the 1.5:1 50-Ω limit.
Chapter 52
Chapter 52
The curves share a common trait: as the soil quality increases, the
frequency differential between resonant points decreases. In fact, the
frequency spacing between SWR minimum points follows the same
pattern with the 2-line matching system, but those curves are too shallow
to detect it easily. The poorest soil yields the highest mid-band SWR
peak values, regardless of antenna height (within the sampling range),
but the spread of the SWR minimum points often accompanies these
peaks with lower band-edge SWR values. In the end, construction and
installation site variables would likely obscure the fine shades of
difference in the plots.
Nevertheless, the similarity in SWR plot families is a function of

adjusting the variables in the antenna and its matching system, and the
differences show up as measureable differences in the dimensions used.
Whatever the matching system, modeling and optimizing the system in
advance of installation yields two beneficial results, even in the presence
of unmodeled site objects. First, it normally leads to first tests that are
Chapter 52
closer to final adjustments. Second, the modeling process gives some

insight into what adjustments are necessary to move the system’s SWR
curves in the desired direction.
Conclusion
Of the two transmission-line matching system, the AI1H version

offers more flexibility in bringing SWR curves under the most stringent
control over a greater range of dipole heights, if we presume the use of a
semi-fat wire simulation, such as the 4-wire cage used in these exercise.
Similar results would accrue to the other equivalent dipoles in ribbon or
cage form. The variability of a dipole’s impedance with height changes in
the region below 1 λ limits any matching system, but for covering the full
80-75-meter band with a single antenna that requires no tuning and that
is at heights normal to serious amateur operation, The AI1H matching
system has a few distinct advantages compared to the simpler two line
system
The more complex matching system also has one disadvantage:

a slight deficiency in efficiency relative to the 2-line system. Table 8
compares the maximum gain of each system to a 4-wire cage dipole fed
directly at its source (with no transmission line at all). The difference is
small and perhaps not operationally noticeable. But it exists and is worth
noting.
Chapter 52
Table 8. Comparative performance of the composite solutions to

broadbanding antennas for 80-75-meters using 4-wire cage dipoles at 90’
above average ground plus a transmission-line matching system
Gain at
System 3.5 MHz 3.75 MHz 4.0 MHz
4-wire cage fed at feedpoint 6.16 6.29 6.48
With 2-line system 5.41 5.75 5.78
(Gain loss) (0.75) (0.54) (0.70)
With AI1H system 5.18 5.56 5.52
(Gain loss) (0.98) (0.73) (0.96)
Whichever system one uses, the combination of a semi-fat dipole

and a transmission-line match, assuming that the antenna height is within
the range of the matching system, does allow a degree of adjustment that
is worth exploration if the goal is to produce the lowest 50-Ω SWR over
the widest possible 80-75-meter bandwidth.
Chapter 52
Chapter 53: Center- & End-Fed Unterminated Long-Wire
A
mong the oldest directional antennas are the ones labeled
"long-wire" antennas. Dating to the late 1920s and early
1930s, we still find some of these antennas in active use--
not only in amateur circles, but as well in government and military
service. Classic names, such as Beverage and Bruce attach to
early developments of long-wire antennas. In the group, we include
bi-directional antennas such as the long center-fed doublet and
end-fed wire, along with more directional arrays such as the
terminated long-wire, the terminated V-beam, and the rhombic.
The theory of long-wire antennas appears early on in most college

antenna texts. Once noted, along with the obligatory collection of
basic equations that describe some long-wire properties, most
authors pass on, never to touch the long-wire group again.
Amateurs come upon one or more representatives of the group and
wonder what they do and how they do it. Few have access to the
seminal articles out of which long-wire technology arose or even to
classic books in the field, such as Harper's Rhombic Antenna
Design or Walter's Traveling Wave Antennas. Today, some of the
terminology surrounding long-wire antennas seems strange. For
example, how long is a long-wire antenna? Some folks see a 135'
doublet (or even a 135' end-fed wire) and think of it as a long-wire
antenna. On 80 meters, where the wire is about 1/2-wavelength, it
is not a long-wire. However, on 10 meters, the wire is 4
wavelengths and is entering into the realm of long-wire aerials.
There is no definite boundary that marks the entry point to long-wire
antennas. However, when we examine the properties of long wires
Chapter 53
to see what performance properties that we want to derive from

them, then we shall quickly learn that "long-wire" means for
practical purposes "many wavelengths long."
The ready availability of a vast literature on long-wire antennas

seemingly makes these notes superfluous. The end of each
episode in this series has a short list of basic references. However,
I receive numerous questions about the properties of long-wire,
enough to suggest that a review of long-wire technology might be in
order. We shall have occasion in these notes to touch upon a few
of the equations defining long-wire antennas, but we shall mostly
try to develop a more visually intuitive understanding of their basic
properties. Antenna modeling software has the ability to provide
polar plots of antenna patterns and other important data that will
assist us in this process. As well, by the judicious use of the
software, we shall discover that some of the more complex
equations that define some of the equally complex forms of long-
wire antennas will become unnecessary: we can design optimized
long-wire arrays wholly within the software.
Along the way, we, we shall encounter some traditional terms, such
as rhombic "tilt angle" and "traveling-wave" antenna. Many college
texts are gradually replacing the term "traveling-wave" with "non-
resonant" or "terminated." As we shall discover, a terminated
antenna is one that ends with a resistance. Since the resistance will
dominate the feedpoint impedance, the antenna becomes non-
resonant over a fairly wide operating bandwidth. How these two
ideas relate to the term "traveling-wave" we shall learn at the
proper place along our path?
Chapter 53
Everything begins with the wire antenna, plain and simple. So our
journey will start with the center-fed doublet that is familiar in its
shorter forms. We shall also look at longer forms of the doublet, as
well as at long end-fed wires. Virtually everything in long-wire
technology depends on how lobes develop as we increase the
length of a wire. Most important will be the direction in which the
strongest or main lobes point relative both to the broadside
direction (that is, the direction for the lobes of a half-wavelength
dipole) and to the axis of the wire itself.
Understanding lobe development is a major part, but only one part

of our foundation in understanding long-wire antennas. In Part 2,
we shall introduce a second critical element to the creation of long-
wire beams, a resistor to terminate the end-fed wire and create a
directional long-wire antenna. Along the way, we shall look at a
number of interesting questions involving antenna height, wire
losses, and ground quality as they bear upon long-wire antennas.
These factors introduce both physical antenna issues and modeling
issues. Therefore, we shall have to reserve the final steps of our
meanderings for the later episodes. There, we shall encounter the
V-beam and the rhombic. Both classic arrays have terminated and
unterminated forms, as well as a few complexities. The V antennas
will occupy the whole of Part 3, while the rhombic will occupy us for
Parts 4 and 5.
Before we can fully appreciate the early work that developed the V-
beam and the rhombic, we must begin our trek in more familiar
territory. Since--as noted--everything begins with the doublet that is
the place to take the first step.
Chapter 53
The Center-Fed Doublet
We shall want to examine what happens to a center-fed wire

doublet as we change its length in 1-wavelength increments from 1
to 11 wavelengths. We might extend the exercise further, but the
rate of change decreases as the antenna becomes longer, and the
limit set here is long enough for us to get hold of all of the
fundamental ideas. One key to understanding long-wire antennas is
to shift our thinking about antenna size. Instead of thinking in
physical lengths, such as X meters or Y feet, we shall think wholly
in terms of wavelengths. Hence, as we increase the frequency, the
physical length of a wave becomes shorter. So a 10-wavelength
antenna at 80 meters is physically 8 times longer than a 10-
wavelength antenna at 10 meters.
The Model: If we are to make fair comparisons among antennas--

even in modeled form--we must set up some parameters that will
remain unchanged from model to model. Obviously, the antenna
length from end to end will always be variable in every exercise.
For simplicity, I shall use the physical length (measured in
wavelengths) rather than the actual electrical length as the
increment. The electrical length of a wire antenna is always slightly
more than the physical length due to end effects. The actual
physical shortening required to obtain an exact electrical length
varies somewhat, but many books cite a general value of about
0.95 as the ratio for a simple 1/2-wavelength dipole. If we cut a
dipole to be physically 1/2 wavelength, then it will be about 5% long
electrically and show inductive reactance at the feedpoint.
However, the so-called end-effect occurs for only 1 half-wavelength
Chapter 53
of a long-wire antenna, since it has only 2 ends, no matter what its

overall length may be. Therefore, the longer the antenna the less
the end effect creates a difference between the physical and
electrical lengths. At 1-wavelength overall, the 5% dipole difference
is only 2.5%. At 10 wavelengths, the differential is only 0.25%. All
antenna models will use 20 segments per wavelength.
All real wire materials have some loss that varies with frequency,
but not in a linear manner. Not only does the material loss decrease
the maximum gain obtainable, it also has a small affect on the
feedpoint impedance. Moreover, it has a further small shortening
effect--like the end effect itself, but somewhat smaller in scale.
However, material loss shortening of the physical wire acts all along
the antenna and not just at the ends. To eliminate this factor, our
models will use lossless or perfect wire.
We need a test environment. I shall place all long-wire models 1

wavelength above average ground (conductivity 0.005 S/m,
permittivity 13). In theory, the main elevation lobe of a horizontal
antenna is tightly connected to the height of the antenna above
ground. Texts on long-wire antennas usually give an equation for
selecting the height of a proposed antenna in terms of the desired
elevation angle required for a communications link.
Hwl = 1 / (4 sin a)
where H is the height in wavelengths and a (usually given as alpha)

is the elevation angle. Since a good bit of science now prefers to
count angles from the zenith (overhead) downward as a theta
Chapter 53
angle, a or alpha is simply 90 - theta, and vice versa. We may

estimate the elevation angle of our antennas initially by reversing
the equation:
a = arcsin 1 / ( 4 Hwl)
You may see arcsin written also as sin-1. Theoretically, our 1-

wavelength height should produce elevation angles that are
consistently 14.48 degrees. We shall set the software to increment
patterns in 1-degree intervals. Since the calculated angle is almost
directly between increments, we shall be satisfied if the angles
appear as either 14 or 15 degrees.
The effects of ground are not constant for all frequencies. Even for
a horizontal wire 1-wavelength above ground, the ground losses
change, increasing as we raise the frequency. To sample the
degree of change, let's set the wire diameter for all models at the
test frequency of 3.5 MHz. We shall use 0.16" diameter wire,
approximately AWG #6. If we perfectly scale our antenna for other
frequencies, then the wire size changes as well. At 7 MHz, it is
0.08" (AWG #12). At 14 MHz, it is 0.04" (AWG #18). At 28 MHz, the
size drops to 0.02" (AWG #24). Next, let's use a 1-wavelength wire
at 1 wavelength height and scale it over the set of frequencies to
sample the maximum gain values.
Chapter 53
Maximum Gain Values: 1 WL Wire at 1 WL Above Average

Ground
Frequency Wire Dia. Maximum Gain
MHz inches dBi
3.5 0.16 9.83
7.0 0.08 9.67
14.0 0.04 9.54
28.0 0.02 9.47
Gain differential 3.5 vs. 28 MHz: 0.36 dBi
Although the differential is small, it is numerically evident. Hence,

we should conduct all modeling tests using as consistent a set of
values for all possible aspects of the antenna and modeling
environment. Our choice of the ground quality also has an effect
upon gain values. Indeed, the effect of changing the ground quality
is more pronounced than the effect of changing the test frequency.
Let's take our 1-wavelength antenna at its 1-wavelength height and
check it using 3 different levels of soil quality.
Maximum Gain Values: 1 WL Wire at 1 WL above Various Grounds
Ground Conductivity Relative Maximum Gain Maximum Gain
Label S/m Permittivity dBi @ 3.5 MHz dBi @ 28.0 MHz
Very Poor 0.001 5 9.41 9.01
Average 0.005 13 9.83 9.47
Very Good 0.0303 20 10.02 9.75
Gain differential: VP to VG Soil 0.61 0.74
Although the differentials between very good (VG) soil and very
poor (VP) soil are similar, it is clear that ground effects on antenna
losses are not completely linear. Nevertheless, the effects do not
change enough to invalidate the general trends in center-fed
doublet patterns if we select any other HF frequency to replace the
3.5-MHz test frequency for our investigation.
Chapter 53
One way to eliminate the effects of all loss sources is to model all
antennas in free space using perfect or lossless wire. These
conditions allow us to scale an antenna with no change in
performance values. Scaling, of course, means proportionately
adjusting for frequency or wavelength the length of elements, the
spacing between elements in a multi-element array, and the
diameter of the elements. However, to make the comparisons
among long-wire antennas reasonably realistic, we shall employ a
given height (1 wavelength) and a specific ground quality (called
"average") and omit only the smallest loss sources, such as wire
material and frequency.
The Center-Fed Doublet and Its Patterns: We are now ready to

show the results of setting up long-wire center-fed doublets ranging
from 1 wavelength to 11 wavelengths in 1-wavelength increments.
For each increment, we shall be very interested in 3 key data items.
First is the maximum gain of the strongest lobe or lobes in the
doublet radiation pattern. We shall call this value simply the
maximum gain. Second, we shall note the elevation angle of
maximum gain for the main lobe or lobes, also called the TO or
take-off angle. The number should--by theory--always be 14
degrees. Finally, we shall note the azimuth angle of one of the main
lobes relative to the antenna wire. If the main lobe is perfectly
broadside to the wire, the angle will be 0 degrees. We shall count in
a consistent direction away from broadside toward one end of the
antenna wire if the main lobe departs from the broadside direction.
The larger the number for the azimuth angle, the closer the main
lobe comes to aligning with the wire end. A value of 90 degrees will
indicate that the main lobe is directly off of and aligned with the
Chapter 53
antenna wire from end to end. Since our investigation is confined to

pattern properties, we shall not list the feedpoint impedance or
other data that models might give us. The following table gives us
the results of our examination.
Center-Fed Doublet Data

Total Length Maximum Elevation Azimuth Angle of
WL Gain dBi Angle deg Main Lobe deg
1 9.83 14 0
2 9.36 14 33
3 10.16 14 45
4 10.93 14 52
5 11.47 14 57
6 11.85 14 61
7 12.14 14 63
8 12.43 13 65
9 12.65 13 67
10 12.82 13 68
11 13.01 13 70
The chart shows the growing gain of the main lobes of the center-
fed doublet, once the number of lobes reaches 4 (at the 2-
wavelength mark). The increased strength of the main lobe is
accompanied by a decreasing beamwidth. As well, the angle
moves steadily toward the ends of the wire, but never reaches that
point. In fact, at 11 wavelengths, the main lobes are still 20 degrees
shy of a true end-orientation. Also note that the elevation angle of
the strongest lobe drops slightly as the antenna length passes the
7-wavelength point. The angle would show a smoother curve if the
increment between sampling points had been smaller than 1
Chapter 53
degree. However, the drop is real and may be more dramatic with
other types of long-wire antennas.
What the chart cannot show is the growth in the number of lobes
and their relative strengths as we increase the length of the
antenna. Fig. 1 provides a gallery of sample elevation and azimuth
plots to illustrate the growth of lobes in both directions. You may
gauge the shrinking beamwidth from the red line marking the half-
power points on the main lobes. The elevation patterns are taken
along a line using the azimuth angle in the table. The azimuth
patterns are taken at the listed elevation angles.
Chapter 53
The pattern selections are closer together for shorter versions of

the doublet, since the azimuth angle of the main lobes changes
more rapidly. As the antenna grows longer, the rate of azimuth-
angle change decreases. However, of considerable note is the total
number of lobes in each pattern. For antennas that are very close
to integral numbers of wavelengths long, we can express the total
number of lobes in a simple equation.
Chapter 53
Ndblt = 2 Lwl
where Ndblt is the number of identifiable lobes and L is the doublet

length in wavelengths. Lobes do not suddenly appear, but rather
emerge, grow, peak, diminish, and finally disappear. The cycle
occurs for every progression from one integral wavelength to the
next. At the midpoint between integral lengths, L.5 wavelengths, the
number of doublet lobes becomes considerable larger. The
antenna pattern shows the growing lobes of the next integral length
plus the diminishing lobes of the preceding integral length. So the
equation becomes somewhat messier.
Ndblt = 2 (Lwl + L+1wl)
where L is the preceding integral wavelength value and L+1 is the

next integral wavelength value. Since a 2-wavelength doublet has 4
lobes and a 3-wavelength doublet has 6 lobes, a 2.5-wavelength
doublet has 10 total lobes. The main lobes are still those furthest
from the broadside angle to the wire. The existence of 10 lobes
forces the azimuth angle of the main or outer lobes to be further
from broadside than for either of the two integral lengths (2 and 3
wavelengths) used in the sample calculation.
The End-Fed Long-Wire Antenna
Understanding the pattern evolution of the center-fed doublet gives

us a baseline against which to measure succeeding steps in the
development of long-wire antennas, and eventually directional long-
wire antennas. The doublet patterns were all very symmetrical as a
Chapter 53
consequence of feeding the antenna at the center. However, most

practical long-wire antennas feed the antenna at one end. In terms
of models, we may simply move the feedpoint to the last segment.
The segmentation remains the same: 20 segments per wavelength.
The test frequency remains 3.5 MHz, and the lossless wire is still
0.16" in diameter. The antennas are 1 wavelength above average
ground.
Therefore, we may proceed directly to the table of results that tells

us the maximum gain, the elevation angle, and the azimuth angle of
the main lobe(s) of the end-fed wires. Note that we here avoid any
use of terms like "end-fed Zepp" and similar informal names for the
antenna. They are all end-fed wires. As well, we by-pass any
discussion of antenna installation practicalities, such as the
imbalance of current magnitudes and phases on the parallel
feedline normally used with such antennas.
However, we shall expand the table of gathered data by reducing

the increment of length between antennas in the list. Instead of
proceeding in 1-wavelength increments, we shall step along in 0.5-
wavelength intervals.
End-Fed Wire Antenna Data

Total Length Maximum Elevation Azimuth Angle of
WL Gain dBi Angle deg Main Lobe deg
1 8.44 14 37
1.5 9.45 14 49
2 10.27 13 56
2.5 10.86 13 60
3 11.32 13 63
Chapter 53
3.5 11.68 13 65
4 11.99 13 67
4.5 12.26 13 69
5 12.48 13 70
5.5 12.71 12 71
6 12.90 12 72
6.5 13.08 12 73
7 13.24 12 74
7.5 13.38 12 75
8 13.50 12 76
8.5 13.64 11 76
9 13.72 11 77
9.5 13.87 11 77
10 13.96 11 77
10.5 14.07 11 78
11 14.15 11 78
The end-fed wire antenna begins at 1 wavelength by showing a

small gain deficit relative to the center-fed doublet. However, the
end-fed wire quickly catches up and shows more gain in the main
lobe than the corresponding doublet. In fact, by the 11-wavelength
version, the end-fed wire has over a 1.1-dB gain advantage. The
added maximum gain accompanies a larger decrease in the
elevation angle of maximum radiation as the antenna grows longer.
The third column adds further information to digest: the azimuth
angles are much larger for any given total end-fed antenna length
than for doublets of the same length. In fact, the 1-wavelength
version shows an azimuth angle that is greater than zero,
suggesting that it has more than 2 lobes. Fig. 2 can go a long way
toward clearing up the differences between doublet and end-fed
wire patterns when both have the same length.
Chapter 53
The increased maximum-gain value of the end-fed antenna over

the doublet arises from the fact that even with lossless wire the
end-fed azimuth pattern shows a displacement away from the fed
end and toward the open end of the antenna. The difference in
strength between the strongest lobes away from the feedpoint and
those toward the feedpoint is just about twice the value of the
improved maximum gain figure. Expressed in other terms, if the 10-
wavelength antenna has a 1.1-dB advantage over the doublet in
Chapter 53
maximum gain, then it also shows about a 2.2-dB front-to-back

ratio. The lobes toward the feedpoint will be about 1.1-dB weaker
than the corresponding lobes for a doublet. The end-fed wire is
already directional, but not to a very significant degree.
The more obvious feature of the radiation pattern gallery is the

increase in the total number of lobes for each antenna length. In
fact, the end-fed wire answers to a quite different equation for
calculating the number of lobes:
Nef = 4 Lwl
where Nef is the total number of identifiable end-fed wire lobes and
L is the end-fed wire length in wavelengths. So the 10-wavelength
end-fed wire has a total of 40 lobes. To squeeze that many lobes
into the same 360-degree pattern requires that each lobe have a
smaller beamwidth (that is, be narrower). As well, the main lobes
have an angle farther from broadside and closer to the wire end
than for a doublet of the same length. In fact, the two main lobes at
each end of the antenna wire begin to fuse into a single large lobe
with a deep inset. Compare these lobes with the very separate
lobes of the doublet.
The data that we gather from the end-fed single long-wire

unterminated antenna will play an important role in the design of
more complex arrays. The data is in many ways height-specific
(with additional cautions regarding the soil quality as a possible
further modifier of the data). The azimuth angle of the main lobe
varies with the antenna height and length. Using an increment of 1
Chapter 53
wavelength between antenna lengths, the following table compares

data for lossless long-wires 0.5-, 1-, and 2-wavelengths over
average ground.
Fig. 3 compares the maximum gain of the end-fed wire antenna at

each height and length. These curves are completely
unexceptional, but may be useful as a reference.
Chapter 53
Although we may be tempted to focus upon the gain data, those

numbers may not be the most important for the long-term use of the
information. The elevation angle columns tells us that the lower we
place a single unterminated long-wire antenna, the faster the
elevation angle of maximum radiation decreases as we increase
the long-wire antenna length. Fig. 4 converts the numbers in
curves. The stair-stepping results from the fact that elevation
angles use a 1-degree increment.
Chapter 53
Still more significant for designing more complex long-wire arrays is

the azimuth angle of the strongest lobe relative to the broadside
direction (in these models). For any given antenna length, the
azimuth angle of the strongest lobes changes with antenna height.
Fig. 5 shows the amount of change with height for each sampled
antenna length. Once more, the 1-degree radiation pattern
increment limits the smoothness of the curves. However, we may
clearly see that the lower the antenna height for any given antenna
length, the closer that the main lobes approach the axis of the wire
and the closer they grow to each other on each side of the wire.
Chapter 53
The azimuth angle has been a very convenient measure for our
initial examination of both center-fed and end-fed long wire
antennas. It has shown us by how much the main or strongest
lobes of the antenna pattern move from the broadside or zero-
degree position as we make the wire longer, as counted in
wavelengths. In other applications, for example, the discussion of V
and rhombic arrays to come in future parts of this series we shall
view the same angle from a different perspective. We shall be
interested in the amount by which the main lobe is displaced from
the axis of the wire, defined as a line drawn along and beyond the
Chapter 53
antenna wire. In literature about long-wire arrays, the off-axis angle

is usually designated as "alpha," although we shall use the letter
"A" as a designation in these notes. Fig. 6 shows the relationship of
the 2 angles.
Chapter 53
We shall eventually convert the azimuth-angle values to angle-A

values with respect to the wire. The relationship is simply this:
Angle A = 90 - (Az Ang) degrees. We need not do the arithmetic
now. However, these angles and their derivatives will come in
handy in later parts of this series.
Since most of our experience is with shorter antennas--say about

1/2-wavelength long--we may not fully appreciate the difference
between center and end feeding for wires that are the same length.
For example, a 1-wavelength doublet has only 2 lobes, while a 1-
wavelength end-fed wire has 4 lobes. Both antennas show 2
complete excursions of current magnitude, showing 2 maximum
current points at approximately 1/4 and 3/4 wavelength along the
wire. The only other significant variable is the phase of the currents
in each excursion. Fig. 7 shows us the difference in this parameter.
Chapter 53
The center-fed doublet graph shows that the currents have the
same phase in each half of the overall antenna length. Hence, the
radiation pattern has only two lobes with contributions from each
half of the total wire length. Not until the antenna reaches a
significantly greater length (2 wavelengths is the next step in our
pattern development sequence) will each half of the doublet show a
current phase reversal. Therefore, we do not find 4 lobes until we
reach the 2-wavelength mark. (Of course, a 1.5-wavelength
antenna will show 6 lobes as the initial 2 diminish and the next 4
emerge and grow.) With the end-fed wire, the currents in each half
of the initial 1-wavelength wire are 180-degrees out of phase
relative to each other. Hence, we see 4 lobes at this shorter length.
Unlike the center-fed doublet, the end-fed wire shows only a single
progression of the number of lobes in the azimuth pattern.
Therefore, the single equation for calculating the number of lobes
applies not only to wire lengths that are at or near integral
wavelengths; as well, it applies to wire lengths at are at or near N.5
wavelengths.
Indeed, the way in which lobes appear and grow differs markedly
between center-fed and end-fed antennas that are the same length.
Fig. 8 provides a glimpse of the process by tracking the lobe
structure of the two types of antennas from 2 wavelengths to 3
wavelengths, in 0.25-wavelength increments. I chose this set of
lengths so that the lobes are clear and countable--even when they
are very small. However, similar graphs are possible between any 2
length markers.
Chapter 53
At 2.5 wavelengths, the two patterns are almost identical differing

only in the end-fed wire's small front-to-back ratio resulting from a
slight forward tilt to the pattern. The center-fed antenna shows its
new lobes at angles outside the existing set of 4 lobes, and in
between any pair of existing lobes. The presence of the new outer-
most lobes forces the existing lobes toward a more broadside
direction. At 2.25 wavelengths, the old lobes are still the strongest,
but show a more broadside angle than when they were alone at 2
Chapter 53
wavelengths. Beyond 2.5 wavelengths, the new lobes dominate

and the old ones shrink. At 2.75 wavelengths, the old lobes are
barely visible. By 3 wavelengths, we find only 6 lobes at their
familiar positions. The following table tracks the progression.
Lobe Development in Center-Fed and End-Fed Wires Between 2 and 3
wavelengths
Antenna Center-Fed End-Fed
Length Max. Gain Main Lobe Max. Gain Main Lobe
WL dBi Az. Angle dBi Az. Angle
2.0 9.36 33 deg 10.27 56 deg
2.25 10.22 28 11.37 59
2.5 10.33 59 10.86 60
2.75 10.33 51 10.91 62
3.0 10.16 45 11.32 63
In contrast to the center-fed lobe development progression, the

end-fed antenna has new lobes that emerge just to the rear of the
broadside direction, where we define "rear" with respect to the
general direction toward the end-fed wire's feedpoint. The 2.25-
wavelength and 2.75-wavelength end-fed antennas are
comparable, as each one introduces a new lobe pair. The lobe
progression acquires symmetry on each side of the wire (except for
the slight differential in the main lobes) only as the antenna
approaches a multiple of a half-wavelength.
We should not neglect the elevation patterns in the gallery shown in

Fig. 2. If we compare the number of elevation lobes for the doublet
and for the end-fed wire, we find more lobes in each corresponding
end-fed wire pattern. This feature of end-fed wire antennas will
eventually play a role in our evaluation of terminated end-fed long-
wire directional antennas. Just how complex the overall pattern of
Chapter 53
an end-fed wire may become, shows up in the 3-dimensional

pattern from a 10-wavelength end-fed wire in Fig. 9. The pattern is
limited to a 5-degree increment between pattern readings, so some
details are missing. However, reducing the increment to show more
detail would convert the line-based sketch into a solid black blob.
Two features of the 3-dimensional pattern are especially prominent.

First, the upper angles in every direction show a plethora of lobes.
A free-space representation of the far-field radiation would show a
tunnel with relatively smooth ridge rings for each new lobe,
counting back from the tunnel entrance formed by the strongest
lobes. However, our radiation pattern takes place over real (or
Chapter 53
"lossy") ground, disturbing the ring structure as we increase the

elevation angle of interest. Many of the upper-angle lobes have
significant strength. Second, the forward-most lobes (along the axis
labeled Y) have an interesting feature. The lowest and strongest
lobe (at 10 degrees in the graphic) shows the deep null along the
Y-axis between lobe peaks on either side. However, at 15 degrees
elevation, the forward lobe structure displays a far-more-even front,
with only a small gain depression along the Y-axis. This feature of
end-fed wire patterns will become very prominent when we tackle
the terminated end-fed antenna in Part 2.
Before we leave the open-ended long-wire antenna, we should

briefly note that the ground plays an ever-more profound role in
end-fed wire antenna performance as the wire grows longer. Let's
compare the 10-wavelength end-fed wire over very good, average,
and very poor grounds. In contrast to our original notes, which used
a 1-wavelength doublet, we shall now be looking at a very long
antenna (856.55 m or 2810' at 3.5 MHz).
Maximum Gain Values: 1 WL Wire at 1 WL above Various Grounds
Ground Conductivity Relative Maximum Gain Elevation Azimuth Angle of
Label S/m Permittivity dBi @ 3.5 MHz Angle deg Main Lobe deg
Very Poor 0.001 5 13.55 10 77
Average 0.005 13 13.96 11 77
Very Good 0.0303 20 14.65 12 79
Gain differential: VP to VG Soil 1.10
The ground quality not only changes the maximum gain attainable
from the antenna, but as well changes the elevation angle of
maximum radiation. The better the soil the higher the TO angle. But
even over very good soil, the elevation angle of maximum radiation
is significantly lower than the calculated value of 14.5 degrees.
Chapter 53
Conclusion
In some respects, we have not gone very far in our exploration of

long-wire antennas. We have merely contrasted the behavior of
center-fed doublets and end-fed wires from 1 to 11 wavelengths.
Along the way, we have examined many of the variables that might
alter the performance progressions in the tables. Our goal has been
to become familiar with the performance parameters of long
unterminated wires. The pattern galleries and tables can serve to
remind us of these properties as we proceed further.
The end-fed wire, in particular, holds great importance for our future
exploration. It is the foundation of all other long-wire arrays. That
collection, of course, includes both complex rhombics and the
simplest of the directional terminated antennas. Hopefully, from the
perspective of developing reasonable expectations from end-fed
wires, the foundation in these notes is sufficiently solid to make
succeeding steps smoother on the trail of terminated long-wire
antennas.
A Few Basic References
Entire books exist on the subject of terminated directional long-wire

antennas, with special attention to the V-beam and the rhombic.
However, for a basic introduction to the subject, the following
college texts, handbooks, and seminal articles might be useful.
Balanis, C. A., Antenna Theory: Design and Analysis, 2nd Ed., pp.
488-505: a college text.
Chapter 53
Boswell, A. G. P., "Wideband Rhombic Antennas for HF,"

Proceedings of the 5th International Conference on Antennas and
Propagation (ICAP87), April, 1987: a source of wide-band rhombic
design information.
Bruce E., "Developments in Short-Wave Directive Antennas,"

Proceedings of the IRE, August, 1931, Volume 19, Number 8: the
introduction of the terminated inverted V and diamond (rhombic)
antennas.
Bruce E., Beck A.C., and Lowry L.R., "Horizontal Rhombic

Antennas," Proceedings of the IRE, January, 1935, Volume 23,
Number 1: the classic treatment of rhombic design, repeated in
many text books.
Carter P. S., Hansell C. W., and Lindenblad N. E., "Development of

Directive Transmitting Antennas by R.C.A Communications, Inc.,"
Proceedings of the IRE, October, 1931, Volume 19, Number 10: a
fundamental treatment of long-wire V antennas, along with the next
entry.
Carter P. S., "Circuit Relations in Radiating Systems and

Applications to Antenna Problems," Proceedings of the IRE, June,
1932, Volume 20, Number 6: the second of the fundamental
analyses behind long-wire V antennas.
Foster, Donald, "Radiation from Rhombic Antennas," Proceedings

of the IRE, October, 1937, Volume 25, Number 10: a more general
Chapter 53
treatment of rhombic design, with the introduction of stereographic

design aids.
Graham, R. C, "Long-Wire Directive Antennas," QST, May, 1937:

an excellent summary of long-wire technology to the date of
publication.
Harper, A. E., Rhombic Antenna Design (1941): a fundamental text

on rhombics, based on engineering experience, with tables and
nomographs as design aids..
Johnson, R. C. (Ed.), Antenna Engineering Handbook, 3rd. Ed.,

Chapter 11, "Long-Wire Antennas" by Laport: similar but not
identical material to the relevant pages of Laport's own volume.
Kraus, J. D., Antennas, 2nd Ed., pp. 228-234; 502-509: a college

text.
Laport, E. A., Radio Antenna Engineering, pp. 55-58, 301-339: a

summary of long-wire technology up to the date of publication
(1950).
Laport, E. A., "Design Data for Horizontal Rhombic Antennas," RCA

Review, March, 1952, Volume XIII, Number 1: rhombic design data
based on the use of stereographic aids developed by Foster.
Laport E. A., and Veldhuis, A. C., "Improved Antennas of the

Rhombic Class," RCA Review, March, 1960, Volume XXI, Number
1: the introduction of the off-set dual rhombic.
Chapter 53
Straw, D. (Ed.), The ARRL Antenna Book, 20th Ed., Chapter 13,
"Long-Wire and Traveling-Wave Antennas." See also older
versions of the volume, for example, Chapter 5 of the 1949 edition,
which gives long-wire technology a more thorough treatment on its
own ground, rather than in comparison to modern Yagi technology.
Stutzman, W. L., and Thiele, G. A., Antenna Theory and Design,

2nd Ed., pp. 225-231: a college text.
Walter, C. H., Traveling Wave Antennas (1965): a classic and very

thorough text on traveling-wave fundamentals for all relevant types
of antennas.
Chapter 53
Chapter 54: Terminated End-Fed Long-Wire Directional

Antennas
I
n Chapter 53 of this Long-Wire series, we examined some
fundamental properties of both center-fed and end-fed
unterminated long-wire antennas. Without the kind of data that
our basic investigation showed, the terminated version of the end-
fed long-wire antenna might seem more odd than natural. As we
move from the symmetry of an unterminated antenna, sometimes
called a "standing-wave" antenna, to the asymmetry of the patterns
of a terminated wire that is the same length, the assimilation of the
nature and growth of both elevation and azimuth lobes will
hopefully carry over to naturalize the new patterns and performance
values. The mark of success in the process might be that we are
able to predict in very general terms "what happens next."
The Terminated End-Fed Long-Wire Directional Antenna
In both of our unterminated antennas, we find an interesting picture

of the current and voltage along the wire. They each form standing
waves (following the accounts of Balanis and of Kraus) with peaks
every half-wavelength and nulls every half-wavelength such that
the peaks and nulls are 1/4-wavelength apart. The voltage peaks
where the current has a null and vice versa. This portrait of voltage
and current behavior forms the basis for a large part of basic
antenna analysis. It derives in part from treating the antenna as an
open transmission line. At the end of any transmission line, an open
condition results in the complete reflection of energy toward the
source. Traditionally, such antennas have received the label
Chapter 54
"standing-wave" antennas, and the group includes most of the

antennas that we commonly use.
In a long-wire antenna, we may add to the end of the wire away

from the feedpoint an impedance or termination. If we select the
right impedance, then the reverse or reflected energy flow is
decreased ideally to zero, as suggested by the top portion of the
sketch in Fig. 1. Under these ideal conditions, the fields or waves
emerging as a consequence of the uni-directional energy flow result
in radiation wholly directed toward the terminated end of the
antenna wire. As well, the current at any position along the antenna
wire will be the same. These conditions define the idea of a
"traveling-wave" antenna.
Chapter 54
Any implementation of the terminated long-wire antenna consists

not only of the wire that is parallel to the ground, but as well to 2
vertical sections. At one end of the antenna, we have a feedpoint,
usually taken between the vertical leg and ground. At the other end,
we find a vertical line as long as necessary to connect to the
terminating impedance. The terminating impedance normally has
one end directly connected to ground with the other end connected
to the vertical wire. When the height of the antenna is very small
relative to a wavelength, the antennas receive the label "Beverage
antennas," after the individual who generated them originally.
Today, such antennas--which are very long and low to the ground--
find use as MF and lower HF receiving antennas. When the
Chapter 54
antenna is an appreciable distance above ground--as in the case of

our wires that are 1-wavelength high--we may simply call it a
terminated end-fed long-wire directional antenna.
The idealization of our terminated long-wire antenna normally does

not account for the vertical wires needed to make both feedpoint
and termination connections. (See Balanis and Kraus for different
approaches to the analysis of such antennas. We shall by-pass
their mathematical accounts, since our goal is to make such
antennas more intuitively sensible.) Ideally, we can find a loading
impedance that will provide the proper conditions for achieving full
traveling-wave status. The calculation is based once more on
treating the wire as a transmission line, and the load impedance
must equal the characteristic impedance of the line. Balanis
provides the following equation to approximate the proper value of
the termination.
RL = 138 log10 (4h/d)
where RL is the value of the impedance load in Ohms, h is the

height of the wire, and d is the wire diameter, when both are in the
same units. Note that the impedance of the line and hence the
approximate load value is independent of frequency and dependent
only upon a set of physical measurements that use the same units
of measurement. Our wires will be 85.655 meters above ground.
The wire diameter is 0.16" or 0.004064 meters. Plugging these
numbers into the Balanis equations gives us an approximate load
impedance of 680 Ohms. As we shall see, values between 600 and
Chapter 54
1000 Ohms are quite usable, although we shall eventually settle on

800 Ohms as a useful value for our initial models.
As Kraus notes, a lumped impedance may greatly reduce

reflections from the termination, but it cannot provide a non-
reflecting termination. In fact, the most common form of termination
is a non-inductive resistor (or series/parallel combination of
resistors). Under these conditions, some standing waves remain,
as shown in the lower portion of the sketch in Fig. 1. The lower
rendition of a 10-wavelength terminated long-wire antenna derives
from an EZNEC model and uses its facility to generate the pattern
of current magnitude along the wires. One consequence of
incomplete reflection elimination is to wind up with a feedpoint
impedance that is not identical to the load resistance. The feedpoint
impedance for the models in this part of the investigation were 600
Ohms or below. However, this impedance value is convenient,
since open ladder line commonly comes in a 600-Ohm value, and
the match is good (SWR 1.25:1 or less). Hence, the user of such
antennas has a wide choice of means at the operating end of the
line for effecting a match to the usual 50-Ohm input/output of a
transceiver.
One common misconception about terminated long-wire antennas

is that the reduction or elimination of reflected energy results in half
the power being dissipated by the terminating impedance (resistor).
In fact, the far end load on the antennas in this exercise dissipates
about 25% of the power, as calculated by NEC.
Chapter 54
Modeling Issues: Modeling the terminated long-wire antenna

presents a number of options and challenges, since NEC has some
limitations that bear upon the models. Fig. 2 outlines the options
available.
Option A brings the vertical elements of the antenna down to

ground. The source or feedpoint is the first segment above ground
of the left wire, while the terminating load appears on the last
segment above ground at the far end of the antenna. In the EZNEC
Pro/4 implementation of NEC, we have at least 4 ways to model the
structure: over perfect ground, with a Sommerfeld-Norton (SN)
Chapter 54
average ground using NEC-4, with an SN average ground using

NEC-2, and with a MININEC ground. Use of a perfect ground
provides a reference baseline for checking the sensibleness of
other models. However, neither NEC-2 nor NEC-4 recommends
bringing a source wire to ground, since at a minimum, the source
impedance is likely to be off the mark. The MININEC ground does
not provide accurate impedance reports for the ground quality
selected, since it is restricted to using the impedance report for
perfect ground.
Despite the limitations, we can tabulate the results. As a test case, I

shall use a 10-wavelength terminated antenna alternately using
termination resistors of 600, 800, and 1000 Ohms. For each option,
I shall list the maximum gain, the reported 180-degree front-to-back
ratio, the elevation angle of maximum radiation, the beamwidth, the
source impedance, and the 600-Ohm SWR at the test frequency.
Test Performance Values for Modeling Option A
Terminating Maximum Front-to-Back Beamwidth Elevation Feedpoint Z 600-Ohm

Load Ohms Gain dBi Ratio dB degrees Angle deg R+/-jX Ohms SWR
1. Perfect Ground
600 13.98 29.04 26.4 15 439 + j 24 1.37
800 13.91 26.38 26.2 15 476 + j 43 1.28
1000 13.87 19.57 26.2 15 504 + j 59 1.23
2. Average SN Ground, NEC-4
600 11.54 11.57 35.2 11 460 + j593 3.01
800 11.49 12.63 35.2 11 495 + j588 2.85
1000 11.45 12.87 35.2 11 524 + j587 2.75
600 10.79 24.23 35.6 11 479 + j 14 1.26
800 10.74 21.78 35.6 11 509 + j 35 1.19
1000 10.72 18.11 35.6 11 532 + j 52 1.16
3. Average MININEC Ground, NEC-4
600 11.09 23.58 35.4 11 439 + j 24 1.37
800 11.01 22.71 35.4 11 476 + j 43 1.28
1000 10.98 18.55 35.4 11 504 + j 59 1.23
Chapter 54
Using the sequence over perfect ground as a background

reference, the NEC-2 results for the SN average ground and the
MININEC average ground data appear to coincide fairly well.
However, the NEC-4 runs for the SN average ground appear to
yield somewhat high gain values with more than anticipated
inductive reactance in the source impedance.
Option B represents an adaptation of NEC-2 techniques for

modeling vertical antennas with ground-plane radials. The return
line between the load resistor and the source is 0.0001-wavelength
above ground, about 3 times the diameter of the wire. Hence, the
model violates no constraints, but as the following results for both
NEC-2 and NEC-4 show, it yields a poor model of the terminated
long-wire antenna.
Test Performance Values for Modeling Option B

600 7.68 16.93 35.4 11 1170 - j 97 1.97
800 7.73 14.44 35.4 11 1182 - j 80 1.98
1000 7.77 13.36 35.4 11 1192 - j 67 2.00
600 7.68 16.10 35.4 11 1167 - j 99 1.96
800 7.72 14.59 35.4 11 1179 - j 82 1.98
1000 7.76 13.50 35.4 11 1188 - j 69 1.99
Although NEC-2 and NEC-4 show a very close coincidence of data,

the low gain, low front-to-back ratio, and high feedpoint impedance
reports combine to suggest that this model is highly inadequate.
However, the beamwidth and elevation-angle reports are consistent
with the other models. NEC-4 does allow the use of a subterranean
return wire, shown in option C in Fig. 2. To test this option, I placed
a return wire 0.01-wavelength below ground level, connecting it to
Chapter 54
the above-ground vertical wires with short segments. Both the

source and the load for the antenna remain above ground. Since
this option is available only in NEC-4, the test-result table is quite
short.
Test Performance Values for Modeling Option C

600 10.38 22.53 35.6 11 526 + j 87 1.23
800 10.37 19.94 35.6 11 556 + j104 1.22
1000 10.36 17.10 35.6 11 579 + j118 1.23
The results are modest, but coincide roughly with the NEC-2 results
in Option A. The front-to-back reports are consistent with those for
perfect ground. The difficulties with the model include the model
size, since the return wire requires as many segments as its above-
ground counterpart, and the return wire may actually yield slightly
low gain reports by carrying more current than the ground itself. A
real installation would not likely use a buried ground wire.
Therefore, I tried option D, which replaces the below-ground

structure of option C with 2 simple ground rods. Each rod is a 1-
segment wire about 0.05-wavelength, which is the length of the
segments in the vertical wires above ground. Therefore, the source
has equal length segments on each side of the feedpoint segment.
0.05-wavelength is about 4.3 meters or 14'. This length may be
longer than the average ground rod, but substituting shorter
segments did not change the reports by any significant amount.
The results of the test appear in the following table.
Chapter 54
Test Performance Values for Modeling Option D

600 10.49 22.94 35.6 11 513 + j 69 1.22
800 10.47 20.30 35.6 11 544 + j 87 1.20
1000 10.46 17.29 35.6 11 567 + j102 1.20
Except for the predicted very slight increase in maximum gain, all of
the values correspond very well with those of the buried-return-wire
model (C), but with a 45% reduction in model size. For users of
NEC-4, it is likely that this style of model is about as adequate as
we may get for a terminated long-wire directional antenna. In fact,
for users of NEC-2, the basic model (option A) coincides well
enough for general guidance. In physical reality, there will be
structural variables that will inevitably limit the precision attainable
by any model. For example, the models presume a flat wire
horizontal to the ground, which is not likely to appear with copper
wire and real supports. Even if all supports provide the same
height, catenary effects will vary the actual wire height above
ground along the antenna pathway.
During the model-testing procedures, I explored 2 other directions.

One direction led to the variety of soil types over which one might
place a terminated long-wire antenna. So I modeled the test series
of 10-wavelength antennas over very good and very poor soil to
see the effect upon the performance parameters.
Chapter 54
Test Performance Values for Modeling Option D over Various Soil Qualities

1. Very Good SN Ground, NEC-4
600 11.86 25.20 33.6 12 474 + j 57 1.30
800 11.81 23.43 33.5 12 508 + j 75 1.24
1000 11.79 19.00 33.4 12 534 + j 89 1.22
600 10.49 22.94 35.6 11 513 + j 69 1.22
800 10.47 20.30 35.6 11 544 + j 87 1.20
1000 10.46 17.29 35.6 11 567 + j102 1.20
3. Very Poor SN Ground, NEC-4
600 9.21 21.93 33-S 10 630 - j 53 1.10
800 9.23 17.54 33-S 10 653 - j 30 1.10
1000 9.25 14.66 33-S 10 671 - j 11 1.12
As we move from better soils to worse soils, the gain decreases by

about 1.3-dB per step. However, note that over very poor soil, the
gain trend reverses relative to the value of the terminating resistor.
The front-to-back ratio reports also decrease with worsening soil.
Each soil quality yields its own consistent beamwidth and elevation
angle. The annotations for very poor soil indicate that the null
between maximum gain peaks is sufficient to record separate lobes
with at least a 3-dB null between. Hence, the beamwidth is an
estimate. The resistive portion of the feedpoint impedance shows a
non-linear rise with worsening soil quality. Nevertheless, all of the
600-Ohm SWR values fall well within the usable range.
The second direction of additional modeling shows the effects of

using copper wire instead of perfect wire in the 10-wavelength
antenna. Both tests use average SN ground.
Chapter 54
Test Performance Values for Modeling Option D with Lossless and Copper Wire

1. Average SN Ground, NEC-4, Lossless Wire
600 10.49 22.94 35.6 11 513 + j 69 1.22
800 10.47 20.30 35.6 11 544 + j 87 1.20
1000 10.46 17.29 35.6 11 567 + j102 1.20
2. Average SN Ground, NEC-4, Copper Wire
600 10.28 23.06 35.5 11 518 + j 70 1.21
800 10.27 19.70 35.5 11 548 + j 85 1.19
1000 10.26 17.37 35.5 11 571 + j 97 1.19
Despite the very long length of the wire, copper losses at the test
frequency only lower the gain by about 0.2 dB. All other
performance values remain quite constant.
The reason that we are taking the trouble to model as adequately

as feasible the terminated long-wire directional antenna is the
difference that we find between its pattern and the pattern of an
unterminated end-fed long-wire antenna. The differences appear in
Fig. 3 for 10-wavelength versions of both antennas. Although the
terminated directional antenna is laden with sidelobes, the entire
pattern provides a good front-to-rear ratio that can enhance
communications by reducing rearward interference levels. Indeed, it
is possible to use a remotely controlled switch to remove the load
and return the antenna to an unterminated state for
communications to the rear.
Chapter 54
When looking over the tabulated results for various ground qualities
during the modeling testing procedure, we met with split lobes over
very poor soil. In order to see better the progression of the forward-
most lobes of the terminated antenna, we can examine Fig. 4. It
provides the azimuth patterns over the 3 soil qualities and over
perfect ground.
Chapter 54
The pattern over perfect ground has a single forward lobe, but all of
the patterns over real ground show two peaks. As the soil quality
decreases, the peaks grow farther apart, with an ever deeper
depression in gain between them. Over very poor soil, the
depression becomes an identifiable null, exceeding 3-dB relative to
the maximum lobe strengths. Hence, the pattern identifies the
peaks as separate lobes. The patterns strongly suggest that
anyone who proposes to construct a terminated long-wire
directional antenna should account in advance for the ground
quality beneath and in the vicinity of the antenna. Depending upon
the specifications of a given communications operation, the 3-dB
null at the center of the 2 peaks over very poor soil might make a
difference to antenna planning.
The terminated long-wire antenna has a very wide operating range

in terms of the feedpoint SWR. The terminating resistor combined
with the antenna height largely controls the feedpoint impedance.
As a specimen test, Fig. 5 provides the 600-Ohm SWR curve for
the test antenna using an 800-Ohm terminating impedance. The
curve involves no change in the antenna, although the height--in
Chapter 54
wavelengths--varies from about 0.66 to 1.34 wavelengths above

ground. It is clear that the 2:1 frequency range of the test run does
not exhaust the usable SWR span for the antenna. However, it
does cover one of the more usual amateur applications of a
terminated wire, that is, operation from 20 through 10 meters.
The End-Fed Terminated Long-Wire Directional Antenna and Its

Patterns: To produce a table of results for terminated long-wire
antennas of various lengths and an associated gallery of patterns, I
settled on an 800-Ohm termination for the models, using option D
as the NEC-4 modeling foundation. The horizontal lossless wire is 1
wavelength above average ground. The total length value is the
length of the horizontal span of the antenna and does not include
Chapter 54
the vertical legs. As in the test data, if the main lobe is split into 2
lobes with a distinct null (>3 dB) between them, the beamwidth is
an estimate with the letter "S" added to denote the split. TR Loss
provides NEC's calculation of the percentage of applied power
dissipated in the terminating resistor.
End-Fed Terminated Long-Wire Directional Antenna Data
Total Length Maximum Front-Back Elevation Beamwidth Feedpoint Z 600-Ohm TR Loss
WL Gain dBi Ratio dB * Angle deg degrees R+/-jX Ohms SWR %
3 7.11 15.32 14 69-S 537 + j92 1.22 26
4 7.99 16.48 13 59-S 539 + j90 1.21 25
5 8.65 17.91 13 51-S 541 + j89 1.21 24
6 9.15 18.30 12 46-S 543 + j89 1.20 24
7 9.57 19.30 12 43.8 543 + j88 1.20 24
8 9.92 19.51 12 40.2 544 + j88 1.20 23
9 10.20 20.12 12 37.0 544 + j88 1.20 23
10 10.47 20.30 11 35.6 544 + j87 1.20 23
11 10.70 20.58 11 33.4 544 + j87 1.20 23
The most constant data are the values for feedpoint impedance,
600-Ohm SWR, and power dissipated in the terminating resistor.
The front-to-back ratio increases with antenna length. However, this
value has a flag, since the value is related to the heading of peak
gain, which is not the center of the pattern, that is, is not aligned
directly with the wire itself. The maximum gain, the beamwidth and
the elevation angle of maximum gain decrease with increasing total
length.
The patterns associated with selected entries in the table appear in

Fig. 6. Because the rate of change slows as we reach the upper
length values, there are more patterns for the shorter lengths than
for the longer. The azimuth patterns reflect both the tabular value
entries plus the anticipated growth in the number of total sidelobes.
However, because there are 2 1-wavelength vertical legs, the total
number of lobes and peaks will be greater than for a corresponding
Chapter 54
unterminated end-fed long-wire antenna. Do not neglect the

elevation patterns. They show a very complex structure that will call
for further comment before we conclude.
Chapter 54
The terminated end-fed long-wire directional antenna is

inexpensive and simple, assuming that one has access to the
required non-inductive terminating resistor. It has 2 chief properties
of merit, neither of which is raw gain. It is quite directional, although
fraught with sidelobes. It is also extremely broad-banded in terms of
SWR. The termination largely controls the feedpoint impedance.
Large frequency excursions, of course, change not only the length
of the antenna, but also the height above ground, when we
measure both in terms of wavelength. However, a single antenna
can cover most of the HF spectrum, if high and long enough at the
lowest frequency. With increasing frequency, we obtain a narrower
beamwidth and higher gain. Offsetting these variable qualities is the
absence of any need for further impedance matching once we
transform the average feedpoint impedance of the antenna to the
value required by the transmitting and receiving equipment. Hence,
the antenna is useful for directional low-angle communications that
may require extreme frequency-changing agility.
The following table compares the maximum gain for terminated and
unterminated end-fed long-wire antennas for lengths from 3 to 11
wavelengths. Note that the unterminated version is essentially bi-
directional, although gain is slightly greater away from the
feedpoint. As the antennas grow longer, the gain deficit for the
directional long-wire antenna grows smaller. However, it is unlikely
to become as low as 3 dB until the terminated long-wire antenna
reaches wholly impractical lengths.
Chapter 54
Gain and Elevation Angle Comparison

Terminated Long-Wire Unterminated Long-Wire Gain
Total Length Maximum Elevation Maximum Elevation Difference
WL Gain dBi Angle deg Gain dBi Angle deg dB
3 7.11 14 11.32 13 4.21
4 7.99 13 11.99 13 4.00
5 8.65 13 12.48 13 3.83
6 9.15 12 12.90 12 3.75
7 9.57 12 13.24 12 3.67
8 9.92 12 13.50 12 3.58
9 10.20 12 13.72 12 3.52
10 10.47 11 13.96 11 3.49
11 10.70 11 14.15 11 3.45
One final property set needs illustration before we close the book
on terminated long-wire directional antennas. We have noted the
complexity of the lobe structure in both azimuth and elevation
patterns. These 2-dimensional slices of the overall radiation pattern
of the long-wire antenna do not do full justice to the overall radiation
pattern of the antenna. To rectify this gap, at least partially, Fig. 7
provides a 3-dimensional pattern for the 10-wavelength terminated
antenna. The pattern is limited to 5-degree increments, lest finer
detail turn the entire graphic into a simple opaque black-ink ball.
The junction of the X, Y, and Z axes represents the antenna
position relative to the pattern. Since the graphic shows a far-field
pattern, the antenna itself is infinitesimally small. However, the wire
extends along the Y-axis, with the terminating resistor on the +Y
end (toward the field's projection of higher gain).
Chapter 54
The graphic shows us two very significant features that might be

lost if we confine ourselves solely to 2-dimensional patterns. First,
the overall field is littered with a morass of sidelobes in virtually
every direction except downward. This facet of very long-wire
antennas concerned early developers of long-wire technology. The
sidelobes waste power that deserves re-direction into the main
forward lobe(s). As well, the sidelobes create and receive
interference. Moreover, they do nothing to secure a point-to-point
Chapter 54
link, but instead allow reception of possibly sensitive

communications to the sides of the antenna.
Second, the forward lobe structure contains an interesting oddity.

Careful inspection is necessary to perceive the anomaly. At the
second-lowest elevation angle (10 degrees in the graphic), we find
the split lobe that marks the highest gain that the antenna can
attain. At the next level (15 degrees in the graphic), the field has
very nearly the same gain across the lower-level split region, but at
a slightly lower gain value. Under some propagation conditions, the
higher-angle smoother pattern might obscure the presence of the
lower-angle split-lobe pattern. The complexity of even the forward-
most lobe structure should be an important planning investigation,
especially if one contemplates installing a terminated long-wire
directional antenna over poor to very poor soil.
Bending the Terminated Long-Wire Antenna: There is a technique

by which we can remove the split radiation lobe of the terminated
long-wire antenna, at least when the wire is many wavelengths
long. We may bend it horizontally in the middle. In effect, we create
a 2-element long-wire antenna, where each element is half the total
horizontal wire length. (In this sample, we shall leave the 1-
wavelength vertical wire and the "ground rods" from model D just
as they are.) Fig. 8 shows the general layout.
Chapter 54
One of the forward main lobes from the feedpoint-end section tends
to align itself with one of the main forward lobes of the termination-
end section, and the two lobes are aligned with the wire termination
points. Fig. 8 provides data for the 8-wavelength (or dual-4-
wavelength) bent terminated longwire antenna. The required angle
relative to the pattern centerline is 24 degrees for maximum gain.
This value is a function of the antenna's 1-wavelength height, the
average soil quality, and the wire length. Since the total horizontal
wire length is 8 wavelengths, the angle creates a maximum
antenna width of 1.63 wavelengths, but shortens the overall length
to 7.31 wavelengths.
Chapter 54
The following brief table compares the performance of the straight

and bent 8-wavelength antennas. Bending the wire adds about 2.5-
dB of overall gain, due to the additive affect of aligned lobes.
However, the front-to-back ratio suffers by a like amount. The
impedance hardly changes between the 2 antennas. The most
notable change of all is the reduction in beamwidth from 40 to 20
degrees.
End-Fed Terminated Long-Wire Directional Antenna Data: Straight and Bent 8-Wavelength Models
Version Maximum Front-Back Elevation Beamwidth Feedpoint Z 600-Ohm
(800-Ohm TR) Gain dBi Ratio dB Angle deg degrees R+/-jX Ohms SWR
Straight 8 WL 9.92 19.51 12 40.2 544 + j88 1.20
Bent 24 deg. 12.39 15.36 13 20.3 531 + j71 1.19
The difference in beamwidth becomes readily apparent when we

examine azimuth patterns for the 2 antennas in the table. Fig. 9
provides the patterns. The bent version has eliminated the null
between peaks by creating a single forward main lobe. As well, the
bent antenna's patterns shows irregular sidelobe structures that
result from off-axis additions and cancellations, relative to the clean
lobe structure of the straight antenna. However, most of the bent
antenna sidelobes tend to be weaker than those of the straight
antenna.
Chapter 54
The bent terminated long-wire antenna is rarely used today. The

straight terminated long-wire beam has lower gain, but it also
enjoys 2 advantages: wider beamwidth and the ability to operate
over a very wide frequency range at a constant impedance. The
bent antenna might match the straight antenna's SWR curve, but
the radiation pattern would become unusable beyond perhaps a 2:1
frequency range. The physical wire angle remains constant, but the
electrical length of the wire--measured in wavelengths--changes for
every change in operating frequency. The angle simply becomes
incorrect to produce maximum gain in a single lobe as the
operating frequency goes too high or too low. If we wish to obtain
the added gain of the bent antenna's aligned main lobes, there are
other designs that achieve the goal with more regular sidelobes
and, in some cases, weaker sidelobes. In future episodes, we shall
encounter some of those designs.
Chapter 54
Conclusion
So far, we have explored some of the performance properties of the

simplest long-wire antennas, a single very long piece of wire placed
horizontally over the ground. The notes have tried to impart a good
sense of what happens as we lengthen the wire under 3 different
feeding conditions: center feeding, end-feeding, and terminated
end-feeding. By the use of extensive tabulated data and patterns
from models of the antennas, I hope to have left reasonable
expectations for the relative performance of the 3 basic types of
long-wire antennas. Along the way, I have explored some of the
modeling issues to reveal both my rationale for use the models
involved and so that anyone else can recreate or improve them.
Bending the wire at the end of the present episode in fact gives us
a preview of the techniques that inform more complex long-wire
arrays.
Still, we have only begun to explore long-wire technology. We have

seen some of the shortcomings of the simple straight terminated
long-wire directional antenna. The lobes are split. There are many
side lobes. The forward gain is low. In an effort to overcome these
problems, early designers ingeniously developed the V-beam and
the rhombic. I have heard that Bruce would have preferred that his
name be attached to the rhombic for which he was a pioneer, rather
than to the planar array that bears his name in many handbooks. In
Parts 3 through 5, we shall not try to change the names of
antennas, but we shall try to understand better both the long-wire
V-beam and the rhombic antenna using some of the same
techniques employed in the notes for Parts 1 and 2.
Chapter 54
Chapter 55: V Arrays and Beams
In Chapters 53 and 54, we examined the simplest unterminated

and terminated long-wire arrays using a single end-fed wire in both
cases. Unterminated wires yield essentially bi-directional patterns in
line with the wire--more in line as the wire grows longer as
measured in wavelengths. There is a small residual front-to-back
ratio associated with long-wire end-fed wires, with the stronger
lobes toward the open or un-fed end of the wire. Adding a
terminating resistor converts the bi-directional wire into a directional
beam, although the gain is about 4 dB lower than the strongest
lobes of the unterminated wire of the same length. At the end of
Part 2, we summarized the shortcomings of the single-wire
terminated end-fed wire beam: "The lobes are split. There are many
side lobes. The forward gain is low." To overcome some of these
problems, early antenna experimenters invented the unterminated
V array and the terminated V beam. We shall look at each of these
antennas in order of sequence since we have some questions that
parallel those connected with the single wire terminated and
unterminated antennas. For example, will the terminated V beam
show the same gain deficit relative to the unterminated V array as
the terminated single-wire did relative to its unterminated version?
The V antennas are so intimately related to the single long-wire
antennas that before we move onward to rhombics, we shall do a
more detailed comparison.
Chapter 55
V-Array Basics
The V array derives directly from the single long-wire antenna. In

fact, a V array is nothing more than two single long-wires
connected at a feedpoint junction and fed in series. The V array
makes use of one of the problems for a single wire: the two main
lobes do not come completely together to form a single lobe. The V
array turns the problem into an advantage. If we angle each leg of
the V in just the right way, we can get two of the lobes--one from
each leg--to point in the same direction and let their gain levels add.
Fig. 1 shows the outline of how we obtain a true bi-directional
unterminated array from 2 long-wire antennas.
On the left is a representation of a single long-wire antenna (bold

solid line) and the headings of its main or strongest lobes (dotted
line). Note that we use the wire center as a conventional origin of
the lobe indicators. Since the dotted lines represent a far field
pattern, the antenna (in relation to the pattern) would have an
Chapter 55
infinitesimal size. When thinking about the pattern, mentally shrink

the antenna until it almost disappears.
In Parts 1 and 2, we represented the angle taken by the individual

lobes as an angle relative to the tangent to the wire, that is, relative
to a broadside direction. In this episode, we are interested in angle
A (usually shown as an alpha in texts). The old angular value and A
add up to 90 degrees, so conversion is easy.
If we now use 2 wires to form a V, we can set each one at angle A

relative to the centerline of the V. So the total angle between wires
is 2A. By aligning the wires in this way, a main lobe from each wire
at each end will fall into alignment and add up to a new higher gain
level. As well, there will be only 1 main lobe in each direction in line
with the wire. The remnant lobes become sidelobes of the array.
Note that this strategy is in principle similar to the strategy of
bending a long single wire in the middle to obtain lobes that add
rather than going in different directions. Indeed, the required angle
for each type of design is almost the same: angle A. Indeed, for the
same quantity of horizontal wire, a directional V beam and a
terminated bent single wire have about the same gain. The
difference is largely one of halving the total overall length (and the
acreage required beneath the antenna) for a doubling of the smaller
required width.
We are fortunate, since we can refer to Part 1 and find the heading
of the main azimuth lobes for each test length of long wire antenna.
The following table lists those headings as well as the resultant
value of angle A. The table also shows several other values. The
Chapter 55
next column lists a calculated value for angle A that we shall

explain following the table. The final columns show the angles
associated with corresponding long-wire terminated beams. These
values will not play a role in our work. They only illustrate the fact
that forming a terminated beam from the long-wire antenna does
compress the angle between the maximum gain points on the
beam forward pattern, in part due to the presence of the vertical
wires necessary to complete a practical installation.
Long-Wire Azimuth angles of Maximum Radiation and Corresponding A-Angles
Unterminated Long-Wire Terminated Long-Wire
Antenna Azimuth Angle Angle A Calculated Angle Azimuth Angle Angle A
Length WL degrees degrees A degrees degrees degrees
2 56 34 35.4 ----- -----
3 63 27 27.6 66 24
4 67 23 23.0 70 20
5 70 20 19.8 72 18
6 72 18 17.6 74 16
7 74 16 15.8 75 15
8 76 14 14.4 77 13
9 77 13 13.2 78 12
10 77 13 12.2 78 12
11 78 12 11.3 79 11
If we did not have access to NEC-calculated values for the azimuth

angles for the strongest long-wire lobes, we could have resorted to
an approximation equation for calculating the value of angle A.
Angle A = arccos [(N-0.5) / N] - 6
Angle A is in degrees, while N is the length of the long-wire legs in

wavelengths. I adapted and adjusted this equation from one found
in Balanis' account of long-wire antennas. Within the confines of the
lengths used for our test NEC-model cases, the equation is quite
adequate for forming models of V arrays. More complex angle
Chapter 55
calculation devices exist, but they turn out to be almost spuriously

precise. The gain of a V array changes very little using angle-A
values that are plus or minus a full degree from the listed values.
The tolerances become considerably tighter, however, if we
increase the leg length well beyond the limits of the table. Hence,
NEC models may be the best way to indirectly obtain the requisite
values for angle A. (For much longer antennas, it may be useful to
increase the resolution of the azimuth patterns from which we
indirectly derive angle A. NEC is fully capable of handling 0.1-
degree increments between pattern samples. In such cases, the
headings for the strongest lobe will also resolve to a tenth of a
degree.)
Note: The models in this part of our work make use of angle A as
derived from our modeling of single long-wire antennas. They do
not necessarily optimize that angle for maximum gain. There is a
slight difference.
For basic model testing, I chose the 10-wavelength V array using

13 degrees as the value of angle A. Relative to the array centerline,
shown in Fig. 1, the array is 9.75 wavelengths long and 4.5
wavelengths wide at the open end. Like the antennas in Parts 1
and 2, this one also uses perfect or lossless wire at 20 segments
per wavelength. The main tests will place the antenna 1 wavelength
above average ground (conductivity 0.005 S/m, permittivity 13).
However, for initial tests on the 10-wavelength model, I placed it
over very good, average, and very poor soil in order to see what
differences ground quality might make to performance. The
following table emerged from those tests.
Chapter 55
10-Wavelength Unterminated V Array 1-Wavelength Above the Indicated Soil

Type
Angle A = 13 degrees; Elevation angle = 10 degrees
Soil Type Gain Front-Back Beamwidth
dBi Ratio dB degrees
Very Good 17.21 2.55 11.0
Average 17.24 2.47 10.2
Very Poor 17.17 2.37 9.8
Unlike other antennas that we have surveyed in this collection of

notes, the V array showed almost no change in its pattern, despite
the wide range of soil qualities. The conductivity of the soils ran
from 0.0303 S/m for very good ground down to 0.001 S/m for very
poor ground. The relative permittivity range from very good to very
poor was 20 down to 5. Fig. 2 overlays the azimuth patterns for the
3 models. Except for a few distinguishable differences in nulls, the
patterns almost perfectly coincide with each other. In the realm of
bi-directional unterminated long-wire antennas, the V array may
prove to be a good selection for use over relatively poor soils.
Chapter 55
In the initial tests, I also tried the 10-wavelength V array using

copper wire over average ground to obtain a sense of what wire
losses might be. As in past models, the wire diameter is 0.16"
(AWG #6) to allow scaling of the 3.5 MHz test models to other
frequencies in the amateur HF range.
Chapter 55
10-Wavelength Unterminated V Array 1-Wavelength Above Average Soil

Angle A = 13 degrees; Elevation angle = 10 degrees
Wire Type Gain Front-Back Beamwidth
dBi Ratio dB degrees
Lossless 17.24 2.47 10.2
Copper 16.73 2.68 10.2
As the simple comparison shows, we lose about 0.5-dB relative to

maximum gain by using copper wire. I would view such losses as
insignificant, especially since we have no way to recover them
without a 20-wavelength supply of super-conducting wire.
In order to compare the performance of a single unterminated wire

to that of a V array, I constructed models of the V array using legs
that ran from 2 to 11 wavelengths. The following table lists the
value of angle A, the elevation angle for maximum gain, the
maximum gain value, the remnant front-to-back ratio, and the
beamwidth of the strongest main lobe. In addition, for easy
reference, the table also lists the maximum gain of the
corresponding single unterminated long-wire antenna and the gain
differential between it and the V array.
Performance of V Arrays 1-Wavelength Above Average Ground Single Long-Wire
Leg Length Angle A Elevation Max. Gain Front-Back Beamwidth Max. Gain Diff.
WL degrees Angle deg dBi Ratio dB degrees dBi dB
2 34 13 13.60 1.37 20.2 10.27 3.33
3 26 13 14.65 1.84 17.2 11.32 3.33
4 23 12 15.48 1.88 14.4 11.99 3.49
5 20 12 15.97 2.05 13.2 12.48 3.49
6 18 12 16.25 2.27 12.2 12.90 3.35
7 16 11 16.56 2.36 11.8 13.24 3.32
8 14 11 16.75 2.44 11.8 13.50 3.25
9 13 11 16.99 2.44 11.4 13.72 3.27
10 13 10 17.24 2.47 10.2 13.96 3.28
11 12 10 17.35 2.56 10.2 14.15 3.20
Chapter 55
The tabulated data shows the usual progression of increasing gain

and decreasing beamwidth as we lengthen the legs of the antenna.
As well, length-for-length, the V array shows a maximum gain that
is somewhat over 3-dB greater than the gain of a single long-wire
antenna having the same length. (One might well dispute the length
equivalence, arguing that the centerline of the V array is always
shorter than the centerline of the corresponding single long-wire
antenna. However, with 10-wavelength legs, the centerline
difference is only about 1/4 wavelength due to the gradual
narrowing of the angle (2A) between the wires.)
Perhaps the most intriguing set of numbers falls in the beamwidth

column. For leg lengths beyond about 3 wavelengths, the antenna
requires careful alignment for the main lobe (or lobes) to hit a
communications target. In fact, V arrays (and beams) found their
main use as antennas having communications targets falling within
a small radius. One technique used to steer the antenna's main
lobe was to set multiple Vs in a physically serial arrangement that
did not necessarily form a straight line Thus, one antenna could
bend the beam of the first. We should also remember that high
quality copper wire in the late 1920s and through the 1930s was not
as cheap as it is today, when measured against other prices. Many
amateurs used less expensive phosphor-bronze wire for antennas,
and government and commercial wire antenna installations were
major investments. Although we today may doubt the precision that
one might achieve by attaching wire to wooden telephone and
telegraph poles, the engineering calculations were as precise a
available techniques permitted. (Laport's Radio Antenna
Engineering from 1952 has an interesting gallery of photos of
Chapter 55
mainly RCA antenna installation going back as far as the 1930s.

Wooden poles--some spliced to increase their height--outnumber
metal masts and towers. We may also find it interesting that many
installers working with hand tools wore neckties and fedora hats on
the job.)
The V array is not an antenna for broad coverage of the horizon. Its
wire foundation makes it immovable, and the gain comes at the
expense of beamwidth. Hence, its best use is as a point-to-point
antenna, where the reliability of a single communications link is
more important than communications with many diverse places on
the horizon. The gallery of sample elevation and azimuth patterns
in Fig. 3 will reinforce this judgment.
Chapter 55
Compared to the single long-wire antenna, the V array shows

significantly smaller elevation lobes above the main lobes. The
azimuth sidelobes, while still pronounced in the off-heading forward
areas, are generally smaller than those of a single unterminated
wire antenna. Many of the sidelobes from each leg tend to counter
corresponding sidelobes from other legs, in part due to having
different headings and in part due to the spacing between the legs.
The azimuth pattern for the 4-wavelength model shows perhaps the
Chapter 55
tightest wasp-waisted pattern. In contrast, the elevation upper lobes

tend to decrease in strength in more direct proportion to the length
of the legs. However, due to the interaction of the lobes from each
leg and the changing included angle from one model to the next,
we cannot characterize the patterns by reference to the number of
lobes, as we did with the single long-wire end-fed antenna.
The 3-dimensional radiation pattern shown in Fig. 4 has a

peculiarly crystalline appearance, given the 5-degree increment
between sampling points. Nevertheless, the main lobe extremities
show well. Still, one might best refer to the 2-dimensional plots
before attempting to characterize the upper-angle lobes. Although
Chapter 55
there are still many lobes--as there will be for virtually any long-wire
antenna--their strength relative to the main lobes is considerably
weaker than is the case for a single wire.
There is no rule that we must always optimize a V array for

maximum gain. At certain values for angle A, the beamwidth will
widen. Of course, the new value for A varies with the length of the
legs. As well, a widening of a few degrees will actually narrow the
beamwidth. However, by judicious modeling or experimentation,
one can find a usable beamwidth before the pattern degenerates
into peaks with a very deep null between them. For example, with
5-wavelength legs, the peak-gain angle is 20 degrees (or 40
degrees between wires). The beamwidth is 13.2 degrees. By
widening angle A to 29 degrees (58 degrees between wires), the
effective beamwidth becomes about 35 degrees. With a pre-
planned selection of centerline headings, it is possible to cover
much of the horizon in a switched set of V arrays in which each
interior leg serves 2 arrays. Fig. 5 shows the general scheme and a
sample azimuth pattern. For some installations, similar schemes
can be tailored to the operating site and communication needs. The
13.4-dBi gain of each V-pair still out-performs individual 5-
wavelength wires.
Chapter 55
The potentials for V arrays are larger than suggested by this

introduction to them. However, it is time to terminate this initial
discussion and the V array itself.
V-Beam Basics
The terminated V array forms a V-beam, that is, a directional

terminated V array. The technique seems simple enough. We
simply place a non-inductive terminating resistor at the end of each
leg. However, the resistor cannot simply float at the terminating end
of the wire. One option is to bring the terminated end of the leg wire
to ground. Alternatively, we may run a wire between the two
Chapter 55
terminated wires end and place the non-inductive resistor at the

center.
Fig. 6 shows 4 classic implementations of the terminated V-beam.

Model A places the feedpoint close to ground and slopes the legs
upward to their normal (1-wavelength) height. (The opposite slope
for the array is also possible. See model A1.) The terminated ends
run vertically to the ground, with the terminating resistors at ground
level. The model will use the same ground-rod technique used in
constructing models of single terminated long-wire directional
antennas. However, none of the models will use a vertical wire at
the feedpoint end. The single long-wire beams could use the
vertical feedpoint end with the actual feedpoint close to ground. If
we apply that same technique to the V-beam, we end up with the 2
legs in parallel, which does not yield much gain or directivity. The
source-ends of the legs must have the feedline across them in a
series connection to yield the correct addition of peak lobes from
each leg.
Selecting the correct values of the 2 terminating resistors is not so

simple as it was with the single long-wire beam. As the following
Chapter 55
trial table shows, the value is not exceptionally critical, although we

may have reasons for choosing one value over another. For design
purposes, the reasons may involve the best compromise among
gain, front-to-back ratio, and impedance. In practical installations,
the reasons generally focus on what non-inductive resistors may be
available. The test table (and others to follow) uses NEC-4 models
with 5-wavelength legs 1-wavelegnth above an average SN ground.
Test Performance Values for Modeling Option A

600 x2 8.89 23.15 12.2 15 988 + j184 1.20

700 x2 8.91 22.40 12.4 15 1043 + j145 1.16
800 x2 8.93 20.58 12.4 15 1091 + j109 1.14
The sloping version of the terminated V-beam shows a serious gain

deficit relative to level models (options B, C, and D in Fig. 6). Gain
is 4- to 5-dB lower than for the other versions. Therefore, we should
test further V-beam designs. NEC calculates that each terminating
resistor dissipates about 21% of the applied power, using the 700-
Ohm resistor in each leg.
If we slope the V-beam in the other direction, with the feedpoint

high and the terminations low, we do not see much change in the
performance, except for a reduction in the front-to-back ratio and a
reduction in the terminating resistor. Let's call the reverse slope
model A1.
Chapter 55
Test Performance Values for Modeling Option A1

400 x2 8.60 18.90 21.0 14 1032 + j107 1.12

500 x2 8.60 18.06 21.2 14 1096 - j 6 1.10
600 x2 8.63 15.99 21.2 14 1141 - j109 1.18
The theory behind the reverse slope is an attempt to lower the

elevation angle of maximum radiation. However, the result is an
antenna that is on average much lower than a model that is level at
1 wavelength. Hence, the net elevation angle, while 1 degree lower
than for version A is still higher by 2 degrees than the other models
(B, C, and D) in this sequence. The model A gain deficit still
remains, with a gain level that is barely 1 dB higher than a 1/2-
wavelength dipole at 1 wavelength above average ground.
Model B uses the same layout as Model A, but raises the feedpoint
to the same height as the remainder of the antenna. Like Model A,
B uses a pair of terminating resistors. The gain and elevation angle
of maximum gain return to normal values, as shown in the following
test table.
Test Performance Values for Modeling Option B

600 x2 13.00 20.62 13.8 12 830 + j133 1.18

800 x2 13.02 18.41 13.8 12 926 + j190 1.30
1000 x2 13.07 16.00 13.8 12 1002 + j242 1.42
The gain level of this model changes very slowly with changes in
the values of the terminating resistors. Hence, the table proceeds in
200-Ohm increments. Selecting the most optimal combination
requires some decision-making based on criteria. In the absence of
Chapter 55
practical operating goals, I chose the 600-Ohm resistors, since they

yielded the highest front-to-back ratio in the group, along with
having the lowest order of feedpoint reactance. The 600-Ohm
resistors dissipate about 22% of the applied power--each.
Model C uses the same feedpoint treatment as model B. However,

instead of bringing 2 vertical wires to ground, with 2 attached
resistors, model C uses a straight connecting wire between the far
ends of each leg. For the 5-wavelength legs of the test model, the
crossing wire is about 3.4 wavelengths. At the center of the wire,
we place a single non-inductive resistor. As the following table will
show, the connecting wire is not inert, but an active part of the
overall antenna.
Test Performance Values for Modeling Option C

800 14.38 12.73 12.6 12 981 + j192 1.25

900 14.35 13.76 12.6 12 949 + j147 1.18
1000 14.34 14.73 12.6 12 919 + j110 1.13
The crossing horizontal wire between the V-leg ends contributes to

the array gain in both directions. Hence, the peak forward gain is
slightly higher than for model B, but the front-to-back ratio is much
lower. If we select the 900-Ohm terminating resistor, NEC
calculates that it will dissipate about 46% of the applied power.
Model D also uses a crossing wire with a single terminating resistor

at its center. However, it brings the crossing wire much closer to
ground level. In the model, the wire is 0.001-wavelength above
ground; just enough for the wire to clear the ground by several wire
Chapter 55
diameters. Each end of the V assembly runs a vertical wire down to

the junction with the low crossing wire. As the table shows, this
arrangement produces one of the most stable configurations
relative to changes of gain with changes of the terminating resistor
value.
Test Performance Values for Modeling Option D

600 13.02 21.26 13.4 12 761 - j 49 1.07

800 13.03 20.64 13.4 12 754 - j 55 1.08
1000 13.03 20.19 13.4 12 749 - j 59 1.08
1200 13.03 19.85 13.4 12 744 - j 63 1.09
Not only is the gain stable across a 2:1 range of resistor values, but
as well both the front-to-back ratio and the feedpoint impedance are
equally stable. NEC calculates that in its altered position, the 1000-
Ohm terminating resistor dissipates only 2.8% of the applied power,
although this result stems from the proximity of the crossing wire to
ground in the model. The actual dissipation may be much larger for
only small increases in resistor and wire height. Nevertheless,
using a very low crossing wire removes it from having a significant
affect on the radiation pattern. In fact, the data for models B and D
are quite similar, although model D appears to be the more stable.
Further test of the V-beam using various leg lengths will employ this
model and its 1000-Ohm resistor.
Chapter 55
Fig. 7 provides azimuth patterns for each of the 5-wavelength V-

beam models. They show a family resemblance, especially in the
forward structure of the lobes. The sidelobes of model A appear
stronger because the forward gain is 4-dB or more weaker than for
the other models. The data had suggested a close correlation
between model B and model D, and the azimuth patterns tend to
confirm the suggestion.
Although the 4 models of a V-beam use different arrangements and

terminating resistor values to arrive at their patterns, all of them
have the wide-band characteristic that we saw in the case of single
long-wire beams. Fig. 8 provides the SWR curves over a 2:1
frequency range using the optimal feedpoint impedance relative to
the indicated values of terminating resistor or resistors. In each
case, for the range tested and beyond, a single impedance-
transformation device would suffice to match the antenna to most
equipment. What all the SWR patterns share in common is the
existence of ripples of non-harmful but noticeable proportions.
These ripples are indications that the selected terminating resistor
value(s) did not result in the closest equality between the
Chapter 55
terminating resistor and the feedpoint impedance. Instead, the final

component selection rested on other criteria, such as the resulting
pattern, etc.
Chapter 55
The broad SWR bandwidth of the single long-wire directional

antenna is completely reliable, since the general pattern of the
antenna is predictable in terms of gain and beamwidth. However,
the V-beam has a more limited usable bandwidth due to restrictions
created by the angle between the wires (2A). At some frequency
above and at another below the design frequency, the value of
angle A will no longer be suitable to support a single forward lobe.
As shown in Fig. 9, a 2:1 operational range is feasible for the 5-
wavelength V-beam that is 1 wavelength above ground at the
center frequency.
Performance of a 5-Wavelength 3.5-MHz V-beam 1 Wavelength Above Average Ground

Model D: Terminating Resistor: 1000 Ohms
Frequency Maximum Front-to-Back Beamwidth Elevation
MHz Gain dBi Ratio dB degrees Angle deg
2.3 9.84 33.30 21.8 17

3.5 13.03 20.19 13.4 12
4.7 14.42 23.77 9.8 9
Chapter 55
When evaluating both the patterns and the tabular data, remember
that at the low end of the sweep, the antenna is only 0.66-
wavelength above ground, accounting for the higher elevation
angle. Similarly, at the top of the sweep, the antenna is 1.34-
wavelengths above ground. The changing height is an additional
variable relative to the departure from an optimal value for angle A,
and both contribute to the listed performance values.
Parallel to our investigation of the unterminated V array, I ran model

D with a 1000-Ohm terminating resistor over several ground types.
As shown in the table below, the gain changes by under 0.5 dB
across the range of soils. The other values are equally stable,
presenting no difficulties to using the V-beam over virtually any
ground environment.
5-Wavelength Terminated V Array 1-Wavelength Above the Indicated Soil Type
Angle A = 20 degrees; Elevation Angle = 12 degrees
Soil Type Gain Front-Back Beamwidth Feedpoint Z 750-Ohm
dBi Ratio dB degrees R +/- jX Ohms SWR
Very Good 13.18 18.89 14.4 753 - j 97 1.14
Average 13.03 20.19 13.4 749 - j 59 1.08
Very Poor 12.72 24.15 13.0 782 - j 27 1.06
Likewise, the use of a real material, such as copper wire, in place of

the modeled perfect wires, offers no hindrance to the V-beam. As
the following table shows, the loss due to the use of copper wire for
the 5-wavelength V-beam is about 0.1-dB over average ground. All
of the other performance values are completely stable.
Chapter 55
5-Wavelength Unterminated V Array 1-Wavelength Above Average soil

Angle A = 20 degrees; Elevation Angle = 12 degrees
Wire Type Gain Front-Back Beamwidth Feedpoint Z 750-Ohm
dBi Ratio dB degrees R +/- jX Ohms SWR
Lossless 13.03 20.19 13.4 749 - j 59 1.08
Copper 12.93 20.43 13.4 752 - j 52 1.07
The full table of performance values below rests on model D, the

version with a single terminating resistor centered on a wire
between the V-leg end, but very close to ground level. The table
does not include power dissipation values, since they likely depend
on the very close proximity of the modeled resistance to the
ground, as well as energy lost to ground due to the proximity.
Hence, the exact dissipation values will vary with the actual height
of the cross connecting wire. The table does include values for
angle A, the elevation angle of maximum gain, the modeled
maximum gain, the 180-degree front-to-back value, the beamwidth,
the feedpoint impedance, and the 750-Ohm SWR. In addition, the
table shows the maximum gain of the corresponding unterminated
V array and the gain difference relative to the V-beam.
Note: Once again, the value of angle A is derived from our long-
wire antennas and is not adjusted to achieve maximum gain.
Chapter 55
The table shows a very normal increase in gain with leg length at
the optimal angle A. Both the elevation angle and the beamwidth
for the V-beam tightly correspond to comparable values for the
unterminated V array, with no decrease in beamwidth as we
experienced with the transition from unterminated long-wire to
terminated long-wire antennas. The 180-degree front-to-back ratio
holds around the 20-dB mark, and the impedance is exceptionally
stable throughout the span of leg lengths. (The stability of the
impedance values is an especially good marker of the adequacy of
using values for angle A derived from the unterminated single long-
wire models.) As a side note, compare the V-beam entry for 4-
wavelength legs to the data for the bent terminated long-wire in
Part 2. The gain values a virtually identical, although the V-beam
improves the front-to-back ratio and reduces many of the sidelobes.
Both antennas require 8 wavelengths of horizontal wire.
The V-beam, like the terminated long-wire antenna, shows a

decrease in maximum forward gain relative to the unterminated
version of the antenna. However, the V-beam decrease is about a
dB less than for the single long-wire beam. Nevertheless, the
reason for using a V-beam instead of an unterminated V array is
the directivity of the pattern, with the loss of gain accepted as a fair
penalty for the reduced sensitivity to the rear. If rearward pattern
reduction is not a priority for a given installation, then the
unterminated V array may be the better choice of antennas. Fig. 10
provides a gallery of selected elevation and azimuth plots that show
the evolution of radiation patterns with increasing leg length in the
V-beam. You may wish to compare these plots directly to
corresponding plots in Fig. 3 for the unterminated V array.
Chapter 55
The azimuth patterns have two major characteristics that we should

note. First is the narrowing of the beamwidth as we make the
antenna longer, a feature that also attaches to the V array. Second
is the development of the secondary lobes in the 2 forward
quadrants. These lobes are a function of the narrowing angle
between wires and the lobes on each wire that does not add to
form the strongest center lobe.
Chapter 55
The most notable elevation-plot feature is the relative absence of

strong secondary elevation lobes. Only the lobes closest to the
main elevation lobe exceed the -20-dB level in strength relative to
the main lobe. We may better gauge the upper-level lobe structure
from a 3-dimensional radiation pattern, such as the one in Fig. 11.
The 10-wavelength V-beam used to generate the plot clearly shows
the lowest level. The apparent second level is actually a part of the
main lobe. The stepped appearance is due to the 5-degree
increments in pattern sampling. The next strongest level to the
main lobe occurs near the 40-45-degree region and is 15-20-dB
weaker than the main lobe. Although there are still many upper-
level lobes in the pattern, their strength is operationally insignificant.
Chapter 55
Perhaps an appropriate way to conclude our exploration of the V-

beam is by comparing it, length for length, with the corresponding
single long-wire terminated beam. Fig. 12 provides a pattern
comparison, using 10-wavelength versions of both antennas. The
elevation patterns show the V-beam's reduction in relatively useless
upper level lobes. The azimuth pattern shows the V-beam's tighter
control of sidelobes, especially in the forward quadrants. However,
for some communications tasks, the terminated long-wire may have
the more useful beamwidth, despite the null between forward
peaks.
Chapter 55
The following table summarizes the gain and beamwidth

differentials between the 2 terminated long-wire directional
antennas.
Long-Wire and V-beam Gain and Beamwidth Values for 3- to 11-Wavelength Arrays
Terminated Long-Wire Terminated V-Beam
Length Gain Beamwidth Gain Beamwidth Gain Diff.
WL dBi degrees dBi degrees dB
3 7.11 69 11.41 17 4.30
4 7.99 59 12.35 15 4.36
5 8.65 51 13.03 13 4.38
6 9.15 46 13.50 12 4.35
7 9.57 44 13.86 12 4.29
8 9.92 40 14.07 12 4.15
9 10.20 37 14.29 11 4.09
10 10.47 36 14.59 10 4.12
11 10.70 33 14.74 10 4.04
The V-beam shows a consistent 4-dB+ gain advantage over the

terminated long-wire antenna, but its beamwidth is consistently 1/3
to 1/5 the values for the long-wire. The terminated long-wire
directional antenna, of course, shows a null between peaks, and for
lengths from 3 to 6 wavelengths, the null is deep enough (>3dB) for
modeling software to recognize two distinct forward lobes. The
table does not itself make a judgment, but simply facilitates a
comparison of the results in Part 2 of this series and the results
obtained for this part.
Conclusion
On this leg of our journey through the classical long-wire antennas,

we have focused on the V antenna in both unterminated and
terminated forms. By properly angling the legs of the V, the antenna
combines a major lobe from each wire to form a single lobe in the
Chapter 55
forward direction. Of course, the unterminated V array has a similar

lobe to the rear and it is is only slightly weaker than the lobe
pointing away from the feedpoint. Terminating the legs of the Vee
creates a directional antenna with superior properties to the single
long-wire in terms of gain and the suppression of both elevation
and azimuth sidelobes. However, the improved directional
characteristics come at the expense of some of the unterminated
V's gain. As well the V antennas have a very narrow beamwidth
that limits the potential applications for either the terminated or
unterminated versions.
Although there may be many variants on long-wire design, classical

literature shows only one more major pathway to traverse: the
rhombic. A Bruce development from the 1930s, the rhombic
sometimes bears the title of the king of wire antennas. The antenna
has had a lure that will take us 2 episodes to cover, and then only
in an introductory way. One humorist has wished for his ideal
antenna, and it was a very long rhombic installed on a rotatable
island. Our task will be to see if there is any good sense hiding
behind the humor.
Chapter 55
Chapter 56: Rhombic Arrays and Beams
Every step along our path through traveling-wave antennas has led
us to new heights of gain per unit of wire length (as measured in
wavelengths)--and to narrower beamwidths. The final steps take us
to the pinnacle of long-wire development: the rhombic antenna.
(We should note that there are some "fishbone" designs that may
be able to achieve more gain per acre of ground than the designs
with which we are working. However, these antennas use a quite
different design and require at least 2 to 4 wavelengths of wire per
wavelength of forward antenna dimension. We shall not cover them
here. However, the ARRL Antenna Book chapter and the Laport
volume, both cited in the short list of references, cover the basics of
these designs.)
The rhombic antenna derives its name from its shape: the rhombus.
In geometry, a rhombus is an equilateral parallelogram, that is, a
closed 4-sided figure with all sides the same length, but with all
corner angles normally using other than right angles. Fig. 1, at the
top, shows a basic rhombus, with indications of the key dimensions.
Chapter 56
An alternative way to look at the rhombus is to see it as 2 V

antennas end-to-end. This orientation makes clear that the
centerline is correctly identified, and it gives the elongated shape
some sense, assuming that Part 3 of this series has had its impact.
The length L, in wavelengths, defines the length of each leg,
suggesting that each rhombic antenna that we examine will likely
be twice as long overall as a corresponding V antenna with the
same leg length.
Also apparent in the sketch is angle A (usually represented by a

Greek alpha). When we examined V antennas, we used the angle
of the strongest lobe of a single long-wire of length L to determine
the value of angle A. We then found that angling each V wire from
the centerline by the value of A produced additive lobes along the
centerline. Since the far end of any rhombic antenna is a mirror
image of the feedpoint end, the lobes for the far-end wires will also
Chapter 56
be aligned with the center line. Hence, we can expect more gain
from a rhombic antenna than from a corresponding V antenna.
The earliest literature, starting with the classic article by Bruce,

Beck, and Lowry ("Horizontal Rhombic Antennas," Proc. IRE,
1935), began the practice of referring to angle B in Fig. 1 as the tilt
angle. The normal character for this angle is a Greek phi, although I
have seen other characters as well. Angle B is simply 90 degrees
minus angle A.
Basic rhombic calculations emerge from a situation that is usually

not very realistic for the average amateur installation. The premise
is that angle A represents 2 different angles in the antenna
installation. First, it represents the elevation angle of maximum
radiation. Hence,
HWL = [1 / (4 sin A)]
where HWL is the required antenna height in wavelengths. As well,

angle A represents the required V'ing angle, the same angle that
we used in the V-antennas. To align the major lobe with the
elevation angle, we calculate the leg-length as follows:
LWL = [0.371 / (sin2 A)]
where LWL is the leg-length in wavelengths. For maximum gain at

the chosen elevation angle,
LWL = [0.5 / (sin2 A)]

Chapter 56
The difficulty faced by amateur installations is that the height is

rarely a matter of open choice. As a matter of fact, neither is the
length open to selection based solely on calculations. Instead, the
maximum height for installations is usually prescribed by any
number of limiting circumstances. All of the examples used in this
Long-Wire series have set the antennas at 1 wavelength above
ground on the premise that most long-wire antennas will ultimately
fall in the upper HF range. 1 wavelength at 14 MHz is about 70'.
Property lines usually define the absolute limits of overall array
length, abetted by complexities such as the availability and
feasibility of supporting very long runs of wire.
Initial and later studies in rhombic antennas provide more complex

equations to calculate compromises where the elevation and the
V'ing angle do not match. Some of the equations appear in
nomographic form. For example, one such nomograph appears in
the ARRL chapter on long-wire and traveling-wave antennas, as
well as in articles and text devoted specifically to the design of
rhombic antennas. (See the Harper volume in the reference list.)
Such nomographs are capable of guiding the rhombic designer to
excellent results, as we shall see before we close this last segment
of our long-wire trek.
However, via NEC modeling, we have an easier route to designing

rhombics. The process started in Part 1, with the modeling of end-
fed unterminated wires, from which we obtained the values of angle
A within the limits of the modeling exercise. We standardized the
wire height at 1 wavelength. We might as easily develop a
compendium of models using the same (or different) increments of
Chapter 56
wire length at a number of different heights. For a practical design

project, we likely would select a single height dictated by whatever
constraints will govern the installation. Then, we can collect data on
angle A for any set of wire lengths desired.
We may use the selected height and the associated values of angle
A to design any number of rhombic antennas. In fact, we can use a
simple long-wire as the starting point. NEC allows us, via the GM
command, to rotate the wire by the required number of degrees
dictated by the value of angle A for a given wire length. (Programs
like EZNEC use a different but equally effective method of rotating
wires.) Hence, we can easily create a V and find its coordinates.
From those coordinates, we can complete the rhombic by doubling
the overall length and bringing 2 new wires back together--or
almost together. See the lower part of Fig. 1 for 2 possible versions
of an unterminated rhombic configuration.
The use of angle A assures us of lobe direction coincidence and

gain addition along the centerline of the antenna. We may then let
NEC calculate the gain and actual elevation angle for the selected
antenna height over any selected soil. Before we close this
discussion, we shall find that NEC's handling of rhombic design and
at least one nomographically based design turns out to be virtually
identical. Traditional methods are quite accurate, but in the present
age of computerized antenna design, the modeling process is often
simpler. As we have seen from our experience with single long-wire
and V antennas, the modeling method also provides ready
supplementary information, for example about sidelobes, feedpoint
Chapter 56
impedances, and power dissipation in the load resistance of

terminated antennas.
In our exploration of rhombic antennas, we shall simply extend our

modeling methods. First, we shall leave the antenna at 1
wavelength above average ground (conductivity 0.005 S/m,
permittivity 13). The test frequency will be 3.5 MHz, and the
lossless wire will be 0.16" in diameter. Part 1 of the series sampled
some of the variations on these choices, so you may readily
extrapolate additional losses or gain from selecting different
background parameters. Better yet, you may easily model most of
the antennas yourself, using your own selection of parameters.
Some beginning programs are limited to 500 segments. A few of
the longer rhombics may require up to 900 segments if we adhere
to our 20-segment per wavelength standard. However, a full 6-
wavelength-per-leg rhombic comes in at under the 500 segment
mark.
Unterminated Rhombic Antennas
The lower portion of Fig. 1 shows two ways of modeling an

unterminated rhombic antenna. We may separate the far end point
by a small space. This configuration is perhaps the most common
understanding of an unterminated (sometimes called a resonant)
rhombic. However, we may equally bring the ends together to
short-circuit the gap. The options expose something of a
misimpression of the rhombic antenna. If we were given to extreme
(and unfortunately, contentious) modes of expression, we might
Chapter 56
suggest that there is no such thing as an unterminated rhombic

antenna.
The single long-wire unterminated antenna and the V array both

make good sense of the idea of a wire without a resistive
termination. Any form of termination requires extra wires and
ultimately a ground connection--although there is a version of the
V-beam that does not use ground at the far end of the array. The
rhombic returns the 2 wires of the antenna to close proximity. In the
models that we shall explore, the gap will be 0.002-wavelength. At
3.5 MHz, that distance is 170 mm, where a wavelength is over 85.6
m long. If we leave the gap open, we can treat the terminating
resistance as simply indefinitely large. One modeling technique for
rhombics is to use a short wire to bridge the gap. To create a
terminated rhombic--as the term is generally used--we place a load
resistor of a desired value on the bridge wire. To create an open
circuit, we might specify the load resistance as 1e10 Ohms or
higher. To short out the gap, we can either remove the load resistor
or give it a value of 0 Ohms. Alternatively, we can remove the
bridge wire and simply bring the 2 legs to the same point on the
coordinate scheme.
Despite the existence of a reasonably plausible claim that all

rhombics are terminated to one or another degree, we shall adhere
to the common referential terms. Without a mid-range non-inductive
resistor at the far end of the antenna, the rhombic will be
unterminated in either the open or closed configuration. The chief
difference between the open and closed versions of the
unterminated rhombic antennas lies in the sidelobes, not in the
Chapter 56
small differences in gain and inherent front-to-back ratio that is a

part of all end-fed long-wire antennas. Fig. 2 contrasts the structure
of the sidelobes for open and closed unterminated rhombics. Note
that the closed version shows larger sidelobes than the open
version, suggesting less complete cancellation of lobes from the
parallel legs.
Chapter 56
For comparison and contrast, Fig. 2 also presents two azimuth

patterns from corresponding unterminated V arrays. The pattern on
the lower left uses 3-wavelength legs, the same length as the legs
in the rhombics. On the lower right is the pattern for a V array using
6-wavelength legs. These legs give the V array the same overall
length as the rhombic with a small margin of difference due to the
difference in the value of angle A. (Both rhombics are 5.39
wavelengths, while the long V is 5.71 wavelengths overall.) On the
whole, the long V antenna pattern resembles in general sidelobe
strength the closed rhombic pattern. However, the V patterns show
the combination of many sidelobes that combine to form fewer
distinct lobes and nulls. In contrast, the double-V configuration of
the rhombic reduces these indefinite lobe formations down to
distinct lobes and nulls. In fact, both rhombic azimuth patterns show
a total of 20 lobes. The lower strength levels of the lobes at near-
right-angles to the 2 main lobes for the open version of the antenna
make lobe counting impossible at the scale of Fig. 2, but expanded
renderings of the plot reveal them all. In contrast, even large
renderings of the V-antennas do not permit an accurate count of
the lobes and the bulges that form incipient lobes.
Clear lobe definition and numeric limitation together comprise one

of the advantages of the rhombic over corresponding V antennas.
The other major rhombic advantage is gain. The following table
provides modeled data for both open and closed unterminated
rhombics with varying leg lengths from 2 through 11 wavelengths.
Remember that the overall length of the rhombic is just under twice
the leg length. Like all long-wire antennas, the rhombic suffers the
blight of diminishing returns as we strive to make it longer. Doubling
Chapter 56
the leg length from 2 to 4 wavelengths provides nearly 2.5-dB more

gain. However, the next doubling to 8 wavelength legs adds slightly
under 2 dB of gain.
Note: The values of angle A derive from our earlier work with single
long-wire antennas. I have not optimized those values to achieve
maximum gain. There is a slight difference.
Performance of Unterminated Rhombic Antennas 1-Wavelength Above Average Ground
Type Leg Length Angle A Elevation Max. Gain Front-Back Beamwidth
WL degrees Angle deg dBi Ratio dB degrees
Open 2 34 14 16.41 2.41 20.4
Closed 2 34 14 15.84 2.90 20.6
Open 3 26 14 17.81 2.40 17.2
Closed 3 26 14 17.50 2.66 17.2
Open 4 23 13 18.89 2.58 14.1
Closed 4 23 13 18.61 2.83 14.4
Open 5 20 13 19.57 2.57 12.8
Closed 5 20 13 19.35 2.77 12.8
Open 6 18 12 20.12 2.55 11.6
Closed 6 18 13 19.95 2.71 11.8
Open 7 16 12 20.53 2.48 11.2
Closed 7 16 12 20.39 2.60 11.2
Open 8 14 12 20.82 2.32 11.0
Closed 8 14 12 20.69 2.42 11.0
Open 9 13 12 21.17 2.27 10.4
Closed 9 13 12 21.03 2.38 10.4
Open 10 13 11 21.52 2.37 9.4
Closed 10 13 11 21.39 2.47 9.4
Open 11 12 11 21.73 2.29 9.0
Closed 11 12 11 21.61 2.38 9.0
At the top of the table, the gain differential between open and
closed rhombics appears to be significant: nearly 0.6 dB. However,
the differential shrinks continuously as we lengthen the legs. By the
time the legs are 11 wavelengths, the gain differential is only a bit
over 0.1 dB. Elevation angles, front-to-back ratios, and beamwidths
Chapter 56
all remain very comparable for both types of unterminated rhombic

antennas.
All of the closed unterminated rhombics show a modest feedpoint

impedance at the integral leg lengths that appear in the table. The
resistive component varies between 235 and 290 Ohms, while the
reactance ranges from -j160 to -j190 Ohms. In contrast, all of the
open rhombics show very high impedance levels, with resistive
components running from 2900 to 3300 Ohms. The reactance
seems to have a wide range--from +j130 to +j460 Ohms. However,
as a fraction of the total impedance, the range is small. The
differential between open and closed rhombic impedances is real,
but in practical terms of designing a system, it is also illusory. The
curves for changes of feedpoint resistance and reactance for the
two types of unterminated rhombics are virtually identical, but
displaced from each other by about 1/4 wavelength of leg length.
Fig. 3 presents the unterminated rhombic gallery of sample

elevation and azimuth plots for leg lengths of 2, 4, 6, 8, and 10
wavelengths. By comparing the plots with Fig. 2, you can verify that
the gallery uses the open version of each rhombic.
Chapter 56
The open unterminated rhombic shows excellent sidelobe control

compared to the other long-wire antennas that we have surveyed.
Chapter 56
In general, azimuth sidelobes are 10 dB of more down, with a very

good front-to-side ratio for headings near or at the 90-degree mark
off the main lobes. Secondary elevation lobes are 10 to 15 dB
down, depending upon rhombic length. Fig. 4 provides a 3-
dimensonal radiation pattern in 5-degree increments of the rhombic
with 10-wavelength legs. Although the upper elevation angles still
bristle with lobes, they are generally all of low strength and
therefore untroublesome to antenna performance.
As a way to summarize our meandering through various

unterminated bi-directional wire antennas, the following table
presents the modeled maximum gain values for each type that we
have surveyed. All values are for perfect-wire antennas 1
wavelength above average ground. Remember that the center-fed
and end-fed long-wire antennas show maximum gain off-axis to the
wire, while the V and rhombic antennas show maximum gain in line
with the antenna centerline. In addition, the rhombics overall are
Chapter 56
twice as long as the single-wire and V antennas listed for the same
leg length.
Maximum Gain of Various Types of Unterminated Long-Wire Antennas
Leg Maximum Gain dBi
Length Center-Fed End-Fed V Closed Open
WL Doublet Wire Array Rhombic Rhombic
2 9.36 10.27 13.60 15.84 16.41
3 10.16 11.32 14.65 17.50 17.81
4 10.93 11.99 15.48 18.61 18.89
5 11.47 12.48 15.97 19.35 19.57
6 11.85 12.90 16.25 19.95 20.12
7 12.14 13.24 16.56 20.39 20.53
8 12.43 13.50 16.75 20.69 20.82
9 12.65 13.72 16.99 21.03 21.17
10 12.82 13.96 17.24 21.39 21.52
11 13.01 14.15 17.35 21.61 21.73
Although some of the gain increase that we see with longer and
more complex long-wire antennas comes from sidelobe control,
most of it emerges at the expense of beamwidth. We have noted
this fact in past episodes, but it needs a reminder here. Short V and
rhombic antennas (2-wavelength legs) have beamwidths just over
20 degrees. With 10-wavelength legs, the beamwidth is less than
half that value. Although the high gain of long Vs and rhombics
seems attractive to many, the utility of a fixed position narrow-
beamwidth antenna is for point-to-point communications, not for
general communications across the horizon. For comparison, a
half-wavelength dipole has a beamwidth of about 80 degrees while
the beamwidth of a 1.25-wavelength extended double Zepp is
about 30-35 degrees. In many cases, the key design question for
fixed long-wire antennas is less "With whom do I wish to
Chapter 56
communicate?" and more "With whom am I willing not to

communicate?"
Terminated Rhombic Antennas
The terminated version of the rhombic antenna is identical to the

unterminated versions with the exception that the far junction of the
wires has an intervening non-inductive resistor (or combination of
resistors in series and/or parallel connection) with the desired
value. Fig. 5 shows the outline of the general arrangement.
Ordinarily, the terminating resistor is somewhat arbitrarily selected
in the 600-800-Ohm range. Angles A (alpha) and B (phi) play the
same role in the terminated rhombic that they play in the
unterminated versions. L remains the leg length measured in
wavelengths, and the leg length plus the angles form unique
combinations to achieve maximum gain at some prescribed
antenna height.
Chapter 56
The models for the unterminated rhombics have used only 4 wires,
one for each leg. The model source consists of a split source, that
is, two sources in series. The sources go on the segments adjacent
to the junction of the wires at the feedpoint end of the antenna. As
the right side of Fig. 5 reveals, I used a similar technique to place
the terminating resistor. Non-reactive resistive loads go on the last
segment of each far-end wire, with each resistance equaling half
the total terminating resistance. These techniques of placing
sources and loads preclude the need to create a short wire at each
end of the rhombic structure. To preserve an equality of segment
lengths, the bridge wire would have to be long enough that it would
not preserve the value of angle A. Alternatively, to maintain the
value of angle A, the source/load wire would be significantly shorter
than adjacent leg segments, a condition on the source wire that
NEC does not recommend for the most accurate calculations. Split
sources and split loads preserve both the geometry of the model
and the best conditions for calculation.
Like all other models in this series, the lossless 0.16"-diameters

wires use 20 segments per wavelength. All terminated rhombics
are 1 wavelength above average soil with a test frequency of 3.5
MHz.
Before we present a table of modeled performance values, we must

select a value for the terminating resistor. Many rhombic builders
rely on the tradition that the terminating resistor controls the
feedpoint impedance. Since 600-Ohm ladder line is readily
available or easily built, 600 Ohms has been a popular resistance
for the rhombic termination. For spot frequencies in otherwise well-
Chapter 56
designed rhombics, a 600-Ohm termination produces a low 600-

Ohm SWR. However, many rhombics find use over at least a 2:1
frequency range. Therefore, I swept the version of the rhombic with
3-wavelength legs from the design frequency to twice the frequency
to observe the likely undulations of resistance, reactance, and 600-
Ohm SWR. Fig. 6 shows the results.
In many ways, the resistance and reactance swings appear to be

modest. Indeed, the SWR curve shows low values for 3.5, 5.25,
and 7 MHz (which would correspond to 14, 21, and 28 MHz on a
properly scaled version of the model). However, the SWR for 4.53
MHz (scale value: 18.118 MHz) is greater than 2:1, and the value
for 6.24 MHz (scale value: 24.94 MHz) is approaching 2:1. These
Chapter 56
values would not be troublesome for a wide-range antenna tuner

between the shack end of the feedline and the transceiver.
However, they may be high enough to defeat the low-loss use of a
wide-range impedance transformation device, such as a
transmission-line transformer balun.
Higher values of terminating resistance yield smaller resistance and

reactance excursions. The result is a set of smaller SWR swings,
all within an acceptable range. Fig. 7 shows the same frequency
sweep using an 850-Ohm terminating resistor, referenced at the
feedpoint to 850 Ohms.
Chapter 56
Comparing the resistance and reactance lines between Fig. 6 and

Fig. 7 reveals the smaller swings in these impedance components.
The SWR (blue) line swings may appear similar in the 2 graphs.
However, note the smaller limit to the Y-axis in Fig. 7: its highest
value is 1.45:1. Although creating a wide-range impedance
transformation device may be more difficult with the higher
reference impedance (850 Ohms), the technique will be applicable
with low losses across the 2:1 frequency range of the rhombic.
Within the usual range of terminating resistor values, the lower the
terminating resistance value, the higher the array gain--but only
slightly so. Fig. 8 overlays the gain values of the rhombic beam for
both the 600- and the 850-Ohm resistors. Throughout the 2:1
frequency range, the 600-Ohm version provides the higher gain,
but by no more than 0.01 to 0.02 dB.
Chapter 56
In the range of terminating resistance between 600 and 900 Ohms,

certain performance parameters remain extremely stable. The
elevation angle of maximum radiation and the beamwidth are two
values that remain the same throughout the range of terminating
resistors, at least for the sample rhombics using leg lengths that
change in 1-wavelength increments between models. The
impedance is also relatively stable at the test frequency for each
model through the 600- to 900-Ohm resistor range. The maximum
spread of resistance goes from a low of about 730 at 600 Ohms to
a high of 870 at 900 Ohms, although the range is a bit smaller for
any one leg-length model. The reactance swing is equally small,
ranging from a -j40-Ohm value at 600 Ohms to a +j40-Ohm value at
900 Ohms.
Chapter 56
My reason for selecting the 850-Ohm terminating resistor has as

much to do with drama than with good electronics. Normal
construction variables and the selection of leg lengths that are not
perfect integral increments of a wavelength would likely alter the
results. However, as the following performance table reveals, 850
Ohms as the termination value yields very high values of 180-
degree front-to-back ratio, resulting in radiation patterns in which
the main forward lobe and the sidelobes take center stage. The
shortest of the rhombics has the lowest front-to-back value because
the 40+-dB ratio occurs with an 800-Ohm terminating resistance. In
practice, values from 750 to 900 Ohms will likely yield
indistinguishable results, although the higher end of the scale will
usually result in the smoothest SWR curve. However, we tend to
obtain the flattest wide-range SWR curves when the terminating
resistance and the feedpoint impedance are as close together as
possible.
The tabular data shows the value of angle A (alpha), the elevation
angle of maximum radiation, the maximum forward gain, the 180-
degree front-to-back ratio, the half-power beamwidth, the modeled
feedpoint impedance, and the 850-Ohm SWR. For reference, the
far-right columns provide the maximum gain values for the
corresponding unterminated open rhombics, along with the gain
differential between the terminated and unterminated versions of
the antenna.
Note: The values of angle A are not optimized for maximum

rhombic gain, but derive from earlier work with single long-wire
antennas.
Chapter 56
As we move from a single long-wire antenna to a V-beam and

finally to a rhombic, the gain differential between the unterminated
and the terminated versions has decreased. The differential was
3.5 to 4.5 dB for the single long-wire terminated antenna. The V-
beam showed a range of 2.7 to 3.7 dB differential. In both cases,
the differential decreased as the length of the legs increased. For
the rhombic, the differentials range from 1.6 to 1.9 dB, a tight range
for which there is no apparent correlation between gain differential
and leg length.
The gallery of sample elevation and azimuth patterns of the

terminated rhombic beam appear in Fig. 9. The gallery includes
patterns for leg lengths of 2, 4, 6, 8, and 10 wavelengths. Because
the arrays are twice as long overall as corresponding V-beams and
single terminated long-wire antennas, the transitions in pattern
shape are smaller from one increment to the next in the series.
Hence, we may use fewer plots to show the evolution of rhombic
radiation patterns.
Chapter 56
Careful inspection of the sidelobe structures will show that the

strength of the forward-most sidelobes--and also the strongest
Chapter 56
sidelobes--is somewhere between the corresponding sidelobes for

the open and the closed versions of the unterminated rhombics.
See Fig. 2 to estimate the limits and where between them the
terminated rhombic sidelobes fall. The phenomenon suggests that
there is continuity in sidelobe strength across a range of termination
values ranging from an open circuit through a mid-range resistance
and ending at a short circuit.
Fig. 10 provides a 3-dimensional pattern for the rhombic with 10-

wavelength legs. It reveals that the terminated rhombic exerts the
most control over the morass of small lobes that populate the
overall radiation pattern. You may directly compare this pattern with
the one in Fig. 4 for the unterminated rhombic to correlate various
lobes and their relative strengths. As well, you may compare it with
corresponding patterns for other terminated long-wire arrays in
earlier parts of this series.
Chapter 56
One quick comparison that we may tabulate is the maximum gain

of each of the 3 types of terminated beams that we have
encountered along the long-wire pathway. Remember that the
maximum gain value for the single terminated long-wire is an off-
axis value, that is, not in alignment with the wire itself.
Maximum Gain of Various Types of Terminated Long-Wire

Antennas
Leg Maximum Gain dBi
Length Single V Rhombic
WL Long-Wire Beam
2 ---- 9.88 14.60
3 7.11 11.41 16.04
4 7.99 12.35 17.27
5 8.65 13.03 17.97
6 9.15 13.50 18.51
7 9.57 13.86 18.85
8 9.92 14.07 18.98
9 10.20 14.29 19.27
10 10.47 14.59 19.73
11 10.70 14.74 19.86
The gain of the single terminated long-wire would not justify its
narrow-band use, since we can obtain similar gain levels from
antenna ranging from dipoles to extended double Zepps at a great
savings in both wire and supporting structures. The single
terminated long-wire acquires its usefulness from the relative
constant feedpoint impedance, allowing great frequency agility. The
terminated V adds about 4-dB of gain, while maintaining a broad
SWR operating bandwidth. However, any angle used as the basis
for the array has frequency limits for a good pattern: outside those
Chapter 56
limits, the forward pattern breaks into multiple lobes. As we change

frequency, the antenna legs change length as measured in terms of
a wavelength at the new operating frequency. Hence, the wire
angles are no longer optimal to add in a forward direction.
The rhombic shares the frequency limits of the V-beam. To sense

its truer gain advantage, you may wish to compare the rhombic with
a given leg length to a V beam with twice the leg length. For
example, a rhombic with 5-wavelength legs and nearly 18 dBi gain
is roughly equivalent in overall length to a V-beam with 10-
wavelength legs and a 14.6-dBi gain level. Like the V beam, the
rhombic is capable of good performance over a 2:1 frequency
range with good gain and a relatively constant feedpoint
impedance. In fact, before we end our trek through long-wire
antennas, we should take one more look at the ARRL rhombic from
Chapter 13 of the 20th Edition of The Antenna Book; but not today.
Conclusion
In this Chapter, we have moved beyond the V array and beam to

examine what some call the highest development in long-wire
antennas: the rhombic. We learned how to close the V with another
V, using the same technique of aligning lobes from each wire to
form a rhombus. Modeling allowed us to develop effective rhombic
antennas without reference to classical equations by setting the
intended height and the leg-lengths that we might use. We explored
both open and closed forms of unterminated rhombic arrays, and
then we turned to the most common rhombic form, the terminated
beam.
Chapter 56
By splitting both the source and load, we found a very economical

way to model the terminated rhombic beam. We also uncovered
some relationships between the value of the terminating resistor
and the feedpoint impedance that bear on the smoothness of SWR
curves that cover a 2:1 frequency range. Indeed, there is more to
be said on this subject. . .
Indeed, I had planned to close the topic at this point. However, we

have a significant amount of unfinished business with the rhombic.
1. The Multi-Band Rhombic: We have not yet evaluated the ARRL

Antenna Book rhombic for 14-28 MHz. This design has its roots in
nomographic design data from Harper's well-known book. (See the
list of references at the end of each Part.) The antenna gives us a
chance to compare modeling design techniques with classical
methods.
2. The Multi-Wire Rhombic: One common method of trying to

improve rhombic beam performance is to use more than 1 wire for
each leg. The usual arrangement consists of 3 wires that come
together at the rhombic points and spread in the middle by
relatively arbitrary distances. The arrangement presents both
theoretical and modeling challenges, and careless modeling of a 3-
wire rhombic can lead to erroneous results.
3. The Multi-Element Rhombic: In the 1950s, Laport developed the

multi-element rhombic beam to improve both gain and sidelobe
suppression. Since the antenna has seen use on the UHF amateur
Chapter 56
bands, the design bears at least an initial exploration to look at both

design and modeling issues.
With so many outstanding rhombic ideas, I would be remiss if I did

not extend the series one more episode. Even then, we shall not
have examined every variation on the long-wire, V, and rhombic
arrays. However, perhaps we shall have encountered enough
designs along our pathway so that you may continue the trek on
your own.
Chapter 56
Chapter 57: Multi-Band, Multi-Wire & Multi-Element Rhombics
B
ecause the rhombic antenna, especially when terminated,
offers very high gain, it has received more design attention
than any of the other long-wire antennas. The
straightforward basic design data sampled in Part 4 does not
exhaust the significant variations on the basic configuration. One
potential particularly suited to amateur service in the upper HF
range is the possibility of operating a rhombic over a 2:1 frequency
range, thus allowing coverage of 20 through 10 meters. We shall
examine one tried and true design and try to find out the basic
design premise that allows it to be successful.
When an antenna is good at what it does, we can count on efforts

to make the good even better. For narrow-beamwidth point-to-point
communications, the rhombic is very good. One very old technique
to improve performance somewhat is the use of multiple wires in
each side of the rhombic. They come together at the feedpoint and
at the terminating resistor end, but spread vertically where the
facing Vs are widest. Some claims about the technique will prove
correct, such as the addition of a small increment of gain. However,
other claims may turn out to have other foundations than the use of
multiple wires.
Finally, we shall address an interesting technique for further

suppressing the remnant sidelobes in the rhombic radiation pattern.
Laport developed a scheme for using closely spaced rhomboid
structures in parallel. The centerlines for each of the independent
rhomboids fed in parallel are offset from each other. The technique
Chapter 57
will offer a small gain advantage over the single-wire rhombic, but
will reduce sidelobes by a very significant amount.
Although these developments are worth our notice here, they will
not exhaust the variations on the rhombic. There is, for example,
the so-called half-rhombic, consisting of one side of a rhombic
played against ground. Unfortunately, lossy soil does not permit the
antenna to play like a true rhombic, due to ground reflections and
losses. Despite its name, the antenna operates more like a
terminated, end-fed, inverted V, and highest performance occurs
with only a slight elevation of the center point above ground. The
antenna appears in Bruce's 1931 article and he calls it simply an
inverted-V. The name "half-rhombic" came later from other builders.
Other variations on the rhombic have emerged in answer to specific
commercial and governmental communication needs. The result
has been highly complex arrangements of wire structures well
beyond the scope of these introductory notes. Nevertheless, the
variations that we have selected should provide a sufficient
foundation to let you examine the classical literature on advanced
rhombic designs with understanding.
Multi-Band Rhombics
Although we have briefly mentioned multi-band use of long-wire

antennas, we have not paused long to investigate their
performance in broadband service. We shall rectify this situation, if
only briefly, by looking the ARRL rhombic intended for upper HF
service from 14 through 28 MHz. The antenna first appeared in The
ARRL Antenna Book somewhere between 1965 and 1974, and has
Chapter 57
been a prime example in the book's treatment of traveling-wave

antennas. Fig. 1 shows the general outlines of the antenna.
One notable feature of the antenna is that its design emerged long
before modeling software became available. Hence, its outline rests
directly on the original rhombic design equations, as filtered into
design nomographs. The design begins with 3-wavelength legs at
14 MHz along with a height of about 70' or 1 wavelength at the
lowest frequency of use. It uses a prescribed tilt angle of 64
degrees and hence an angle A value of 26 degrees. These values
coincide perfectly with the values developed via computer
modeling. For this model, I followed the typical amateur
conventions and used a 600-Ohm termination and an SWR
reference impedance of 600 Ohms. The following table lists the
Chapter 57
modeled performance of the antenna over the 5 amateur bands

between 14 and 28 MHz.
Modeled Performance of the ARRL Upper HF Rhombic with a 600-Ohm Termination
Frequency MHz 14.0 18.118 21.0 24.94 28.0
Parameter
Gain dBi 16.04 17.89 18.38 18.31 17.33
El. Angle deg 14 10 9 7 6
Front-Back dB 19.93 15.28 24.68 15.27 32.12
Beamwidth deg 17.0 13.0 10.8 8.6 7.0
600-Ohm SWR 1.25 1.79 1.22 1.65 1.22
The gain values parallel almost exactly the curves in Fig. 8 in Part
4, which is also for a rhombic with 3-wavelength legs and an angle
A of 26 degrees. The three differences between the earlier model
and the present one are the design frequency (3.5 vs. 14 MHz), the
wire (perfect 0.16" vs. copper AWG #12 or 0.0808"), and the
terminating resistor value (850 vs. 600 Ohms). Fig. 2 shows a
gallery of elevation and azimuth patterns at each of the test
frequencies. Note that this gallery differs from the galleries in the
earlier parts of this series because angle A is optimized in
combination with the leg length only at the lowest operating
frequency.
Chapter 57
The sidelobe structure (including the rear-most lobe) of the patterns

for frequencies above 14 MHz does not parallel any of the patterns
Chapter 57
in the earlier galleries (Fig. 9 in Part 4, for example) because angle

A (and the tilt angle B) remain constant while the leg length
changes as a function of the ever higher operating frequency. As a
result, we find lobes that do not appear in the main gallery of
optimized designs for each leg length. They result from incomplete
cancellations that occur with a non-optimal combination of leg
length and angle A. As well, the use of the relatively low terminating
resistor value (600 Ohms) results in a set of SWR values that
approximates those shown for the frequency sweep in Fig. 6 of
Part 4.
The ARRL rhombic design nevertheless shows itself to be a very

competent performer over its 2:1 frequency range. It captures
perhaps the key element in multi-band rhombics: optimize the
design for the lowest anticipated frequency, accounting for both
antenna height and anticipated leg length. As the frequency
increases, the gain will rise, as indicated by 2 of the leg-length
equations early in Part 4. According to those equations, peak gain
would occur somewhere close to 15 meters. With a satisfactory
terminating resistor, the antenna will perform quite well over a 2:1
frequency range. With a higher value than 600 Ohms, the SWR
curve would smooth out more completely, if we use a reference
impedance to match the termination (and hence a feedline with a
higher characteristic impedance than 600 Ohms).
The general procedure has exceptions. For example, the idea of

optimizing the rhombic at the lowest frequency in the 2:1 requires
careful selection of the value of angle A. If we increase the angle in
order to raise the gain at the lowest frequency, we shall find that we
Chapter 57
have limited the operating frequency range upward. The gallery of

azimuth patterns shows that, at 28 MHz, the innermost sidelobes
are almost as strong as the main lobe. If we select a maximum gain
value of angle A for 14 MHz, the 10-meter pattern will show 3
lobes, and the lobe that is on-axis with the array will no longer be
the strongest. Such a condition defeats the main goal of creating a
rhombic in the first place: the desire to achieve point-to-point
communications on a heading in line with the two acute angles of
the rhombus. If we reduce the value of angle A at 14 MHz, then the
main lobe broadens with a loss of gain. For the selected height, the
ARRL rhombic antenna selects a value of angle A at 14 MHz that
yields roughly equal gain on both 20 and 10 meters, which is
generally a good selection for amateur service. It also illustrates
why much of the classical rhombic literature recommends no more
than a 2:1 frequency range for the antenna, even though the range
of acceptable matching is much wider.
Multi-Wire Rhombics
Perhaps the most common variation on the single-wire rhombic

beam involves the use of multiple wires running from the feedpoint
to the terminating resistor on each side of the centerline. The added
wires join the level wire at both the feedpoint and the terminating
resistor. However, they spread above and below the level wire at
the widest points in the array. In general, the wires are the same
length as the level wire, theoretically resulting in the wires being
further offset from any support post toward the centerline. However,
the amount of differential is a very small fraction of the total wire
length along each leg, and allowing the spread wires to be slightly
Chapter 57
longer in order to align the supports will create no performance

problems.
In order to model the multi-wire rhombic, using 3 wires as a sample

version, we must alter the means by which we create the antenna
geometry. The left side of Fig. 3 shows the method used in Part 4.
It consists of only 4 wires per rhombic, with a split source and a
split load. At the source end, we simply place a source on each of
the segments adjacent to the wire junction. Since they are in series,
the feedpoint impedance is the sum of the source impedance
values reported for each source. The split load simply creates a
balance at the far end of the array by placing a load resistor on
each of the wire segments adjacent to the junction. The overall
terminating resistor value is simply the sum of the 2 load resistance
values. To use a real example from the last episode, the 4-
wavelength-leg version of the terminated rhombic used legs that
are 4.00 wavelengths long. The distance from centerline to a side
peak is 1.563 wavelengths, while the distance from the midline to
either end junction is 3.682 wavelengths. The resulting angle A is
23.0 degrees, and the overall rhombic length is 7.364 wavelengths.
Chapter 57
The "pointy" ends of the model do not permit ready feeding for a
multi-wire version of the antenna. Therefore, we must revise the
modeling system to allow the wires to terminate together for a
common feedpoint and for a common load resistor. The right side
of Fig. 3 shows the general technique. We create a flat or blunt end
at each rhombic point. To ensure that the source segment has
adjacent segments of equal length on each side, we make the blunt
end-wires 3 segments long. So that the wires will have segments
as close as possible in length to the segments in the long side
wires, the blunt end wires are 0.14-wavelength, based on the use of
20 segments per wavelength in the side wires. Now let's set the
total length of the rhombic to 7.36 wavelengths, with a 3.68-
wavelength distance from either end to the midline. The distance
from the centerline to the peaks will be 1.56 wavelength. The angle
(A) from the centerline to a peak will be 22.97 degrees. However,
the overall wire length will not be exactly 4.0 wavelengths. Instead,
the sloping portion of the side wire will be 3.97 wavelengths, added
to half of the blunt end-wire (0.07 wavelength) for a total length of
Chapter 57
4.04 wavelength. All figures are for rhombics 1 wavelength above

average ground with lossless 0.16" wire at 3.5 MHz.
I have recorded seemingly insignificant variations in models

because these variations do create differences in the reported
performance of the antennas. The following table explores the
performance of the 4-wire "pointy" version of the antenna using
various terminating resistor (RL) values.
Performance of a Pointy Single Wire Rhombic with 4-Wavelength Legs and
Various Terminating Resistors
Terminating Maximum Front-Back Feedpoint Z
Resistor (Ohms) Gain dBi Ratio R+/-jX Ohms
600 17.30 18.07 737 - j 40
700 17.28 23.13 793 - j 13
800 17.27 33.22 844 + j 14
850 * 17.27 43.97 869 + j 27
900 17.28 32.75 892 + j 41
1000 17.29 24.29 936 + j 67
1100 17.30 20.40 977 + j 94
1200 17.32 17.94 1015 + j120
We should note 2 special items in this table. First, the starred item
represents the version of the antenna selected for inclusion in the
larger table in Part 4. There are 2 reasons for selecting this
terminating resistor value. It does result in the highest front-to-back
ratio, although this reason is secondary to another. Without
becoming too finicky, the load resistor and the resistive component
of the feedpoint impedance are most closely matched. With smaller
values of terminating resistance, the resistive component of the
feedpoint impedance is always higher than the load resistance. For
all terminating resistors larger than the selected value, the
feedpoint resistance is always lower than the terminating
Chapter 57
resistance. Since a terminated long-wire antenna operates in a

similar manner to a transmission line, matching the load resistance
to the feedpoint resistance results in the widest SWR bandwidth
when referenced to the load resistance value. The required value
does not change with changes in the leg length so long as the
angle A is selected to align the lobes for maximum gain. However,
it will change with even small departures from the ideal geometry. It
will also change with the height of the antenna above ground and
with the quality of the ground itself, since both of these factors will
change the effective impedance of the antenna when viewed as a
length of transmission line.
Second, note the remnant inductive reactance in the feedpoint

impedance. The reactance is inductive. One traditional reason for
using multiple wires in the rhombic legs is that it introduces a
compensating capacitive reactance due to interactions among the
wires. A capacitive reactance represents--with respect to feedpoint
impedance--a slight electrical shortening of the antenna
circumference. Wire interaction is unnecessary to explain the
electrical shortening of the overall rhombic loop. All closed loops of
a preset total circumference become electrically shorter if we
increase the wire diameter--exactly the opposite effect of fattening
elements in open-ended elements. Since the 3-wire rhombics will
have effectively a fatter element, even though variable in equivalent
diameter along the leg lengths, the loop will become electrically
shorter and thus show a more capacitive reactance at the
feedpoint.
Chapter 57
The blunt-end version of the 4-wavelength-leg rhombic makes only

one change among the factors that tend to affect the optimal value
of load resistance: the geometry. The shape changes are very
small overall, but they do have consequences, as shown in the
following table that parallels the one for the pointy version of the
same rhombic.
Performance of a Blunt Single Wire Rhombic with 4-Wavelength Legs and
600 17.40 15.26 806 + j121
700 17.37 18.48 857 + j 81
800 17.35 22.87 903 + j 41
900 17.35 30.23 945 + j 2
975 * 17.35 38.04 973 - j 27
1000 17.35 35.88 982 - j 37
1100 17.36 26.68 1016 - j 74
1200 17.38 22.27 1046 - j110
The closest match between the terminating resistor and the

feedpoint resistance occurs with a value of about 975 Ohms. The
difference between the 2 models of 125 Ohms may seem
significant, but it is likely that construction variables would wash out
the difference in terms of trying to determine which model better
captures a physical rhombic with 4-wavelength legs at a height of 1
wavelength above average ground. As well, small changes in the
segmentation per wavelength will also change the reported values
somewhat. Note also that the progression of inductive to capacitive
reactance is the reverse of the pointy geometry. Nevertheless, the
pattern of the feedpoint resistance remains: below the optimal load
resistance, the feedpoint resistance is higher than the load resistor
Chapter 57
and above the optimal load; the feedpoint resistance is less than
the load resistance.
The blunt-end version of the modeled 4-wavelength-leg rhombic will

become the standard against which we measure 3-wire rhombics
using the same leg length. However, modeling the 3-wire rhombic
presents another modeling challenge of its own. Theoretically, the
wires must join on each side of both the feedpoint wire and the load
resistance wire. The relevant modeling sketch of this situation
appears on the left in Fig. 4. There is a difficulty built into this
scheme. Because the wires are not widely spaced relative to their
length, the segments at the junction interpenetrate for a
considerable distance along the segment length. Even though the
level of inter-penetration may not reach a level that raises flags
within NEC, it may still be sufficient to alter the performance reports
of the array, since the inter-penetration does affect NEC's current
calculations.
To test the model, let's explore what happens as we pass the

model through a number of loading resistor values. The side wire
Chapter 57
expansion is very modest, reaching only 0.0125 wavelength at the

midline. That distance amounts at 3.5 MHz to about 1.06 m or
3.49', with an antenna that is over 630 m (2068') long. Like all of the
models, the 0.16"-diameter wire is lossless and the wires are 1
wavelength above average ground.
Performance of an Angled 3-Wire Rhombic with 4-Wavelength Legs and Various
Terminating Resistors
600 18.92 16.76 795 + j335
700 18.92 18.57 834 + j319
800 18.92 19.64 870 + j305
900 * 18.93 19.68 902 + j291
1000 18.94 18.96 933 + j278
1100 18.95 17.93 961 + j266
1200 18.96 16.87 987 + j255
Although we are not yet positioned to evaluate the gain

improvements, the impedance column should give us pause. The
very large rise in inductive reactance relative to the blunt single-
wire model exceeds what we might otherwise reasonably expect
from adding 2 wires with fairly narrow spacing relative to the
frequency. In addition, the indicated "ideal" termination resistor
value (900 Ohms), does not coincide with long-standing empirical
experience, which suggests a value closer to 600 Ohms.
We may reformulate the model using some techniques that have

proven useful with quad loops and similar structures. The right side
of Fig. 4 outlines the techniques at each and of the antenna. At the
feedpoint end, we prevent the wires from meeting, but bring them to
a 0.001-wavelength spacing (about 86 mm or 3.4"). Next, we create
Chapter 57
a bridge wire for each loop. The source excitation goes to the
center (level) wire on the middle segment of the bridge wire. From
the corresponding segments on the upper and lower section, run
600-Ohm transmission lines to the source segment. The
impedance is not critical, because the lines will be only 0.000001-
wavelength long, a number that the modeler specifies in the
transmission line entry. Hence, the three wires have a common
source in parallel, while preventing the inter-penetration of any
wires.
The termination end of the beam uses the same modeling

technique of bringing the wires close (0.001 wavelength) but not
allowing them to touch. We cannot create a single parallel
connection using the transmission line technique, because any load
resistor would be in series with the line and hence outside it.
Instead, we provide each bridge wire with a load resistance that is 3
times the desired terminating resistor value. If we run the same
tests on the reformulated model, we obtain the results in the
following table. Note that the actual terminating resistance values
are 3 times the value in the table, but occur on 3 bridge wires.
Chapter 57
Performance of a Separated 3-Wire Rhombic with 4-Wavelength Legs and

Narrow (0.0125-Wavelength) Maximum Wire Separation
400 18.60 17.14 586 + j 22
500 18.60 22.29 619 - j 4
600 18.60 31.34 648 - j 32
650 * 18.61 36.44 662 - j 37
700 18.61 31.37 675 - j 42
800 18.63 24.01 695 - j 73
900 18.64 20.33 714 - j 95
1000 18.66 18.02 733 - j105
The gain improvements over the single-wire model are more

modest: about 1.3 dB. The rounded ideal load value comes very
close to matching the feedpoint resistance and also corresponds to
the highest 180-degree front-to-back ratio value. As expected, the
capacitive reactance is slightly higher than for the blunt single-wire
model, but only slightly so, since the average wire-diameter
increase for the closed loop is not great as a function of a
wavelength. Finally, the selected terminating load and feedpoint
impedance tend to match reasonably with reported experience with
these types of rhombic beams.
Most amateur rhombics cover the upper HF spectrum, and the

spacing used at these frequencies is 3' to 4'. Therefore it seems
prudent to test our 3.5 MHz model with a wider spacing than the
0.0125-wavelength used in the initial model. Using the same loop
separation techniques, I increased the spacing at the midline to
0.025-wavelength (about 2.1 m or 7'). All other modeling
parameters remain constant. The results appear in the following
table.
Chapter 57

Medium (0.025-Wavelength) Maximum Wire Separation
400 18.74 17.46 597 + j 26
500 18.74 22.45 629 + j 10
600 18.74 30.19 656 + j 7
650 * 18.75 33.08 669 - j 11
700 18.75 30.20 682 - j 15
800 18.76 24.04 701 - j 55
900 18.78 20.56 721 - j 63
1000 18.79 18.30 739 - j 71
As one might expect, by enlarging the average wire diameter by a

significant amount, the gain reports increase by a very small but
numerically noticeable amount. More telling is the array of front-to-
back values. The peak value does not reach the level attained by
the narrower 3-wire array, and that value, in turn, did not reach the
peak value of the single wire blunt-end rhombic beam. However,
the wider 3-wire array shows a smaller fall-off in front-to-back value
as we vary the terminating load across the same range as used
with the narrower 3-wire version. Compare values for this antenna
with 600-Ohm and with 1000-Ohm loads with the corresponding
values for te narrow 3-wire rhombic.
The near-ideal load resistance remains unchanged at 650 Ohms or

thereabouts. However, the capacitive reactance at that load value
is not as great as with the narrow 3-wire rhombic. The important
data on the reactance is not its value at the ideal load resistance so
much as it is the total range of reactance across the total set of load
resistors. The narrow 3-wire rhombic shows a range of 162 Ohms,
Chapter 57
while the medium spacing (twice the narrow spacing) reduces the
range to 134 Ohms--for the same set of load values.
Let's increase the maximum wire spacing at array midline one more
time. We shall again double the spacing to 0.05-wavelength (about
4.3 m or 14.1'). All other parameters remain the same. Each outer
leg is now about 0.0003-wavelength longer than the level center
wire--about 1". With all other model parameters unchanged, we
obtain the following table of modeled values.
Wide (0.05-Wavelength) Maximum Wire Separation
400 18.88 17.79 607 + j 59
500 18.88 22.46 638 + j 37
600 18.89 28.31 664 + j 23
650 * 18.89 29.64 676 - j 10
700 18.90 28.16 686 - j 14
800 18.91 23.71 707 - j 9
900 18.92 20.62 724 - j 38
1000 18.93 18.50 738 - j 56
Once more, we find the small improvement in gain, which is now

about 1.5-dB higher than the blunt single-wire array. The peak
front-to-back ratio continues to diminish, but the values with a 400-
Ohm and with a 1000-Ohm load are higher. The curve--as we might
expect for increasing wire diameter--has less of a sharp peak and
covers a broader range with higher values. Although I might have
increased the ideal terminating resistor to 700 Ohms, continuing to
use the 650-Ohm value allows us to see the other curve changes
more easily. The reactance range has shrunk to 96 Ohms total. The
Chapter 57
anomalous value for the 800-Ohm terminating resistor is accurate

to what NEC reports. It may be a function of secondary effects that
the other tables do not show given the 100-Ohm increment in
terminating resistor values.
The use of 3-wires, whatever the spacing, does not change the
essential elements of the rhombic pattern. Fig. 5 compares the
patterns for the blunt single-wire model and for the widest 3-wire
model in both separate patterns and with an overlay. The overlaid
patterns show the comparative raw gain of each lobe. The separate
pattern establishes that there is no essential change in the relative
strength of the lobes. The only exception, of course, is the 180-
degree lobe.
Chapter 57
Amateur lore on rhombic antennas suggests that the 3-wire design

may be capable of a smoother SWR curve across a broad
passband than a single wire model. That lore tends to neglect the
need to match the terminating resistor to the feedpoint impedance--
and that impedance to the characteristic impedance of the feedline.
To test this way of looking at the impedance question, I ran each of
the 4 main blunt models through an SWR sweep from the design
frequency to twice that frequency (3.5 to 7.0 MHz). The single-wire
blunt model used a 975-Ohm SWR reference impedance, while the
3 3-wire models used a 650-Ohm reference impedance. The results
appear in Fig. 6.
Chapter 57
Chapter 57
In practical terms, we have no way to make a selection among the

antenna models. All 4 curves remain below 1.2:1 relative to their
reference impedances across the entire range. Any device capable
of broadband impedance transformation at the desired ratio would
operate under very low-loss conditions. The exercise, however,
does show one interesting fact: none of the 3-wire models improves
upon the blunt single-wire model SWR curve. The only advantage
shared by the 3-wire models is that they may better use a
commercial 600-Ohm parallel transmission line than the single-wire
model. However, a 975-Ohm line requires more patience than skill
to fabricate in one's own shop.
The 3-wire rhombic, then, has 3 advantages over a single-wire

rhombic. First, the gain improvement is real, but might not be
sufficient to be noticeable in practice. Second, from a practical
perspective, the ideal conditions for a 3-wire rhombic--at least one
that is 1 wavelength above average soil--yield a terminating resistor
and feedpoint impedance that more nearly coincides with off-the-
shelf components. (Note: this result applies only to the subject
antenna and requires verification for any variation in height and soil
condition.) Third, the "fat-wire" effect of using wider spacing
gradually widens the operating curves of some operating
parameters.
Besides mechanical complexity, the 3-wire rhombics have only one

almost insignificant down side. The front-to-sidelobe ratio shows a
very small but steady decline as we increase the effective wire
diameter. Between the blunt single-wire model and the widest 3-
wire model, the decline is only about 0.2 dB. However, it appears to
Chapter 57
be a real phenomenon and runs counter to the design goals of

many rhombic designers. The design goal of reducing rhombic
sidelobes leads us to the third of our bits of unfinished business.
Multi-Element Rhombics
Rhombic development persisted long after its primary period of HF

service in the 1930s and 1940s. With the advent of commercial
broadcast VHF television in the 1950s, followed by UHF television
in the 1960s, engineers searched for wide-band antennas with high
gain to satisfy consumer needs in fringe reception areas. In this
period, Laport published his work on the adaptation of the rhombic
for this and other services. The sidelobes for a single rhombic with
an overall length of about 5 wavelengths were down less than 10
dB, a situation that made the antenna susceptible to multi-path
ghosting and other forms of interference. Laport's solution to the
problem was to develop a dual rhombic antenna with offset axes.
Laport's dial offset rhombic is a variant of the basic idea of using

two rhombics of different sizes, each with its own terminating
resistor. Only certain combinations of rhombics are eligible for such
use. The main criterion is that the sidelobes of one size align
closely with the side nulls of the other. The result is a significant
decrease in the net sidelobe strength. The combination of a
rhombic with 3.5-wavelength legs and one with 6-wavelength legs
provides a prime candidate for dual rhombic service. We can
shorten the overall length of the combination by combining one leg
from each rhombic on each side of a pair of rhomboids. The dual
offset rhombic offered higher gain and greater sidelobe
Chapter 57
suppression. Fig. 7 shows both the general outline and the critical
dimensions.
Chapter 57
The lower half of the sketch shows the dimensions needed. If we

set L1 at 3.5 wavelengths and L2 at 6.0 wavelengths, then angle A
becomes 26.1 degrees and angle B is 18.85 degrees. Simple trig
relations yield the physical dimensions, including the amount of
offset of the far junction from the array centerline (c). To compare
the dual rhombic with a single rhombic I scaled my early VHF
model down to our test frequency (3.5 MHz) and set it 1 wavelength
above average ground. Since the 0.16" wire diameter is much
thinner at 3.5 MHz than AWG #12 is at 100 MHz, I set the spacing
between wires at 0.08 wavelength and used 900-Ohm terminating
resistors in each rhombic in the pair. Even so, the front-to-back
ratio is only good, but not optimal. However, the combination of
spacing and the terminating resistor values are adjustable in the
design to improve these figures without affecting the forward gain
or the sidelobe suppression.
The best single rhombic for comparison with the dual version is the
model using 5-wavelength legs. It is only slightly longer overall (9.4
wavelengths vs. 8.95 wavelengths for the dual rhombic). The
following table presents some of the basic performance data.
A Preliminary Comparison of Equal Length Single and Dual Rhombics
Antenna Leg Length Elevation Max. Gain Front-Back Beamwidth Feedpoint Z
WL Angle deg dBi Ratio dB degrees R +/- jX
Ohms
Single 5 13 17.97 44.71 12.8 867 + j23
Dual 3.5/6.0 12 19.82 25.03 12.2 447 + j 9
The feedpoint impedance is the parallel combination of the

impedances of the individual offset rhombics in the pair. At VHF
and UHF, where the wire is proportionately thicker as a function of
Chapter 57
a wavelength, dual rhombics would normally use lower values for

the terminating resistors and have feedpoint impedances closer to
300 Ohms. The table shows that the dual rhombic has a 2-dB gain
advantage over the single rhombic. However, the benefit of the dual
design is less the added gain than the sidelobe suppression. Fig. 8
provides elevation and azimuth patterns for the 2 antennas. It also
overlays the two azimuth patterns for a more direct comparison of
relative sidelobe strength.
Chapter 57
The dual rhombic's strongest sidelobe is about 5-dB weaker than

the strongest sidelobe of the single rhombic. We can add 2-dB to
that figure when considering the sidelobe strength relative to the
strength of the main forward lobe. The sidelobe strength has
diminished to a level that equals the sidelobe strength of many (but
not all) long-boom Yagi designs with approximately the same
forward gain and front-to-back ratio values. For a further discussion
of dual rhombics in VHF and UHF service, see the upcoming
chapters.
Conclusion
The study of long-wire antennas--both terminated and

unterminated--is far from complete in these notes. There are
numerous theoretical directions one can take to intensify one's
understanding of the relationship of these antennas to fundamental
mathematical concepts governing all antennas. Likewise, both
historical practical applications and future possibilities leave much
room for exploration, in terms of both available literature and
physical experimentation. (I am, for example, unaware of any
experiments using dual rhombics in the GHz range, with both
rhomboids using copper strips bound to separate sides of a
substrate.)
Nevertheless, this series of notes has reached its end. Beginning

with all-too-often overlooked fundamentals, we explored the basics
of lobe formation on both center-fed and end-fed wires ranging from
1 to 11 wavelengths. The galleries of elevation and azimuth
patterns should provide a handy reference. At the same time, we
Chapter 57
looked at the modeling issues and variables involved in portraying

long-wire antennas, including changes of ground quality, changes
of wire and material, and changes of height. We also saw that as
we lengthen a long-wire, the elevation angle of maximum radiation
gradually decreased below the traditionally calculated value. We
next explored antennas that add a terminating resistor between the
far end of the long-wire and ground. These end-fed terminated or
traveling-wave antennas formed the simplest fixed beams, although
the use of such a resistor reduced the available forward gain
relative to unterminated wires of the same length. The terminating
resistor largely--but not completely--controls the feedpoint
impedance of the antenna, allowing the use of a terminated long-
wire beam over 2 or more octaves of frequency change.
The unterminated single long-wire antennas provided us with a

critical piece of information in the development of more complex
long-wire arrays. The maximum gain for any long-wire antenna
does not coincide with the wire end itself, but occurs at an angle
that varies with the wire length. V and rhombic arrays depend on
this angle to align a major lobe from each individual wire so that the
lobes add to increase array gain. Long-wire V antennas are usable
in both unterminated and terminated forms. In both cases, the gain
is considerably higher than for a single long-wire antenna, and the
strongest lobe is in line with the wire. However, the higher gain
comes at the expense of beamwidth, as the main lobe becomes
very narrow at longer wire lengths. Once more, the terminated V-
beam has somewhat less gain than the more bi-directional
unterminated V array, but the termination provides considerable
bandwidth. The limiting factor for bandwidth is that the leg length
Chapter 57
changes when measured in wavelengths as the operating

frequency changes. As a result, the wire angle no longer is correct
for aligning the lobes from the individual wires and the pattern
breaks down.
The rhombic is perhaps the largest and most refined of the long-
wire antennas, consisting of two Vs, open-end to open-end. The
result is 4 wires contributing aligned lobes for higher gain and
narrower beamwidth. Although the rhombic suppresses unwanted
sidelobes better than the V antenna, significant sidelobes remain.
The effort to further suppress the sidelobes has resulted in the
development of more complex rhombic designs using multiple
rhombic elements offset from each other. Although the
unterminated rhombic is usable and has more gain than the
terminated version, the gain differential is less than for other types
of long-wire antennas. If we optimally design a terminated rhombic-
-by reference to the correct wire angle relative to the antenna
height and leg length--we may obtain at least a 2:1 frequency ratio
of high performance at a nearly constant feedpoint impedance.
Although the facts about long-wire antennas are readily available

from a variety of sources, these notes have used antenna modeling
software as an alternative technique in determining the correct wire
angle for maximum antenna performance for any given height and
leg length. Starting with the unterminated end-fed long-wire, we can
determine the lobe angle and use this information in designing both
V and rhombic antennas that use the same wire length for their
legs. Although the models used to provide basic comparisons
within each antenna type and among types employed a set height
Chapter 57
(1 wavelength) and lossless wire of a suitable size for the test

frequency, modeling software, such as NEC, allows one to vary
these elements and rapidly optimize a complete design. Allied to
these basic design techniques are methods of placing sources (the
feedpoint) and loads (the terminating resistor) to produce accurate
calculations without disturbing the basic geometry of the antenna.
As the antennas grew more complex, the modeling issues became
more significant, although they grew in a stepped fashion with the
step-wise increase in the complexity of long-wire antenna
geometry.
Long-wire technology dates back to the earliest attempts to control

antenna radiation patterns and to obtain gain beyond the levels of
single wires. However, the techniques may still have application
today and tomorrow. At the same time, modeling design methods
can shorten at least some of the calculation time needed to
produce a workable long-wire antenna, whatever the type. Our trek
through long-wire technology ends here, but the antennas
themselves may still have far to go.
Chapter 57
Chapter 58: The Dual Rhomboid for 1296 MHz
I
n the late 1950s, Edmund Laport of RCA hand calculated a
number of improved rhombic-type antennas. The improvements
for a dual rhomboid consisted in the main of higher gain (with
claims of 27 dB over a dipole) and lower side lobe values. The
horizontal beamwidth was calculated at about 11 degrees to -3 dB
points. Thus the antennas represent appropriate choices for fixed
point-to-point communications or reception.
Interest in the design has periodically peaked in various parts of the

overall communications field, including amateur VHF and UHF
efforts and the TV reception (cable and individual) industry. For
either application arena, improved rhombics offer the potential for
an inexpensive antenna (some wire and wood) with high gain and
relatively easy construction.
Cliff Buttschardt, K7RR, graciously provided me with some

background material appearing in the October, 1976 CATJ, and
other information has appeared in 73 and QST. The article's
references include several Radio-Electronics articles between 1953
and 1960, mostly referenced to TV uses of the rhombic. As well,
there are references to Laport's original papers in the RCA Review
(March, 1952, and March, 1960). Bill Parker, W8DMR, wrote on the
"Dual Rhombic for VHF-UHF" in 73 for August, 1977, and the
information there was edited and relayed by Emil Pocock, W3EP, in
his VHF column (p. 89) in QST for March, 1997. The reason for the
resurgence of interest in 1997 stems from the 1296 MHz version of
the dual rhomboid built by Dayton Johnson, W0OZI, which won the
Chapter 58
1996 Central State VHF Conference antenna gain test with a

measure 17.3 dBi gain value. (See QST for December, 1996, p.
90.)
Although Laport developed several advanced multi-element

rhomboid antenna designs (hand-calculated), the most favored for
its ease of implementation is the dual rhomboid. (The elements are
rhomboids, but not true rhombi, since the sides are not necessarily
perfectly parallel.) It is on the dual rhomboid that I shall
concentrate, since it presents a number of challenges to the
antenna modeler.
In this note, I shall focus on the 1296 MHz version of the antenna
derived from the work of W8DMR as revised by W3EP, since that is
likely the antenna design most accessible to most hams.
Apparently, W3EP scaled the antenna design from a 1255 MHz
ATV version in Parker's article. Among the claims made for the
antenna are the following of interest to an inveterate modeler. 1.
The gain may be 20 dB better than a dipole. 2. The antenna allows
for "sloppy" construction without jeopardy to success.
In all of this background material, no mention is made of the

antenna's front-to-back ratio. Moreover, Laport's theoretical
calculations and HF applications of the antenna suggested that
terminating resistors for each section of this traveling wave design
should be about 660 Ohms and yield a net feedpoint impedance of
about 330 Ohms. In ham writings, this has been uncritically
translated into 600 Ohm resistors and a 300-Ohm feedpoint
impedance.
Chapter 58
To see how this works, see Fig. 1, a general outline--with

dimensions--of the 1296 MHz version appearing in QST. The two
rhomboids are offset from each other--left and right--by a small
distance at their terminating points so that the separate patterns
maximize the main forward lobe and minimize troubling side lobes
that are characteristic of single rhombic designs. Both rhomboids
are fed in parallel. Laport's original designs called for no separation
between the "upper" and the "lower" wires, but only insulation at the
crossing points. Typical ham practice has mounted the two
Chapter 58
rhomboids on opposite sides of a frame, usually about 3/4" to 1"

thick (at UHF, a minimum size for sturdiness).
At 1296 MHz, a wavelength is about 9.11" long, so the length of the

antenna from feedpoint to terminating resistors is about 8.4 wl and
the maximum width is about 4.7 wl. (This may account for the fact
that no ham has yet constructed a rotating HF version of the
antenna.) At 1296 MHz, the antenna is about 77" long and 42.5"
wide--quite manageable dimensions.
There are two sets of antennas to be explored: the QST model and
the CATJ versions derived directly from Laport's analysis. In this
part, I shall look only at the QST model. One important reason for
this is that modeling the antenna is tempting for anyone with a
basic modeling program using NEC-2. However, creating a useful (I
shall not use the term "precise") model of the Laport dual rhomboid
is not so easy a task as it may seem, and I shall point to some
dangers in the enterprise before seeing what the QST model yields.
Modeling a Dual Rhomboid
A single rhombic antenna that is 8 wl long will tax many basic NEC-
2 modeling programs. The core will handle the geometry easily, but
the number of segments required to achieve a relevant degree of
convergence (as a test of model adequacy) may quickly approach
the standard 500-segment limit attached to basic programs. If we
create a dual rhomboid antenna with closely spaced wires crossing
each other and sharp angles, the number of segments required for
Chapter 58
convergence to even a reasonable degree quickly passes the 1000

mark, and some of my models approached 1600 segments before
achieving an acceptable level of convergence.
Modeling a rhomboid shape with a feedpoint and two terminating

resistors also requires small distortions of the ideal acutely angled
points to the geometry. For the 1296 MHz model, I used 1" multi-
segment wires at the points in which to place the resistors and the
source. Although an inch seems small compared to a total length of
77", it is 11% of a wavelength and thus cannot be neglected as a
potential error source. These wires used at least 3 segments (and
some as high as 7) to ensure centering of the source and resistors
and to ensure that segments adjacent to the source and load were
the same length of the source and load segments.
The wires for the longer and shorter sides are equally highly
segmented. I developed two models, the chief difference between
them appearing in Fig. 1A.
Chapter 58
Model A brings the two wires on each side of the feedpoint to a

common junction. This is a somewhat dangerous modeling
practice, since the wire segments closest to the junction intersect--
even for small diameter wire--along an appreciable portion of the
segment. This can create modeling errors. Convergence to a
reasonable, but not perfect, degree required models using nearly
1600 segments.
Model B changes all of the angles to right angles, minimizing the

mutual wire penetration effect. It may also reflect ham construction
using a wood frame. These models converged reasonable with
about 800 segments.
Chapter 58
However, the results obtained from just the change in feedpoint

area treatment differ by enough to warrant presentation of both sets
of figures. For many purposes, the differences may not make a
difference, but that is not something that a modeling exercise can
establish from the outset. For example, the feedpoint impedance of
Model A is higher than the theoretical 300 Ohms by about as much
as the feedpoint impedance of model B is below that value.
In all azimuth patterns, to add to the slowness of model runs, I used

a 0.1 degree resolution. The patterns of rhombics of any form are
too complex for the 1-degree resolution we habitually use with
Yagis.
Interestingly, in no case did I obtain anything close to the 20 to 27

dB gain over a dipole. All modeling was done in free space using
copper wire losses, so a comparison with a free space dipole
should reduce the reported figures by about 2.1 dB. This does not
make the dual rhomboid a poor antenna, since 16 dBi free space
gain from a hank of wire and a few slats of wood is still excellent
performance potential.
Chapter 58
For reference, here is the description of Model B as used below.

Dual Rhombic-QST 3-97, p89 Frequency = 1296 MHz.
Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
--------------- WIRES ---------------
Wire Conn.--- End 1 (x,y,z : in) Conn.--- End 2 (x,y,z : in) Dia(in) Segs
1 W8E2 -0.500, 0.000, 0.000 W2E1 -0.500, 0.000, 0.500 # 12 2

2 W1E2 -0.500, 0.000, 0.500 W3E1 -15.250, 27.500, 0.500 # 12 75
3 W2E2 -15.250, 27.500, 0.500 W4E1 5.500, 77.000, 0.500 # 12 120
4 W3E2 5.500, 77.000, 0.500 W5E1 6.500, 77.000, 0.500 # 12 3
5 W4E2 6.500, 77.000, 0.500 W6E1 21.250, 50.000, 0.500 # 12 75
6 W5E2 21.250, 50.000, 0.500 W7E1 0.500, 0.000, 0.500 # 12 120
7 W6E2 0.500, 0.000, 0.500 W8E1 0.500, 0.000, 0.000 # 12 2
8 W15E2 0.500, 0.000, 0.000 W9E1 -0.500, 0.000, 0.000 # 12 3
9 W1E1 -0.500, 0.000, 0.000 W10E1 -0.500, 0.000, -0.500 # 12 2
10 W9E2 -0.500, 0.000, -0.500 W11E1 -21.250, 50.000, -0.500 # 12 120
11 W10E2 -21.250, 50.000, -0.500 W12E1 -6.500, 77.000, -0.500 # 12 75
12 W11E2 -6.500, 77.000, -0.500 W13E1 -5.500, 77.000, -0.500 # 12 3
13 W12E2 -5.500, 77.000, -0.500 W14E1 15.250, 27.500, -0.500 # 12 120
14 W13E2 15.250, 27.500, -0.500 W15E1 0.500, 0.000, -0.500 # 12 75
15 W14E2 0.500, 0.000, -0.500 W7E2 0.500, 0.000, 0.000 # 12 2
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type

Seg. Actual (Specified)
1 2 8 / 50.00 ( 8 / 50.00) 1.000 0.000 I
--------------- LOADS ---------------
Load Wire Wire #/Pct From End 1 R (Ohms) X(Ohms)

1 2 4 / 50.00 ( 4 / 50.00) 600.000 0.000
2 2 12 / 50.00 ( 12 / 50.00) 600.000 0.000
Ground type is Free Space
Chapter 58
Modeling Results
The data derived from the models will appear mostly in tabular
form, with a few patterns interspersed. This is a consequence of my
usual procedures of systematically exploring certain variables in the
antenna design.
One question of interest is whether wire size plays any significant

role in antenna performance. The easiest way to find out is to run
identical antenna dimensions with various wire sizes. Here are the
results for 1296 MHz, using the prescribed 600-Ohm terminating
resistors. In the tables that follow, gain is the free space value in
dBi, F-B is the 180-degree front-to-back ratio in dB, B/W is the -3
dB beamwidth in degrees, F/S is the ratio of the forward lobe to the
most major side lobe in dB, and the Feed Z is the source
impedance.
Model A (1581 segments)
AWG Gain F-B B/W F/S Feed Z

Size dBi dB deg dB R+/-jX
12 16.23 15.99 10.0 10.24 347 - 81
14 16.25 16.55 10.0 10.23 372 - 58
16 16.29 16.90 10.2 10.26 391 - 46
18 16.22 17.49 10.2 10.23 411 - 33
20 16.17 18.18 10.2 10.21 429 - 23
Although the gain does not change in practical terms, it does show
a peak with #16 copper wire. Interestingly, the QST article
suggested that #12 would be the smallest wire likely to be used. I
am not certain that is a sound statement, since the #16 version of
the model also showed the highest front-to-side lobe ratio. Note
Chapter 58
also the increasing front-to-back ratio and feedpoint impedance as

the wire size decreases. These phenomena are likely effects of
increasing wire losses, which do not affect gain significantly.
Model B (797 segments)
AWG Gain F-B B/W F/S Feed Z

10 15.71 14.98 10.3 10.74 186 - 17
12 15.76 15.54 10.4 10.66 200 - 8
14 15.80 16.20 10.4 10.57 213 - 1
16 15.81 16.92 10.4 10.48 226 + 10
18 15.81 17.71 10.4 10.40 239 + 18
20 15.80 18.59 10.4 10.33 251 + 26
The antenna gain for this model is systematically about a half dB

lower than for Model A, and the reported source impedance is
below 300 Ohms. Interestingly, the front-to-back ratio is almost
identical for each wire size between the two models. One of the
reasons that I tend to trust Model B more than Model A is the
smaller excursion of reactance with the changes in wire size (noting
that I added #10 wire to Model B just to see what would occur).
Moreover, the gain peak is less pronounced and the front-to-side
ratio makes a steady progression downward as the front-to-back
ratio climbs.
Chapter 58
Fig. 2 provides a free space azimuth pattern for Model A, which is

virtually identical to the pattern for Model B with a slight adjustment
of gain. Despite the careful calculations made by Laport, this
version of his work cannot suppress the main side lobe by more
than 10 dB relative to the main lobe.
Chapter 58
It is interesting to compare the azimuth plot to a free space vertical

(or elevation) plot for the antenna (Fig. 3). In this plane, we see a
broadening of the main forward and rear lobes (to about 30
degrees between -3 dB points). We may also note that the largest
side lobe also appears in this pattern, giving the impression that it
may form a cone around the main lobe.
Chapter 58
A 3-D view of the pattern, shown in Fig. 4, can give us a better view
of what is happening with the main side lobe--or side lobes. First,
we must allow for the fact that the reduced resolution of the 3-D
pattern converts smooth petals into crystalline points. Nonetheless,
we can see that the main side lobe is actually a series of undulating
lobes and nulls around the main lobe. (Those given to such things
can make any sort of desired Rorschach test out of the 3-D
pattern.)
Chapter 58
To some degree, then, the dual rhomboid is sensitive to wire size in

the 1296 MHz model we are examining. We may increase the front-
to-back ratio by decreasing the wire size. We should also wonder
what effect we might achieve by changing the values of the
terminating resistors. The next data set for both models explores
two versions of each model: #12 wire and #16 wire--that latter
because it coincides with the gain peaks shown by the preceding
data. One of the basic questions to pose is whether there is a value
of terminating resistor that will maximize the front-to-back ratio. The
following data set systematically reduces the terminating resistor
values in 100-Ohm increments from 600 to 200 Ohms.
Model A (#12 wire; 1581 segments)
Res. Gain F-B B/W F/S Feed Z

600 16.23 15.99 10.0 10.24 347 - 81
500 16.21 17.77 10.0 10.17 338 - 81
400 16.17 20.23 10.0 10.07 327 - 83
300 16.14 21.97 10.0 9.95 313 - 85
200 16.09 18.31 10.0 9.77 295 - 89
Model A (#16 wire; 1581 segments)

600 16.29 16.90 10.2 10.26 391 - 42
500 16.26 19.15 10.2 10.17 379 - 46
400 16.23 21.91 10.2 10.06 364 - 51
300 16.20 21.50 10.2 9.92 346 - 58
200 16.17 16.37 10.2 9.74 323 - 68
Chapter 58
Despite differences occasioned by the smaller wire size

occasioning more rapid property changes than the larger wire size,
the two tables show an interesting coincidence. The maximum
front-to-back ratio occurs with a load between 300 and 400 Ohms--
closer to 300 Ohms for the #12 wire and closer to 400 Ohms for the
#16 version. Fig. 5 shows the resultant azimuth pattern for the #12
version with terminating resistors of 300 Ohms.
Chapter 58
Model B (#12 wire; 797 segments)

600 15.76 15.54 10.4 10.66 200 - 8
500 15.74 17.64 10.4 10.55 194 - 8
400 15.72 20.92 10.4 10.42 186 - 8
300 15.69 24.15 10.4 10.23 177 - 9
200 15.67 18.91 10.4 10.00 165 - 10
Model B (#16 wire; 797 segments)

600 15.81 16.92 10.4 10.48 226 + 10
500 15.79 19.64 10.4 10.37 218 + 9
400 15.77 23.64 10.4 10.23 209 + 8
300 15.75 23.11 10.4 10.06 197 + 7
200 15.74 16.59 10.4 9.83 182 + 5
As with Model A, Model B shows its maximum front-to-back ratio

with terminating resistors between 300 and 400 Ohms. The
consistency between the source impedance values for the two wire
sizes gives me additional reason to trust Model B more than Model
A, even though the primary trends coincide.
Whether the source impedances reported by Model B are accurate

to a real antenna involves a number of variables. Some of those
variables include limitations of the model itself, as described earlier.
Other variable emerge from the construction process itself. Ideally,
the support structure for the antenna should be RF-transparent at
1296 MHz. Likewise, construction practices should involve no metal
Chapter 58
supports--not even nails--close to the wire. Even a few 1-inch brads

can add up to a wavelength of nails very quickly. As a
consequence, any real version of the dual rhomboid is likely to
show a source impedance somewhat at variance of even the most
precise model.
One final question that occurred to me resulted from the claims that
the dual rhomboid forgives sloppy construction. In more precise
form, one may ask to what degree the antenna may be frequency
sensitive. As a partial answer to this question, I ran Model A
through a few wire sizes but on the ATV frequency of 1255 MHz,
about 3% lower. (Some claims for the broad-banded nature of the
antenna suggested that +/- 40% of the design frequency would be
usable.) The following table compares the results for Model A at
1296 and 1255 MHz for 3 wire sizes, using the standard 600-Ohm
terminating resistors.
Model A (1581 segments)
Freq. AWG Gain F-B B/W F/S Feed Z

MHz Size dBi dB deg dB R+/-jX
1296 12 16.23 15.99 10.0 10.24 347 - 81
1255 12 16.20 19.37 10.6 10.30 313 -108
1296 16 16.29 16.90 10.2 10.26 391 - 46

1255 16 16.26 21.48 10.8 10.20 362 - 80
1296 20 16.17 18.18 10.2 10.21 429 - 23

1255 20 16.14 23.96 10.8 10.12 409 - 61
With respect to gain, no especially frequency sensitivity can be

found. However, the front-to-back ratio with a given value of
terminating resistor is quite frequency sensitive. At the lower
Chapter 58
frequency, the 600-Ohm terminating resistors are close to optimal

for maximizing the front-to-back ratio. Moreover, the added
capacitive reactance at the source is quite evident for all of the wire
sizes.
Whatever the final evaluation of the adequacy of these models, it is

clear that the Laport dual rhomboid antenna is not quite the "set-
and-forget" item that some sources portray it to be. Its properties
vary with wire size, terminating resistor value, and frequency.
Whether any of those variations are significant to a given operation
can only be judged by reference to the operating specifications.
Moreover, the realizable gain from at least the QST version of the
antenna is considerably less than claims derived from theory (which
rarely takes into account wire losses). What I hope to squeeze time
for is a look at the dimensions derived more directly from Laport's
work--perhaps something in the 100 MHz range (about 8 times
longer than the 1296 MHz model). When I am semi-satisfied with
models of that antenna, I shall add Part 2 to this report on modeling
the dual rhomboid.
Chapter 58
Chapter 59: The Dual Rhomboid, a True Laport Version
I
n looking at the CATJ article referenced in Chapter 58 of these
notes, I was initially struck by the fact that the author tried to
show as exactly as possible the dimensions of a true Laport dual
rhomboid. Modeling this antenna might provide a comparison with
the 1296 MHz QST model examined in Chapter 58.
Of course, some scaling would be necessary. The CATJ versions

were cut for the television channels, with a 100 MHz model for
reference (or for FM reception use). So we can expect in this part to
find antennas over 12 times larger than the 1296 MHz model.
Replacing inches with feet for the Chapter 58 model will give an
idea of the size difference.
Chapter 59
Fig. 6 repeats the sketch in Chapter 58, but without dimensions.

Just why will become immediately apparent.
Sometimes a casual reading must give way to a close reading, and

in the process, what seemed clear becomes a bit muddy. The
CATJ article provides dimensions in two ways: approximations of
the distances from the feedpoint to the supporting cross members
and angles between the two short legs and between the two long
legs. (There is a further ambiguity because the picture of the angles
refers to angles A and B but references a table where the only
angles given are called X and Y.) The result was two sets of
dimensions. One was based on using the prescribed leg lengths
plus sines and cosines of the angles given, which resulted in what I
call the narrow model. The second version was based on the
approximated cross member dimensions, which yielded what I call
the wide model. We shall look at a third model before we are done.
The dimensions for the narrow and wide models are as follows,
using #12 AWG copper wire and the prescribed 600-Ohm loads.
Refer to Fig. 6 to place each dimension.
Narrow Model
0-A 31' A-A' 30.30'
0-B 56' B-B' 38.12'
0-C 88.5' C-C' 7.8'
Wide Model
0-A 31' A-A' 31.50'
0-B 56' B-B' 39.35'
0-C 88.5' C-C' 7.8'
Chapter 59
For model construction in each case, I used the method of creating

right angles among wires at the feedpoint area as perhaps yielding
a more trustworthy model than bringing the wires together at a very
shallow angle. The following model description table illustrates the
modeling technique.
Dual Rhomboid: Laport-CATJ Frequency = 100 MHz.
--------------- WIRES ---------------
Wire Conn.--- End 1 (x,y,z : ft) Conn.--- End 2 (x,y,z : ft) Dia(in) Segs
1 W8E2 -0.100, 0.000, 0.000 W2E1 -0.100, 0.000, 0.100 # 12 1

2 W1E2 -0.100, 0.000, 0.100 W3E1 -15.750, 31.000, 0.100 # 12 75
3 W2E2 -15.750, 31.000, 0.100 W4E1 3.800, 88.500, 0.100 # 12 125
4 W3E2 3.800, 88.500, 0.100 W5E1 4.000, 88.500, 0.100 # 12 3
5 W4E2 4.000, 88.500, 0.100 W6E1 19.670, 56.000, 0.100 # 12 75
6 W5E2 19.670, 56.000, 0.100 W7E1 0.100, 0.000, 0.100 # 12 125
7 W6E2 0.100, 0.000, 0.100 W8E1 0.100, 0.000, 0.000 # 12 1
8 W15E2 0.100, 0.000, 0.000 W9E1 -0.100, 0.000, 0.000 # 12 3
9 W1E1 -0.100, 0.000, 0.000 W10E1 -0.100, 0.000, -0.100 # 12 1
10 W9E2 -0.100, 0.000, -0.100 W11E1 -19.670, 56.000, -0.100 # 12 125
11 W10E2 -19.670, 56.000, -0.100 W12E1 -4.000, 88.500, -0.100 # 12 75
12 W11E2 -4.000, 88.500, -0.100 W13E1 -3.800, 88.500, -0.100 # 12 3
13 W12E2 -3.800, 88.500, -0.100 W14E1 15.750, 31.000, -0.100 # 12 125
14 W13E2 15.750, 31.000, -0.100 W15E1 0.100, 0.000, -0.100 # 12 75
15 W14E2 0.100, 0.000, -0.100 W7E2 0.100, 0.000, 0.000 # 12 1
-------------- SOURCES --------------

1 2 8 / 50.00 ( 8 / 50.00) 1.000 0.000 I
--------------- LOADS ---------------

1 2 4 / 50.00 ( 4 / 50.00) 600.000 0.000
2 2 12 / 50.00 ( 12 / 50.00) 600.000 0.000
Chapter 59
Before looking at the results of modeling these 100 MHz models,

let's review Fig. 7. This is a free space azimuth pattern for one of
the best 1296 MHz models, using #12 wire and 300-Ohm
terminating resistors to achieve maximum front-to-back ratio.
Remember that #12 wire is about 12 times fatter at 1296 MHz
relative to a wavelength than it will be at our new test frequency of
100 MHz.
At 100 MHz, with 600-Ohm terminating resistors, the basic

numbers given by NEC-4 for the performance of the narrow and
wide models are as follows:
Chapter 59
Model Gain F-B B/W F/S Feed Z

dBi dB deg dB R+/-jX
Narrow 14.96 21.94 12.2 11.56 388 - 144
Wide 15.26 24.11 11.8 11.36 364 - 148
The respective free-space azimuth patterns are shown in Fig. 8

and Fig. 9.
Chapter 59
Both models show less gain than the 1296 MHz model, but
considerably better front-to-back ratio with the prescribed 600-Ohm
terminating resistors. The beamwidth at 100 MHz is wider by a
small amount, and the front-to-side lobe ratio is better, also by a
small amount. Perhaps the major fact that becomes evident,
especially in the narrow model, is the reduction in the amount of
power overall in the rearward lobes. Every lobe past 60 degrees
from the main lobe is down by at least 20 dB and mostly more. One
goal of the Laport dual rhomboid design is at least partially met in
these models.
To see what effect wire size might have on performance, I ran the
wide model using wire sizes from #12 through 0.5" in diameter.
Chapter 59
Throughout the exercise, the dimensions remained constant and

the terminating resistors were a constant 600 Ohms.
Wire Dia. Gain F-B B/W F/S Feed Z
Size In. dBi dB deg dB R+/-jX
12 0.0808 15.26 24.11 11.8 11.36 364 - 148
10 0.1019 15.29 25.39 11.8 11.29 345 - 147
8 0.1285 15.31 26.81 11.8 11.21 327 - 145
6 0.1620 15.33 28.27 11.8 11.13 309 - 144
4 0.2043 15.34 29.69 11.6 11.04 292 - 143
2 0.2576 15.35 31.07 11.6 10.95 275 - 141
-- 0.3 15.36 31.94 11.6 10.89 264 - 140
-- 0.4 15.40 33.49 11.6 10.76 242 - 136
-- 0.5 15.49 33.62 11.6 10.66 222 - 131
Obviously, the performance of the dual rhomboid benefits from the

use of fatter wire, whether used as a single wire or as a simulated
fat wire composed of separated parallel wires. The chart does not
peak within the range of values checked (nor does a similar chart
for the narrow model). As we saw with the 1296 MHz model, the
front-to-side lobe ratio and the feedpoint impedance both decrease
with increases in the front-to-back ratio and gain.
It may be the case that using a single wire size of #6 AWG may be
the most practical compromise for a 100 MHz dual rhomboid. Wire
of this size or larger might best be aluminum for weight saving.
Therefore, I compared the performance figures for both #12 and
0.5" wire in copper and aluminum.
Chapter 59
Wire Wire Gain F-B B/W F/S Feed Z

Size Type dBi dB deg dB R+/-jX
12 copper 15.26 24.11 11.8 11.36 364 - 148
12 alum. 15.24 24.10 11.8 11.39 364 - 148
0.5" copper 15.49 33.62 11.6 10.66 222 - 131

0.5" alum. 15.49 33.59 11.6 10.68 222 - 131
Since the performance differences between copper and aluminum

wire are non-existent at the limits of the chart, any wire size within
the chart will give equivalent performance, whether copper or
aluminum.
As I did with the 1296 MHz model, I checked the new models to
determine whether different values of terminating resistors would
yield better performance than the standard 600-Ohm values. As a
quick reference, here are numbers for the wide models using #12
wire and using #6 wire (copper).
#12 Copper Wire

600 15.26 24.11 11.8 11.36 364 - 148
650 15.26 27.13 11.8 11.34 356 - 146
700 15.27 30.13 11.8 11.33 350 - 145
750 15.27 31.06 11.8 11.30 344 - 143
800 15.27 29.15 11.8 11.28 338 - 142
#6 Copper Wire

600 15.33 28.27 11.8 11.13 309 - 144
650 15.33 31.22 11.8 11.10 304 - 142
700 15.34 31.05 11.8 11.09 299 - 141
Chapter 59
The gain of this model (and likewise, the narrow model) rises very
slowly (insignificantly so) as the value of the terminating resistors
increases. However, the front-to-back ratio shows a peak that result
from the interrelationship of the wire size and the terminating
resistor values. The 650-Ohm value for #6 wire is close to the value
recommended by Laport's original design. For reference, Fig. 10
shows the azimuth pattern for the #6 wire wide model with the
optimal terminating resistor values.
Chapter 59
The Scaled QST Model
There remains the question of what happens if one simply scales

the 1296 MHz model to 100 MHz, while retaining the #12 wire. The
dimensions will be somewhat different from those of either the
narrow or wide models, with a shorter overall length and somewhat
wider cross supports at all positions. The scaled dimensions are
these:
Scaled QST Model

0-A 29.7' A-A' 32.94'
0-B 54.0' B-B' 45.90'
0-C 83.16' C-C' 11.0'
To translate the model to 100 MHz, certain modifications were

necessary. Relative to pure scaling, the spacing between
rhomboids had to be reduced (to 0.2') and the spacing between
feedpoint area leg junctions also had to be reduced to manageable
values (0.2'). For reference, here is the model description.
Dual Rhombic-QST 3-97, p89 Frequency = 100 MHz.
--------------- WIRES ---------------
1 W8E2 -0.100, 0.000, 0.000 W2E1 -0.100, 0.000, 0.100 # 12 2

2 W1E2 -0.100, 0.000, 0.100 W3E1 -16.470, 29.700, 0.100 # 12 75
3 W2E2 -16.470, 29.700, 0.100 W4E1 5.940, 83.160, 0.100 # 12 120
4 W3E2 5.940, 83.160, 0.100 W5E1 7.020, 83.160, 0.100 # 12 3
5 W4E2 7.020, 83.160, 0.100 W6E1 22.950, 54.000, 0.100 # 12 75
6 W5E2 22.950, 54.000, 0.100 W7E1 0.100, 0.000, 0.100 # 12 120
7 W6E2 0.100, 0.000, 0.100 W8E1 0.100, 0.000, 0.000 # 12 2
Chapter 59
8 W15E2 0.100, 0.000, 0.000 W9E1 -0.100, 0.000, 0.000 # 12 1

9 W1E1 -0.100, 0.000, 0.000 W10E1 -0.100, 0.000, -0.100 # 12 2
10 W9E2 -0.100, 0.000, -0.100 W11E1 -22.950, 54.000, -0.100 # 12 120
11 W10E2 -22.950, 54.000, -0.100 W12E1 -7.020, 83.160, -0.100 # 12 75
12 W11E2 -7.020, 83.160, -0.100 W13E1 -5.940, 83.160, -0.100 # 12 3
13 W12E2 -5.940, 83.160, -0.100 W14E1 16.470, 29.700, -0.100 # 12 120
14 W13E2 16.470, 29.700, -0.100 W15E1 0.100, 0.000, -0.100 # 12 75
15 W14E2 0.100, 0.000, -0.100 W7E2 0.100, 0.000, 0.000 # 12 2
-------------- SOURCES --------------

1 1 8 / 50.00 ( 8 / 50.00) 1.000 0.000 I
--------------- LOADS ---------------

1 2 4 / 50.00 ( 4 / 50.00) 600.000 0.000
2 2 12 / 50.00 ( 12 / 50.00) 600.000 0.000
Here is a small chart comparing #12 models with 600-Ohm

terminating resistors for all three models:
Model Gain F-B B/W F/S Feed Z

dBi dB deg dB R+/-jX
Narrow 14.96 21.94 12.2 11.56 388 - 144
Wide 15.26 24.11 11.8 11.36 364 - 148
Scaled 15.52 32.65 10.4 10.12 293 - 96
Chapter 59
Fig. 11 presents the free-space azimuth pattern for the scaled QST
model as adjusted. Note the slightly higher gain and front-to-back
ratio, but the narrower beamwidth and lower front-to-side lobe ratio.
Among the more subtle features to notice when comparing patterns
is the first lobe off the main lobe. In the narrow and wide CATJ
models, it is a low-level distinct lobe. In the scaled QST model, the
first lobe is stronger and melds with the main lobe. Whether
features like these make an operational difference in most ham
circumstances is dubious. However, they are interesting
theoretically when considering what Laport was trying to
accomplish with his design.
Chapter 59
If the side lobes are not especially troublesome, the scaled QST
1296 MHz model may be the more advantageous design,
considering the gain, front-to-back ratio, and feedpoint impedance.
However, if the power to the rearward lobes is of concern for a
particular operation, the CATJ version may end up as more
suitable.
A Note on Feedpoint Reactance
Virtually all of the models have shown a remnant capacitive

reactance of proportions to disturb a match with 300-Ohm or similar
line. Because of limitation in the models, it is not certain to what
degree this reactance will appear in a real antenna. However,
modeling uncovers a simple technique for changing the reactance.
See Fig. 12.
Chapter 59
Where the wires of the legs join, the spacing between leg pairs can
be widened or narrowed. Narrowing the spacing tends to push
reactance further into the capacitive region. Widening the spacing
pushed the reactance less capacitive and more toward inductive.
Although the models may not predict the exact reactance value to
be encountered with a dual rhomboid, the trends should be quite
reliable in field adjusting the feedpoint reactance.
Conclusion
By judiciously using the figure that emerged from the 1296 MHz
model and those that emerged with these 100-MHz models, it is
possible to estimate the properties of scaled versions of the dual
rhomboid for 144-, 225-, and 440-MHz versions of the antenna. The
key item to remember is that the "standard" #12 wire becomes
effectively fatter relative to a wavelength as the frequency
increases.
The dual rhomboid models produce consistent narrow beamwidth

gains between 15 and 16 dBi in free space. At 100 MHz, the
require length is 83-89 feet, with a 38 to 45 foot maximum width.
What these numbers do not tell us is whether the antenna is worth
building. So far we have produced no standards of comparison. For
example, what would be the performance of a simpler single wire
rhombic at 100 MHz? Does the dual rhombic have enough of a gain
advantage to warrant the added construction difficulties? How large
would a Yagi or equivalent gain be?
Chapter 59
It may be useful to add one more part to this series to provide some
basis for the individual to decide if the dual rhomboid is indeed the
way to go.
Chapter 59
Chapter 60: The Dual Rhomboid, Some Comparison Standards
I
n thinking about building a dual rhomboid, we should carefully
evaluate whether the results will be worth the effort involved.
Despite its inexpensiveness at UHF, the dual rhomboid is not the
simplest antenna to build.
Moreover, the dual rhomboid does not offer in modeled

performance the gain theoretically claimed for it. Consistent gain
figures between 15 and 16 dBi free space have emerged from the
models. Even if we allow that the models have not caught the
precise dimensions by which the side lobes come in for complete
control, it is dubious that any constructed version of the antenna will
achieve much more than 16 dBi free-space gain.
Therefore, it is reasonable to look at some other antennas in order

to make some evaluative comparisons. In this note, I shall explore
only two: the single-wire rhombic and a standard Yagi.
The Single-Wire Rhombic
The ARRL Antenna Book has carried an HF rhombic since time

immemorial. It is possible to scale this antenna to 100 MHz and to
use #12 wire in order to see by how much the dual rhomboid
outperforms it.
Chapter 60
Fig. 13 provides the essential dimensions for the 100 MHz single-
wire rhombic. At 79.3' long by 38.6' wide, the antenna occupies a
footprint just a tad smaller than the dual rhomboids. The model
description follows.
Chapter 60
ARRL rhombic scaled to 100 MHz Frequency = 100 MHz.
--------------- WIRES ---------------
1 W6E2 -1.200, 0.000, 14.469 W2E1 1.200, 0.000, 14.469 # 12 7

2 W1E2 1.200, 0.000, 14.469 W3E1 19.291, 39.638, 14.469 # 12 100
3 W2E2 19.291, 39.638, 14.469 W4E1 0.344, 79.275, 14.469 # 12 100
4 W3E2 0.344, 79.275, 14.469 W5E1 -0.344, 79.275, 14.469 # 12 3
5 W4E2 -0.344, 79.275, 14.469 W6E1 -19.291, 39.638, 14.469 # 12 100
6 W5E2 -19.291, 39.638, 14.469 W1E1 -1.200, 0.000, 14.469 # 12 100
-------------- SOURCES --------------

1 4 1 / 50.00 ( 1 / 50.00) 0.707 0.000 V
--------------- LOADS ---------------

1 2 4 / 50.00 ( 4 / 50.00) 600.000 0.000
The values in the Z columns are remnants of the source of this

scaled model and can be replaced by zeroes for free space
analysis. The wide spacing of the wires near the feedpoint
represents an attempt to control some of the capacitive reactance
at the feedpoint.
As I did for the CATJ dual rhomboid models, I ran the scaled single-
wire rhombic through various wire sizes to develop a sense of the
trends in performance. Note the reduction of the terminating
Chapter 60
resistor to 600 Ohms from the HF value of 800 Ohms. Here are the
results.
Wire Dia. Gain F-B B/W F/S Feed Z
Size In. dBi dB deg dB R+/-jX
12 0.0808 13.85 45.30 11.4 8.50 625 - 96
10 0.1019 13.93 34.76 11.4 8.53 606 - 105
8 0.1285 14.01 29.84 11.4 8.56 585 - 114
6 0.1620 14.09 26.68 11.4 8.59 563 - 122
4 0.2043 14.16 24.40 11.4 8.61 540 - 130
2 0.2576 14.24 22.57 11.4 8.65 516 - 137
Fig. 14 presents the free space azimuth pattern for the single-wire
rhombic using #12 wire, where the terminating resistor has been
optimized for maximum 180-degree front-to-back ratio. Obvious
from the figure is the fact that a 180-degree front-to-back ratio
reveals the rearward lobe behavior over only a very small portion of
the rear quadrants. The number is impressive on paper only.
Chapter 60
Optimizing the front-to-back ratio for wire sizes other that #12 AWG
will require adjustment of the terminating resistor. Larger wire
versions may be preferable to the #12 model in order to increase
both the antenna gain and the front-to-side lobe ratio.
The front-to-side lobe ratio numbers can be misleading if one does

not also account for the strength of the main lobe. In fact, the lower
front-to-side lobe numbers for the single-wire rhombic--relative to
the dual rhomboid models--only indicate lobes that have about the
same intrinsic strength as those of the dual rhomboids. We can see
this by overlaying patterns, as in Fig. 15.
Chapter 60
The red and blue patterns in Fig. 15 clearly show the higher gain of
the dual rhomboid. However, with respect to the other lobes in the
pattern, only the positions and not the strengths change from one
pattern to the next. With respect to the secondary lobes, there is
not much to choose between a single-wire rhombic and a dual
rhomboid. Of course, this must be qualified with the recognition that
the models in this collection may not have caught the precise
dimensions that yield maximum lobe control. However, we have
looked at enough models to suggest that if there is such a "perfect"
dimension set, it is unlikely to be replicated in the home workshop.
Chapter 60
In terms of forward gain, the difference between the best 100 MHz
#12 wire dual rhomboid and the #12 wire single rhombic is less
than 1.7 dB.
A 16-Element Yagi
A second standard of comparison one might use in evaluating the

dual rhomboid is a standard design Yagi of comparable gain.
DL6WU designs have been around for a long time. They feature
50-Ohm feedpoint impedances and fairly broad-banded
characteristics. One interesting facet of the DL6WU design is that
one can cut off a longer design and still end up with good
characteristics and a 50-Ohm feedpoint impedance.
For this exercise, I cut off a 26 element DL6WU design at 16

elements and then scaled the result to 100 MHz to provide a
comparator for the dual rhomboid. The antenna has the
appearance of Fig. 16.
Chapter 60
For reference, here is the model description.

DL6WU Original, 26 el 432 MHz Frequency = 100 MHz.
Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
--------------- WIRES ---------------
1 0.000, 2.414, 0.000 0.000, -2.414, 0.000 6.80E-01 19

2 1.967, 2.339, 0.000 1.967, -2.339, 0.000 6.80E-01 19
3 2.704, 2.137, 0.000 2.704, -2.137, 0.000 6.80E-01 19
4 4.476, 2.120, 0.000 4.476, -2.120, 0.000 6.80E-01 19
5 6.591, 2.095, 0.000 6.591, -2.095, 0.000 6.80E-01 19
6 9.048, 2.071, 0.000 9.048, -2.071, 0.000 6.80E-01 19
7 11.803, 2.049, 0.000 11.803, -2.049, 0.000 6.80E-01 19
8 14.753, 2.030, 0.000 14.753, -2.030, 0.000 6.80E-01 19
9 17.851, 2.014, 0.000 17.851, -2.014, 0.000 6.80E-01 19
10 21.098, 2.000, 0.000 21.098, -2.000, 0.000 6.80E-01 19
11 24.491, 1.987, 0.000 24.491, -1.987, 0.000 6.80E-01 19
12 28.032, 1.976, 0.000 28.032, -1.976, 0.000 6.80E-01 19
13 31.720, 1.966, 0.000 31.720, -1.966, 0.000 6.80E-01 19
14 35.556, 1.956, 0.000 35.556, -1.956, 0.000 6.80E-01 19
15 39.491, 1.947, 0.000 39.491, -1.947, 0.000 6.80E-01 19
16 43.425, 1.940, 0.000 43.425, -1.940, 0.000 6.80E-01 19
-------------- SOURCES --------------

1 10 2 / 50.00 ( 2 / 50.00) 1.000 0.000 V
This model happens to be symmetrical in the X axis. The longest

element is under 5' and the element diameter for the model is a
little larger than 5/8". Note that the boom length is only about 43.5'
long or about half the length of a dual rhomboid.
Chapter 60
Fig. 17 presents the free space azimuth pattern for the 16-element
Yagi. For comparative purposes, the modeled performance figures
at 100 MHz are these.
Gain F-B B/W F/S Feed Z

dBi dB deg. dB R+/-jX
16.30 17.98 29 17.41 48 - j4
Although the front-to-back ratio of this particular model is under 20

dB, the overall power found in side lobes is much smaller than that
in any of the rhomboid models. The front-to-side ratio is very good
for rejection of QRM from those regions.
Chapter 60
The beamwidth (29 degrees between -3 dB points) makes the

antenna considerably easier to aim than any of the rhomboid
models, whose beamwidths are only a third as wide. The Yagi's
wider beamwidth can be either an advantage or a disadvantage,
depending upon the operating requirements for the antenna.
The DL6WU antennas scale easily, so long as one remembers to

scale the element diameter as well as the lengths and spacings. At
432 MHz, the element diameter for optimal performance is 4 mm.
Conclusion
I have not presented the single-wire rhombic or the DL6WU Yagi

either to encourage or discourage construction of a dual rhomboid.
That decision belongs to the individual user. However, making that
decision requires reference to relevant comparators, and the ones
we have examined here seem like good choices with which to start.
A More Precise Laport Dual Rhombic
Although the models examined in these notes will likely provide

highly satisfactory dual rhomboid antennas, I have remained
unsatisfied with the presentation of numbers for the builder to use.
The "narrow" version of the Laport in Part 2 used a combination of
lengths calculated from angles and some of the "approximations."
So I decided to see what we might obtain by calculating from
ground zero.
Chapter 60
The basic information is this:
L1 = 3.5 wl = 34.425' at 100 MHz

L2 = 6.0 wl = 59.014' at 100 MHz
Angle A (for L1) = 26.1 degrees
Angle B (for L2) = 18.85 degrees
Let us assume that Laport used true rhombi, with parallel sides.
The result is a set of calculations, sketched in Fig. 18.
The figure shows only one of the two rhombi. The horizontal line
will have coordinates 0,0 at the left.
Chapter 60
Side a, from the through horizontal line upward to the end of L1 will
equal sin A * L1 = 15.144'. Side b, from the through horizontal line
downward to the end of L2 will equal sin B * L2 = 19.067'. If the
sides are parallel, the distance c will equal side b - side a = 3.923'.
Distance d from the origin to the end of L1 will equal cos A * L1 =
30.915'. Distance e from the origin to the end of L2 will equal cos B
* L2 = 57.031'. Distance f from the origin to the far peak of the
rhombus will equal d + e = 87.946'.
These numbers provide us with coordinates for both rhombi of the

Laport antenna. They appear in the model description below.
Dual Rhomboid: Laport-CATJ Frequency = 100 MHz.
--------------- WIRES ---------------
1 W4E2 0.000, 0.000, 0.100 W2E1 -15.144, 30.915, 0.100 # 12 150

2 W1E2 -15.144, 30.915, 0.100 W3E1 3.923, 87.946, 0.100 # 12 257
3 W2E2 3.923, 87.946, 0.100 W4E1 19.067, 57.031, 0.100 # 12 150
4 W3E2 19.067, 57.031, 0.100 W1E1 0.000, 0.000, 0.100 # 12 257
5 W8E2 0.000, 0.000, -0.100 W6E1 -19.067, 57.031, -0.100 # 12 257
6 W5E2 -19.067, 57.031, -0.100 W7E1 -3.923, 87.946, -0.100 # 12 150
7 W6E2 -3.923, 87.946, -0.100 W8E1 15.144, 30.915, -0.100 # 12 257
8 W7E2 15.144, 30.915, -0.100 W5E1 0.000, 0.000, -0.100 # 12 150
-------------- SOURCES --------------

1 1 1 / 0.00 ( 1 / 0.00) 1.000 0.000 SV

2 1 5 / 0.00 ( 5 / 0.00) 1.000 0.000 SV
Chapter 60
--------------- LOADS ---------------

1 257 2 / 99.81 ( 2 /100.00) 300.000 0.000

2 1 3 / 0.33 ( 3 / 0.00) 300.000 0.000
3 150 6 / 99.67 ( 6 /100.00) 300.000 0.000
4 1 7 / 0.19 ( 7 / 0.00) 300.000 0.000
You may notice several alterations in this model relative to those

used in preceding parts of these notes. First, two independent
rhombi are used, each with its own feed and load. This move
preserves the geometry of the rhombi. Second, to avoid flat wires at
either end of the rhombi, split loads are used for the terminating
resistors and split feed is used for each rhombus. This technique
involves a compromise and a modeler's judgment of priorities. In
this case, preservation of wire geometry was given priority over
exact equalization of segment lengths for each fed and load
segment. The model employs a high number of segments (1648),
but may still not be perfectly converged. The segment lengths are
equal to two decimal places, but very slight differences in segment
length for split loads and feeds can prevent convergence until a
very high number of segments is used in a model.
Despite these potential shortfalls of perfection, certain trends make

the results close to precise. First, for all stages of convergence
testing from about 800 segments upward, the same terminating
resistor values produced maximum front-to-back ratio in each
model tested with different wire sizes. Gain, beamwidth, and front-
to-side lobe ratio remained very close during the tests, although the
Chapter 60
higher the number of segments, the better the reported front-to-

back ratio. Only the feedpoint impedance remained somewhat
variable.
The following results were obtained for #12 and #6 copper wire. In
the table, the given value of terminating resistor--chosen for the
best front- to-back ratio--represents a series combination of two
load resistors in the model description. The feedpoint impedance
given is the composite parallel impedance for the two sources
connected in parallel. The rhombi are vertically separated 0.2'
(2.4").
Wire Dia. Res. Gain F-B B/W F/S Feed Z
Size In. Ohms dBi dB deg dB R+/-jX
12 .0808 600 15.01 23.38 12.4 12.10 398 - 122
6 .1620 550 15.08 23.48 12.4 11.94 348 - 130
The most interesting facet of the exercise in trying to make the

Laport antenna model more precise does not appear in the
tabulated numbers. Rather, it appears in the azimuth pattern of Fig.
19.
Chapter 60
The Laport antenna does indeed have potential for controlling the
side lobes of the rhombic configuration. Only 3 forward side lobes
rise much above -20 dB relative to the main lobe, and they are
down by more than 12 dB. The reduction in rearward lobes is
significantly improved relative to any of the preceding models used
in these notes. Whether or not this model has succeeded in
capturing the Laport dual rhombic in exact precision, it is clear that
Laport was on the right track in his efforts to reduce side lobes from
rhombic antennas. Perhaps the only thing not yielded by the design
is the absolute maximum in gain.
Spacing between the two rhombi does make a difference in

performance characteristics, including the feedpoint impedance,
Chapter 60
which rises as the wires are brought closer together. If the spacing
is increased, we obtain a lower source impedance, higher gain,
high front-to-side lobe ratio, and--up to a peak value--higher front-
to-back ratio. I ran a small table of ever-increasing spacing using
the #12 wire, 600-Ohgm terminating resistor model, and I obtained
the following results.
Space Space Gain F-B B/W F/S Feed Z
Feet WL dBi dB deg dB R+/-jX
0.2 0.020 15.01 23.38 12.4 12.10 398 - 122
0.4 0.041 15.05 29.04 12.4 12.18 342 - 105
0.6 0.061 15.07 34.27 12.4 12.23 316 - 88
0.8 0.081 15.08 35.21 12.4 12.26 303 - 77
1.0 0.102 15.10 33.13 12.4 12.30 295 - 68
1.2 0.122 15.11 31.45 12.4 12.32 290 - 62
The gain rises continuously with increasing space, although the

peak cannot be far off the chart. The front-to-back ratio increases
until the spacing reaches 0.8' (0.081 wl). There is no sign where the
increase in front-to-side lobe ratio may peak. Given the reported
impedance figures, a spacing in the region of 0.081 wl may be most
optimal for a balance of operating characteristics. Why increased
spacing tends to improve performance appears to be a function of
the fact that the wires of the two rhombi cross at less than right
angles. THus, there is significant coupling between them. For any
given geometry for the individual rhombi, there is likely a spacing
that optimizes the operating characteristics. Fig 20 provides an
azimuth pattern of one of the most fully optimized Laport dual
rhombic antennas obtained in this series of experiments. Even so,
note the fact that, relative to the rear lobes in Fig. 19, some of the
rear lobes in this pattern are beginning once more to grow.
Chapter 60
The Laport design deserves further study, with special reference to

the designer's original papers. These notes have gone only so far
as the available information will permit. Hopefully, they have
indicated some useful directions for additional effort.
Chapter 60
Chapter 61: Folded X, Hex, Square & Moxon Rectangle Beams
F
rom time to time, interest reemerges in some long-standing
designs for compact planar (2- dimensional) beams.
Unfortunately the interest seems to focus on a single design
at a time rather than on the design as a member of a family of
designs. Equally unfortunately, the interest usually stems from the
publication of some peak performance figures for a particular
design rather than from the antenna's performance across an entire
band. Consequently, misunderstandings of antenna potentials
multiply endlessly.
One of the families of beams whose members rouse periodic

interest is the end-coupled clan. If the ends were connected, these
would all make versions of a loop. However, with the ends spaced
properly, each member forms a directional beam. Another apt
name for the group might refer to the semi-closed geometry of the
antennas. With closed loops, these antennas share the feature of
tending toward larger dimensions with significant increases of
element diameter.
Under any name, the family has two branches: those whose center
structures form Vees that point at each other bottom to bottom and
those whose centers parallel each other. Among the features that
clan members have in common is a flat structure with an area that
is just over 0.6 square wavelengths--in other words, about 1/4 by
1/4 wavelength. Hence, the lure of the family is its compact size.
Chapter 61
It may be useful to explore the main members of the family

individually to seek out their potential. I have selected 20 meters as
the test band. To keep comparisons fair, I have constructed all
models of #12 copper wire. However, some of the family members
lend themselves to self-supporting aluminum tubing construction,
and I shall note the potential performance changes that may result
from building a tubing version of the antenna. The use of tubing for
part or all of the structure, of course, will alter the dimensions from
the ones used with the #12 wire versions.
The antennas that we shall examine are these:
• 1. The folded X-beam

• 2. The hex beam
• 3. The VK2ABQ square
• 4. The Moxon rectangle
As yet, I do not have any parallelograms, pentagons, or octagons in

my collection.
Chapter 61
The Folded X-Beam
Fig. A shows the outlines of a folded X-beam. If you are interested

in the history and details of the folded X-beam, see "Modeling and
Understanding Small Beams: Part 1: The X-Beam,"
Communications Quarterly, 5 (Winter, 1995), 33-50. Ordinarily, the
Chapter 61
Vee portions of the folded X-beam are constructed of tubing

supported by a center hub. Then wire tails for the driver and
director are run from one corner toward the other, often taped to a
perimeter cord that also holds the four arms in a fixed arrangement.
Modeling the usual construction of an X-beam is not feasible with

NEC, since the program has an invariant tendency to yield
inaccurate results with angular junctions of wires having different
diameters. So, I have fashioned a model using #12 copper wire
throughout. The performance differences are these: the all-wire
version has a slightly lower maximum gain (by about 0.2 dB) and a
slightly narrower 2:1 SWR bandwidth (about 50 kHz narrower) than
the hybrid tubing/wire version. Incidentally, the hybrid version can
be directly modeled with public-domain MININEC if one uses
length-tapering toward the sharp angle corners.
Folded X-beams are normally designed for driver-director

arrangements, since it is difficult to obtain significant performance
with a driver-reflector arrangement. In the folded configuration of
Fig. A, the parasitic element almost "wants" to be a director. In less
metaphorical terms, a modestly performing driver-reflector design,
with only a slight change of reflector length will reverse its pattern
and hold that reversal, even though the parasitic element is
considerably longer than one might expect for a director. It is also
possible to tune the director to move the peak front-to-back portion
of the operating curve across the band. By lengthening the director
and adding a remotely adjusted bit of capacitive reactance at the
center, the peak performance region can be moved across an
Chapter 61
amateur band. However, the model used here employs a fixed

construction, as the following table shows.
X-Beam Frequency = 14.1 MHz.
--------------- WIRES ---------------

Wire Conn. --- End 1 (x,y,z : in) Conn. --- End 2 (x,y,z : in) Dia(in) Segs
1 -99.000, 17.000, 0.000 W2E1 -99.000, 99.000, 0.000 # 12 15
2 W1E2 -99.000, 99.000, 0.000 W3E1 -6.000, 3.000, 0.000 # 12 25
3 W2E2 -6.000, 3.000, 0.000 W4E1 6.000, 3.000, 0.000 # 12 3
4 W3E2 6.000, 3.000, 0.000 W5E1 99.000, 99.000, 0.000 # 12 25
5 W4E2 99.000, 99.000, 0.000 99.000, 17.000, 0.000 # 12 15
6 -99.000,-11.000, 0.000 W7E1 -99.000,-99.000, 0.000 # 12 15
7 W6E2 -99.000,-99.000, 0.000 W8E1 -6.000, -3.000, 0.000 # 12 25
8 W7E2 -6.000, -3.000, 0.000 W9E1 6.000, -3.000, 0.000 # 12 3
9 W8E2 6.000, -3.000, 0.000 W10E1 99.000,-99.000, 0.000 # 12 25
10 W9E2 99.000,-99.000, 0.000 99.000,-11.000, 0.000 # 12 15
-------------- SOURCES --------------

1 2 8 / 50.00 ( 8 / 50.00) 1.000 0.000 V
Chapter 61
In Fig. 1, we find both the gain and front-to-back curves of the

folded X-beam. Because the direction of the beam reverses
between 14.3 and 14.35 MHz, the curves are cut off at 14.3 MHz.
(The reversal to a driver-reflector beam yields only poor results,
never reaching a 10 dB front-to-back ratio.) One of the inherent
difficulties of the folded X-beam is that the maximum gain and the
Chapter 61
maximum front-to-back ratio are always separated in frequency.

The gain at the maximum front-to-back peak is about 0.5 dB below
peak. Both the gain and the front-to-back curves are quite steep,
indicating a narrow operating passband, whatever the feedpoint
impedance characteristics might be. In the past, the chief use of the
folded X-beam has been on 10 meters as a home-brew project for
those interested in the 28.3 to 28.5 MHz region of the band.
Chapter 61
The SWR curve, in Fig. 2, is referenced to 20 Ohms, which is

approximately the impedance at the maximum front-to-back peak.
Indeed, this design shows operating characteristics that are directly
tied to the feedpoint impedance. A near 50-Ohm impedance is
possible at the lowest frequency in the passband, with a low gain
and relatively poor front-to-back ratio. Where the front-to-back ratio
peaks, the impedance is from 20 to 25 Ohms, depending on the
thickness of the element materials. At the maximum gain point, the
feedpoint impedance drops to the 10-15-Ohm region. Wire versions
of the antenna tend to show impedance values at the low end of the
ranges indicated, while tubular and hybrid versions yield
impedances values at the higher ends of the ranges.
Chapter 61
The peak gain and 180-degree front-to-back ratio figures can give a
misimpression. The peak gain of about 6 dBi (free space) rivals that
of a 2-element Yagi whose elements take twice the space side-to-
side. Likewise, the peak 180-degree front-to-back ration of over 32
dB sounds impressive. However, the patterns in Fig. 3 tell a
somewhat different tale (as do the passband graphs we have
viewed. An averaged front-to-rear ratio for the entire rear area of
the beam has, within the 200 kHz of prime operation, a value of
between 10 and 15 dB--no better than a common 2-element driver-
reflector Yagi. The Yagi would also have superior gain over X-beam
at every frequency and be able to cover the entire 20-meter band.
A 2-element Yagi with about 1/8 wavelength element spacing and
loaded elements that are about 3/4ths full size would occupy about
the same area as the X-beam with broader performance curves.
Hence, the folded X-beam has fallen into relative disuse.
Chapter 61
The Hex Beam
If we fold the X-beam tails outward, we obtain the basic

configuration of the hex(agon) beam, although true hex beams are
built as closely to the hexagon geometry as the support structure
will permit. Fig. B shows the outline of the model used to generate
Chapter 61
performance curves. The details of the model used in this study,

which is a significantly modified version of a model originally
provided by N7CL, follow in the chart.
hex beam: 20 meters Frequency = 14.1 MHz.
--------------- WIRES ---------------

1 -108.00, 19.500, 0.000 W2E1 -61.800,113.000, 0.000 # 12 22
2 W1E2 -61.800,113.000, 0.000 W3E1 -9.950, 25.900, 0.000 # 12 26
3 W2E2 -9.950, 25.900, 0.000 W4E1 9.900, 25.900, 0.000 # 12 5
4 W3E2 9.900, 25.900, 0.000 W5E1 61.800,113.000, 0.000 # 12 26
5 W4E2 61.800,113.000, 0.000 108.000, 19.500, 0.000 # 12 22
6 -112.00,-12.900, 0.000 W7E1 -61.800,-113.00, 0.000 # 12 23
7 W6E2 -61.800,-113.00, 0.000 W8E1 -9.950,-25.900, 0.000 # 12 26
8 W7E2 -9.950,-25.900, 0.000 W9E1 9.950,-25.900, 0.000 # 12 5
9 W8E2 9.950,-25.900, 0.000 W10E1 61.800,-113.00, 0.000 # 12 26
10 W9E2 61.800,-113.00, 0.000 112.000,-12.900, 0.000 # 12 23
-------------- SOURCES --------------

1 3 3 / 50.00 ( 3 / 50.00) 1.000 0.000 I
-------- TRANSMISSION LINES ---------

Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/
Actual (Specified) Actual (Specified) Ohms Fact Norm
1 3/50.0 ( 3/50.0) Short ckt (Short ck) 12.000 in 600.0 1.00
One feature of this model is the relatively wide spacing of the

centers of the Vee-ed sections. This move tends to lower the
feedpoint impedance to the 25-Ohm region, and the model uses a
12" stub of 600-Ohm shorted transmission line as a beta hairpin to
effect a 50-Ohm match. It is possible to bring the center points of
the driver and reflector closer together to obtain a direct 50-Ohm
match. However, two deficits emerge with this move. First, the 50-
Ohm match does not extend across the entire 20-meter band
Chapter 61
because the sharpness of the geometry yields a corresponding

tuning sharpness. In contrast, the beta-matched 25-Ohm
impedance does cover the entire 20-meter band with a 50-Ohm
SWR of under 2:1. Second, with the center Vee points brought
closer together, array performance smoothes out across the band,
but at much lower levels of gain and front-to-back ratio than we
obtain from the wider-spaced center region. Therefore, I have
chosen to look at the lower impedance version of the antenna with
its better performance peaks.
The hex beam has a design affinity with a number of other

members of the end-coupled clan that we shall not examine here.
The slope of the outer sections of each end toward the other
element is a property shared by several interesting antenna
designs, including a 2-element reversible wire beam for 40 meters
developed by AA2NN. The antenna uses a double slope, since the
elements each form an inverted Vee. As well, each element end
approaches the corresponding end of the other element. The result
is a beam that requires only two center supports. As well, by using
rope on the ends of the elements, the tie down points will also be
reduced to 2. Equally related to the outer structure of the hex beam
is the 3-element 40-meter reversible Yagi developed by WA3FET. It
uses a linear driver and a pair of parasitic elements, each of which
is sloped toward the end of the driver. One parasitic element is
loaded for reflector duty. One advantage of element tips that slope
toward each other rather than point directly at each other, is the
greater ease of adjustment. Small changes of spacing of the tips
produce less radical effects than when the tips are end-to-end.
Chapter 61
Fig. 4 presents the gain and 180-degree front-to-back ratio figures

across 20 meters. The gain variation across the band is nearly 2
dB, a fairly high figure among common 2-element beam designs.
The front-to-back ratio shows a very sharp peak, but decreases
rapidly to band-edge values in the 8 to 12 dB range. Peak operation
of this antenna has a bandwidth of 100 to 150 kHz, with the
Chapter 61
remainder of the band showing relatively mediocre performance.

Nonetheless, like all members of the semi-closed geometry family,
the hex beam permits a high front-to-back peak whose decline is
steeper below the peak frequency than above it.
Fig. 5 illustrates one of the illusions of SWR. One could suggest

that this model of the hex beam antenna has an operating
bandwidth that covers the entire band, since the 50-Ohm SWR is
Chapter 61
less than 2:1 across 20 meters. However, operating bandwidth

involves more parameters than just the SWR. Evaluating the gain
and front-to-back ratio is equally as important, if not more so, than
the SWR. For this particular design of the hex beam, the only wide-
band parameter is SWR. Gain and front-to-back ratio values are
relatively narrow band properties.
Fig. 6 shows free-space azimuth patterns for the first 200 kHz of 20
meters. The pattern at 14.1 MHz is well controlled, but off peak, the
rearward pattern spreads to average values in the 15 dB range.
Beyond 14.2 MHz, the rearward pattern spreads larger and the
forward gain decreases rapidly.
Chapter 61
In general, like the X-beam and other beams based upon vee-ing
the center parts of the elements, the hex beam shows a quite
narrow operating bandwidth relative to gain and front-to-back ratio.
The rate and total gain change across the band and the band-edge
front-to-back ratio values are very important in evaluating the
operating bandwidth of an antenna.
For further extensive information on home-brew hexbeams, see

G3TXQ's website http://www.karinya.net/g3txq/hexbeam/ or
K4KIO's site
http://www.leoshoemaker.com/hexbeambyk4kio/general.html
NOTE: URLs may go stale over time.
Chapter 61
The VK2ABQ Square
The VK2ABQ Square (and the Moxon Rectangle) are more fully
described in "Modeling and Understanding Small Beams: Part 2:
VK2ABQ Squares and The Modified Moxon Rectangle,"
Communications Quarterly, (Spring, 1995), 55-70. The origins of
the square go back to the 1930s, only to disappear and re-emerge
in the 1960s. Fig. C shows the outlines of a modified square. The
modification consists of loading the reflector with a shorted
Chapter 61
transmission line stub about 6" long to move the peak performance
point without disturbing the square shape.
The original VK2ABQ square used very close-spaced element tips--

only a literal coat button apart. However, very close tip spacing
creates an array with narrow-band properties, and small variations
in construction can yield large variations in performance. Therefore,
the model below uses fairly wide spacing (34") for the element tips.
VK2ABQ 20 Meters Frequency = 14.15 MHz.
--------------- WIRES ---------------

1 -118.22, 16.889, 0.000 W2E1 -118.22,106.159, 0.000 # 12 6
2 W1E2 -118.22,106.159, 0.000 W3E1 118.222,106.159, 0.000 # 12 13
3 W2E2 118.222,106.159, 0.000 118.222, 16.889, 0.000 # 12 6
4 -118.22,-16.889, 0.000 W5E1 -118.22,-106.16, 0.000 # 12 6
5 W4E2 -118.22,-106.16, 0.000 W6E1 118.222,-106.16, 0.000 # 12 13
6 W5E2 118.222,-106.16, 0.000 118.222,-16.889, 0.000 # 12 6
-------------- SOURCES --------------

1 7 2 / 50.00 ( 2 / 50.00) 1.000 0.000 I
-------- TRANSMISSION LINES ---------

Line Wire #/% From End 1 Wire #/% From End 1 Length Z0 Vel Rev/
Actual (Specified) Actual (Specified) Ohms Fact Norm
1 5/50.0 ( 5/50.0) Short ckt (Short ck) 5.892 in 600.0 1.00
As the model shows, this version of the antenna is off square by

about 12 inches. In this highly square (if imperfectly square)
configuration, the feedpoint impedance is about 100 Ohms, making
the antenna a candidate for a 2:1 balun at the feedpoint.
Chapter 61
As shown by Fig. 7, the VK2ABQ square is a relatively low gain

beam, although the gain varies only about 1.1 dB across the band.
Hence, the 4.05 dB gain at the high end of the band equals that of
the hex beam. The square's 180-degree front-to-back ratio peaks
above 34 dB. Although the curves are fairly steep, the band edge
Chapter 61
values are about 15 dB--not bad for a 2-element parasitic beam

that is about 1/4 wavelength on a side.
As Fig. 8 shows, the real surprise of the modified VK2ABQ square

is the 100-Ohm impedance curve. Across all of 20 meters, the
resistive portion of the feedpoint impedance varies by under 6
Ohms, and the reactance varies by a similar amount. Hence, the
Chapter 61
SWR curve is very flat indeed. A 2:1 balun would permit operation
across the entire 20-meter band with an exceptionally low SWR
and no conditions to incur losses within the balun.
The VK2ABQ was the basis for the later Moxon Rectangle. The key
performance feature absorbed from the square was the excellent
control of the rear portion of the radiation pattern. Fig. 9 shows the
band-edge and mid-band pattern for the square. If the square is
constructed of 1" aluminum tubing, the band-edge front-to-back
ratio improves to nearly 20 dB, with a small increase in array gain
as well.
In all, the square is a relatively wide-band array whose

characteristic remain reasonably level across the band (gain and
Chapter 61
impedance) or hold to minimal acceptable levels (front-to- back

ratio). However, the chief deficit of the square is gain. In fact, one
can preserve the front-to-back performance while improving gain--
and as a bonus achieve a direct 50-Ohm match. The cost is going
considerably out of square.
The Moxon Rectangle
Because the 3 family members we have so far examined use

relatively wide spacing between facing element tips, many
designers have ignored the effects of this dimension. The result has
been a number of fairly poor designs. The element tip spacing
influences the relative proportions of every other dimension of any
of the family members. Nowhere is this more apparent than with the
Chapter 61
optimized Moxon rectangle, sketched in Fig. D. The combination of

close tip coupling as well as more extended parallel element
coupling allows the Moxon rectangle to recover the gain lost by the
square while maintaining fairly wide-band operating characteristics.
It is the longer sections of parallel elements that permit the close tip
spacing to be controllable without sudden shifts in the direction of
the pattern.
The #12 copper wire model for this study reveals that the side-to-
side length is about 3/8 wavelength, while the front-to-back size is
about 1/8 wavelength. Hence, the total area of the antenna is less
than the 1/4 wavelength squares, although the turn radius is
greater. The details of the model used here are as follows:
Moxon rectangle Frequency = 14.175 MHz.
--------------- WIRES ---------------

1 -151.74, 64.188, 0.000 W2E1 -151.74,110.377, 0.000 8.08E-02 5
2 W1E2 -151.74,110.377, 0.000 W3E1 151.740,110.377, 0.000 8.08E-02 35
3 W2E2 151.740,110.377, 0.000 151.740, 64.188, 0.000 8.08E-02 5
4 -151.74, 56.433, 0.000 W5E1 -151.74, 0.000, 0.000 8.08E-02 7
5 W4E2 -151.74, 0.000, 0.000 W6E1 151.740, 0.000, 0.000 8.08E-02 35
6 W5E2 151.740, 0.000, 0.000 151.740, 56.433, 0.000 8.08E-02 7
-------------- SOURCES --------------

1 17 2 / 47.14 ( 2 / 47.14) 0.707 0.000 V
As the model shows, the rectangle is about 50% longer (side-to-

side) than the squares. Tip-to-tip spacing is about 8". In the August,
2000, issue of antenneX, I published a small program that inputs
Chapter 61
only the design frequency and wire diameter to yield optimized

dimensions for Moxon rectangles for the HF and VHF regions. The
designs provide a direct 50-Ohm match, whether used for rotatable
or reversible beams.
Chapter 61
The gain curve in Fig. 10 for the Moxon is a full dB better than for
the square, although the total change in gain across the band is
about the same. Since the Moxon rectangle can easily be
fabricated of aluminum tubing, the result will be another 0.2 dB of
gain and slightly less change in the gain across the band. As well,
the band-edge front-to-back ratio values will improve to nearly 20
dB from the wire values of 15 dB. As with all of the semi-closed
geometry designs, the front-to-back ratio is peaked just below the
center of the band in order to achieve relatively similar front-to-back
values at the band edges.
Both the square and the Moxon use the combination of parallel
element coupling and end-coupling to achieve a very high front-to-
back ratio at a design frequency. Indeed, in both cases, the current
magnitude and phasing on the parasitic element center is very
close to the precise values needed for a maximum front-to-back
ratio if each element were to be independently fed and phased.
Only the existence of the "tails" which radiate (if only weakly),
prevents the pattern from becoming the deep dimple of a perfectly
phased pair of elements.
Chapter 61
The 50-Ohm SWR curve in Fig. 11 is for a direct match to coaxial

cable with no matching required (although a common-mode current
suppression choke or 1:1 balun is always in order). Unlike the SWR
curve for the VK2ABQ square, the Moxon SWR curve shows a
definite slope, although the band edge figures are acceptable under
most conditions. The curve flattens further if one uses aluminum
tubing of about 1" diameter for the antenna.
Chapter 61
The Moxon rectangle shares with the VK2ABQ square a nearly

cardioidal pattern. The deepest "side" nulls do not occur at 90
degrees off the bearing of maximum gain, but somewhat further
toward the rear, as is evident in Fig. 12. The rear lobes are well
behaved, that is, they have no large quartering side lobes. The
rearward lobes for the band edges shrink as the element diameter
becomes larger.
Some Tentative Conclusions
This survey of semi-closed geometry end-coupled beams should

suffice to reveal the family resemblances among the members of
the clan. It may be useful to summarize some of the properties that
both link and separate the individual members.
Chapter 61
1. Designs with element center regions that are parallel or only

gently sloped outward toward the ends tend to show wider-band
characteristics than those whose element centers are Vee-ed
toward each other.
2. Element tips display two regions of coupling. Wider spacing

between tips tends to produce lower gain, although small changes
in spacing yield less radical effects. Closely spaced tips tend to be
more critical and may be effectively usable only if most of the
element length is either parallel or only gently slopes to bring the
tips closer together.
3. Semi-closed beam designs tend toward loop properties, such as

an increase in perimeter dimensions with an increase in element
diameter. Sloping element designs are most immune to this effect
and may show more typical linear element properties.
4. Designs that strive for a minimum turning radius tend either to

have narrow-band characteristics or lower gain. The Moxon
rectangle represents a compromise geometry that achieves as
good or better gain than the other 2-element members of the clan
while achieving a high front-to-back ratio and relatively broad-band
characteristics. Sometimes the best square is a rectangle.
5. Both the front-to-back ratio and SWR curves tend to deteriorate

much faster below the design frequency than above it. Therefore, to
achieve relatively equal performance at both the lower and upper
band edges, the appropriate design frequency is about 1/3 the way
up the band. For 2-element driver-reflector designs, whether using
Chapter 61
a standard Yagi configuration or one of the end-coupled designs,

the gain will decrease as frequency increases.
I have over the years built and used most of the designs we have
discussed here in 10-meter versions, using both wire and aluminum
construction. The models employed here are variants of those
antennas, as well as of published data. No commercial antennas
are modeled for these notes. Their intent is simply to show both the
resemblances and differences among members of the end-coupled
clan of beams.
Chapter 61
Chapter 62: The EDZ Beams
S
ome time back, I wrote a piece for Communications Quarterly
on the Extended Double Zepp ("Modeling and Understanding
Small Beams: Part 3: The EDZ Family of Antennas," Fall,
1995, 53-71). My hope was to improve our understanding of the
EDZ and look at some of its possibilities.
The EDZ in its simplest form is a non-resonant wire antenna about

5/4 wavelengths long. Being non-resonant, exact length is non-
critical. Shorter versions have smaller side lobes but higher
capacitive reactance; longer versions the reverse. Feedpoint
impedance ranges from 100 to 150 ohms resistive with well over
600 ohms capacitive reactance. The chief reason for using the EDZ
is its 1.5+ dB gain over a dipole comparably situated.
Brian Egan, ZL1LE and I had been discussing EDZ potentials since
about 1991. He initially suggested a 2-element beam consisting of
an EDZ driven element plus two Yagi-type reflector elements
spaced a few feet behind the driven element and each pushed
sideways to the wire end limits of the driven element. Modeling this
configuration seemed to make a different arrangement preferable.
From this arose the 2-element (driven element- reflector) beam
noted in the article. The center of each element is inductively
loaded, one for matching the feedline, the other for optimizing the
rear element as a reflector. With 1/2 wavelength parallel lines down
to near ground level, the two matching/loading units could be
reversed, reversing the direction of the beam. This installation was
tested for a couple of years at W4RNL and worked quite credibly.
Chapter 62
Well, folks, as the old song says, "Everything old is new again." Bill
McDowell, K4CIA, sent me a copy of an article from the June,
1938, QST, "The Extended Double-Zepp Antenna." In the back
pages is a description of how to add a parasitical element to the
EDZ. Author Hugo Romander, W2NB, describes a 0.2 wavelength
spaced array. The driven element is stub matched to the source
feedline. The other element is stub loaded inductively, but at two
points: one for use as a reflector, the other for use as a director.
Hence, a different system for a reversible beam--and a perfectly
competent one. W2NB's system has the advantage of simplicity,
while ours has the advantage of convenience. It can be fun to
discover that one has reinvented the wheel. Fortunately, the
information I added to the end of my article reviewing the principles
of stub matching and loading would aid one to replicate the W2NB
EDZ beam, so I do not feel totally disconnected from the 1938
work.
From time-to-time, folks discuss the possibilities for a 3-element

EDZ beam. Henry Pollock, WB4HFL, is actually planning to build
one. The idea led me to try to verify his modeling results and to
compare his configuration to an alternative.
As with the 2-element EDZ, one has two main choices of

configuration: 3 long elements or a long driven element with pairs of
Yagi elements (directors and reflectors) at the extreme limits of the
EDZ driving element.
Chapter 62
Henry has chosen the double-Yagi version, and very likely wisely
so. Since he plans to put it at 60' for 10 meters, let's look at
modeling results for both arrangements centered at 28.5 MHz.
The 3-wire EDZ beam can be built from 3 41'8" lengths of #12 wire,
each with a center load. The director requires about 800 ohms, the
reflector 1150 ohms, and the driven element 980 ohms. The
resulting antenna has a resonant feed resistance of about 90-95
ohms, just about right for a 1/4 wl matching section of 70 ohm coax
Chapter 62
to the regular 50-ohm feedline. You can make the director and
reflector inductive loads from coils or from 450-ohm parallel vinyl
covered feedline stubs 5.5' and 6.25' long each. If you do not use a
split coil for the driven element feed point, you may wish to design a
stub matching system--or perhaps use an ATU and parallel line all
the way.
The potential beam performance at 60' is quite good: 15.5 dBi gain
with about 30 dB front-to-back ratio. Adding the director to our old
2-element EDZ beam really improves the front-to-back ratio more
than it helps raw gain.
But here is the rub:
The 3-wire EDZ beam is quite narrow-band in pattern--and even

more so in feedpoint impedance and loading. At 28 and 29 MHz,
the front-to-back ratio drops to the 7-9 dB range. The feedpoint
shows a 250-ohm reactance change across the band. This is a
beam that needs adjustment of all 3 elements if one hopes to cover
more than 100 kHz of 10 meters. (For lower band versions, narrow
the bandwidth in proportion of the ratio of the desired lower
frequency to 28.5 MHz.)
Chapter 62
The double Yagi EDZ tells a somewhat different story. WB4HFL did
not give me detailed dimensions, so I modeled my own version,
with directors and reflectors spaced 5' from the driven element.
Parasitical elements had outer limits in line with the end of the EDZ
element (41'8"). Reflectors were 17'1" and directors were 16'0.5"
long. #12 wire, of course, for consistency throughout.
Chapter 62
The results at the design center frequency were interesting: 16.0

dBi gain with a front-to-back ratio of 38 dB at 60' height. The front-
to-rear quadrants had a minimum ratio of about 21 dB. What the 3-
wire gives us in a slightly better front-to-rear ratio at design center
is offset by the added gain of the double-Yagi version. Feedpoint
impedance of the double Yagi version is about 90 - j1000 ohms,
calling for a stub match or an ATU feed system.
However, the WB4HFL-style design has two hidden advantages,

partially revealed by a frequency sweep:
First, the double-Yagi version retains a better figure from 28 to 29

MHz, never sinking below 11 dB front-to-back ratio at those
extremes. While not superlative, the ratio climbs to nearly 20 dB at
the 28.25 and 28.75 marks. These numbers are far superior to the
3-wire beam.
Chapter 62
Second, the only adjustment needed across the band is the driven
element tuning. Like its counterpart, the double-Yagi version shows
a 250-ohm reactance excursion across the band, along with a 75-
ohm change in the resistive component. However, parallel feedline
and a good ATU would take care of the problem. Because of the
high reactance-to-resistance ratio, one might have to carefully
select the line length in order to present the ATU with a load it can
Chapter 62
handle most efficiently. Nonetheless, no other adjustments are

necessary, a plus for the double-Yagi design.
Now why does the double-Yagi version work?
If you look at the current distribution along the EDZ, it consists of a

small central peak with outward dips. The outer 1/2 wavelength of
the EDZ wire on either side is a perfect dipole current distribution
pattern. Parasitical elements aligned with these peaks perform just
as they would with independent in-phase separate driven elements.
The 3-element double Yagi EDZ beam is actually a form of two in-
phase-fed side-by-side 3-element Yagis with ¼-wavelength tip-to-
tip spacing. And the performance is just about the same.
One question that often arises with EDZ beams is how do we get
rid of the ears in the pattern, those quartering side lobes. W1GQL,
David Billheimer, sent me a design that accomplishes just that--an
Chapter 62
ear-less EDZ beam. Figure W1GQL-1 shows the azimuth pattern of

this 20-meter 2-element wire beam.
Dave's technique is to create what looks to me like a "gull-wing"

design: the driven element is drawn in to midway between the 2
elements, while the parallel sections are drooped like a Vee. See
Figure W1GQL-2.
Chapter 62
Dave's 20-meter CW beam has a 50' maximum height. The

elements are about 5' apart. The two reflectors begin about 14.5'
apart and droop to the 33.6' level at a maximum width of 39.4' each
side of center. The driven element legs (beginning at center) move
outward and forward to a little over 8' each side of center and then
parallel the reflectors. (I have rounded the dimension numbers.)
Chapter 62
The natural feedpoint of this ear-less EDZ beam is about 60 ohms

resistive and -j1000 ohms reactive. Dave uses stub-tuning to match
50-ohm coax for his narrow-band CW needs. However, the pattern
of the beam holds up across 20-meters and can be fed with parallel
feedline and an ATU quite effectively.
I have added Dave's beam to demonstrate that we have not yet

exhausted all the possibilities with either EDZs or wire beams.
Among these notes and two articles, we have look at EDZs,
stacked EDZs, parasitical EDZs, bent EDZs, and phased EDZs. I
must be overlooking something. . .
Of course: co-linear EDZs, George Goldstone, W8AP, sent me

some correspondence he had with Hugo Romander, W2NB (W6CH
in the 1960s), and Henry Pollock, WB4HFL, sent me a copy of a
Ham Radio article by Alvan Mitchell, W6QVI. The article was an
update on Hugo's co-linear EDZ array, which the ARRL Antenna
Book of 1943 still carried. Since few folks have access to either
Hugo's 1938 article or the 1943 Antenna Book, let's take a look at
this version of the EDZ, outlined in the figure below.
Chapter 62
The antenna is given in terms of electrical degrees. The phasing

lines are shorted parallel-line stubs. Here are Hugo's 20 meter
dimensions and Alvin's 15 meter dimensions as samples:
dimensions are in feet.
Band A B C
14 43 53.5 11.5
21 27.5 35.5 7.7
The 15 meter version, which I modeled extensively, is 126' long,

about the length of a 75-meter dipole. So what do you get for all
that linear space on 15 meters?
You get almost precisely what Hugo predicted in 1938: about 7 dB

gain over a dipole similarly place in a bi-directional pattern that is
Chapter 62
very narrow: 16°-17° between -3 dB points to be as exact as my

model will permit. Modeled gain is about 14.3 dBi in a pattern like
this one:
The best points for installing the parallel line stubs in the 15-meter
model were actually 1.5' farther inboard than W6QVI suggests:
about 29' from the ends and 34' from the antenna center. 67°
proved the length required for maximum gain. The feedpoint
Chapter 62
impedance is about 170 - j740 ohms, requiring an ATU, stub

matching, or something similar.
As W2NB pointed out, careful aiming is required. (The EDZ beams

earlier noted had beamwidths between 32 and 38 degrees, while a
standard Yagi or quad has a beamwidth between 50 and 60
degrees, depending on the number of elements.) This is no
antenna for casual worldwide DXing. Rather, it is a serious point-to-
point antenna. Within that context, it is an antenna that proves that
narrow beamwidths are not impossible at HF. I have expensive
flashlights with wider beamwidths.
If you want a bi-directional antenna with a gain of about 18 dBi

each way, while retaining the narrow (16-17°) beamwidth, try
stacking two of these antennas at 5/8 wl separation. For the 15-
meter sample, that places the two at 50' and 79' respectively. The
feedpoint impedance, when fed in phase with 450-ohm line at the
midpoint between the two, is about 65 + j350 ohms. A pair of series
capacitors would cancel the reactance, providing a direct
connection to 70-75-ohm cable (through a choke balun).
Let's carry the experiment one step further. To each of the vertically
stacked EDZ arrays, one might arrange a series of 1/2 wl reflectors
to achieve some further forward gain and reduce the rear lobe.
Alternatively, one might place a second vertically stacked array 1/8
wl behind the original vertical stack. Then, feed the rear array with a
current magnitude and phase to maximize forward gain and front-
to-back ratio. At 21.2 MHz, the spacing would be just about 5.8'.
Chapter 62
With proper feeding of the rear elements, we might achieve an

azimuth pattern like this:
21 dBi forward gain, over 26 dB front-to-back ratio, and a 16-17°

beamwidth are figures that amateur radio operators rarely see from
antenna arrays whose bases are about 1 wl up and whose tops are
1.7 wl up. Of course, for most operations, such figures are contrary
Chapter 62
to what is need for effective ham operation, but they might be

useful for some specialized operations.
Antennas spaced 1/8 wl apart call for 135° phase differences in the
elements on the currents: this is the received wisdom.
Unfortunately, it is wrong. Dipoles with this spacing might call for
something close to this figure. However, for any two elements
spaced more than a small fraction of a wavelength but less than 1/4
wl, there will be for each spacing a relative current magnitude and
phase for the rear element that will yield maximum gain and
maximum front-to-back ratio. With real materials, these two maxima
may occur on very slightly different frequencies. For the array
shown here, the maxima occurred with the rear elements fed at
0.75 the forward element current at a phase angle of 142 degrees.
Slightly better performance might have been obtained if the upper
and lower phased pairs had been individually optimized.
It is unlikely that standard ZL Special techniques would achieve

perfect phasing. Instead, one should most likely use phasing
networks to establish the operating conditions. Since the arrays are
identical, one could use this method to flip the direction of the beam
electronically. "But in the end, this is all hypothetical, isn't it? No
one could or would build such an array." Given that all the
techniques needed are standard in the field, I am not so sure of
this. Some folks might engineer such an array just to say that they
have an array with 21 dBi forward gain and to listen to the long-path
echoes of their own signals. Hams have done far stranger things in
the history of the service. I wonder what might be heard if one of
these reversible arrays were aimed directly toward one of the poles.
Chapter 62
We are still far from done with the EDZ. I am looking forward to the
next step. These notes are simply the update so far. I'll add more
as soon as I learn more about this interesting antenna. If I read
enough old articles, I could learn more very shortly.
Chapter 62
Chapter 63: Feeding the EDZ
T
ypically, Extended Double Zepp (EDZ) users employ one of
two methods in feeding this highly capacitively reactive 1.25
wl long antenna. Some users, especially those who employ
the antenna as a simple center-fed long wire on bands other than
the design band, simply use parallel feedline and an ATU. Others,
with single-band use in mind, use a matching stub arrangement to
find a 50-ohm point for a coax feedline. Of course, one can also
place a split coil at the feedpoint to provide the inductive reactance
necessary to cancel out the antenna's inherent capacitive
reactance, although the resulting resistive impedance will still be
100 ohms or greater.
In the Summer, 1997, issue of Communications Quarterly, Rick

Littlefield, K1BQT, presents a 2-meter EDZ that bears close
examination. Besides an interesting construction method, designed
to make a very durable EDZ for vertical use in hearing 2-meter
repeaters, the key unique feature of Rick's design is the match and
feed system that eliminates the usual center inductor to cancel out
the heavy capacitive reactance at the feedpoint.
An EDZ at almost any frequency has a variable feedpoint

impedance and capacitive reactance, depending on the exact
length to which it is cut. However, without altering performance by
more than a tenth or so of dB gain, one can cut the antenna for a
feedpoint impedance in the 100-140 ohm resistive range, which
gives a capacitive reactance in the 500-600 ohm range.
Chapter 63
Rick applied a technique used with 5/8 wl vertical gap antennas:

instead of an inductor, he uses a length of coax about 10.875" long,
with a rod element beyond that point. Let's think of a 5/8 wl vertical
and then simply place 2 of them feedpoint to feedpoint to get the
final EDZ. The feed goes to the center conductor of the coax
length. At the feed end, the braid is not connected to anything. At
the far end, the center conductor and the braid are connected
together and this junction goes to the 38" rod element. Rick calls
this a delay line.
When two of these assemblies are put end to end, the coax center
conductors are the two terminals making up the feedpoint. The
braid ends are about an inch or two apart (and must NOT be
connected together). The result is a nearly purely resistive
feedpoint impedance of 100 ohms in the 2-meter model. Rick uses
a 75-ohm 1/4 wl (+ 1/2 wl added) to make a combination matching
section and balun for a 50-ohm coax feedline.
The delay line is interesting, because the name does not describe
its function. Actually, it is a simple shorted feedline stub providing
the inductive reactance necessary to cancel the antenna's
capacitive reactance. Let's look at the figure to see the evolution of
the arrangement.
Chapter 63
Part A shows the conventional split coil arrangement so familiar to

EDZ builders (who do not use either open feedline to an ATU or a
stub tuning method for a 50-ohm match). Part B replaces the
inductors with a pair of shorted feedline stubs calculated to provide
the same inductive reactance as the coil sections. Note that I have
designated the outer part of the antenna line as "a" and the inner
part as "b" in the sketch. When I substituted the parallel feedline, I
designated on side of it as "c." "C" is as long as "b".
Chapter 63
There is no rule that says you cannot sometimes make a wire do

double duty. There is no incompatibility between wire "c" and wire
length "b" so that we can combine them together as in Part C of the
sketch. And Part C is essentially the arrangement used in Rick's
coax "delay" line. Because the coax is now doing double duty, the
exact length may change from simple calculations for stubs, but it is
very close.
Although the final arrangement looks like a Tee match, it is not. The
center must have a gap, forming at best a split-T top. The open
ends of the non-feedpoint center are actually the ends of the
inductive stubs away from the feedpoint and thus must be kept
independent of each other by a gap.
The use of coax was possible in the original model, because the
resistive portion of the feedpoint impedance was near 50 ohms on
each side of center (for the 100-ohm total). Hence, the use of 50-
ohm coax did not alter the feedpoint impedance.
If we use feedlines of higher impedance, two things will happen.

First, the feedpoint impedance will be reduced. Second, the length
of the stub will increase, placing the junction of "c-b" and "a" farther
outward on each side of center. The next figure is a sketch of a
model I developed while exploring this subject.
Chapter 63
To create as reliable a NEC model as possible, I used 0.125"

diameter aluminum for all parts. This kept the diameter constant,
thus allowing a greater reliability of the result with NEC-4. I
modeled the parallel lines 1" apart, give about a 330-ohm
characteristic impedance for the resultant line. With a connection
point about 14.5" outward from center and a 2" gap between the
open ends, the stub/line or split-T match provides about 54 ohms
resistive impedance and no reactance at the feedpoint. Hence,
direct 50-ohm coax feed is now possible.
The revised feed provides both capacitive reactance cancellation

and resistive impedance transformation together. The length of the
section is about the same as the combination of a 330-ohm shorted
stub plus a length of the same line necessary to transform the
overall impedance to nearly 50 ohms on its own, although treating
this way of looking at the sections as a correct analysis of actions
and interactions involved is far from certain at this point.
Chapter 63
However, the model's parallel feedline section is close enough to

300 ohms to suggest that experiments may be useful with twinlead,
taking into account the line's velocity factor of 0.8, of course. The
technique may also be applicable using 450-ohm window line or
600 ohm ladder line, experimentally finding the correct length to
use. And the technique is likely applicable at all HF and VHF
frequencies at which EDZs are in use.
One advantage of the technique is that it is fairly broad-banded,

giving full 2-meter coverage either in Rick's coax version or in the
modified parallel line version shown here. I have not explored the
consequences of this feed for use of the EDZ as a simple long wire
on other HF bands--yet.
Henry Pollock, WB4HFL, took up the challenge of creating a #14

copper wire HF version of the impedance transformation "delay"
line EDZ. His initial version was 42' long with 450-ohm match lines
either side of center, each 66.5" long. The antenna resonated at
28.9 MHz on this first try. Modeling the exercise suggested that
lengthening the antenna a bit (to 44.7') and shortening the match
sections to about 65.5" (adjusted after physical modeling for
velocity factor) would likely bring the antenna closer to a 28.5 MHz
target. The 2:1 SWR bandwidth of the model appears to be about
600 kHz, although the use of a coax feeder will likely widen the
bandwidth operationally at the shack end of the line. These figures
are not unlike the bandwidth numbers for stub-tuned versions of the
EDZ.
Chapter 63
As a general rule, lengthening the antenna wire tends to reduce the

resistive component of the feedpoint impedance, while lengthening
and shortening the match section changes the reactance without
affecting the resistance much. In general, it appears that the higher
the characteristic impedance of the feedline used to effect the
impedance transformation, the narrower the 2:1 SWR bandwidth of
the antenna.
So here is one more experimental way to feed an EDZ. The K1BQT

and WB4HFL experimental antennas prove that the principle works,
yielding an EDZ with no need for stubs or ATUs: matching is built
into the antenna structure itself. Have fun creating some interesting
prototype EDZs for 50-ohm feeds.
Chapter 63
Chapter 64: NVIS: Some Background
Near-Vertical Incidence Skywave or NVIS propagations has proven

useful, if not vital, to radio communications since at least the World
st
War II era in the 1940s. The mode has reemerged in the 21
century as a focal point of research and practical field
communications. The military, especially, has made it an essential
part of its overall message-handling system. In the civilian arena,
the mode has become a significant part of emergency plans.
Amateur use of NVIS propagation has grown almost exponentially

over the last decade. Some amateurs use the mode for close in
communications on 75 and 40 meters, with some work on the 60-
meter channels and some activity on 160 meters. Hurricane Katrina
proved the importance of NVIS communications when all terrestrial
landline, cellular, and VHF modes fell to the fury of the storm.
This overall collection of notes concerns the evaluation of amateur

radio antennas for NVIS operation. The first section provides
background on a number of matters that we must understand if we
are to choose the correct antenna for NVIS work. In our initial
discussions, we shall confine ourselves to antennas for the
amateur bands that use NVIS and to fixed or base station
permanent or long-term installations. Our goal for such antennas is
not merely borderline success, but instead, optimal antenna
installations that maximize the chances of successful
communications.
Chapter 64
Our first step will be to look at the ionospheric mechanisms that

allow and define NVIS communications, and we shall integrate
them with the typical NVIS operational situation. Together, these
factors tell us what basic properties an “ideal” NVIS antenna should
have in order to be effective. Although we shall not perform any
evaluations of real antennas until the next episode, we can set up
the conventions used to describe NVIS antenna performance,
along with some good reasons to depart from the sorts of
descriptions we might use with long-distance antennas. The final
step in our preliminary notes will be to examine our primary tool for
antenna analysis: antenna-modeling software. We shall see why
only some of the available software is suitable for working with
NVIS antennas.
NVIS Propagation and Situations

Apart from ground-wave signals, virtually all upper MF and HF
communications occurs as a result of refracting radio waves
through various layers of the ionosphere. The F-layers are the
most important ones, although in a negative way, the D-layer also
has significance. We identify layers mostly by reference to their
height above ground. The D-layer is relatively low, while the F-
layers are much higher—in the vicinity of 250 miles above the
earth. We used to think that we needed very low angles of
incidence between the F-layers and radio signals to effect
communications of any strength. However, we later discovered that
we obtained returns from signals transmitted directly upward.
Initially used for radiosonde work, the realities of battlefield
situations showed that we could transfer information by this mode
of operation.
Chapter 64
Ionized layers of the rarified upper atmosphere form under the

influence of ultra-violet radiation from the sun. Some layers exist
only when there is direct sunlight (the D-layer, for instance), while
others persist after dark, although they may change some of their
properties between daylight and nighttime hours. Fig. 1 shows the
day and night propagation situation as it directly applies to NVIS
communications.
Each panel shows nearly vertical radiation from (and to) an

arbitrary antenna. In daylight hours, the D-layer forms and absorbs
radiation in the upper MF range and even in the lower HF range.
Therefore, virtually all skip or ionospheric communications
disappears from the 80-75meter band in daylight. However, 40-
meter communication is generally possible via refractions from the
Chapter 64
F2-layer (and occasionally from the F1-layer, although it is usually

too weak to sustain good signal returns). After sundown, the D-
layer dissipates and the two F-layers usually coalesce into a single
layer that is weaker than in daylight hours. The single F-layer is
capable of supporting effective communications, especially on 75
meters, with some work on 160 meters.
The sketches are not to scale, as suggested by the average range

of NVIS communications compared to ionospheric layer height. In
general, the NVIS range is about 200 miles from a reference
station, with possible communications up to about 300 miles. The
exact distance on any day depends on numerous factors. The
quality of the station equipment (at both ends of the path) is critical.
As well, the antenna installation design (our key interest in these
notes) is a second contributor to success or failure. Although we
can control these first two factors within the limits of the state of the
art of radio, the third factor lies outside our control: the variables
associated with the existence, strength, and height of the ionized
atmospheric layers that make communications possible. These
factors, as already noted, vary daily. They also vary seasonally,
both in obvious ways (such as the relative length of daylight and
nighttime) and in less obvious ways that stem from the changing
angle of our station locations to the sun. Nevertheless, on most
days and nights, we can achieve successful NVIS communications
on one or another amateur band. Indeed, despite the severe power
restrictions attached to the amateur channel allocations on 60
meters, the band is finding some good use during the twilight or
transition hours between true daytime and true nighttime
operations.
Chapter 64
The importance of the NVIS mode of operation shows up clearly in

Fig. 2, which portrays in very general terms the NVIS situation. For
many practical—sometime vital—reasons, we need to
communicate over a range that exceeds VHF and UHF line-of-sight
abilities. However, the range is far shorter than we normally
associate with HF skip transmissions. As well, the terrain may
contain obstructions to ground-wave communications of any sort.
The NVIS communications mode allows us to leap tall mountains in

a single bound, if we choose the correct frequency and if the
ionosphere cooperates. Military applications are instantly clear. In
fact, military research into NVIS operations is pressing the
frequency limits of the mode, with investigations spreading from just
above the AM BC band up to 12 to 14 MHz. Amateur applications
generally focus on 75 and 40 meters, with SSB the primary method
of encapsulating intelligence. However, as emergency service
efforts expand, we shall find increasing use of digital message
transfers and a host of other forward-looking methods.
Chapter 64
The figure also hides an important facet of NVIS communications

for our work. We shall focus initially on the antennas for the central
station and presume that we have no major constraints for their
installation. We shall treat the central station as having relatively
unlimited power and resources with a location outside the troubles
that may beset field locations. In contrast, field locations may lie
within highly troubled areas—in military terms, a battlefield, and in
civilian terms, a disaster area. In both cases, the field station may
have limited transmitting power, limited receiving sensitivity, and
somewhat primitive antennas. The field antennas may include
bent-over whips, hastily erected dipoles using very low supports,
and similar inefficient radiators (and receivers) of RF energy. As a
consequence, a fixed position central station antenna should be—
within the limits of the installation site—as efficient and effective as
possible. Anything less places additional strains upon the field
station, which is by definition operating under highly taxing
situational stresses.
Having noted the importance of optimizing the central station

antenna to the degree possible, we must also recognize that few
amateur installation sites have unlimited space or other resources
to erect a seemingly perfect NVIS antenna. The analysis of various
antenna options for various relevant bands may help in the
selection of the antenna design to implement on a given site, but
the discussion will not create any automatic decisions. (The
discussion will also help dispel some older misguided rules of
thumb that some amateurs misapply to their NVIS antennas,
thinking them to be optimal when they are not.) Equally critical to
antenna decision-making is the overall mission of the NVIS station.
Chapter 64
Some stations devote their activity solely to NVIS communications.

Others may have both short and medium range communications
goals and require a compromise antenna system that allows both
types of operation, even if neither is truly optimal.
In the field of antennas for NVIS service, there are many options.
Fortunately, most of them involve rather basic antenna designs.
Antenna Analysis Conventions Used in These Notes
The analysis of NVIS antenna candidates requires that we alter

some of the conventions that we use to portray information
applicable to low-angle long-distance antennas. Most often, we
show both the elevation and azimuth patterns of the subject
antenna, especially for directional and bi-directional arrays. When
our main radiation focus is straight upward, we need to change our
perspective on the antenna. Fig. 3 provides a guide to the
conventions that we shall employ in these notes.
Chapter 64
On the left, we find a 3-dimensional radiation pattern for a simple

NVIS antenna. The strongest radiation is upward at the zenith
angle. Although the pattern is horizontally very round, it is not a
perfect circle. On the right, we find a portrayal of the antenna with
two nearly circular black outlines. One outline is broadside to the
antenna wire—a simple dipole. The other circle aligns with the wire
ends. (Virtually every NVIS antenna has a definable broadside and
endwise pair of directions, even closed horizontal loops.) In the
center of the sketch we find two elevation patterns, one broadside
to the loop and the other endwise. We shall use these patterns—at
right angles to each other—to characterize the far-field radiation
patterns of all of the NVIS antennas that we consider.
In each elevation pattern we find a central line defining the direction

of strongest radiation. Very often, the line may be a few (2-4)
degrees off the zenith angle (90°) because in a given plane, the
region of maximum gain is quite wide. We also find a pair of lines
angularly equidistant from the maximum gain line. These lines
define the half-power points along the pattern; the points at which
gain is 3-dB lower than maximum gain. The angular distance
between these lines is the conventional beamwidth of the antenna
in each direction. We may define the circularity of the pattern by
taking the ratio of the broadside beamwidth to the endwise
beamwidth (in that order). Almost all patterns will show a larger
beamwidth in the broadside orientation than in the endwise
direction. Hence, most (but not absolutely all) antennas will have
ratios greater than 1:1, the value for a perfectly circular pattern.
Chapter 64
The beamwidth information will be as important to some

installations as the maximum gain value associated with a given
antenna. Since the beamwidth of the sample dipole is wider in the
broadside direction than endwise, if a station has medium-range
duties in addition to NVIS functions, orienting the wire broadside
to the medium-range targets may increase communications
reliability.
The analysis will

bypass the azimuth
patterns that we
associate with long-
range, low-angle
radiation from the
usual set of amateur
antennas. Fig. 4
shows part of the
reason why we do
not use azimuth
patterns. The same sample dipole used to produce the elevation
patterns in Fig. 3 yields the set of azimuth patterns, which vary in
shape according to the elevation angle at which we take the
pattern. The patterns seem to change shape as we raise the
elevation angle, starting at 30° as a sharp oval, but becoming a
circle at the zenith angle. The patterns show very little relationship
to the 3-dimensional pattern that we viewed in conjunction with the
elevation patterns.
Chapter 64
Part of illusion fostered by the azimuth patterns arises from a

systematic error that attaches to azimuth patterns as we raise the
elevation angle at which we take the pattern. The higher the
elevation angle for a given azimuth pattern, the greater the error
that we find in the beamwidth of the azimuth pattern. The error is a
function of the fact that the azimuth pattern actually forms a conical
section that we then flatten into a planar azimuth pattern. At low
elevation angles, the error is not sufficient to void the reported
beamwidth (whether as a numerical value or as a visual
impression).
Chapter 64
As we raise the elevation angle, the error becomes very significant.

Fig. 5 shows a sample of the error. The views show only a single
lobe, since the sketch slices the cone in half, eliminating one of the
lobes. The flat azimuth pattern on the right shows and reports a
wider beam angle than we find on the left. The differential
increases as we increase the elevation angle at which we take the
azimuth pattern. Let’s let BWa be the actual horizontal beamwidth
on the conical section, BWr be the NEC report of the beamwidth,
while the indicated angles are the elevation or theta angle at which
we take the phi/azimuth pattern. (Some NEC software employs the
original notation of theta angles that count from the zenith angle
downward, while most NEC implementations convert those angles
to more familiar elevation angles from the horizon upward.
Elevation + theta = 90°.) To correct the reported beamwidth we
may perform a simple calculation.
BWa = BWr cos(elevation) or BWa = BWr sin(theta)
For example, at an elevation angle of 45°, we might have a

reported horizontal beamwidth of 27.8 degrees. The cosine of 45°
is 0.707. Multiplied times the reported horizontal beamwidth, we
obtain 19.7° actual beamwidth. The 10° difference is significant.
The cosine of an elevation angle of 60° (theta angle 30°) is 0.5,
resulting in a more nearly correct beamwidth that is half the value
reported on the azimuth pattern. (The correction is only
approximate, since the cone itself is a curved surface.)
For low-angle azimuth patterns, the correction is not significant.

For example, at an elevation angle of 20°, the cosine of the
Chapter 64
elevation angle is about 0.94, resulting in only a very slight change

in the reported beamwidth. The importance of the required
correction emerges at high elevation angles, typical of those we
might use to try to portray a NVIS pattern in azimuth form. For
general analysis of NVIS antennas, using a pair of elevation
patterns is far more revealing of the antenna’s far-field radiation
pattern.
Modeling and Evaluating NVIS Antennas
The broadside pattern of a proposed NVIS antenna is often a

key element in its evaluation. For virtually all NVIS antennas, free-
space patterns that emerge from models or basic antenna theory
have little or no bearing on the antenna’s NVIS performance.
Instead, the critical factors that create the far-field pattern are the
antenna geometry, the height above ground, and the soil quality in
the region of the antenna.
Antenna geometry is an obvious factor, since we do not expect

a closed 1-λ loop to perform identically to a linear dipole or to an
inverted-V dipole. Other antenna possibilities will each show
performance differences from these three most basic forms in part
due to their particular geometric features, that is, their shape
overall and their shape relative to the position of the feedpoint in
the assembly. Indeed, we may even press certain forms of beam
antennas into NVIS service, not so much to create a clearly
definable forward lobe as to tilt the upward NVIS pattern in a
desired direction.
Chapter 64
In the course of evaluating various candidates for NVIS service, we

shall also discover that the proximity of the antenna to the ground
magnifies the influence of the ground quality on various aspects of
performance. The difference that ground quality makes will show
up both in the maximum gain attainable from a given type of
antenna and in the height above ground at which we attain the
maximum gain. Moreover, when we supplement an active NVIS
antenna element with additional structures in the form of
reflectors—either as a single wire or as a ground screen—the
degree of additional gain that we may obtain from the supplement
will vary with the quality of the ground below the antenna and in the
region surrounding the antenna. As is the case with all antennas,
the far-field forms as a consequence not only of the ground
immediately beneath the element, but as well at considerable
distances from the antenna, where downward radiation intersects
the ground and is reflected upward to combine with the upward
incident radiation from the element.
The height above ground for a NVIS antenna is perhaps the key
ingredient to the formation of the basic far-field or radiation pattern.
Sometimes, individual elevation patterns (in this case, broadside
patterns) can be misleading, as is the case with the patterns on the
left in Fig. 6. The upper pattern, with the antenna 0.4-λ above
average ground, is clearly less than optimal for NVIS work. The
pattern shows a distinct null at the zenith angle.
Chapter 64
Lowering the antenna to 0.25-λ above the same quality of ground

produces a pattern without the distinct null, but the two maximum-
gain lines indicating at least a small reduction in gain at the zenith
angle. Further reduction of the height to 0.1-λ, still above average
ground, produces a pattern that is similar to the one shown in Fig.
3. To resolve any question about which pattern of the three is best
for NVIS operation in the absence of tabular data, we may simply
overlay the elevation plots. The right side of the figure shows the
result. The pattern for the highest antenna level shows the highest
maximum gain, but at angles that clearly depart from the desired
zenith angle. The nearly circular pattern at a height of 0.1-λ shows
deficiencies in gain compared to the seemingly less perfect pattern
Chapter 64
for the antenna at 0.25-λ. The mid-level antenna placement not

only yields more NVIS or zenith gain, but as well has (in the
broadside direction) a wider beamwidth that might also serve for at
least some medium-range communications needs.
Evaluation of NVIS antenna candidates requires close attention to

the maximum gain, both overall and in the zenith direction, as well
as to broadside and endwise beamwidth values. Because virtually
all NVIS antennas will require heights that are less than ¼-λ above
ground for some or all of their horizontal structures, we are limited
in the computer-based antenna modeling tools that will produce
reasonable accurate views of performance potential. The key
limiting factor is not the basic core itself (NEC-2, NEC-4, or
MININEC).
Chapter 64
The chief limiting factor is the ground calculation system. Only the
Sommerfeld-Norton (SN) calculation system has sufficient accuracy
to provide usable data on horizontal antennas closer than about
0.2-λ above ground. The SN system is a part of both the NEC-2
and NEC-4 calculating cores. One implementation of MININEC
called Antenna Model has successfully grafted the SN system to its
core. NEC contains an alternative ground calculation system that
uses a Reflection Coefficient Approximation (RCA). The simplified
calculations originally allowed faster core runs in the days of slow-
speed personal and mainframe computers, but the results grow
more inaccurate as any horizontal wire approaches ground level.
Even less accurate is the ground calculation system that is part of
the public domain version of MININEC (abbreviated here as a
ground calculation system as MIN). In fact, the MIN system
produces only feedpoint impedance values for perfect ground and
not for the soil quality specified for the far-field pattern.
To illustrate the differences in the ground calculation systems, I

used identical dipoles at identical heights above average ground to
derive results for each of the ground calculation systems. Table 1
lists the outcome of the exercise, which ran the dipole in 0.05-λ
increments from a maximum height of 0.4-λ down to ground level
(simulated by a height of 0.001-λ). The table lists the height in feet
for each level as well as the height in wavelengths.
Chapter 64
For each antenna height, the table reports the maximum gain and
the TO (take-off) angle (the elevation angle of maximum gain) in
degrees elevation. In some cases, the angle is close to but not
exactly the zenith angle, because there is a range of elevation
angles over which the gain does not change. The dipole is
resonant in NEC-4 at 0.4-λ above ground and does not change its
dimension as the height decreases. Therefore, the columns
labeled R and X show the feedpoint resistance and reactance that
results from using the unadjusted dipole.
For ease of seeing the differences, Fig. 7 plots the maximum

gain values of the dipole at each height using each of the three
ground calculating systems. The SN and RCA systems show
good coincidence down to a height of about 0.2-λ, below which
we find a systematic departure. The RCA system somewhat
overestimates the maximum gain as the antenna approaches
ground level.
Chapter 64
The MIN system begins to show a departure from the baseline SN

system values at about 0.25-λ above average ground. One of the
shortcomings of the MIN system, made publicly available in the
1990s in QST by Roy Lewallen, W7EL, the developer of ELNEC
and EZNEC, is the radical overestimation of gain by the MIN
ground calculation system for antenna at or below 0.2-λ above
ground. The system provides wholly unreliable gain values for
horizontal antennas close to ground. It is responsible for many
misestimates of gain for 1990s 160-meter and 80meter antennas.
As well, the MIN system, when only it was available to PC users,
created misimpressions about very low-height NVIS antennas.
Chapter 64
Chapter 64
Fig. 8 shows the feedpoint resistance values reported under all

three ground systems. At lower heights, the RCA system reports
values below those reported with the SN system. More radically
different are the values reported by the MIN system. The
excessively low feedpoint resistance values accompany the
excessively high gain values that the system produces for heights
below about 0.25-λ for antennas with any degree of horizontal
component to the radiation pattern.
The end result is that we must set aside virtually all old reports
on the performance of antennas installed at NVIS heights. In
fact, we must begin again with an evaluation of basic antennas
using only antenna modeling software with the SN ground. In
fact, these notes will employs NEC-4 throughout, with the SN
ground calculation system implemented. Equally important to
our effort will be a systematic exploration of basic antennas
using a variety of ground quality conditions.
The following soil descriptions are commonly used in antenna

modeling. Always substitute more precise values wherever known.
The table represents an adaptation of values found in The ARRL
Antenna Book (p. 3-6), which are themselves an adaptation of the
table presented by Terman in Radio Engineer's Handbook (p. 709),
taken from "Standards of Good Engineering Practice Concerning
Standard Broadcast Stations," Federal Register (July 8, 1939), p.
2862. Terman's value for the conductivity of the worst soil listed is
an order of magnitude lower than the value shown here.
Chapter 64
For our work, we shall use Very Good and Very Poor soil as
extremes and Average soil as an intermediate value set between
the two. Between any two of the three value sets, you can
interpolate values close to reality.
NVIS antennas find applications under many circumstances for

which the standard soil categories do not apply. For example, we
find them in Antarctic regions placed over a mile or more of ice and
snow. Therefore, as a further reference, the following table of
values may have some useful data for special installations.
Chapter 64
We generally think of signals incurring greater losses as we reduce

the ground’s conductivity and permittivity. However, between the
worst dry-land soil (city industrial areas) and icy regions, we
discover an interesting phenomenon. With conductivity values
Chapter 64
below about 1e10-4 and permittivity values that drop close to the
minimum value of 1 (the value of a vacuum), the region beneath the
antenna begins to act more like a free-space environment than like
what we think of as earth. The effect has interesting consequences
for practical antenna operation.
The next step is to review some very fundamental antenna types:

the linear dipole, the V dipole (with a droop or slope of 30° from the
horizontal or a 120° included angle between legs, and the 1-λ
closed loop. These three types of antennas are perhaps the
backbone of fixed station NVIS work. We shall look at all three
antennas in versions for 160 meters (1.85 MHz), 75 meters (3.9
MHz), and 40 meters (7.2 MHz). We shall try each antenna over
each type of soil, seeking the best zenith-angle gain, but with an
eye toward ensuring that we have an acceptable NVIS pattern
throughout.
Although incidental to our work, you may wonder why I speak of “a

NVIS antenna,” rather than “an NVIS antenna.” The acronym
“NVIS” (at least where I come from) has acquired the pronunciation
[nee’-vis], hence the article “a.” If you prefer to say [en vee eye
ess], you may substitute the “an” at every suitable place.
Chapter 64
Chapter 65: NVIS Some Basic Antennas Used
T
he most fundamental NVIS antennas for fixed station
operations are the linear dipole, the inverted-V dipole, and
the 1-λ closed loop. Each has its own set of mechanical
advantages and disadvantages in terms of the complexity of
installation. Despite the very commonness of these antennas, their
properties when installed at heights appropriate to NVIS operations
remain somewhat murky to many radio amateurs. Advice ranges
from the idea of placing the antenna as close to the ground as
possible to placing it as high as may be feasible.
There is a range of heights that optimizes the performance of each

of these basic antennas in the zenith direction, that is, straight
upward. The idea of straight upward in this context means a cone
of radiation offset from the true zenith by enough to allow contact
with stations up to 200 to 300 miles away. All HF antennas have
rather broad patterns in this regard, so using the concept of zenith
gain will capture the properties of the antenna within the required
cone.
In this set of notes, we shall use the antennas alone, without

supplementary wires or ground improvement screens. Our goal is
to find out what we may obtain from the antenna relative to its
height and the quality of the ground beneath it. Performance
supplements will arise in later sets of notes. Our working tool will be
NEC-4 with the SN ground calculation system. We shall examine
each antenna over three of the soil quality values from standard
charts. At the extremes are very good soil (conductivity 0.0303 S/m,
Chapter 65
permittivity 20) and very poor soil (conductivity 0.001 S/m,

permittivity 5), while the middle ground will be average soil
(conductivity 0.005 S/m, permittivity 13). As well, we shall explore
each antenna on three bands: 40 meters (7.2 MHz), 75 meters (3.9
MHZ), and 160 meters (1.85 MHz) to uncover any possible
differences in performance for equivalent heights above ground (as
measured for each antenna in fractions of a wavelength). The
results will create a considerable body of data and some fairly
definite conclusions.
The Linear Dipole
Of all NVIS antennas, the linear dipole is the most basic. Fig. 1
outlines the dipole and the critical properties necessary to examine
its performance at possible eights above ground. We shall start with
a 40-meter dipole and then proceed to lower frequencies. We shall
evaluate each dipole at heights from 0.075-λ up to 0.255-λ in 0.01-λ
increments.
Chapter 65
The 40-meter dipole is cut for near resonance at 7.2 MHz at a

height of about 0.175-λ above average ground. The length remains
constant for all tests: 0.4806-λ using AWG #14 copper wire. (The
length of dipoles for the lower bands will be the same. On 75
meters, we shall also use AWG #14 wire, but for 160 meters, we
shall increase the diameter to AWG #12 wire.)
The basic data collected for the 40-meter dipole appears in Table
1. The table has separate sections for each soil quality. The left-
most columns list the antenna height in wavelengths and in feet.
The uppermost height used is 0.255-λ, just over ¼-λ, which is only
about 35’ above ground. Hence, on 40, at most installation sites,
the antenna height falls wholly within the operator’s range of
choice. On lower bands, not all heights may be feasible.
The gain columns record zenith or straight-up gain on the left. The
maximum gain column only has entries where the value differs from
the zenith gain value. Both values are in dBi. The need for the
second column results from the standard evolution of the NVIS
pattern with increasing antenna height. Fig. 2 shows a sample set
of patterns for a 160-meter NVIS dipole at several heights above
very poor ground. Patterns for 75 and 40 meters and for other soil
qualities will be similar, although the final step of showing different
zenith and maximum gain values varies in height with different soil
qualities. As the antenna height increases, the broadside
beamwidth grows continuously, while the endwise beamwidth
varies by slightly.
Chapter 65
At a height near the upper limit of our sampling range, the elevation
pattern begins to split into broadside lobes, resulting in two
maximum gain directions with a slightly depressed zenith gain
value. The broadside elevation patterns and the 3-dimensional “top-
down” plots provide alternative views of the phenomenon. The
broadside axis line has a constant total length from the 3-D plot
Chapter 65
center to provide a visual estimate of the growth of the broadside

beamwidth with increasing dipole height.
The elevation plots contain lines showing the half-power or 3-dB

beamwidth in both the broadside and endwise directions relative to
the dipole. Table 1 and subsequent tables record these values as
BS BW and as EW BW. In addition, the tables contain a column
recording the ratio of the broadside to the endwise beamwidths as
a rough measure of the circularity of the pattern. A ratio of 1:1
would indicate a perfectly circular pattern. Values greater than 1:1
indicate an elongation of the pattern in the broadside direction. An
antenna builder may productively use this information if the antenna
requires an orientation favoring certain directions—and if there is
available space to satisfy this need.
The final columns of the table list the feedpoint resistance and
reactance at each height. Horizontal antennas close to ground
undergo considerable swings of feedpoint impedance values, a fact
recorded by the data in the tables. As we change the quality of the
ground beneath the antenna, we also encounter some interesting
variations in feedpoint impedance values for each height in the
survey.
Chapter 65
Because the tables do not allow rapid scanning of certain critical

information, I have graphed two significant data items. Fig. 3 shows
the zenith gain values for the entire span of heights, with separate
lines for each soil quality. The fact that better soil quality yields
higher gain is self-evident. As well, it is also clear that as we reduce
the soil quality, we also increase the optimal height range for
maximum gain from the dipole.
Chapter 65
Chapter 65
On 40 meters, the maximum zenith gain occurs at heights between

0.165-λ and 0.175-λ over very good soil. Reducing the soil quality
to average raises the maximum gain height to about 0.195-λ. A
further reduction in soil quality to the very poor level results in a
maximum gain height of about 0.205-λ. As the graph lines in Fig. 3
show, the gain goes not change very rapidly near the optimal
height. For practical purposes, there is a window of heights perhaps
0.04-λ wide in which the gain changes over an operationally
undetectable range (including changes in the broadside
beamwidth). This range amounts to a spread of about 5.5’ of height
on 40 meters or +/-3’ or so relative to the optimal height for
maximum gain. If one does not know the local ground quality,
placing the antenna at the optimal height for average ground will let
it fall close to the best height for other soil values.
The differences in ground quality values from very good to very

poor not only affects the peak-gain antenna height, but also have
perhaps even more profound effects on the feedpoint impedance.
Fig. 4 graphs the feedpoint resistance values of the dipole across
the range of heights, with separate lines for each ground quality
surveyed. At very low heights, the resistance values very widely for
the different soils. They gradually converge so that at a height of
0.205-λ, they meete, only to separate again above that height. The
convergence height coincides with the maximum gain height for
very poor soil. In general, selecting an antenna height that is near
the level for best gain will yield an impedance value over any soil
that will produce few, if any, surprises when it comes to matching
the antenna to the feedline. The convergence resistance is close to
75 Ω, with up to about +/-j10 Ω reactance.
Chapter 65
The table reveals another facet of NVIS dipole behavior worth

noting. If we decrease soil quality levels for any given height near
the optimal range, the beamwidth ratio systematically increases. As
the soil quality grows worse, the broadside beamwidth increases
more rapidly relative to the slowly changing endwise beamwidth. At
a height of 0.195-λ, for example, the broadside beamwidth changes
by about 14° across the rage of soils. In other terms, each half-
power point is about 7° lower over very poor soil than over very
good soil. Since antenna gain drops very rapidly beyond the half-
power points, the difference may make a difference in the
Chapter 65
performance of antennas designed for both NVIS and medium-

range communications. In such cases, one may wish to place a 40-
meter NVIS dipole above rather than below the maximum gain
height with average or better soils. However, the height should in all
cases be below the level at which the zenith gain suffers
significantly.
On 75 meters, if we continue to count height in increments that are

a fraction of a wavelength, we may not have the option of placing
an antenna above the maximum gain height. Indeed, many sites
will have difficulty raising the antenna to its best-gain height. Still,
the behavior of the dipole on 75 meters over the same three soil
qualities differs enough from the 40-meter properties to warrant a
separate table and graph set. Table 2 provides the parallel set of
data to the 40-meter information in Table 1. Fig. 5 graphs the
zenith gain across the span of heights, which are, in feet, almost
double those on 40 meters. At first glance, the graph lines appear
to be the same as those for 40, but there are some interesting
differences in the 75meter set. Most significantly, the maximum
gain values occur at lower heights: 0.165-λ for very good soil,
0.185-λ for average soil, and between 0.195-λ and 0.205λ for very
poor soil. Although the individual changes from 40 meters are small
(about 1% of a wavelength), they indicate a trend that we should
anticipate to continue when we examine 160-meter dipoles. In
addition, the peak zenith gain values that we may obtain on 75
meters are all higher than those we can obtain on 40 meters. For
horizontal antennas over ground, especially at the low NVIS
heights, the ground absorption increases with rising frequency for
any given soil quality. We normally notice this effect only in lower
Chapter 65
HF surface-wave communications, but the phenomenon also

affects the maximum obtainable NVIS gain.
Chapter 65
Chapter 65
Apart from the difference in maximum possible gain from an un-

supplemented dipole and the modeled height of occurrence,
virtually every other comment on the 40-meter dipole applies
equally to the 75-meter dipole. Heights in the range of 40’ (for very
good soil) up to about 50’ (for very poor soil) yield maximum gain. If
we select an arbitrary but common amateur dipole height of 35’
above ground, then the gain deficit relative to maximum possible
gain varies with the soil quality. It ranges from about 0.1 dB over
very good soil to more than 0.6 dB over very poor soil. At 75
meters, the maximum value of the beamwidth ratio also decreases
slightly relative to the values at 40 meters.
Chapter 65
The feedpoint resistance curves for 75 meters, shown in Fig. 6,

resemble those in Fig. 4 with a small but significant difference. The
convergence region is slightly higher on 75 meters: between
antenna heights of 0.205-λ and 0.215-λ. Since the optimal gain
region shows lower heights on 75 meters, we can expect a wider
variation in the feedpoint impedance values as we move from very
good to very poor soil. In fact, if we return to the arbitrary but
common amateur dipole height of 35’ above ground, the impedance
range runs from close to 50 ° over the worst soil to nearly 70 Ω over
the best.
The trends that we have noted relative to the 40-meter and 75-
meter dipoles continue unabated when we examine a 160-meter
dipole (set for 1.85 MHz in this sample). If the patterns hold true,
we should expect higher maximum gain values, lower optimal gain
heights (in wavelengths), lower maximum beamwidth ratio values,
and a greater height of feedpoint resistance convergence. Table 3
provides the numerical data to confirm each of these trends, while
Fig. 7 and Fig. 8 supply visual references for the gain and
feedpoint resistance curves. Indeed, with only a few exceptions, we
may bypass extensive commentary on the 160-meter dipole’s
behavior, although we can hardly avoid a note on the usual
amateur 160-meter horizontal antenna installation.
Chapter 65
Chapter 65
For the most typical amateur installations, a height of 35’ falls below
the lowest height in the survey. In fact, at 35’ above ground, a 160-
meter dipole will lose between 1.5 dB (over very good soil) to 2.8
dB over very poor soil relative to placing the antenna at an optimal
NVIS height. Since the gain of the antenna at 160 meters is higher
for a given height (in wavelengths) above any given soil quality, the
deficit is not quite as severe as the internal 160-meter numbers
suggest, but the installation at a low height has far less
performance potential than it might have. As well, at the low height,
Chapter 65
the feedpoint impedance may range from 25 Ω up to 50 Ω,

depending upon soil quality.
We may better gauge the relative gain for the three bands covered
by this survey by graphically sampling at least one set of antennas.
Fig. 9 compares the gain values over average ground for 160-, 75-,
and 40-meter dipoles across the surveyed heights as measured in
wavelengths. Just the change in operating frequency produces
nearly a full dB difference in maximum gain when we take the
values that coincide with the maximum zenith gain for each band.
Chapter 65
As we increase the height of the antenna above ground, the

differentials decrease, but remain notable even at a height greater
than ¼-λ above ground. Curves for other soil qualities will be
similar. The idea that ground quality has very little effect on
horizontal antenna performance may be true for antenna that are 1
λ up or higher, but in the range of NVIS heights in the upper MF
and lower HF region, horizontal antennas show considerable
effects from both height changes and from ground quality changes.
Chapter 65
We may summarize the findings—to a degree, at least—by

encapsulating some of the key data from the individual data tables
in a single place. Table 4 uses a cross-matrix of the 3 bands vs. the
soil quality levels. It lists the peak zenith gain for each band and the
height in wavelengths at which that gain occurs. In addition, it lists
the height in wavelengths at which the feedpoint resistance values
converge. Wherever individual values occur at two adjacent
heights, the table lists the average of the pair. Although highly
incomplete, the table provides at a glance a view of some of the
trends that we have noted along the way. It may also allow a fairly
quick interpolation of probable values for NVIS dipoles at other
frequencies, for example, 60 meters. It may also serve to make
comparisons easier with other antennas in our collection.
Chapter 65
The 1-λ Closed Loop
In basic antenna theory, the inverted-V is a dipole form and

perhaps ought to come next in our survey. However, the inverted-V
has some special limitations that divorce it from its close family ties
to the dipole. More akin to the dipole by virtue of using a level plane
for installation is the 1-λ closed loop. In these notes, we shall deal
only with a square loop, although we might in principle approximate
any polygon ranging from a triangle to an almost perfect circle.
Performance differences among the closed loops will be minimal.
As shown in Fig. 10, we may feed the square either at mid-side or

at a corner with no change in the loop dimensions, the feedpoint
Chapter 65
impedance, or the performance. Corner feeding may be more

convenient, since the post at that location can support the vertical
run of feedline. We define the broadside direction of the loop as
running between the feedpoint and a point directly opposite. The
endwise direction is at 90° to this line. For modeling convenience,
these notes use a mid-side feedpoint. The patterns do not differ
significantly from those produced by selecting the more convenient
corner feed position.
The 1-λ loop is subject to the same constraints as the dipole. The
height above ground and the quality of the ground both below the
antenna and in the region of far-field reflections largely determine
the pattern shape and strength. Mechanically, the side dimension of
the loop is about half that of a dipole, but the loop does require 4
support posts and occupies an area at the installation site. As well,
the loop feedpoint impedance is higher than the impedance of a
dipole, resulting in the need for a matching section if the main
feedline is a standard 50-Ω coaxial cable.
At 40 meters (7.2 MHz), total circumference of the 1-λ loop is

actually close to 1.03 λ at NVIS heights. Table 5 provides the
numerical data derived from surveying the loop over the same
height range as the dipole and over the three selected ground
qualities. The range of reactance variation may seem striking
compared to the values for the dipole. However, its affect upon the
SWR relative to resonance is about the same, given the ratio of
reactance to resistance at the feedpoint.
Chapter 65
The gain curves in Fig. 11 are very similar to those for the dipole,
with two major exceptions. First, the values at all heights are higher
for the loop. (Whether the added gain justifies the more complex
construction is a user judgment.) Second, the loop has a narrower
broadside beamwidth and a very slightly wider endwise beamwidth
at all heights. Hence, the column for maximum gain in the table is
blank, since the broadside beamwidth never reaches a value that
creates a dual line for the maximum gain direction. In essence, the
loop more closely approximates the circular pattern that represents
Chapter 65
the theoretical ideal (although that ideal may be less applicable to

given installations).
Chapter 65
If you compare Table 5 with Table 1, you will discover that the
maximum gain occurs at the same heights over each type of
ground quality for both loops and dipoles. As well, the feedpoint
resistance tends to converge in the same manner as we found for
the dipole, although the convergence is less complete in the case
of the loop. The loop’s convergence region is considerably wider as
a span of heights, so we may bypass a graph. However, the tabular
data will show the spread. Of special note are the beamwidth
numbers, especially the ratio of broadside to endwise beamwidth.
Note that the loop and the dipole both use the same wire: for 40
meters, AWG #14 copper wire.
In the case of the dipole, we found that as we lowered the operating

frequency from 40 meters to 75 meters, the maximum gain value
rose, while height of maximum gain decreased. These facts applied
to all three ground qualities. We encounter the same phenomena in
the case of the 75-meters 1-λ loop. The numbers appear in Table 6
(for comparison with the corresponding dipole values in Table 2).
Fig. 12 compares the loop gain values for the three qualities of
ground.
Chapter 65
As both the graphs and the tables make clear, the heights of
maximum gain on 75 meters are virtually identical for both the loop
and the dipole. Unlike either antenna at 40 meters, where we may
easily construct the antenna at the optimal height, on 75 meters, we
may need to be satisfied with a slightly lesser height. The loop is
like the dipole in the fact that gain does not fall off sharply over any
of the soil types as we lower the antenna by modest amounts.
However, the effect may be more noticeable over the worst soils
where the maximum gain height in wavelengths is greatest, while
the antenna construction project may have a strict physical limit.
Chapter 65
For example, compare the gain values at 35’ (about 0.14-λ) with the
maximum gain possible for each of the individual ground quality
values.
Chapter 65
The 75-meter loop continues the trends that we encountered with

the 40-meter loop. The broadside beamwidth never reaches a
value that creates a difference between the antenna’s maximum
gain and the zenith gain. (The exact broadside beamwidth at which
the maximum gain splits into to vectors with a slight depression in
the zenith gain varies from one antenna and ground quality to the
next. The general region of the split is a broadside beamwidth
above 125°, a value that the 1-λ loop never reaches with the survey
height limit of 0.255-λ.) The 75-meter beamwidth ratios parallel
those for 40 meters, as do the progressions of feedpoint resistance
and reactance.
If we followed the band-by-band progressions for the dipole and

have digested the values for the 40-and 75-meter 1-λ loops, we can
almost predict the values that we meet for the 160meter loop. We
expect increased gain and slightly lower heights for maximum
zenith gain, and the 160-meter loop does not disappoint us. Fig. 13
graphs the gain curves to supplement the numerical information in
Table 7.
Chapter 65
Perhaps the most limiting factor for the 160-meter loop, which also
applies to the 160-meter dipole, is the physical height limit to which
most horizontal antennas are subject on that band. The lowest
height on the survey is almost 40’ (for 0.075-λ), which is very much
below the height of maximum gain, even over the best of soil
qualities. This height presents deficits of gain, as well as
considerably different feedpoint resistance values. Moreover, the
feedpoint resistance values (assuming one field adjusts the
antenna to resonance) vary considerably with soil quality at the
very low height. Almost inevitably, then, any 160-meter NVIS
Chapter 65
installation will suffer relative to performance values that are

possible for 75-meter and 40-meter NVIS antennas. However, if the
antenna height may reach between 80’ and 100’ (depending on soil
quality), the 160-meter loop is capable of excellent performance.
Chapter 65
Chapter 65
Some Preliminary Dipole and Loop Comparisons
The dipole and the loop have numerous similarities in their

performance curves relative to height and ground quality. They also
display a number of differences worth noting. The differences are
real, but their import for a given NVIS operation will vary from one
installation to the next. We can here only note the differences, but
the user must assign them weight in the overall decision on what
sort of antenna to construct for a given fixed station system.
Mechanically, the dipole requires only two end-support posts

(towers, trees, etc.) but the linear space is about ½-λ at the
operating frequency. In contrast, the loop requires 4 supports, but
at a spacing just over ¼-λ per side. The dipole’s feedline has only
the antenna wire for support, but a corner-fed loop may use the
support post to minimize feedline stress on the antenna wire.
Electrically, one of the most interesting differences between the

dipole and the loop is the beamwidth ratio, that is, the broadside
beamwidth divided by the endwise beamwidth. Fig. 14 graphs the
beamwidth ratios for to 75-meter dipole and loop for all ground
qualities in order to clarify the difference. In the region of higher
gain, the dipole values range from 1.6:1 up to nearly 1.9:1. Values
increase as we lessen the quality of the soil beneath the antenna.
In contrast, the loop ratios for the same region vary from 1.2:1 to
1.4:1. Again, the values increase with worse soils in the antenna
region.
Chapter 65
The significance of the numerical values shows more clearly if we

present the information in the form of far-field antenna patterns.
Fig. 15 provides a sample of elevation and 3-dimensional (top-
view) patterns for the same dipole and loop. The sample uses
average soil and 2 heights: 0.175-λ and 0.255-λ. The heights
correspond to near-maximum zenith gain and the upper limit of the
survey. For reference, the 3-dimensional patterns show the same
length of broadside axis line in all cases.
Chapter 65
At both heights, the dipole shows a greater broadside elongation of

its patterns. In fact, at 0.255-λ, the broadside elevation pattern
displays the dual maximum gain lines, although the zenith gain
depression is operationally insignificant. In contrast, the loop
patterns are more nearly circular, even at the maximum height
surveyed. (Close inspection of the 3-dimensional loop pattern at
0.255-λ reveals a slight asymmetry or egg-shape, with the broad
end at the antenna feedpoint side of the mid-side fed loop used in
the sample.) In operation, either pattern may prove to be the more
desirable, depending upon the mission specifications for a given
Chapter 65
station. Nevertheless, the differences are real and may play a role
in operations under difficult physical or ionospheric conditions.
We have noted in passing that the loop provides a gain

improvement over the dipole. Conventionally, we tend to compare
dipoles and loops in free space. In that environment, the loop has a
gain advantage of about 1.1 dB over the dipole. When we place
horizontal antennas close to ground, as is necessary for NVIS
operations, we must set aside conventional numbers and examine
the effects of the ground upon the two antennas.
Table 8 summarizes some of the key features of the 1-λ loop in

NVIS operation. (See Table 4 for a parallel treatment of NVIS
dipoles.) Just as was the case with the dipole, lowering the
operating frequency shows a greater increase in gain over very
poor soil than over better soils. The table also shows the increase
in the height of maximum zenith gain as we raise the operating
frequency over each of the soil types.
Chapter 65
The table also contains an extra set of columns showing the zenith
gain advantage of the loop over the dipole when we set each
antenna at the height of maximum gain (a height that is the same
for each antenna type over each soil type). The gain advantage of
the loop increases as we reduce the quality of the ground in the
antenna region. Fig. 16 graphs all 6 of the relevant gain curves (3
for the dipole and 3 for the loop) to shows the variation in the loop’s
advantage over the full spectrum of surveyed heights. The curves
appear in pairs for each of the soil quality value sets. For each pair,
the loop is always the higher curve. One interesting facet of
comparing the curves is the more rapid drop in gain of the dipole
above the height of maximum zenith gain. The loop curves are
shallower above the maximum gain height. Below the height of
maximum gain, the dipole and loop curves show a highly parallel
shape. You may correlate this data to the beamwidth ratio
information in the following way. At the maximum surveyed height,
the dipole has already passed the beamwidth at which the
broadside pattern begins to split into two lobes, but the loop
beamwidth remains short of that value.
Chapter 65
The feedpoint impedance levels for NVIS dipoles are generally

suitable for use with 50-Ω coaxial cable feedlines, although at the
heights of maximum zenith gain, 70-Ω coax may yield better SWR
values. Loop impedance values at the heights of maximum zenith
gain range between 100 Ω and 130 Ω, depending upon the quality
of the soil. In most cases, the simple ¼λ 70-Ω series matching
section shown in Fig. 17 will transform the impedance to a level
compatible with a 50-Ω main feedline. Since the matching-section
line is in series with the main feedline and counts toward the total
Chapter 65
feedline length from the antenna to the equipment, it does not

measurably increase line losses.
Neither antenna shows an advantage with respect to the SWR

bandwidth once well matched. Fig. 18 overlays the SWR curves for
both antennas, with each referenced to the resonant impedance, on
75 meters at 0.175-λ above ground over average soil. The curves
are virtually indistinguishable.
Chapter 65
These comparative notes on the dipole and the 1-λ loop as NVIS
antennas make no decisions about which one (or which height)
may be best for a given installation. That decision rests on the total
span of considerations that go into planning and building an
antenna with a certain set of mission specifications. The whole
point of the extensive notes, graphs, and tables is to provide
sufficient background information on the anticipated electrical
performance of the antennas to make the decision as well informed
as possible. However, among our basic antennas, we still have one
more to consider. The inverted-V dipole is a form of dipole, but has
a special property when placed close to ground in a NVIS
environment: the V-shape.
Chapter 65
The Inverted-V Dipole
When we consider the inverted-V with a modest slope (or a large

included angle) in a free-space environment or placed higher than
½-λ above ground, we consider it to be a slightly modified dipole
with almost as much broadside gain and with a smaller gain null off
the ends of the wire. In those contexts, we tend to truncate the
discussion of the V and its performance. As a NVIS antenna, the
inverted-V requires close attention to details of its performance.
Fig. 19 provides some of the reasons for special focus.
We ordinarily define an inverted-V in one of two ways: by reference

to the slope of the line from the horizontal or by reference to the
included angle between the wires. For our work, we shall select a
slope angle of 30°, which yields an included angle of 120°. Larger
slope angles are generally impractical for NVIS work on the lowest
three amateur bands. Shallower angles will have performance
Chapter 65
reports between the 30° V we have selected and a linear dipole, so

you may interpolate the probable values.
The chief mechanical advantage of the V is that it needs only one

central tall, study support. The wire-end supports can be shorter
and therefore lighter. In addition, the V version of the dipole has a
lower feedpoint impedance value than a linear dipole. If the
standard dipole has a NVIS feedpoint impedance close to 70 Ω,
then the anticipated V impedance value should approach 50 Ω, a
good match for the ubiquitous coaxial cables used in most amateur
installations. Of course, we shall allow the data to eventually tell us
what the most likely values are for each soil type in our survey.
The 30° inverted-V sets some limits to the lowest height at which
we can set the center point. The ends must not only clear the
ground, but as well leave a safety margin to prevent human or
animal contact with the high-voltage end of the wires. A reasonable
standard is probably about 10’. However, we shall show results for
one step below this level. On 40 meters, the minimum center height
will be 0.175-λ, which results in an end height of about 7.4’ above
ground. On 75 meters, the center minimum is 1.55-λ, for an end
height of 8.7’. The 160meter center height of 0.135-λ results in an
end height of 7.7’ above ground. For each band, we shall use the
center-height as a reference and increase that value in 0.1-λ
increments to the survey limit of 0.255-λ, regardless of whether that
value is practical on any particular band.
One of the most interesting aspects of the inverted-V configuration

is the difference in the endwise patterns relative to either the dipole
Chapter 65
or the 1-λ loop. Fig. 20 compares elevation patterns for a dipole

and a V for 160 meters, both with center heights of 0.175-λ. The
broadside patterns show very little difference. However, the
endwise patterns have quite different general shapes as well as
beamwidth values. The sloping elements, even with only a 30°
droop, show considerable radiation off the ends. The end radiation
is not sufficient to dominate the pattern, but it is enough to widen
the endwise beamwidth and to retain more than expected levels of
radiation at lower angles. The patterns are similar on all three of our
surveyed bands.
Because the V enforces a minimum height for the antenna center,

our data tables will be smaller than for the other two antennas. The
40-meter V has the smallest data set of all, as evidenced by Table
Chapter 65
9. However, the span of values is large enough for use to see some
interesting differences in V behavior relative to the behavior of the
two level antennas.
Chapter 65
The gain tracks in Fig. 21 show two important V idiosyncrasies.

First, the center height for maximum gain is uniformly high. Only
over very good soil do we find a distinct gain maximum followed by
at least one lesser value. For average and very poor soil, maximum
zenith gain occurs either at or above the 0.255-λ survey-height
Chapter 65
limitation. Ground coupling to the lower wire ends and the sloping
elements combine to reduce the effective height of the V if we take
the maximum gain heights of the level antennas as standards.
Second, with a center height only at the level of the dip[ole or loop
maximum-gain heights, the V shows a much lower gain. Despite
this apparent disadvantage, the anticipated lower feedpoint
impedance values—close to the characteristic impedance of
common coaxial cable—do show up in the data set.
The trends established by the 40-meter inverted-V reappear in the

75-meter version. As we move downward in frequency, we can add
two more steps of data to the collection and maintain the minimum
wire-end height. Only over very good ground does the progression
of values in Table 10 show a distinct peak zenith gain value,
although the doubled value at the highest limit over average ground
indicates a clear peak at that level. The required center height for
peak zenith gain over very poor soil remains outside the table
limits. We may also note that the inverted-V, unlike the dipole, only
shows a difference between maximum gain and maximum zenith
gain at the highest levels and only over very poor soil. The oddity of
this phenomenon relative to the dipole and the 1-λ loop is that the
differential occurs before the V over the worst ground quality has
reached its peak zenith gain value.
Chapter 65
The gain curves in Fig. 22 add two lower-level steps to the chart
and thereby reveal the rapidly decreasing gain level that occurs as
Chapter 65
the V wire ends approach ground. Even though the overall gain
level for any height (in wavelengths) is higher on 75 meters than on
40 meters, the gain of a V with its ends at about the same height on
both bands will be lower on the lower band. In addition, as we lower
the inverted-V, the feedpoint resistance shows more parallels to the
impedance of the dipole at very low levels, with a strong divergence
of values as we change the quality of soil. However, in the case of
the V, the divergence occurs largely as a result of the average
height of the antenna, not the center height. The divergence shown
by the 75meter V at its minimum height of 0.155-λ corresponds to
the divergence displayed by dipoles closer to the lower survey limit
of 0.075-λ.
Chapter 65
Chapter 65
Chapter 65
160 meters creates an additional two steps to the tabulated data

and shows how low that zenith gain values may go when the V
ends are close to ground. Both Table 11 and Fig. 23 show that
lowering the operating frequency also lowers the heights of
maximum zenith gain, although only slightly. Still, over very poor
soil, we cannot from the existing data certify that the highest listed
gain value is in fact the peak value. Once more the V over very
poor ground begins to split its broadside elevation lobes prior to
reaching the peak zenith gain value. The trends among all three
sample inverted-V NVIS antennas are consistent with prior trends.
Chapter 65
Fig. 24 provides graphic evidence of how the zenith gain behavior

of the inverted-V differs from corresponding behavior in a dipole (or
by extension in a 1-λ loop). In the primary span of heights within
which the dipole reaches its peak gain, the inverted-V shows
considerably lesser gain, since this portion of the inverted-V height
span is marked by a rising gain figure. Since amateur tend to build
antennas within total height limitations dictated by available
materials, skills, expense, and zoning restrictions, the comparison
is fair. Table 12 provides a summary view of the gain disparity
between the V and the level antennas. The table uses height
values for peak zenith gain, and we have already seen that the
required heights for peak inverted-V gain are considerably higher
than for the other antennas. If you change the table to record a
constant height—perhaps 0.175-λ as an average of the heights of
maximum gain of the level antennas over all soil types—the
disparity is even greater. For example, a 75-meter dipole at 0.175-λ
above average ground has a zenith gain of 6.4 dBi, while the 75-
meter loop under the same conditions shows 7.0 dBi. However, a
75-meter inverted-V with a center height of 0.175-λ provides less
than 4.5 dBi zenith gain.
Chapter 65
The behavior of an inverted-V NVIS antenna differs in further ways

from the behavior of the level antenna. For example, the beamwidth
ratio (broadside to endwise) increases more rapidly with increases
in center height than we find in the case of dipoles of 1-λ loops. Fig.
25 shows the phenomenon in a 160-m V in contrast to the rates for
the dipole on the same band. The faster rate of increase for the V
coincides, at least in part, with the V’s endwise elevation pattern,
and both are results of the greater radiation off the ends of the
element due to its slope. (Although 1-λ loop beamwidth ratios are
smaller than those for a linear dipole, their curves are equally “flat.”)
Chapter 65
As we increase the height of a dipole or a 1-λ loop, the feedpoint

impedance components show particular patterns. Except for the
lowest heights, the resistance tends to rise over all soil qualities,
although the rate varies with the soil type. Hence, we saw the
resistance values converge toward the top of the height range
within the survey. In contrast, the reactance values tend to change
fairly slowly. On 75 meters over average ground, the SWR curves
in Fig. 18 were equivalently wide for both level antennas, with a 2:1
SWR ratio relative to the resonant impedance (at 3.9 MHz) from 3.8
to 4.0 MHz.
If we track the feedpoint impedance in terms of the resistive and

reactive components for an inverted-V, we find opposite trends.
Fig. 26 tracks the resistance and reactance of a 75-meter dipole
and a 75-meter inverted-V over average ground—restricting the
height coverage to the V’s limited range. Although the patterns of
lines may be difficult to follow, the two rising curves represent
feedpoint resistance. The steeper curve belongs to the dipole, as
the resistance of the V changes more slowly. Both descending
curves belong to the feedpoint reactance values. The V’s reactance
changes more rapidly and radically than the dipole values. At the
left in the graph, the V’s reactance changes most rapidly when the
wire ends are closest to the ground. Although the rate of change
remains relatively high, it slows as the wire ends increase their
height. In contrast, the dipole curve in the left part of the graph
coincides with the region of highest gain, and the rate of change is
very slow. The rate increases as we raise the antenna well past the
region of maximum zenith gain.
Chapter 65
The differences in the patterns of resistance and reactance change

have very little effect upon the available SWR bandwidth. Fig. 27
overlays SWR curves for a 75-meter dipole and V, both with center
heights of 0.175-λ above average ground. If we judge by the
endpoints of the sweeps, the V curve is not quite as broad as the
dipole curve. Nevertheless, the SWR bandwidth is fully adequate to
NVIS operations on the specified band. Allowing for the changes in
frequency, similar curves would apply to NVIS antennas for the 40-
meter and 160-meter bands.
Chapter 65
Conclusion
The three most basic NVIS antennas—the dipole, the 1-λ loop, and
the inverted-V configuration of the dipole—share many properties,
most often as a result of the close proximity of the antenna to
ground. Hence, we discovered that ground quality plays an
important role in determining the maximum possible zenith gain on
each of the bands surveyed. As well, it plays a role in setting the
optimal height for maximum zenith gain, although for all types of
antennas, precision is not necessary in order to achieve excellent
results. However, we did discover that an old idea that gives very
low heights a presumed gain advantage is simply false. Averaging
both level antennas over all soil types, a height of approximately
0.175-λ above ground places the antenna within the expanded
range of best zenith gain performance.
Chapter 65
The inverted-V, with its wire ends close to ground and a 30° slope
angle, presents a conundrum for the NVIS antenna builder.
Although easier to construct than either a linear dipole or a 1-λ
loop, the inverted-V antenna shows a considerable gain deficit
relative to level antennas with the same center height. The deficit
may reach up to about 2.5 dB or close the half an S-unit. Although
the inverted-V may be necessary for field antennas, a fixed station
antenna might well enjoy the advantages of one of the level
antennas.
The data compendium provided by these notes likely has surplus

information. However, the extra data serves the twin goals of these
notes. Not only is the information useful in making decisions about
what type of antenna to create, it also aids in a better
understanding of the behaviors of each antenna type. Despite the
wealth of numbers and facts, these notes have only scratched the
surface of even basic NVIS antennas.
Chapter 65
Chapter 66: NVIS Antennas with Reflectors
A
n interesting facet of basic NVIS antennas—the dipole, the
1-λ loop, and the inverted-V—is the suggestion that we can
improve antenna gain by placing some form of wire structure
below it. The possibilities are numerous, but the most common
suggestion is the addition of a single-wire element. In fact, with
proper consideration, the suggestion will work, but with limitations.
As well, there may be better, although more complex, solutions to
obtain better zenith gain from the basic NVIS antenna.
The structure that we place below the driven wire has acquired two
names, one correct, the other misplaced and misleading. The
correct name for the element is a reflector. If the reflector is a
single-wire element optimized in size for best performance, then it
is a parasitic reflector. Still, the circumstances of its use will force
us to modify the expectations that we have of such elements when
used with highly elevated beam antennas. If the structure below the
driven element consists of a screen or a series of wires parallel to
the endwise orientation of the driven element, then we have a
planar reflector (sometimes called a sheet, curtain, or screen
reflector). We shall eventually examine both types of reflectors for
NVIS applications.
The incorrect name for the element—usually applied to the single-

wire reflector—is “counterpoise.” Although widely bandied about,
the term “counterpoise” actually applies only to a certain form of
monopole completion structure that substitutes for buried radials.
Very slightly elevated from the ground and not connected to ground
Chapter 66
by any direct means, the counterpoise serves the monopole by

capacitive coupling to the ground. Although quite effective for its
function, the counterpoise has disappeared from active use,
seemingly freeing the terms for other uses. Unfortunately, the terms
has greatest use in lazy applications, where an investigator or
writer does not take the trouble to analyze the structure’s role in an
application and further does not go on to optimize its physical
parameters relative to the application. This situation too often
applies to NVIS applications with careless element sizing and
placement. Perhaps it is time to drop both the term and the
associated carelessness from not only NVIS concerns, but from
any antenna considerations whatsoever—except, of course, when
working with the original engineering designs for monopole-
counterpoise antenna systems.
In these notes, we shall treat NVIS antenna reflectors, whether

parasitic or planar, as parts of an antenna system consisting of a
driven element and the element or structure below it. For parasitic
reflectors, we shall size them for nearly optimal performance and
carefully consider their placement. We may measure placement in
two ways: as their height above ground or as their separation from
the driven element. For both perspectives, we shall discover that
the height of the driver above ground plays a significant role in
reflector placement. In addition, the ground quality also dictates the
placement of a carefully designed reflector element.
We shall also discover that dipoles and 1-λ loops, despite the
similarities of their optimal heights over various ground qualities
when used alone, do not respond identically to reflector elements.
Chapter 66
Eventually, we shall look at the inverted-V to let it reveal further

oddities. Although planar reflectors improve gain most when placed
close to their driven elements, practicalities dictate that we place
them on or very near to the ground. Nevertheless, they will prove
their merits, especially when we give proper attention to their size.
We have much to explore, even if the concept of a NVIS reflector

seems simple. Let’s begin with the dipole.
The NVIS Dipole and a Parasitic Reflector
At its optimal height, the common linear or level dipole provides

quite good NVIS performance with a range of about 5 to 7.4 dBi
zenith gain, depending upon the operating frequency and the
quality of the soil beneath it. Under certain conditions, we can
increase the gain by adding a parasitic reflector somewhere
between the dipole and the ground. Unfortunately, we cannot
specify a specific place for the reflector, since numerous variables
enter into the optimal placement. Fig. 1 provides indicators of the
most relevant variables.
Chapter 66
Like almost all parasitic reflectors, the element length must exceed
the length of the resonant dipole. As well, the proper placement will
vary with the dipole’s height above the ground and with the quality
of the ground. As shown in the sketch, we may specify the
placement by two measures: the height of the dipole above ground
or the separation of the dipole from the driver. Unfortunately for
ease of analysis, both parameters tend to vary with the height of
the dipole itself and the quality of the ground beneath.
In these notes, we shall confine ourselves to 75-meter and 40-

meter dipole arrays. Rarely are 160-m dipoles high enough to
sustain a reflector element. On 60 meters, one may interpolate
between the 75-and 40-meter data to arrive at a reliable value,
since the gain curves are not sharp enough to modify performance
drastically with small variations.
Chapter 66
Beginning with the 75-meter dipole, we shall again use AWG #14
copper wire for all elements. The main unit of measure will be the
wavelength, and the dipole will be 0.4803-λ long. The reflector
element will be 0.5-λ long. The reflector length theoretically will
change as we move the reflector around, but not enough to disturb
the trends that we find with a constant length. We shall catalog the
results of modeling the dipole at three heights (to reduce the
number of continuously changing variables). Heights of 0.15-λ,
0.175-λ, and 0.2-λ will surround the optimum heights over all three
of our standard ground types: very good, average, and very poor.
Tabulated results (Table 1) will include, for each dipole, reflector

heights from 0.005-λ to 0.06-λ in 0.005-λ increments. In addition,
we shall include two special heights: -0.001-λ to cover the potential
for a buried reflector element and 0.001-λ to cover the case of a
reflector so low that someone might trip over it. The table shows the
height in feet for every increment of reflector height. It also
indicates in boldface the reflector height of maximum zenith gain
and shows on the right side the indicated separation from the
dipole. For each height, the tables show the zenith gain and the
broadside beamwidth.
Chapter 66
Chapter 66
Chapter 66
Chapter 66
Chapter 66
As the pages following the table show (in Fig. 2 through Fig. 7) we
may graphically examine the data in two different ways. The easy
way is to graph the gain curves for each dipole height using
separate lines for each quality of soil. The first three graphs follow
this plan and resemble the curves in the last set of notes for dipoles
alone. They establish that the dipole-reflector over very good soil
has more gain at any height than equivalent systems over lesser
soil types. The three graphs vary by virtue of the dipole height since
a dipole and a dipole-reflector array both reach maximum gain at
lower dipole heights with very good ground than over lesser ground
qualities. In contrast, the lines close up somewhat as we raise the
dipole height, since the version over very good ground has passed
its optimal height, while the versions over average and very poor
soil reach their peak values at higher dipole altitudes.
Although the initial three graphs relate easily to past performance

graphs, Fig. 5 through Fig. 7 may prove more revealing. In this set,
each graph uses a single soil quality, with individual lines in each
graph for the three selected dipole heights. With very good soil, the
0.15-λ-dipole height is clearly most nearly optimal. Over average
soil, the peak values for dipole heights of 0.15-λ and 0.175-λ
approach each other as most nearly optimal. Over very poor soil,
the values for the two lower heights are nearly the same, while the
values for a dipole at 0.2-λ above ground have nearly caught up to
the other lines. These graphs are more than merely interesting;
they indicate a fundamental property of all enhancements that we
may bring to basic NVIS antennas. The enhancement—in this case
a parasitic reflector—becomes more effective in raising zenith gain
as the soil decreases in quality. In Table 1, compare for each major
Chapter 66
subdivision the delta values for the three soil types. The maximum
improvement for an optimized reflector over very good soil is only
about 0.2 dB over very good soul. The overall performance
improvement is between 0.4 and 0.7 dB over average soil, but it
grows to a full dB or more over very poor soil.
Soil quality determines in part whether adding a parasitic reflector

to a given dipole is worth the effort involved for both installation and
maintenance. It also tells us something very significant about
parasitic reflectors in NVIS service. The added element may
supplement ground reflection as the source of zenith gain, but it
does not replace the ground. Note also that even though we find
the greatest gain improvement over very poor ground, the total
space of gain value ranges in each graph do not overlap those in
another graph. Ground quality tends to dominate zenith gain, even
with a parasitic reflector added to the NVIS dipole.
The table shows the antenna gain of the dipole at each height over
each ground quality with no reflector. Compare the gain values to
the next two entries, which show a slightly buried reflector and one
just above ground. In both cases, the gain improvement is minimal
to marginal, at best. The reflector does not significantly improve
performance until it is well above ground. For very good soil, the
reflector height is between 0.01-λ and 0.015-λ, regardless of the
height of the dipole (within the surveyed range). Over average soil,
the best reflector heights have an equally narrow range, but a
different one: 0.025-λ to 0.03-λ. Over very poor soil, where the
reflector has maximum effect in improving the dipole’s zenith gain,
Chapter 66
the ranges are split, running in the region of 0.04-λ for the lowest
dipole up to about 0.055-λ for the highest.
Over very good and average soil, the reflector height remains
constant, but the separation between the dipole and the reflector
changes with a change in the dipole’s height. The separation
between the dipole and the reflector also changes for each dipole
height over very poor soil, but that change combines with a change
in the best height above ground to produce a more complex picture.
In just the region of soil quality for which a parasitic reflector effects
a worthy improvement, uniformity disappears. In fact, over poorer
soils, one cannot recommend either a single height above ground
or a single spacing between elements that will cover the remaining
variables, such as dipole height. As soils improve, we can
recommend some reasonably good reflector heights above ground,
but not without also considering whether the potential improvement
justifies the installation and maintenance efforts.
Because the reflectors are parasitic, the overall array is a tuned

system with operating bandwidth limits. Like all parasitic systems,
the SWR bandwidth (referred to the resonant impedance) is
narrower than the bandwidth of the dipole alone. Fig. 8 provides a
sample comparison of dipoles at a 0.175-λ height, one with no
reflector and the other with a reflector at 0.025-λ above ground. The
dipole covers the 3.8-4.0-MHz spread of 75 meters completely, but
the dipole-reflector array manages to cover only about ¾ of the
range.
Chapter 66
One purpose in adding 40-meter arrays to this initial examination is

to determine if the trends that we saw on 75 meters are general or
idiosyncratic to the lower of the two bands. From our study of
dipoles alone, we know to expect slightly lower gain values for each
dipole height when measured as a fraction of a wavelength and
from each soil quality. Looking at 40meter dipole-reflector arrays
can tell us if there are other variations in the trends that are
frequency sensitive.
Table 2 provides the data for 40-meter dipoles at the same three
heights (measured in wavelengths. Of course, the physical heights,
as shown in the table, will be only about half the 75-meter values.
Otherwise, the data takes the same steps as for the longer
antenna. The reflector height increments are 0.005-λ between
0.005-λ and 0.06-λ, with the addition of –0.001λ to simulate a
buried reflector and 0.001-λ to simulate one very close to ground
Chapter 66
level. The table also includes reference data for independent

dipoles so that we can see the level of improvement created by the
addition of a parasitic reflector.
The data for each entry includes the zenith gain and the broadside
bandwidth. The beamwidth data has an obvious story to tell,
namely, that for practical operating purposes, the beamwidth does
not vary enough to be a concern over any soil quality with any
dipole height. However, for both 75 and 40 meters, the beamwidth
information conveys some subtle pattern changes. Over very good
soil, the beamwidth continuously rises. Over average soil, the
general trend is a rise in beamwidth value as we raise the reflector
height, but we find in some cases an initial drop in value for the
lowest reflector height. Over very poor soil, the beamwidth
decreases from the initial value until we approach or reach the
reflector height for maximum zenith gain, after which point, the
value rises. We might also note that the rate of beamwidth value
change slows or stops just before we arrive at maximum zenith
gain for each soil and dipole height combination.
Chapter 66
Chapter 66
Chapter 66
The graphs in Fig. 9 through Fig. 11 catalog the tabular differences

by separating soil types. In each graph, we have individual lines for
each dipole height. Hence, we can directly compare these 40-meter
graphs to those in Fig. 5 through Fig. 7 for 75 meters. In the main,
we find the same data trends at work for each soil type, but with
variations. For example, over very poor soil, the lines for each
dipole height are closer together than in the corresponding 75-
meter graph. Nevertheless, the overall gain ranges for each chart
show no overlap from one soil quality to the next.
Chapter 66
Like the 75-meter reflector heights that yield maximum zenith gain,
the 40-meter reflector heights over very good and average soil
show only a small range, regardless of the dipole height. However,
on 40 meters, the ranges are slightly higher: 0.015-λ to 0.02-λ over
very good soil and 0.03-λ to 0.035-λ over average soil. Over very
poor soil, the ranges are also higher on 40 meters than on 75
meters, reaching 0.06-λ for dipole heights from 0.175-λ to 0.2-λ. In
all cases, we find a change in the spacing from the dipole to the
reflector as we change the soil quality.
One interesting, although perhaps small difference between the 75-

meter and the 40-meter systems is the net improvement created by
adding a reflector to the dipole over all soil qualities. The
improvement is a bit better on 40 meters. This fact is consistent
with the increased ground losses that we find on 40 meters relative
to 75 meters. As a result, the reflector helps a bit more on the upper
band. Whether the slightly higher improvement offered, for
example, over average soil warrants a reflector on the upper band
is a user judgment.
The 40-meter dipole-reflector arrays are just as tuned a set of

systems as they are on 75 meters. Therefore, we also find a
narrower operating bandwidth (measured here in terms of SWR
relative to the resonant impedance of the individual antennas). Fig.
12 provides a comparison of a solitary dipole and a dipole-reflector
array. Both dipoles are at 0.175-λ, while the reflector is at 0.03-λ
above ground. By a simple adjustment of the element lengths, one
can better center the SWR curves within the band. However, for our
purposes, the comparison of the two curves is sufficient.
Chapter 66
At this point, we can see the relatively close parallel behavior

between the two dipole-reflector arrays despite their frequency
differences. In both cases, adding a reflector to a dipole over very
good soil makes little sense, while adding one over very poor soil
may be justified if an additional dB or more of zenith gain will
enhance operations. Average soil on both bands presents a case in
the margins.
We have two directions in which we might now go. One involves

the question of whether there are any reflector systems that might
bring about better results than a parasitic array, considering both
gain and operating bandwidth. A subsidiary question will focus on
whether such systems can materially improve antenna performance
over very good and average soil as well as over very poor soil.
Chapter 66
The second direction involves our alternative level antenna, the 1-λ
loop. To what degree loops follow or depart from the trends
established by the dipole arrays is a significant inquiry, since we
found a close correlation between the heights of maximum zenith
gain for both dipoles and loops. Because any differences might
impact the investigation of alternative reflector systems, we likely
should turn down the loop road first.
The 1-λ Loop and a Parasitic Reflector
The 1-λ loop inherently has more gain than a ½-λ dipole. Its
advantages for NVIS operation lie both in the gain and the greater
circularity of its upward radiation patterns. As we saw in the study
of the loop alone, the gain advantage of the loop tends to be about
0.6 dB (on average) over the dipole. Adding a reflector to the NVIS
loop is simply a matter of creating a second loop below the first.
Like the 2-element dipole parasitic array, the loop array requires a
larger reflector loop circumference relative to the driven loop
circumference.
The loop presents essentially the same open question as the

dipole. To what degree does soil quality play a role in the final array
zenith gain and in the placement and size of the reflector loop? Fig.
13 outlines the loop situation. As with the dipole, we shall sort
possible loop reflector heights from the ground upward and add
special notes the show the optimal separation of the loop at its best
height for each ground quality.
Chapter 66
We may shorten the data gathering by omitting some of the

improbable lower reflector heights from the survey, although we
shall retain an entry for 0.001-λ above ground to reinforce the
relative futility of trying to improve NVIS performance with
essentially a trip wire. As well, we may reduce the number of
graphs to one per band per ground quality to capture of trends in
performance. As with the dipoles, we shall track data with driven
loop heights of 0.15-λ, 0.175λ, and 0.2-λ to surround in finite steps
the region of highest gain of the loop over all soil types.
Table 3 provides the data applicable to loops with reflectors for 75

meters, again using 3.9 MHz as the test frequency. Fig. 14 through
Fig. 16 graph the performance over very good, average, and very
poor soil. Perhaps the most notable feature of adding parasitic
reflectors to NVIS loops is the fact that the optimal reflector heights
employ only a very small range for all ground qualities: from 0.02-λ
(for very good soil) up to 0.04-λ (for very poor soil). Since the
Chapter 66
reflector heights change very little with driven loop height, the
separation values vary a lot.
Chapter 66
Chapter 66
The gain benefits of a reflector follow the dipole pattern: over very
good soil, added gain is minimal. Even over average soil, the
maximum gain addition is under a half dB. Over very poor soil, the
reflector may add up to 1 dB of gain, depending upon the driven
loop height.
Chapter 66
Similarly to the dipole-reflector combination, the loop-reflector

combination results in a narrowing of the operating bandwidth
compared to a loop without supplement. Fig. 17 overlays SWR
curves relative to the resonant impedance values for a loop by itself
and for a loop with a reflector when both driver loops are at 0.175-λ
above ground. The sample case uses a reflector that is 0.03-λ
above ground, about optimal for the antenna height over average
ground.
Chapter 66
On 40 meters, we find the same parallels with the dipole cases, as

modified by the narrower range of optimal reflector heights that we
found with the 75-meter loops. Table 4 provides the numerical
information. Fig. 18 through Fig. 20 graph the gain data for each
antenna height over each of the soil qualities. The 40 meter gain
values are universally slightly less than those for 75-meters. As
well, we find some differences in other details of array behavior.
Chapter 66
Chapter 66
Chapter 66
If you compare Fig. 14 with Fig. 18, you can see that over very
good soil, the gain level at the two lower heights on 40 meters
result in overlapping lines, rather than separate lines. Similarly,
over very poor soil, the 40-meter lines for the two higher levels
overlap, whereas on 75 meters, they are separate. Compare Fig.
16 with Fig. 20.
Chapter 66
Nevertheless, the loop-reflector combinations for both bands are

consistent with each other and in the main are consistent with
results for the dipole-reflector combinations. The consistency
extends to the reduction in operating bandwidth on 40 meters, as
shown in the SWR curves in Fig. 21. The addition of the reflector at
an optimal height (0.035-λ) for average soil and a loop at 0.175-λ
results in a significant reduction in the bandwidth. With respect to
gain increase, on 40 meters, the use of a reflector is questionable
over very good soil, marginal over average soil, and possibly
productive over very poor soil.
Chapter 66
As noted with respect to dipoles, the use of a parasitic reflector with

a driven element creates a tuned system, although not fully isolated
from ground effects. Besides limiting the operating bandwidth, the
tuned system also tends to reduce the resonant impedance relative
to a loop without a reflector. However, the parasitic reflector
element is not the only method of improving NVIS performance.
Dipoles, Loops, and Planar Reflectors
An alternative method of provide improved reflection of energy

upward relative to reflections from the bare ground is the use of a
planar reflector. In other applications, HF planar reflectors go under
a variety of names, including screens, curtain, and billboards. A
planar reflector operates according to principles largely derived
from optics. In general, the reflections from an essentially flat
conductive surface depend upon the size of the planar reflector and
Chapter 66
its distance from the driven element—in this case, either a dipole or
a 1-λ loop. Although it is possible to elevate a planar reflector closer
to the driven element to optimize performance, we cannot simply
reduce the height of the driven element toward a ground-level
reflector. The far-field gain is a function not only of the area covered
by the reflector, but depends on the region several wavelengths
away from the reflector. As a result, we shall only be able to obtain
benefits that result from a practical ground-level reflector and an
elevated driver.
As the best compromise among all possibilities, I have placed the

driver at 0.175-λ above all ground qualities. Very good soil would
prefer a slightly lower height, while very poor soil prefers a slightly
greater height. However, to achieve some consistency within the
results of systematic modeling, a common height is best.
The dimensions of an optimal planar reflector vary according to the

method used to construct it. In these notes, we shall consider two
forms of planar reflectors, as illustrated by Fig. 22. The simpler
reflector consists of at least 9 wires (using the same diameter wire
as the driven element) spread to cover an area at least 0.4-0.5-λ
beyond each limit of the antenna.
The sample array, which yields the best performance at ground

level, is 1.2-λ in the direction of the wires and 0.8-λ broadside to the
antenna. One might add additional wires within the field.
Chapter 66
As an alternative, one might cover the ground with conductive

screening with holes smaller than 0.05-λ. In this case, a full screen
that is 1.0-λ by 1.0-λ proved to be the most effective version. The
modeled screen has twice as many wires as shown in the sketch,
although to add them would have made it impossible to find the
dipole above them.
Chapter 66
One advantage of the planar reflector in either form is that it does

not alter the impedance or the operating bandwidth of the driven
element above it. Fig. 23 provides the SWR curves for both types
of reflector overlaid on the SWR curve for the dipole alone for both
Chapter 66
75 and 40 meters. With or without the planar reflector, the curves

are essentially identical.
We obtain similar properties is we place either type of planar

reflector at ground level beneath a 1-λ loop, as suggested by the
sketches in Fig. 24. The same 9-wire and full screen reflectors
used with the dipole also serve the loop very well. Like the dipole,
the loops are at 0.175-λ above all ground types to ease the problem
of performance comparison.
Also like the dipole with a planar reflector, the loop-planar-reflector

combination results in an operating bandwidth essentially identical
to the bandwidth of a loop alone. Fig. 25 provides SWR curves for
loop-reflector combinations for 75-and 40 meters, with the loop-
along curve superimposed. Separating the curves visually is
virtually impossible.
Chapter 66
Table 5 provides data on the planar reflectors for both dipoles (on
the left) and loops (on the right). However, it also includes data for
isolated NVIS antennas and for antenna-reflector combinations
using the same set of limiting constraints. In all cases, the driven
antenna is 0.175-λ above ground. The table indicates the antenna
Chapter 66
dimensions and, where relevant, the reflector dimensions. For

dipoles, the element dimensions are linear lengths, while for loops,
they are circumference values. The arrays are sized for resonance
over average ground, and the changes of impedance for very good
and very poor soil are indicators of stability. For example, the
arrays with parasitic reflectors show the least change with changes
in soil quality, which is consistent with one role of a parasitic
reflector, namely, to control the driver feedpoint impedance.
Chapter 66
Reading from left to right provides a guide to the gain advantage in

all cases of the 1-λ loop over the dipole, whether alone or in the
surveyed arrays. Reading within an array type summarizes the gain
change with soil quality. Reading from one group to the next
provides a guide to the increasing gain advantage offered by
successively more effective arrays. The table includes broadside
and endwise beamwidth values to allow estimates of pattern
circularity.
The entries for the full screen planar reflector may seem odd at first
sight. For all preceding arrays, we find that very good soil yields the
highest zenith gain. However, with a full screen, using either a
dipole or a loop, the highest gain occurs over very poor soil. The
difference is not operationally significant within each full screen
group, but the phenomenon is interesting. Only the full screen
provides sufficient coverage to isolate the antenna from the ground
to the degree that very poor soil approaches the quality of free
space. Even the 9-wire screen has ground losses between wires,
losses that one can reduce by increasing the reflector wire diameter
or by increasing the number of wires—or both.
Measured against the performance benefits of a 1-λ-by-1-λ full

ground screen must be the site preparation difficulties, factors that
lie beyond the scope of these notes. However, to focus more
clearly on the potential gain benefits, Table 6 provides a summary
view. Even though the exercise does not place single-element
reflectors at their optimum heights for very good and very poor soil,
the maximum improvement in the gain values for those cases
would be about 0.05 dB.
Chapter 66
Chapter 66
The gain-table is not only useful in estimating the benefits of

supplementing a basic level NVIS antennas in various ways, but it
also sets in bold relief the overall range of gain values that we may
expect from these antennas as a group. That data is useful in
comparing basic antenna performance with the performance of
more complex antenna types, such as variations on the lazy-H.
More relevant to our discussion of basic antennas is the one that is
missing so far: the inverted-V.
The Inverted-V with Parasitic and Planar Reflectors
I have set aside the inverted-V from the discussion because it

represents a special case when we consider adding a parasitic
reflector to the antenna. Within the range of our survey, which has
a maximum (center) height of 0.255-λ, an inverted-V obtains
maximum gain over almost any ground quality only near the
maximum height. In NVIS operation, the effective or virtual height of
an inverted-V relative to its performance falls between half and 2/3
the physical center height. For most amateur installations, 0.255-λ
is practical on 40 meters (about 35’), but less so on 75 meters
(about 64’). However, we need to consider such heights if we wish
relatively good performance from an inverted-V over the full range
of soil qualities.
Inverted-V antennas with lower center heights will work, as shown

in the preceding set of notes, but they do not permit the addition of
a parasitic reflector. The reflector element must have at least some
spacing from the driven element and still clear the ground at the
reflector wire ends. In fact, ground effects upon a reflector for an
Chapter 66
inverted-V impose interesting geometry requirements that oppose

our natural desire to flatten the slope angle of the element. Fig. 26
shows the general requirements for an effective inverted-V with a
parasitic reflector.
For all soil qualities, the sketch shows the average optimal height
for an inverted-V with a 30° slope (or a 120° included angle). The
reflector, by virtue of its need for greater length than the driven
element requires a center height of about 0.155-λ, but the slope
angle is greater than 30°. The precise angle is a function of the
wire-end heights, which tend to be between 0.01-λ and 0.015-λ
above ground. With respect to user safety, the reflector ends are
too close to ground, but we shall bypass this legitimate concern in
order to evaluate antenna performance.
Chapter 66
One facet of the inverted-V array’s performance that we may

readily compare to the performance of the level antennas is the
operating bandwidth as measured by SWR curves referenced to
the antenna resonant impedance. Fig. 27 superimposes the curves
for an inverted-V alone at the optimum height with the curve for the
same antenna supplemented by a parasitic reflector. Both are over
average ground, although the general shape of the curves would
apply equally to all soil types. The figure records separate sweeps
for 75 meters and for 40 meters. In the case of level antennas
(dipoles and loops) using parasitic reflectors, we found moderate
shrinkage of the 2:1 SWR bandwidth. See Fig. 8, Fig. 12, Fig. 17,
and Fig. 21 for samples. In contrast, the SWR bandwidth shrinkage
for the inverted-V with a parasitic reflector is more radical, reducing
the 2:1 SWR region by more than half relative to the inverted-V
alone. One immediate consequence of this phenomenon for
antenna builders is that field adjusting the antenna to a desired
frequency will be a somewhat finicky task.
Chapter 66
There are means to obtain additional gain from the inverted-V while
preserving the SWR bandwidth available with the V alone. We may
place a ground-level planar reflector below the V using essentially
the same techniques that we employed for the dipole and the loop
antennas. Indeed, as shown in Fig. 28, the 9-wire and full-screen
Chapter 66
reflectors may use the same dimensions as used with the level
antennas. The same application rules also apply. We may improve
the 9-wire reflector performance by adding either thicker wires or
more wires. The full screen may use materials with opening no
larger than 0.05-λ, although common materials will normally have
much smaller openings relative to NVIS operating frequencies.
Table 7 summaries the performance values for all of the variations

on supplementing an inverted-V, beginning with the V alone to form
a reference data set for the three ground types. All driven inverted-
V elements have a maximum center height of 0.245-λ and a 30°
slope. Because the total element length varies from one design to
the next, the end heights will vary slightly but fall within the range of
0.123-λ and 0.125-λ. The reflector ends are about 0.01-λ above
ground.
Chapter 66
Chapter 66
The impedance columns for both 75 and 40 meters are instructive

in accounting for the relatively narrow SWR bandwidth of the
inverted-V with a parasitic reflector. On both bands, the
average feedpoint impedance for the V is about 65 Ω, a value

preserved with either planar reflector. However, with a parasitic
reflector, the resistive component of the impedance drops to about
30 Ω. At this impedance, small changes in the reactive component
of the impedance have more notable effects upon the SWR.
For all of the entries, the inverted-V arrays have gain levels about a
full dB below the levels achieved by the level dipole, despite the V’s
greater center height. (Loop arrays, of course, provide an additional
gain increment.) Over very good ground, the gain benefits of any of
the reflector systems are quite marginal, but over very poor soil, the
gain increase can approach 3 dB. The gain of the full screen (using
a model with twice the wire density shown in Fig. 28) over very
poor ground parallels the value increases that we observed with the
level antennas. To approach this level of performance with the 9-
wire screen would require extensive revisions to cover the ground
more thoroughly with conductive wires.
Conclusion
The idea of adding a reflector element to a basic NVIS antenna to

improve performance has lived in sound bites and mythology since
the initial uses of the propagation mode. Therefore I decided to
perform a more thorough modeling analysis of the idea to see what
order of improvement might be possible and the conditions under
Chapter 66
which we might optimize the improvement. This compendium of

data is the result. For all three types of basic antennas— dipoles, 1-
λ loops, and inverted-Vs—the addition is questionable or marginal
until we reach very poor soil qualities. In addition, the use of a
parasitic reflector (which is not under any circumstances a
counterpoise) requires attention to its height above ground and its
separation from the driven antenna, although the gain curves are
broad enough to allow for variation from the ideal. Over any soil, a
single wire reflector close to the ground proves to be an
unproductive expenditure of materials and energy. Variations in
reflector size will require element pruning to reach a resonant
impedance value. In all cases, the use of a parasitic reflector will
lower the feedpoint impedance relative to the impedance of the
basic antenna alone. As well, the reflector will narrow the operating
bandwidth. Both consequences are more extreme for the inverted-
V than for the level antennas.
An alternative to the parasitic reflector is a planar reflector. In

theory, we might elevate a planar reflector to a position below the
main antenna at which we may obtain very significant gain
improvements. The required size of a planar reflector militates
against the elevated version, so we confined our examination to
near-ground versions. In general, a planar reflector needs to have
dimensions that exceed the driven antenna dimensions by about
0.4-λ to 0.5-λ on all sides. The 9-wire and full-screen reflectors that
we sampled showed that these guidelines are not absolutes. In
fact, smaller planar reflectors will work, but they will seriously
reduce the gain benefits. Both the parallel-wire and the full-screen
reflectors significantly improved the gain performance of the basic
Chapter 66
antennas, especially over lesser soil qualities. In addition, they

preserved the impedance level and the SWR bandwidth of each
individual basic NVIS antenna type.
The goal of these notes has been to provide as full and complete
information as possible on reflectors for basic NVIS antennas. The
notes make no recommendations about the selection of any
reflector technique beyond the very general notes concerning the
relative size of the gain benefits over the range of soil types in the
survey. Such comments merely state the obvious. If blessed with
very good soil, the antenna installation needs no supplementation,
since reflectors in general only improve gain to the level of the
antenna alone over very good soil. However, over lesser soils,
including very poor soil, the use of a reflector can be beneficial,
although one must measure the potential level of gain improvement
against a host of other factors. Among these factors are the NVIS
station mission, the difficulty of coverage, the available antenna
site, and the investment of resources required for the improvements
that might come from a reflector.
In general, parasitic reflectors require no additional supports or

ground preparation. The investment comes in the field adjustments
necessary to bring the antenna to best operation. In contrast, one
may add a planar reflector to an existing antenna that is near an
optimum height and incur very little need for subsequent
adjustments. However, the work of installing either an extensive
parallel-wire or full-screen reflector is very significant and requires
access to a considerable area around the antenna. These factors
Chapter 66
are only some of the mechanical considerations that go into the

decision to add a reflector to a basic NVIS antenna.
Chapter 66
Chapter 67: NVIS Dipoles, Inverted-Vs, 1-λ Loops & Doublets
T
he preceding Chapters have developed a data compendium
on the performance of basic NVIS antennas, with special
reference to the dipole, the inverted-V, and the 1-λ loop. Our
focus on these antennas has centered on fixed stations with well-
prepared installation sites. Therefore, we sought to identify for each
of the three soil types in our survey the antenna height for peak
zenith gain, along with other trends that are relevant to
performance. One collection worked with isolated or
unsupplemented antenna elements, while the other collection
featured both parasitic and planar reflector systems for the fed
elements.
In the present exploration, we shall change our perspective. Instead

of letting the antenna reach its peak zenith gain at whatever height
might emerge, we shall work with some practical antenna heights
that are typical of amateur installations. Fortunately, some of these
heights happen to correspond closely with the natural heights for
maximum zenith gain. For most level NVIS antennas, a height of
0.175-λ is close to the center of the range of optimal heights for all
soils. Very good soils need a slightly lower height, while very poor
soils need a bit more height. However, we saw that gain changes
fairly slowly in the region of maximum zenith gain, so our use of a
single value to capture the best NVIS height for level antennas
(such as linear dipoles and 1-λ loops) will not be far from perfect.
Two of the heights amateurs often use for wire antenna supports
are 50’ and 25’. The former comes close to the proper height on 75
meters, while the latter is about right for 40 meters. Along the way,
Chapter 67
we shall look at some alternative heights for inverted-V antennas.

As well, we shall look at 35’ in two ways, first, as an alternative to
the optimal height and second, as a compromise so that we may
connect two antennas together with a common feedpoint.
We shall look at a number of antennas and combinations of

antennas. Of course, the dipole, the inverted-V, and the 1-λ loop
will undergo some close scrutiny within the confines of our height
limitations. Then we shall begin pairing 75-and 40-meter antennas,
initially stacking them both in-line and at 90° angles but keeping the
feedpoints independent of each other. Next we shall look at the
performance of crossed dipoles and inverted-Vs that use a
common feedpoint. We can also create a 2-band array of nested 1-
λ loops, one inside the other. Our next antenna will be both simpler
and more complex than the others. It consists of a single center-fed
104’ wire, but using it will require an antenna tuner at some point
between the equipment and the antenna proper. Finally, we shall
briefly look at a trap dipole and trap inverted-V for 75-and 40-meter
NVIS use. All of the antennas will use AWG #14 copper wire.
These selections do not exhaust our options for practical NVIS

antennas. Still, they provide a broad selection of possibilities for
performance comparisons. As well, they provide some broad
outlines of the 3-dimensional space requirements required for a
NVIS antenna installation. Their true function is not to guide actual
antenna construction, but rather to form a background for antenna
planning. To the antenna performance specifications, the antenna
planner must bring detailed information on the antenna site,
available resources, and mission specifications. Engineering—even
Chapter 67
at an amateur level—an antenna installation is not as casual an

affair as some beginners believe. Good electrical and mechanical
design and construction become even more important if the NVIS
station has emergency communications as part or the entirety of its
mission. The data in this set of notes provides only one set of
pieces in a relatively complex jigsaw puzzle.
The Practical NVIS Dipole for 75 and 40 Meters
The standard linear or level dipole is so common a wire antenna on

the lower HF bands that it seems to scarcely need mentioning. In
fact, the most common backyard lower HF dipole installations are
NVIS antennas, since amateurs rarely can achieve heights
approaching ½-λ or more on 75 and 80 meters. Indeed, 40-meter
dipoles rarely reach ½-λ (about 70’).
Chapter 67
Fig. 1 shows the main components of a dipole installation, including

two end supports, end insulators and ropes, a wire element fed at
its center, and a feedline, normally coaxial cable. Most installation
would also add a common-mode current attenuator at the feedpoint
of the dipole and almost any other antenna. As a NVIS antenna
within the constraints of these notes, the height above ground will
be either 50’ or 35’ on 75 meters and either 35’ or 25’ on 40 meters.
Table 1 provides performance data for these options.
The table lists modeled dimensions for the dipole if composed of

AWG #14 copper wire. On 75 meters, 121.2’ will resonate at 3.9
MHz at either height over average soil. The dimensions must
change very slightly for both better and worse ground qualities. As
well, the dimensions might also change due to the proximity of
objects within the installation site, since the model presumes flat,
uncluttered terrain. Still, the numbers provide a starting point for
field adjustments.
Chapter 67
As the 75-meter entries show, the 50’ height, if achievable,

provides superior zenith gain performance, since the height is close
to the generalized optimum height of 0.175-λ. The advantage
shows up more clearly as we decrease the soil quality. In addition,
the pattern becomes more oval and less circular for either height as
we decrease ground quality. Fig. 2 provides broadside and
endwise elevation patterns for both heights. As we raise the height
of a NVIS dipole, the oval becomes more elongated in the
broadside direction. This fact may have a bearing upon the
orientation of the antenna for some installations and missions.
A wire dipole will not allow coverage of the entire 80-75-meter

band, but it does suffice for the main part of the SSB portion at 75
meters. Fig. 3 shows the SWR curves for both heights referenced
Chapter 67
to the resonant feedpoint impedance over average ground. As the

curves indicate, the 50’ curve is flatter than the 35’ curve. In
addition, the tabular impedance data suggests that the lower height
is a better match for a 50-Ω feedline, while the 50’ heights better
matches a 70Ω coaxial cable.
On 40 meters, the table offers a choice between heights of 35’ and

25’. In this case, we obtain better zenith gain performance at the
lower height, which is closer to 0.175-λ above ground. On 75
meters, our choices were a near-optimal height and a height below
optimum. On 40 meters, we can select between a near-optimal
height and another above the optimal level. If we examine the
patterns in Fig. 4, we can see one effect of raising the antenna too
height for best NVIS operation. At 35’, the broadside pattern has
already split into two maximum gain lobes offset from the zenith or
straight-upward direction. The beamwidth ratio reflects the greater
Chapter 67
ovalization of the pattern. For strict NVIS operation, a more circular

pattern is desirable, but some missions may favor the pattern
stretch broadside to the wire.
At either height, the wire dipole may cover the entire 40-meter band
in terms of the SWR curves referenced to the resonant impedance
over average soil. Fig. 5 provides both curves. An actual
installation might wish to lengthen the listed length values for the
element to center the curves within the band. Note that on 40
meters, the two listed heights call for about a 5” difference in
element length, with further adjustments needed as the soil quality
changes. At 25’, the feedpoint impedance favors a match with 70-Ω
cable, while at 35’, the impedance is a bit higher. In a practical
installation at 35’, the length of coaxial cable usually needed to
Chapter 67
reach the equipment would introduce sufficient loss to reduce the

equipment end SWR levels.
In principle, a NVIS dipole should use the height that yields best
performance. However, as a practical matter, most installations
may be forced to use other reasonable heights based on available
supports and other site factors. The tabular data shows a modest
degradation of performance at the alternative heights, but the
overall level of performance is close enough to optimal that we can
expect good performance from the alternative. The 75-and 40-
meter NVIS dipoles provide a standard against which we can
measure other basic NVIS antennas.
Chapter 67
The Practical NVIS Inverted-V for 75 and 40 Meters
As we found in earlier notes within this series, the inverted-V

center-fed dipole requires a greater center height for maximum
performance than a level dipole. Wire-end coupling to ground tends
to reduce the effective height of the inverted-V relative to its
effective height when placed well above ground for long-distance
communications. Fig. 6 outlines the inverted-V that we shall use:
AWG #14 copper wire with a 30° slope from the horizontal (or a
120° included angle). Shallower slope angles will produce
performance intermediate between the sample V and the linear
dipole. Greater slope angles generally produce weaker zenith
performance.
The 75-meter center height options are 60’ and 45’, while the 40-
meter options are 35’ and 25’. Table 2 provides the modeled data
Chapter 67
for all of these options over the standard three types of ground
quality.
The table shows the total element length, but adds two other
figures for each version of the inverted-V. The end height is the
height of the wire tip (excluding end ropes and insulators) above
ground. The end length is the horizontal distance parallel to the
ground from the center of the antenna to the wire end. Double the
end length to obtain the total horizontal distance needed for an
inverted-V installation. One advantage of the V-configuration for
some sites is the reduced linear space needed for the antenna,
while the need for a single tall center support and two shorter end
supports is often a second attraction.
Chapter 67
On 75 meters, the available zenith gain, even at the 60’ center

height, does not match the gain of a level dipole at optimal height.
However, the performance is quite adequate for many situations,
and the pattern does show greater circularity relative to a dipole
pattern. The V radiates more effectively in the endwise direction
than the level dipole, contributing to the reduction in the ovalization.
Fig. 7 shows the broadside and endwise elevation patterns of the V
at both center heights. You may wish to compare the shapes of the
endwise patterns, especially at low elevation angles, to
corresponding 75-meter dipole endwise patterns.
The inverted-V provides adequate SWR coverage of the SSB

portion of the 75-meter band, as shown by the SWR curves in Fig.
8. The impedance data in the table show the 60’ center height to
Chapter 67
have a stable resistive component that favors a match to 70-Ω

cable. However, at 45’ above ground, wire ends are sufficiently
close to ground to create a wide swing (nearly 20 Ω) of the
feedpoint resistance with changes in ground quality.
Some amateurs attempt to install 75-meter NVIS antennas using

center heights below the shorter of our two options. The cost is a
continued reduction in zenith gain, which tends to fall off very
rapidly as we bring down the center height and tie off the ends very
close to the ground.
On 40 meters, the two alternative center heights are 35’ and 25’.
The lower height proved better for the level dipole, but for the
inverted-V, the higher center support provides superior zenith gain.
As well, the 25’ height for the V results in wire ends only about 8.5’
above ground, which may fall below the safety level for a fixed
Chapter 67
installation. (A temporary field installation may need to use lower

heights for wire ends—with suitable safety flagging for personnel—
but with consequential further reductions in performance.) Fig. 9
provides broadside and endwise elevation patterns for the 40-meter
options. Unlike the dipole at 35’, the V at that center height does
not show the splitting of the broadside lobe, although the canted
angle of the maximum gain indicator line suggests that that the
height is approaching the limit prior to splitting. In general,
broadside beamwidth angles greater than 130° usually accompany
the splitting of the maximum gain angles.
As the SWR curves in Fig. 10 indicate, a wire V, even at the lower

center height, is capable of covering all of 40 meters relative to the
resonant impedance (over average ground). One may wish to
Chapter 67
lengthen the listed element length to better center the SWR curve
within the band. The 35’ center height tends to favor 70-Ω
feedlines, while the lower 25’ height yields feedpoint impedance
values closer to 50 Ω.
The inverted-V is often mechanically simpler as a NVIS antenna.

However, even with an optimal center height, its performance, while
adequate, does not match the performance of the standard dipole.
The critical factor in inverted-V installations is not to install the
antenna at optimal dipole heights, but to select a higher center
height to best optimize the effective height of the antenna.
The Practical NVIS 1-λ Loop for 75 and 40 Meters
As a level antenna, the 1-λ loop shows height properties similar to

those of the level dipole. Therefore, we shall look at the 75-meter
Chapter 67
version at 50’ and at 35’. The 40-meter height options will be 35’
and 25’. Fig. 11 outlines some of the critical aspects of loop
installation, including the need for four tall corner supports.
(Although the number may seem problematical for a single
antenna, it will become less so when we consider multi-band
installations.) We may select either a mid-side feedpoint (used in
the models) or a corner feedpoint. The latter allows feedline support
along the support post with no change in the tabulated data in
Table 3. The only differences are the physical axes for the
broadside and endwise radiation patterns that move from a side-to-
side orientation to a corner-to-corner perspective.
Chapter 67
Although 50’ is close to optimal over average ground on 75 meters,

the best height for very good ground is slightly lower—in the 40’ to
45’ range. Hence, the zenith gain values for both heights over very
good ground are the same. The advantage of a 50’ height appears
Chapter 67
as we reduce the ground quality, although the decline is slow. In all

cases, the zenith gain of the loop is greater than the gain from a
dipole at the same height and soil quality. In addition, the patterns
for a loop are more circular than those for either a dipole or a V, as
indicated by the lower values in the beamwidth-ratio column. The
circularity of the loop patterns also appears in the broadside and
endwise elevation patterns for both heights in Fig. 12. (It is possible
to further circularize the NVIS pattern by shortening the fed wire
and its opposite wire, and by lengthening the “side” wires—and to
obtain a very small gain increase as well. However, this refinement
is rarely practical in an amateur installation.)
The impedance data shows wider swings of reactance as we

change soil quality than we find with dipoles, but the effect of the
Chapter 67
swings on the SWR relative to a resonant impedance value is

proportional to the resistive component value. The 75-meter SWR
curves in Fig. 13 are very similar to those for the dipole, despite the
higher loop impedance. For a match to a 50-Ω coaxial cable, a ¼-λ
series section of 70-75-Ω cable is usually satisfactory for
impedance values up to about 130 Ω. For higher feedpoint
impedance values, 93-Ω cable may prove more effective for the
matching section.
On 40 meters, the greater loop height shows its gain disadvantage

over every soil type. Like the dipole, the loop at 25’ is closer to an
optimal height for NVIS operation and shares many of the
properties of the 75-meter loop at 50’ above ground. The broadside
and endwise elevation patterns for 40 meters appear in Fig. 14 to
confirm the near circularity of the loop patterns when the antenna is
Chapter 67
at its best height. As we raise the loop above its best height, the
pattern becomes more oval.
The 35’ loop, being above optimal height, shows higher feedpoint
impedances that suggest the use of a 93-Ω matching section. At
25’, the impedance values are on the borderline that allows testing
of each matching section impedance value for the widest 50-Ω
SWR curve. The curves in Fig. 15 are relative to the resonant
feedpoint impedance over average ground for each antenna height.
They confirm the ability of the loop easily to cover the entire 40-
meter band.
Chapter 67
Despite the requirement for 4 tall corner supports, the 1-λ loop is a
highly usable antenna. The dimensional values show the
circumference of the wires, with each side having ¼ the value
shown. The loop fits a square location that may not fully support a
dipole’s ½-λ total length. Moreover, the zenith gain level is
somewhat higher for any height above any ground. A corner
feedpoint permits full cable support, reducing strain on the element-
to-cable junction. For some missions, the greater circularity of the
patterns may also be an advantage.
Practical Multi-Band Antennas: Multiple Independent Dipoles
So far, we have looked in detail at monoband antenna installations.

There are a number of highly practical ways to create antenna
systems for both 75 and 40 meters besides widely separating
independent monoband antennas. Our first candidate is simply to
Chapter 67
place two independent dipoles, each at its own best height, close to
each other. Fig. 16 outlines two options for us to consider. In each
case, we shall place the 75-meter dipole at 50’ above ground, with
the 40-meter dipoles at 25’.
The in-line version of the dual independent antennas requires the

fewest support structures. We only need to add two ropes to the
75-meter dipole support posts to hold up the 40-meter dipole
element. In contrast, the crossed version demands 4 supports
posts, a pair for each band.
Chapter 67
Table 4 provides the performance data on models of the two

systems. In both cases, the 75-meter dipole performance is
unaffected by the orientation of the 40-meter antenna. If we cross
the two antennas, each performs almost identically to independent
antennas over the same average ground at the same height. You
may confirm the values by comparing the present table with the
appropriate entries in Table 1. However, the lower band dipole
does have some significant effects upon the upper band element
when both are aligned with each other. The required length for
resonance changes, and the zenith gain decreases. Whether the
gain difference between the two systems is enough to offset the
differential in mechanical requirements is a user judgment, taking
into account site, resource, and mission factors. In either case, the
system requires two feedlines running to either a switch at the
equipment room or to a remote switch closer to the antennas.
Chapter 67
Practical Multi-Band Antennas: Crossed Dipoles and Vs with a

Common Feedpoint
We may simplify the feeding system by using a dipole for each

band, but at 90° to each other to minimize interactions. By using a
common feedpoint, each dipole will resonate on its own band with
minimal current on the element for the other band. Fig. 17 shows
the general outline of a pair of dipoles, although the system will also
work with inverted-V elements. Like crossed independent dipoles,
the common-feedpoint system requires at least 4 full-length support
posts, one at the end of each element wire. As well, when we cross
dipoles, the wider broadside beamwidth also changes by 90° as we
switch bands. This aspect of the system may or may not be
meaningful to a given installation or mission. In many cases, the
site dimensions may override the desire to direct the broadside
beam.
Table 5 provides modeled data for the crossed dipoles at two

heights over average soil. (Past tables will allow close estimates of
performance over other soil types.) For the moment, we need only
Chapter 67
examine the upper portion of the table for dipoles at 35’ and at 25’.
We find a disparity of gain at both heights between the values for
75 meters and for 40 meters. In addition, we find that the
interactions between dipoles are minimal in terms of performance,
but they do require adjustments to dipole lengths relative to the
required lengths of independent dipoles at each height.
The lower height is close to ideal for 40 meters, but very low for 75
meters. 35’ is somewhat low for 75-meters, but already high for 40
meter NVIS dipoles. Although 50’ would provide better 75-meter
performance, 40-meter zenith gain would drop, because the
broadside pattern would be split into two lobes with a very
noticeable zenith null between them. Fig. 18 provides broadside
patterns for both bands at both array heights. At the upper height
Chapter 67
(35’), the 40-meter pattern already shows a split maximum-gain line

pair with a tiny (operationally insignificant) gain decrease at the
zenith angle. Further increases in height will rapidly increase the
zenith null on 40 meters. The final selection of installation height for
crossed dipoles will necessarily involve a compromise between the
requirements of the two bands.
A mechanically attractive alternative to crossing level dipoles is to

cross inverted-V elements. As suggested by the outline in Fig. 19,
the system requires only a single tall center support, with shorter
posts for the wire ends. For our sample, we shall use a 50’ center
support and a 35’ center support to compare performance values
on both bands.
Chapter 67
Crossed inverted-Vs have performance disadvantages relative to

crossed dipoles. Despite using elevated center heights for both the
higher and the lower arrays, the overall gain values are less than
the values for the dipoles. In addition, we find a wider disparity
between the zenith gain values for each band. Even if we find a
“perfect” center height that yields nearly equal zenith gain values on
each band, those values will fall well below the gain values that we
can obtain from crossed dipoles.
Chapter 67
Finding the ideal height for crossed inverted-Vs will involve more
than just gain equalization. As shown in Fig. 20, the 40-meter
broadside elevation pattern shows serious lobe splitting and a very
wide broadside beamwidth. We may also examine the dimensions
for the Vs in Table 5 and uncover an additional installation
temptation. At either height, the 30° sloping Vs place the 40-meter
wire ends much higher above ground than required by the 75-meter
V. The temptation would be to use a greater slope angle (that is, a
smaller included angle) for the 40meter V. The smaller angle also
promises to lower the 40-meter impedance to a value that more
closely matches the 75-meter value. However, as we decrease the
included angle of an inverted-V (or any half-wavelength V-element),
the gain decreases along the V-axis. The already low zenith gain of
the 30° V element would drop to even less desirable levels.
Chapter 67
The sequence of crossed-element arrays has shown a continuously

growing number of performance compromises. With crossed
independent dipoles, each at a nearly optimal height, we obtained
full performance from each, although with wider broadside
beamwidths 90° apart. When we simplified the feed system by
using a common feedpoint for both dipoles, we encountered
reductions in the maximum available zenith gain due to the need to
find a common height for both antennas. Converting the linear
dipoles to an inverted-V configuration further reduced available
zenith gain. From the starting point to the final inverted-V array, we
lost as much as 3 dB, depending upon the final selection of
antenna height and the slope angle of the inverted-V elements.
Such losses may be mandated by temporary field installations, but
a fixed station antenna system should carefully weigh the
performance penalties of simplified mechanical construction if the
station mission includes more than casual operation.
Practical Multi-Band Antennas: Nested 1-λ Loops
Multi-band dipoles and inverted-Vs require four to five support

posts. When we compared monoband dipoles to 1-λ loops, we
noted that the somewhat higher zenith gain of loops often fell prey
to the desire for the simpler mechanical requirements of the dipole:
2 posts instead of
4. However, the mechanical advantage of dipoles and inverted-Vs

becomes moot when we consider multi-band loop installations. We
may nest 1-λ loops for 75 and 40 meters within a single 4-post
support system. Moreover, we may set each loop at a favorable
Chapter 67
height. For our sample, outlined in Fig. 21, we can set the 40-meter
loop at 25’ above average ground, with the 75-meter loop 10’
higher to obtain matched gain levels. One advantage of the nested
loops is that we may also orient the broadside patterns in the same
direction.
Table 6 provides numerical data for the pair of loops. Not only do
both loops share a nearly common zenith gain value, but as well,
the beamwidth ratio is almost the same on both bands. Despite
nesting, the performance data for the individual loops is nearly the
same as for independent loops, such as those shown in Table 3.
However, the proximity of the loops yields some revision of the loop
dimensions relative to monoband versions. Since the 75-meter loop
is nearly 2-λ in circumference on 40 meters, it shows a low but not
wholly negligible level of activity when we drive the 40-meter loop.
Chapter 67
The relationship between the two operating frequencies militates

against trying to feed both loops from a common feedpoint. The two
independent feedpoints have significantly different impedance
values, and both require ¼-λ series matching sections. The
columns showing the alternative feedpoint impedance values
employ a 70-Ω matching section on 75 meters and a 93-Ω section
on 40 meters. Fig. 23 shows the 50-Ω SWR curves on both bands
with the prescribed matching sections. Of course, in an actual
Chapter 67
installation, the builder would measure the resonant feedpoint

impedance on each band before deciding upon the proper
matching-section characteristic impedance.
Chapter 67
For multi-band service, 1-λ loops become more attractive since

they do not require more support structures than we would need for
crossed dipoles or inverted-Vs. Their additional gain and the ease
of matching them to a 50-Ω main feedline suggest that they
deserve serious consideration, especially for installation sites that
may strain to handle a full half-wavelength of linear space. Nested
loops require a little over ¼-λ per side on the lowest band in the
loop nest.
Practical Multi-Band Antennas: A Center-Fed Doublet
Those who can manage only two supports may wish to consider a
largely overlooked option for a NVIS antenna: a center-fed doublet.
Fig. 24 shows the outline of one possibility. Although it looks like a
common dipole, it is not. Rather, it will function as a center-fed
element that ranges from about 0.4-λ on 75 meters to about 0.75-λ
on 40-meters. In addition, we may operate the doublet on 60
meters, where it is just over 0.55-λ long. For our sample, we shall
use a height of 35’, which is higher than ideal for a ½-λ 40-meter
dipole, but nearly ideal for the longer length of the doublet.
Chapter 67
The length of the doublet resembles the length of a G5RV

antenna/feed system. The resemblance is no accident, but has little
to do with the reasoning behind the original system. It is possible to
use a doublet that is a full half-wavelength long at the lowest
operating frequency. However, as we nearly double that frequency
(from 75 meters to 40 meters), the feedpoint impedance increases
to values of resistance and reactance that are both over 2000 Ω. To
restrict the impedance excursions of the antenna, we cut the
doublet short for 75 meters, but still within a reasonable impedance
range for most antenna tuners (ATUs). As a consequence, we
obtain impedance values on 40 meters that are also more
amenable to normal ATU tuning ranges. The feedpoint impedance
values in Table 7 for each band over all three soil qualities give a
good feel for the values that require matching.
Chapter 67
Using a doublet requires an ATU somewhere along the line

between the antenna feedpoint and the station equipment. As
shown in Fig. 25, we may select among three main positions for the
ATU. On the left is perhaps the most common system for feeding a
doublet: the use of parallel transmission line (600-Ω ladder line or
450-Ω window line) from the antenna to the equipment room with a
balanced ATU located indoors. A manual tuner with a record of
settings for each band usually provides adequate speed when
switching bands except where automatic link establishment (ALE)
procedures may be in use.
The system shown at the center of Fig. 25 uses a length of parallel

feedline to effect an initial impedance transformation to reduce the
impedance range required of an ATU Table 7 adds two columns to
record the modeled impedance values that result from the insertion
of the line. Although the range for 75 and 40 meters is small, the
values are not direct matches for a standard coaxial cable. In
addition, if one adds 60 meters to the set of operating bands, then
the value range does not vary differently from the range of values at
the feedpoint. The high impedance values simply occur of different
Chapter 67
bands. With the added line, system requires a weatherproof remote

tuner located below the feedpoint. The weight of such a unit would
likely require a third support for the antenna. Nevertheless, the
remote tuner, if equipped with memories, would permit rapid band
switching.
We may also install the remote tuner directly at the antenna

feedpoint, again with weatherproofing and a suitable support for the
weight. Remote ATUs currently available have different matching
ranges, running from quite small to very wide. Therefore, selection
of the ATU for either remote system is a major installation decision.
Chapter 67
A doublet at about 35’ above ground provides relatively even band-

to-band performance as a consequence of the increasing length of
the element as we raise the operating frequency. The zenith gain
numbers for comparable soil qualities confirm the near uniformity of
performance. The broadside and endwise elevation patterns in Fig.
26 confirm the impression left by the tabular data.
As we increase the length of a center-fed wire element (or raise the

operating frequency, which amounts to the same thing), the zenith
gain rises and the beamwidth narrows. However, with a fixed height
above ground, increasing the operating frequency also increases
the height in wavelengths above ground, which results in a wider
beamwidth broadside to the antenna element with a lower zenith
gain value. By judiciously selecting a physical height for the
antenna, we may balance the conflicting trends—at least to a level
that yields adequate performance over a wide range of frequencies.
In general, the doublet at 35’ above ground provides performance
Chapter 67
that is similar to the performance of 3 independent half-wavelength

dipoles, each near its optimum height for maximum zenith gain.
The one deficiency in performance, relative to the independent
monoband dipoles, is that the endwise beamwidth continues to
diminish with rising operating frequencies.
Although the preceding set of notes has adequate information for

estimating the benefits of a full screen at ground level for the major
type of antennas that we have been reviewing, we have no data
directly applicable to the doublet. Therefore, I created a near-
ground screen below the doublet, as shown in Fig. 27. The screen
is 1-λ per side at 75 meters, making it larger than necessary for
higher frequencies.
Table 8 provides numerical data that parallel the values shown in

Table 7, without the screen in place. (The new table omits the extra
impedance columns.) Pattern shapes do not significantly change,
Chapter 67
and the impedances values are not very far apart in the two tables,
especially considering the application of an ATU to the feed
system. As expected, the key benefit is to the zenith gain over
lesser quality soils. Note that the gain values for 40 meters do not
keep pace with those for the lower bands. The screen is simply
oversized for that band.
Additional engineering investigations might turn up a better

compromise set of dimensions for the ground screen. Its use with
the doublet will depend upon many factors, and so the information
is not inherently a recommendation. Nevertheless, the basic
doublet with any of the ATU systems shown is worthy of
consideration, especially if land and support posts materials are
limited.
Chapter 67
Practical Multi-Band Antennas: Trap Dipoles and Inverted-Vs
Trap dipoles and inverted-Vs represent an alternative means of

providing multi-band performance with only two end supports—and,
of course, a center support for the V-configuration. Fig. 28 provides
a general outline of a trap inverted-V. The trap dipole has the same
dimensions using a level wire element.
Traps are parallel-tuned L-C circuits that we tune slightly lower in

frequency than the lowest frequency used on the higher of the two
bands. The traps used in the model require 60-pF capacitors and
8.7-μH inductors. Most conventionally wound coils have Q-values
of about 200 or so, although a careful builder might achieve a
higher value. As a compromise between the bands, both the
inverted-V and the dipole versions of the 75-40-meter antenna have
peak heights of 35’, a level that is high for 40 meters and low for 75
meters, if we use the ideal heights for dipoles as our reference
Chapter 67
standard. In practice, the inverted-V peak height should be higher—

perhaps 45’ or so—but most amateurs who limit themselves to only
two or three supports are unlikely to exceed the 35’ height in the
sample.
The modeled data appear in Table 9. The zenith gain for the
inverted-V is low by virtue of the V-configuration and the low height.
The dipole model over average ground has more equal gain values,
but the 75-meter performance shows a deficit relative to individual
dipoles over the same ground. The 40-meter gain value for the
portion of the antenna inside the traps is comparable to the value of
the 40-meter dipole at the same height for crossed dipoles using a
common feedpoint.
Chapter 67
The use of traps imposes no revisions on the radiation patterns

produced by the antenna. In Fig. 29, we find perfectly normal
broadside elevation patterns for both versions of the antennas. The
dipole version on 40 meters shows the split maximum-gain lines
typical of dipoles above their optimum NVIS height.
One advantage of the trap multi-band NVIS antenna is the reduced

linear space it requires. The level dipole version requires only 103’
plus a mall space required for end insulators and support ropes to
the end posts. The inverted-V, with a 30° slope, needs less than 90’
plus end-attachment space.
On 75-meters, the trap antenna exhibits impedance values that are

compatible with 50-Ω coax. However, the 40-meter impedance
Chapter 67
values are higher. Prior to building a trap antenna for NVIS work,
one might experiment with trap components, including the trap
resonant frequency, to arrive at a better match for the usual coaxial
cable feedline. The dipole version of the antenna has a total length
similar to the length of the doublet. Both antennas have
complexities, in one case the traps, in the other the need for an
ATU.
Conclusion
Our survey of practical NVIS antennas has included many basic

types and variations, but it is by no means exhaustive. Beginning
with basic dipoles, inverted-Vs, and 1-λ loops for monoband
service, we progressed to various multi-band arrangements. Our
goal has been to lay out the general structures of practical NVIS
antennas and to compare performance level both at various normal
amateur antenna heights and also among the antennas included.
The overall goal of this set of notes has been to provide data that
may be useful in planning and implementing a fixed-station NVIS
antenna system for the two most commonly used amateur bands.
Unlike field antennas, which must employ simplified construction

methods for rapid deployment, the fixed-station NVIS antenna
system deserves careful attention to detail. Some NVIS stations
engage almost solely in casual operation in order to sample the
propagation mode. Such stations can take shortcuts with
construction and live with the modest outcome. Many stations have
more significant missions that include emergency communications
work. Unfortunately, not all of them have the resources to
Chapter 67
implement optimal antenna systems. Of the systems that we have

surveyed, one of the best—in terms of pattern circularity and zenith
gain—is a set of nested 1-λ loops supplemented by a full ground
screen for soil qualities less than very good. In amateur and local
community terms, such a system is a relatively expensive
proposition. As well, the antenna site often dictates antennas with
different shapes and heights. Nevertheless, a fixed NVIS station
with more than a casual mission would do well to engineer the best
antenna system possible for the site and the operating goals. In
many instances, the fixed station gain and radiation pattern
properties must compensate for deficiencies in the field stations
with which communications are essential.
For the fixed NVIS station with an important mission, casual design
is not good enough, simply because we can do better. The notes in
this collection provide some background data that I hope will
contribute toward better NVIS antennas.
Chapter 67
Chapter 68: Fixed 3-Band NIVS Antennas
I
n the past, most amateur NVIS activity occurred on 75 and 40
meters. Recently, amateurs have begun expanding their
coverage to include 60 meters. That has brought requests and
suggestions for NVIS antennas that cover all three bands—without
resorting to lossy terminated antenna configurations. An added
requirement often cited is the need to switch bands rapidly without
having to readjust an antenna tuner. Although it is possible to set
up a single wire with a parallel feedline to a tuner and by careful
selection of both the antenna height and length to achieve
adequate pattern from 75 through 40 meters, this last requirement
effectively precludes this option without the use of very fast
automatic tuners with memories to eliminate tuner searching for
settings while changing bands. Let’s omit this option from our
exercise.
The goal, then, is to develop wire antenna options for 3-band

operation in the NVIS mode so that we may ideally switch bands
without attention to the antenna. (We shall add a final option that
requires only a single antenna switch.) Next, let’s face reality. The
ideal height for a linear or level antenna for maximum NVIS of
upward gain falls in the 0.15-λ to 0.22-λ range. The upper end of
the range places an 80/75-meteer antenna at about 60’. Higher
antennas—up to 0.25-λ above ground—will work well for NVIS, but
are physically prohibitive for most amateur installations. The upper
limit of the NVIS height range also increases the radiation at lower
elevation angles, a fact that favors an antenna that must do double
duty by providing both NVIS and medium-range communications
Chapter 68
duty. However, for pure NVIS work, such antennas tend only to
increase atmospheric noise levels while receiving.
Therefore, let’s restrict, for our exercise alone, the maximum height
of our NVIS antennas to 35’. Some of our examples will also use a
25’ height. As the data in Table 1 show, these heights are very low
on 75 meters, but approach optimal NVIS heights on 60 and may
even exceed them on 40 meters. The main reason for using heights
of 35’ and 25’ is that most amateur installations cannot usually
exceed these heights without considerable difficulties.
With very low antenna heights come a few very important cautions.
The antennas in these notes will use either AWG #12 (0.0808”
diameter) or AWG #14 (0.0641” diameter) copper wire. Dimensions
will be in feet but may show up to 2 decimal places. These
decimals result from the antenna modeling software used to
generate the models. In fact, all dimensions are only starting points.
Any replication of the antenna designs shown will require
considerable field adjustment and dimensions may depart by a
noticeable amount from the listed dimensions.
Chapter 68
There are two major reasons for the potential variance between the
model and reality. Antennas at very low heights vary their
impedance values and their resonant lengths with only small
changes in height. In addition, at very low heights, the resonant
length and impedance of a basic antenna types vary with the
quality of ground beneath the antenna. All of the models use
average ground with a conductivity of 0.005 S/m and a permittivity
(relative dielectric constant) of 13. Your ground quality may differ
considerably from these numbers, ranging very likely from very
good (0.0303 S/m, 20) down to very poor (0.001 S/m, 5). Ideally,
you should plan your antenna by remodeling the samples in these
notes for the most precise height values that you can obtain and for
the best estimate of ground quality. Even so, expect significant field
adjustment when you assemble the antenna.
Ideally, a perfect NVIS antenna in the abstract would have a

circular azimuth pattern at any elevation angle with peak gain in the
zenith or straight upward direction. Real antennas only approximate
this condition. Fig. 1 shows the 3-dimensional pattern of an
inverted V. Beside the obviously imperfect pattern are two 2-
dimensional elevation plots that we shall use to characterize the
radiation patterns of the antennas we discuss. Broadside to the
inverted V (and to all of the antennas in these notes) we find a
pattern with a rather broad 3-dB beamwidth (as indicated by the red
lines). Off the ends of the antenna, the pattern tends to have a
somewhat narrower beamwidth. We shall use the dual elevation
pattern system to characterize all of the antennas under discussion.
High-angle azimuth patterns have systematic conical section errors.
Chapter 68
From the two elevation patterns, you may infer the general
departure from the ideal circular pattern. The inference may prove
useful in orienting an actual antenna to provide a desired degree of
coverage. As you continue to raise the height of a NVIS antenna,
the broadside pattern tends to increase its beamwidth until the top
flattens and the radiation pattern evolves into a pair of lobes, one in
each broadside direction.
The reason that we may usefully spend some time looking at basic
antennas for 3-band operation has to do with the properties of NVIS
propagation. At night, the ionosphere lacks the absorbing D-layer
and so 75 meters (and 160 meters) become very useful for
refracting (reflecting) radiation from the nighttime F-layer, which
may not be strong enough for usable return signals on 40 meters.
In the daytime, the F-layer strengthens, but the D-layer reforms,
Chapter 68
effectively closing 75 meters (and below) to NVIS propagation.

However, the stronger F-layer allows good use of 40 meters. The
attraction of 60 meters is for those transition time periods between
the closing of one band and the opening of the other. Of course,
like all HF communications making use of ionospheric refraction,
there will not only be daily cycles of change, but as well both
seasonal and sunspot-cycle variations, not to mention special
conditions, such as solar flares.
Numerous web sites provide details of basic NVIS propagation

phenomena as well as other basic data on the propagation mode
and its use by radio amateurs. Essentially, NVIS propagation is
most relevant to communications at distances from zero to about
200 to 300 miles, especially where intervening terrain may block
ground wave communications or VHF/UHF line-of-sight activity.
The following notes will examine three basic candidates for a 3-

band NVIS antenna covering 75, 60, and 40 meters, with emphasis
upon SSB operation. The first section evaluates the pros and cons
of a 3-band trap inverted V antenna. The second looks at the
potential for converting a common arrangement into a slightly more
complex configuration. The use of crossed 75-40meter dipoles, laid
out at 90° angles but with a single feedpoint, is common. We shall
explore both level and inverted V versions of dipoles for the three
bands, each separated by 60° from an adjacent element. Finally,
we shall look at the advantages and disadvantages of nested 1-λ
loops for each band. Each arrangement has both physical and
electrical properties that go into the evaluation process. Our goal is
Chapter 68
not to make a final decision, but instead to organize some of the

factors on each side of the ledger.
A Trap Inverted V for 75-60-40-Meter NVIS Use
The design of a trap dipole is straightforward. Beginning with the

highest band, we create a dipole or inverted V and place a trap at
the end. The trap is tuned to a frequency just below the lowest
frequency used on the highest band. When we wish to add the use
of a lower band, we add wire to the assembly to extend its length.
Since at the lower frequency, the trap acts like an inductive load for
the lower frequency, the total element length is shorter than would
be a full dipole or V for that frequency. We may continue the
process indefinitely, but we need add only one more set of traps to
achieve 3-band operation.
Chapter 68
Fig. 2 shows the dimensions for a trap inverted V for 75, 60, and 40
meters using AWG #12 wire, which is normally strong enough to
support the weight of the traps. The dimensions are suited to a 35’
center height above average ground with a 30° element slope (or a
120° included angle below the center point). The dimensions place
the wire ends 9.25’ above ground. The design aims for feedpoint
impedance values that are compatible with either 50-Ω or 75-Ω
coaxial cable. (I might note in passing that most cables, such as
RG-59, have 70-Ω characteristic impedance values, but tradition
allows a collective reference to 75-Ω cable.) The overall leg length
for 75-meter operation is less than 48’, although a simple inverted V
for 75 meters might use leg lengths of about 60.5’. Hence, the trap
3-band V has the smallest footprint of all of our test designs. It
requires less than 90’ of horizontal length and only the wire or cable
thickness for width. As well, it normally requires only one 35’
support pole, while 10’ poles can support the wire ends. Of course,
the antenna design allows instant band changing with no required
action upon the antenna itself once successfully installed. These
are perhaps the major advantages of using a 3-band trap inverted
V.
Chapter 68
Table 2 supplies some of the major properties, both physical and

electrical, for the antenna. Trap design is standard and almost any
antenna handbook will provide guidance in construction. To the list
of conditions that may require adjustment of the wire lengths for
each band, we can add that small variation in trap values will also
change the required length of the 60-meter and the 75-meter
extensions. To reinforce the need to create a final design using
height and ground quality values as close as possible to reality, we
can compare the modeled resonant impedance values to free
space values for the same assembly. On 75 meters, the free-space
impedance is about 50 – j50 Ω. On 60, the value is 69 – j29 Ω,
while on 40 meters, the resonant free-space impedance is 63 – j19
Ω. Note that the free-space values depart more radically from the
values over ground—especially in the reactance column—as we
place active parts of the antenna closer to ground.
In Fig. 3, we find pairs of elevation patterns for each band at the

frequencies of resonance. Off-resonant patterns do not depart from
the ones shown. As we increase the operating frequency, the
antenna height increases as a fraction of a wavelength. The
broadside patterns show an accompanying increase in beamwidth.
In fact, the 40-meter pattern levels at the top, as indicated by the
tilted line. The endwise patterns show a slight decrease in
beamwidth with rising frequency.
Chapter 68
One deficiency of the trap inverted V is the relatively low possible

gain. The tabular gain values show that the closer we place active
parts of the antenna to the ground, the less gain that we can obtain
from the antenna. As well, the inverted V structure inherently has
less gain than a level trap dipole would have if at a 35’ height. The
combination of close ground spacing and inverted-V structure may
provide mechanical simplicity to an installation, but it limits the
antenna’s possible performance. The gain at 40 meters (4.8 dBi) is
typical of an inverted V at 0.25-λ above ground, but the gain of a
level dipole can be up to a full dB or more higher. Moreover, on the
two lower bands, there are trap losses, about a half-dB per trap
pair.
The design does not use a lower wire as what some call a
“counterpoise” (in a total misuse of that term). Extensive modeling
has shown that a single wire near ground below a NVIS element
does not significantly change the antenna gain. The ground itself is
Chapter 68
the primary reflective surface and it extends far beyond the limits of
a low reflector wire. A way to improve performance is to lay out a
series of 7-9 wires or a full (chicken-wire) screen that exceeds the
active element dimensions by 0.4 λ to 0.5 λ in every dimensions.
Then the local ground acts like a planar reflector, but only to a
certain point. A full ground screen improves performance only to
the level of very good ground. For a basic installation, the antenna
element itself is all that one needs unless one creates ground
screening or an elevated tuned reflector.
The SWR curves in Fig. 4 show the relative sizes of the operating
windows for each band. Since the antenna would require field
adjustment as a matter of course, you can adjust the wire lengths to
move the windows anywhere within the bands. Compared to other
Chapter 68
antenna types, the SWR windows of the 3-band trap inverted V

tend to be fairly narrow, calling for careful field adjustment. A final
set of lengths for one installation my not prove satisfactory for
another. One limitation of the trap inverted V is the fact that on
bands with trap ends, the impedance tends to be higher than on the
lowest band. As a result, 75-Ω coax provides wider SWR windows
on 40 and 60 meters, while 50-Ω coax is best for 75 meters. If we
add a significant length of coax between the antenna center point
and the station equipment, line losses will broaden the SWR
windows. However, the total energy available for radiation (and the
receiving sensitivity) will undergo proportional reduction. These
notes do not include a level version of the trap dipole at 35’ for a
significant reason. Leveling the antenna yields impedance values
on 60 and 40 meters close to 90 Ω, while the 75-meter impedance
remains close to 50 Ω. With even a 75-Ω feedline, the operating
windows shrink on at least one band below a usable level. The
inverted V configuration tends to lower all of the impedance levels
to yield a usable antenna. However, obtaining usable feedpoint
impedance values comes at a price: on all three bands, the
maximum gain of a level 3-band trap dipole at 35’ above ground
falls between 5.3 and 5.7 dBi. Compare these gain values to those
listed in Table 2.
For those unfamiliar with the action of traps, Fig. 5 presents a set of
current magnitude distribution curves along the inverted V on each
of the three bands. The center gap is a function of the sloping
element halves, since the magnitude is measured from the wire
itself. On the two lower bands, note the increase in the slope of the
curve as it passes a trap, which acts like a non-radiating load
Chapter 68
inductance on the lower bands. Only on 40 meters do we find a

normal current distribution up to the first pair of traps. Although we
normally think of the current magnitude in wires beyond an
operative trap as zero, the value is not quite that low. This fact adds
to the somewhat finicky adjustments required of any multi-band trap
antenna.
Assuming that trap construction is not a hindrance, the trap inverted

V for 75, 60, and 40 meters in NVIS operation provides one of the
simplest physical installations. Offsetting that advantage is the
relatively low gain on the two lower bands and the relatively narrow
Chapter 68
SWR windows for operation. In addition, the antenna requires

careful adjustment to the conditions of the installation site.
Crossing Dipoles for 3 Bands
One popular system for obtaining 75-and 40-meter operation with

an antenna having only one feedline employs dipoles for each band
in a cross, with each dipole oriented 90° from the other to minimize
interaction. The system often uses the inverted V configuration so
that a single center support with shorter wire-end supports
simplifies the mechanical needs. We may expand the system to
include 3 bands by separating the dipoles by 60°, as shown in
outline form in Fig. 6. The legs may be level or slope to form Vs.
The interactions among the dipoles are greater than we find in the
2-band version but are completely manageable.
Chapter 68
Feeding the antenna requires only a feedline, although adding a

common-mode current attenuation device at the feedpoint is a
useful precaution to take. Fig. 7 shows the relative current
magnitude distribution as we operate the array on each band. The
distribution does not change with height or by using an inverted V
configuration. Note that the unused elements are relatively
quiescent, but not completely inactive. The chief effect of the low
currents on the inactive elements is to require careful pruning of the
dipoles for each band to place the low SWR passband to cover the
operating frequencies on each band.
For NVIS operation, a level system of linear dipole would likely

require seven full-length supports, one at the center and one at
Chapter 68
each wire end. Although this system is probably more complex than
most amateurs wish, let’s examine it to see what level of
performance we can obtain. We shall place the system at 35’ above
average ground and then drop it to 25’ above ground. If you refer to
Table 1, you can gauge the height of each dipole as a fraction of a
wavelength and estimate the probable performance relative to
performance at an optimal height (0.15-λ to 0.22-λ above ground).
Table 3 provides the modeled dimensions and performance data
for both heights.
A single set of dipole lengths is sufficient for both heights chiefly

because the 50-Ω low SWR windows are considerably broader than
those we encountered with the trap inverted-V 3-band antenna.
Fig. 8 provides SWR curves for both heights with the level dipole
system. The current magnitude curves showed higher off-band
current activity on the 60-meter dipole than when using either 75 or
40 meters. This condition shows itself in the numerical impedance
data and in the SWR curves in the form of a higher resonant
Chapter 68
impedance value and a narrower SWR operating window.

However, the 60-meter SWR window extends beyond the limits of
the 60meter channel assignments.
The broadside and endwise beamwidth and the gain values in the
table are worth noting. At a height of 25’, only the 40-meter dipole is
at optimal height for maximum gain straight up. The other dipoles
fall increasing below the optimal height and therefore show lower
gain, largely due to ground absorption. All patterns follow the model
in Fig. 1 with wider broadside beamwidth values than endwise
values. When we move the antenna upward by 10’, the 75-and 60-
meter dipoles are closer to optimal NVIS height and show better
gain than at 25’. However, the 40meter maximum gain value
decreases relative to the value at 25’. As well, the beamwidth
Chapter 68
significantly increases. Fig. 9 compares the broadside elevation

patterns of the 40-meter dipole at both heights. Above optimal NVIS
height, the pattern begins it evolution into two separate broadside
lobes. Note that there are two peak-gain lines equally spaced (in
degrees) from the zenith angle. As well, the gain straight up is
slightly less than maximum. The differences between the two
patterns are not sufficiently great to disrecommend the higher
installation level. In fact, if the station is also used for medium-
range communications, the higher level provides more energy at
lower elevation angles to enhance this operation. The increased
beamwidth is the chief reason for finding a slightly lower maximum
gain value at 35’. The exercise is useful as a caution against raising
NVIS antennas too high. Eventually, the very slight reduction in
zenith gain will develop into a very deep upward null.
Although the crossed-dipole array requires too many supports for

most amateur installations, the exercise provides us with a
reasonable perspective on dipole performance in NVIS service. It
also shows us that 3 crossing dipoles separated by 60° angles is a
Chapter 68
perfectly feasible multi-band array. Its final function will be to

provide a baseline for comparing the performance of an inverted V
form of the same array. The top-down outline would follow the
pattern in Fig. 6, but the horizontal dimensions would shrink to
about 0.866 of the dipole lengths as a result of sloping each dipole
30° below the level dipole line. Table 4 provides the dimensions
and performance data from the model.
The V system uses a standard 30° angle for the wire slope. One
result is a variation in the wire-end heights, which range from 5.8’
on 75 meters up to 19.15’ on 40 meters. A practical installation
might wish to select a common height for all wire ends. For
example, 10’ end supports would place all wires above the potential
for accidental contact but with reduced gain on the higher bands.
However, to obtain a 30° slope angle, the center height needs to be
about 35’ to prevent the 75-meter V from touching ground.
Veeing a set of elements tends to lower the feedpoint impedance

relative to level dipoles. However, in the crossed V configuration,
interactions tend to limit the degree of feedpoint impedance
decrease. Hence, the 50-Ω SWR windows shown in Fig. 10 are
about the same size as those for the level dipoles. To place the
windows within approximately the same frequency limits on each
Chapter 68
band requires a slightly different set of overall element lengths.

Because the element ends are close to ground level, the actual
lengths needed for the three bands will vary with small structural
variations from the model and with changes in the ground quality
below the antenna. The width of each SWR passband is great
enough to keep the adjustment task from becoming too onerous.
We often hear a sound bite about inverted V antennas, namely, that

their gain values are nearly as good as the gain of level dipoles.
Unfortunately, this nugget of wisdom applies to inverted V antennas
at significant heights above ground for use in long distance
communication. Close to the ground and used for NVIS
communications, the proximity of the antenna ends to ground
creates a significant gain deficit straight up. Compare the gain
Chapter 68
values to those for the level dipoles at 25’ and 35’. Only the 40-
meter V dipole, with its ends at over 19’ above ground is clearly
competitive with the level dipole versions. As the V ends more
closely approach ground level, the gain decreases. The 75-meter
maximum gain is nearly 3 dB lower than the gain of the dipole at
35’. Although the inverted V version of the cross dipole array is
mechanically simpler than the level dipole version, there is a gain
price for the convenience. (As a side note, compare the crossed V
array gain values to those of the trap dipole in Table 2 to obtain a
rough estimate for the further losses due to trap construction.)
Fig. 11 provides broadside and endwise elevation plots for the

crossed V array for each of the three bands. All but one pattern
follows the nearly ideal NVIS pattern form. The broadside 40-meter
pattern, with a center height of 35’ above ground, shows similarities
to the 40-meter pattern for a level 35’-high dipole in Fig. 9. Because
the V element ends droop, the effective height of the 40-meter V is
Chapter 68
slightly lower than its center height, so the pattern is less distinctly
split into separate broadside lobes.
A 3-band crossed dipole or V array can provide quite adequate

NVIS service on a single feedline. However, there are trade-offs for
each version. The dipole system provides better performance, but
requires up to 7 tall supports. (A little ingenuity with ropes might
reduce the required number of supports to 5.) The crossed V
configuration reduces the required height of wire-end supports, but
imposes a penalty on performance on at least two of the bands.
A Nest of Three 1-λ Square Loops
An alternative to the crossed dipole system can reduce the number

of required supports to 4, one at each corner of the array. Fig. 12
shows the very general outline of a set of three 1-λ loops that are
the core of this NVIS array.
Chapter 68
Each loop is independent and assumes an antenna switching

arrangement. Depending upon the installation and its distance from
the operating equipment, the switch may be either at the station
(with three lines) or at the antenna at the equipment end of the
required ¼-λ 70-75-Ω matching sections The feedpoint impedance
of the loops themselves falls in the range of 90 Ω to 130 Ω. The
series matching sections are a very simple way to yield impedance
values compatible with 50-Ω coaxial cable. The sketch shows a
mid-side feedpoint. However, the alternative feedpoint at the array
corner is just as apt. As well it would allow cable support along the
support post at that corner.
Although the basic sketch shows the loops on a level plane, the
model for them places the 75-meter and the 60-meter loops at 35’,
heights closer to optimum for those frequencies. (In fact, a height of
45’ to 50’ would be best for the 75-meter loop, but we started this
Chapter 68
exercise with a 35’ height restriction.) In fact, even within our

restriction, we might lower the 60-meter loop slightly so that ropes
from the corner support posts would place each loop at a slightly
lower height, with a 25’ height minimum for the 40-meter loop. 60-
meter performance would drop to about the 75-meter level. With
the 35’/25’ split, Table 5 provides dimensions and performance
data for the nested loops using both mid-side and corner
feedpoints.
Note that we need not change any dimensions when we change

the feedpoint position; indeed, all performance values show only
undetectable differences in the modeled performance values. (Of
course, like the dipoles, the loops may require dimension
adjustments with small changes in height or significant changes in
soil quality.) In the table, we determine the broadside pattern by
drawing a line from the feedpoint to a point just opposite on the
Chapter 68
loop. Endwise patterns are along a line at right angles to the

original line. Broadside for a corner-fed system means a line from
one corner to the opposite corner, while mid-side feeding defines
broadside from wire center to wire center.
Even with separate feedlines, the loops do show some interaction

between the most active loop and the next adjacent loop. As shown
in Fig. 13 for mid-side feeding, the 60-meter loop shows activity on
both the 75-and the 40-meter loops. These interactions have a
bearing on the final loop dimensions, but are low enough to create
no hindrance to the formation of typical NVIS patterns. A sampling
of those patterns (with mid-side feeding) appears in Fig. 14.
Chapter 68
The 75-meter loop is below its optimum height and shows a slightly
narrower broadside beamwidth than the broadside patterns for 60
and 40 meters, both of which are at close to optimal heights. Loops
tend to produce more circular patterns than dipoles, as suggested
by the endwise patterns, which vary from the broadside
beamwidths by only about 20°. As well, loops have slightly higher
gain values than dipoles. For the nest shown, the gain varies
between 6.4 and 6.8 dBi.
Chapter 68
Fig. 15 provides another advantage inherent in the nested loop

array. With series ¼-λ 75-Ω matching sections, all of the loops
show the widest 50-Ω SWR bandwidths of any of the options under
discussion. The worst case is 75 meters: the 90-Ω loop impedance
under conversion by a standard ¼-λ 75-Ω cable only drops to about
62 Ω. However, the SWR passband changes values very slowly,
allowing access to the entire top 200 kHz of the band.
The nested loops do have constraints. They require a square

installation region about 70’ per side, including support posts. As
well, the system needs 4 full-height posts. Finally, the loops require
independent feedlines with either a station or a remote switch.
Chapter 68
Unlike quad beams, some of which use a common feedpoint, the

nested NVIS loops should use separate feedlines and line
switching. Fig. 16 shows why. On 40 meters, with a common
feedpoint for all loops (simulated but not shown in the model), we
obtain significant activity on the 75-meter loop, which is close to 2 λ
long. Each side of the 75-meter loop is about ½-λ long on 40
meters. One consequence appears in the offset broadside pattern,
with the main lobe tilting away from the feedpoint. A second
consequence follows from the fact that the impedance of the 75-
meter loop, when excited on 40 meters, is about 220 Ω. The
parallel combination of impedances for the 40-and 75-meter loops
yields a net impedance value that is more difficult to match. The
impedance challenge is not insurmountable by careful adjustment
of loop lengths. However, the pattern offset will remain.
If the 4-corner support system is feasible, the nested 1-λ-loop array

provides the highest performance of any of the systems in these
notes, all of which have observed a 35’ maximum height restriction.
Chapter 68
Conclusion
Our goal has been to explore some basic 3-band antenna systems
for NVIS operation on 75, 60, and 40 meters. We have tried to
portray reasonably the advantages and disadvantages of each
system. As well, we have used the occasion to address some basic
issues in NVIS antennas, such as the ineffectiveness of so-called
single-wire reflectors or “counterpoises,” and the effects of using
the inverted V configuration in contrast to level dipoles. The trap
inverted V uses the least real estate as measured by its area, but
has overall the lowest performance level. Crossed dipoles improve
performance significantly but require an extensive structure. Setting
the dipoles into a V-configuration eases the support requirements
but at the cost of severe performance reductions, especially on 75
meters. The nested 1-λ loops require 4 full-height supports and
separate, switched feedlines, but provide the highest level of
performance of the group of candidates.
These notes have not covered all possibilities. For example, we did
not discuss using a single antenna across the entire spectrum by
employing either a lossy terminating resistor (or set of resistors) or
by using high-speed matching systems. Our aim was to stick to
basic antennas and basic installation techniques. These notes do
not form in any way a complete menu of tri-band NVIS coverage.
Indeed, they are at most appetizers, food for thought.
Chapter 68
Chapter 69: NVIS Antennas for Special Needs
N
ot all NVIS missions are the same, and so not all antenna
requirements are the same. In this set of notes, we shall
examine a few of the special requirements that some
missions might impose upon antennas and look at a few samples
ways to fulfill the needs. Not all of the antennas that we shall
explore fall in the category of basic NVIS antennas, but they are all
buildable by experienced radio amateurs.
We shall, somewhat arbitrarily, divide the effort into three sections.

The first part of our work will be to design a good NVIS antenna
that has as circular a pattern as possible. In other words, the
beamwidth ratio will be within the limits from 0.9:1 to 1.1:1. Our goal
will also be to ensure that the zenith gain of the antenna matches or
exceeds the gain of a dipole at the same height above ground. The
second section will explore ways of maximizing zenith gain
regardless of the beamwidth ratio. Ultimately, we shall aim for a
gain of perhaps 12 dBi over average ground, compared to a
dipole’s maximum zenith gain of about 6.4 dBi over the same
ground.
A perfectly vertical pattern is not always the best fit for a station’s
mission. In the third and final part of our work on special purposes
NVIS antennas, we shall examine some ways in which we might
reliably tip the pattern of a NVIS antenna in a desired direction
while maintaining adequate zenith gain. In fact, we shall begin with
a tempting proposal that simply does not work. Then we shall
examine a few workable ideas, exploring along the way the
Chapter 69
parameters of any antenna that we might use to do the job. As

always, the final part of this set of notes is in no way the final word
on the many possibilities for NVIS antennas.
Nearly Perfectly Circular NVIS Pattern Production
Suppose that the NVIS mission includes a requirement for a

perfectly circular pattern in which the broadside and endwise
beamwidths are the same—or as close to the same as we may
achieve. The lowest value of beamwidth ratio achieved by any of
the basic antennas was about 1.25:1 for some of the square loops.
Still, that value is far from the 1:1 goal of the present hypothetical
requirement. We can do better. Fig. 1 outlines a relatively basic
way to attain the desired beamwidth ratio, increase zenith gain, and
provide a direct match to the standard 50-Ω amateur feedline. We
simply create a rectangle, fed on a narrow side, either alone or with
a ground-level screen.
Chapter 69
The development of vertically and horizontally polarized rectangular

antenna shapes has a long history, and we may easily adapt those
designs to NVIS service by laying out the wires parallel to the
ground. If the ratio of long side wires to the fed wire (and its
opposite) is about
2.29 to 2.30 to 1, several beneficial consequences emerge (along

with one limitation as well). First and most relevant to our project,
the radiation from the side wires increases, widening the
beamwidth relative to the broadside beamwidth that we measure
from the feedpoint through the center of the opposing wire. In fact,
the suggested ratio (applicable to the AWG #14 wire antennas that
we are modeling) produces a nearly perfect 1:1 ratio, depending
upon the antenna height and the ground quality beneath the
antenna. Fig. 2 shows a set of typical patterns for a rectangle with
the specified dimensions.
The broadside and endwise elevation patterns are virtually

indistinguishable. The 3dimensional version of the radiation pattern
is about as close to a sphere as one may achieve with a ground-
based antenna system. The second consequence of constructing a
Chapter 69
rectangle of the suggested dimensions and fed at the center of one

of the short wires is that the feedpoint impedance changes its value
relative to the impedance value for a square loop. Instead of an
impedance level greater than 100 Ω at resonance, the impedance
value decreases as we elongate the rectangle. At the proportions
necessary for a circular pattern, the feedpoint impedance is
approximately 50 Ω, the value we need for our coaxial cable.
The third consequence of elongating a square loop into a rectangle

is increased zenith gain for the 1-λ loop. (Like square loops, the
rectangle will actually have a circumference that is slightly greater
than 1-λ at resonance. The circumference values for our samples
will be between 1.03 λ and 1.033 λ.) In NVIS service, the additional
gain may not be enough to be truly decisive in deciding to install a
rectangle. However, the combination of advantages may have more
weight than the simple sum of the three individually.
An AWG #14 copper wire rectangle for 75 meters will require side
wires about 0.358-λ long, with end wires about 0.157-λ long. For
the numerical data in Table 1, I first resonated the loop at a height
of 0.175-λ above average ground and then sought the height of
maximum zenith gain over our three standard soil varieties: very
good, average, and very poor. (See the first set of notes for soil
quality specifications in terms of conductivity and relative
permittivity.) For each soil quality, I recorded the zenith gain,
beamwidths, and feedpoint impedance between 0.145-λ and 0.235-
λ above ground in 0.01-λ increments. The table indicates by italics
the heights of maximum zenith gain for each soil quality. For this
class of antennas, there is no difference between zenith gain and
Chapter 69
maximum gain, since the patterns are so circular. BS BW and EW

BW indicate the broadside and endwise beamwidth values
respectively, while the ratio is always broadside over endwise.
Hence, where the endwise beamwidth is greater than the broadside
value, it is possible to obtain ratios less than 1.00. The Feed R and
Feed X columns show the feedpoint impedance based on the initial
resonance of the sample model.
Chapter 69
Chapter 69
Fig. 3 provides a graphic view of the gain curves for the three soil
qualities. They are quite shallow and selecting a mounting height
that differs a bit from the optimum height would yield undetectable
differences in performance. In fact, the optimum heights for
maximum zenith gain for the rectangle are uniformly slightly higher
(by about 0.01-λ) than those for the square loop. We may note in
passing that the fed wire and the opposite wire are significantly
farther apart in the rectangle than the corresponding wires are in
the square loop. Although not very significant relative to building a
loop, this fact will take on more importance when we examine other
types of antennas in these notes. We should remember that we
may analyze the square loop and the rectangle as two dipoles in
phase, bent so that the ends join at the center of the side wires.
Chapter 69
Besides having circular patterns and 50-Ω feedpoint impedance

values, rectangles also show very good gain over each soil type.
However, they have one limitation relative to a square loop. The
SWR bandwidth is much narrower. Fig. 4 shows overlaid SWR
curves relative to the respective resonant impedance of a square
loop and a rectangle. The 2:1 bandwidth is about 1/3 the width
achieved by the square loop. As a consequence, the rectangle will
likely require considerably more field adjustment effort than a dipole
or square loop.
Chapter 69
We may retrace our steps on 40 meters (7.2 MHz) to assure

ourselves that the trends that apply to 75 meters are quite general.
Table 2 provides data over the same span of heights (in
wavelengths) and the same soil types that we applied to 75 meters.
Because ground losses at 40 meters are slightly higher than at 75
meters, we expect a slight reduction in gain values for comparable
heights. The rectangle is 0.36-λ by 0.157-λ using AWG #14 copper
wire.
Chapter 69
Chapter 69
In general, the heights required for maximum zenith gain are about
one step higher on 40 than on 75. In addition, they are equivalently
higher than for the square loop on 40 meters. Fig. 5 provides a
graphic view of the gain curves for each soil type in the table. Like
the curves for 75 meters, the 40-meter gain graphs show very slow
changes in the zenith gain in the general height region of maximum
gain, a fact that allows the user to vary the physical height of the
antenna with no perceptible difference in operational performance.
The feedpoint impedance values remain tame in the sense that

small changes of the rectangle’s dimensions can easily yield a
precise 50-Ω impedance. Since resonance is a function of the
circumference, every modification to either the long or the short
sides will require a comparable modification to the other sides.
Elongating the long sides will reduce the resistive component value,
while increasing the length of the short sides will raise the value.
Since the amount of change for the side lengths will be small, the
beamwidth ratio will not change much.
Chapter 69
Like the 75-meter rectangle, the 40-meter version also displays a

narrower SWR bandwidth than a square loop, as measured relative
to the resonant impedance of each type of antenna. Fig. 6 displays
the narrowing on 40 meters by superimposing loop and rectangle
SWR curves. The rectangle’s 2:1 SWR bandwidth is about 1/3 the
value for a square loop.
Chapter 69
The tables have shown zenith gain values that may seem high
compared to those we developed in the second set of these notes
for the dipole and the square loop. To confirm this impression,
Table 3 presents maximum zenith gain data for each type of
antenna over each type of soil, along with the height above ground
at which the maximum zenith gain occurs. The heights of maximum
gain for both the dipole and the square loop are almost identical,
but the rectangle requires about 0.01-λ greater height to reach
maximum gain. As noted earlier, this is a fact worth remembering
for the moment.
Chapter 69
The rectangle provides an added increment of gain over the square

loop with any soil type. The increment is not as great as the
increment of the square loop over the dipole. However, the
rectangle provides an average of about 1 dB higher gain than the
dipole when both are at optimal heights above ground. The
increase is highest over very poor soil and least over very good soil
and slightly higher on 40 meters than on 75 meters. Whether the
gain increase offsets the narrower SWR bandwidth of the rectangle
is a complex judgment that requires consideration of all mission
and resource information applicable to a given installation site.
Fig. 1 provided the outlines of the rectangle in isolation, the case

with which we have been working, and of the rectangle with a near-
ground screen. The screen is 0.001-λ above ground to allow the
modeled wires to avoid ground penetration. It uses openings that
Chapter 69
are 0.05-λ per side to simulate better the sorts of screening that
might actually find use at a site. For uniformity over the three soil
types, the antenna is fixed at 0.175-λ above ground and uses the
dimensions set for resonance without a screen. Table 4 presents
the results of the screen test.
Although the screen is 1 λ by 1 λ, making it a bit short for the

broadside dimension of the loop, the supplement does improve
gain, even over very good soil. More significant is the uniformity of
both gain and feedpoint impedance values over all three soil types.
The total variation in feedpoint impedance on either band is about 4
Ω of resistance. As we saw with the dipole and the square loop in
past notes, the gain value over very poor soil is (by an insignificant
operational amount) the highest on both bands. Over very poor soil,
installation of a ground screen may be a worthy investment, since
Chapter 69
the gain improvement can be up to about 2.5 dB over the same

antenna without the screen.
Our exercise has been largely hypothetical, since it rests on the

assumption that for some given mission, a circular beamwidth
pattern is required or desired. The rectangle proves to be one of the
simplest means for achieving the goal—and for obtaining slightly
more gain than the other basic antennas and for achieving a
feedpoint impedance close to 50 Ω. The cost, as we have seen, is a
major narrowing of the SWR bandwidth of the resulting antenna.
Maximum Zenith Gain
In theory, we may produce much higher gain than we obtained

even with the rectangle. One very basic way to achieve this goal is
to create a large array of parallel dipoles spaced ½-λ apart and fed
in phase. The net gain will be a function of the number of dipoles in
the array. The array achieves its increased gain by reducing the
beamwidth of the zenith lobe. A very long collection on in-phase
collinear sections can achieve similar ends by the same beamwidth
narrowing means.
Within the realm of practical antennas for NVIS work, most

suggested high-gain arrays have restricted themselves to 2
elements fed in phase. Past suggestions have acquired some odd
names, but all of the 2-element arrays are variations on the lazy-H.
In this section, we shall look at two of the past arrays and then
create a third version of the lazy-H with superior gain. Along the
way, we shall acquire a better understanding of the relationship of
Chapter 69
an array’s broadside dimension and the required height above

ground for maximum zenith gain.
One of the earliest antennas in this group has carried the label
“Shirley” array. As shown in Fig. 7, it is a form of lazy-H that uses
relatively short (1/2-λ) elements with a wide spacing (0.65λ)
between them. The lines joining the elements are transmission line
sections. To achieve in-phase feeding of the elements, we use
equal length sections to a central feedpoint.
In our notes, shall omit feedpoint impedance values. The feedpoint

impedance depends upon the length of the elements, the
characteristic impedance and velocity factor of the phasing lines,
along with the length of the lines. Because the ½-λ elements are
still within a range that permits mutual coupling, the impedance of
Chapter 69
½-λ elements will not be identical to the impedance of each

element in isolation. As well, different installations may opt for
different feedpoint positions, some using an elevated feedpoint and
others using longer lines for a feedpoint at or near the ground. With
judicious element pruning, one might develop the array to use ¾-λ
(electrical length) sections of phasing line with a 70-75-Ω
impedance to transform element 50-Ω impedance values to 100 Ω.
In parallel, the array might then be fed with a 50-Ω coaxial cable.
The lazy-H configuration with two elements fed in phase increases

the broadside gain relative to a single element. The particular
configuration used in the Shirley array employs ½-λ elements with a
spacing that approaches maximum gain for the element length.
Table 5 summarizes the potential performance of the array over
each ground type. We may omit the scanning of many heights with
the understanding that for the height region around maximum
zenith gain, the change per height increment is relatively small. The
table lists only the heights of maximum gain and the zenith gain
value for each soil on each of our two bands.
Chapter 69
The phased dipoles at wide spacing produce an average of about

3.5 dB over single dipoles. The required height for maximum zenith
gain averages about 0.02-λ higher than for the single dipole. The
height values are about 0.01-λ higher than for the rectangle. Note
that the Shirley array uses a spacing between dipoles that is close
to twice the spacing of the broadside wires in the rectangle. The
increased height of maximum gain from the reflective surface—in
this case, the ground—is also noticeable with planar reflector
arrays. In fact, the required height increase of the array over a
single dipole is less with very poor soil, a relatively poor reflector.
Chapter 69
Fig. 8 in conjunction with the beamwidth ratios shows other

interesting facts about the performance of two dipoles spaced more
than ½-λ apart. First, the broadside beamwidth narrows
considerably to yield the higher gain levels. However, the endwise
beamwidth remains close to the value for individual dipole
elements. As a consequence, the array has beamwidth ratios well
under 1.00. Still, the motivation for employing a phased array to
obtain higher gain is the gain itself. In most such cases, designers
are not concerned with the beamwidth ratio. The higher-gain NVIS
antennas tend to focus solely upon NVIS effectiveness, to the
exclusion of almost all other missions. The second interesting fact
about the present array is the development of secondary broadside
lobes. Such lobes are typical of any phased array in which the
element spacing exceeds ½-λ.
Chapter 69
Fig. 9 shows Shirley array over a ground-level screen. Because the

spacing between elements is so wide, the modeled screen uses a
broadside dimension of 1.5 λ. The results of modeling the antenna
at a height of 0.2-λ above ground with the screen beneath appear
in Table 6.
Chapter 69
With a ground screen, the array provides only a very small gain
improvement over very good ground, but about 2-dB of
improvement over very poor soil. The reported gain values are
insignificantly different as we change soil types once we add the
screen. Indeed, the uniformity of operating characteristics tends to
apply to all of the antenna parameters.
The second of our older antenna systems bears the label “Jamaica”
array. In fact, as shown by the outline sketch in Fig. 10, the array is
nothing more or less than a traditional lazy-H. The elements are 1 λ
long, which presents to the individual phase lines a very high
impedance value. Normally, a lazy-H builder uses equal lengths of
parallel transmission line to a central feedpoint. Again, the precise
impedance at the feedpoint is the parallel combination of individual
impedance values, as transformed by the lines. The transformation
will depend upon the characteristic impedance, velocity factor, and
length of the lines employed. In many cases, the net feedpoint
impedance will consist of a relatively low resistive component and a
high reactance. As a result, matching at the feedpoint generally
results in lower losses than using a long run of parallel transmission
line.
Chapter 69
Because the Jamaica or standard lazy-H uses longer elements, its

gain potential is higher than we can obtain from the Shirley array.
Table 7 summarizes the heights and values of maximum zenith
gain from the standard lazy-H configuration.
Chapter 69
The Jamaica array provides about a dB higher gain than the

Shirley. However, it is more notable for what it reveals about array
performance in general. The longer elements result in a narrower
endwise beamwidth, as shown in Fig. 11. The broadside
beamwidth exceeds the endwise beamwidth, resulting in
beamwidth ratio values greater than 1.00. Still, the values average
only about 1.25:1, indicating a fairly circular NVIS pattern. In
addition, because the spacing between the elements does not
exceed 1/2-λ, the broadside pattern has no secondary lobes.
Finally, the closer element spacing also produces maximum zenith
gain heights that are very similar to those for a single dipole.
As we did for the Shirley array, we may place a ground-level screen

below the Jamaica array. The greater element length requires a
screen enlargement. For this exercise, I used a screen that is 1.5 λ
per side. All of the screens used in these notes use 0.05-λ
openings. Fig. 12 shows the general outline of the Jamaica array
and its screen. The results of the modeling appear in Table 8.
Chapter 69
The table provides no surprises. The screened array over very

good soil provides very little added gain, but about 1.7 dB more
gain over very poor soil. Across all soil types, the performance
values a very consistent, with very poor soil showing again the
highest numerical gain values. Indeed, for all implementations, the
Chapter 69
standard lazy-H provides high-gain NVIS service compared to the

basic antenna. The remaining question is whether we can further
improve zenith gain without adding further elements to the lazy-H
configuration.
There is a version of the lazy-H, sometimes called the extended or

expanded lazy-H, that uses 1.25 λ elements with a spacing value of
about 0.65-λ (sketched in Fig. 13). The individual elements are
called extended double-Zepps, which provide about the maximum
gain possible from a simple length extension before the pattern
breaks into multiple lobes with a reduced broadside lobe. The
elements are spaced as far apart as possible to yield maximum
gain when fed in phase with each other. The combination produces
the maximum possible broadside gain (measured from the plane of
the element pair). Table 9 provides a glimpse into the gain and
other performance attributes of the extended lazy-H when pressed
into NVIS service.
Chapter 69
The maximum zenith gain of the extended lazy-H array averages

about 6 dB more than we can obtain from a single dipole. However,
the antenna height at which the array reaches maximum gain
averages about 0.04-λ higher than the maximum gain heights for
the dipole. The increases spacing between elements explains only
part of the required heights, for the extended lazy-H has the same
spacing distance as the Shirley, which has lower maximum gain
heights. The extended lazy-H shrinks both the broadside and
endwise beamwidths to achieve its gain. As a result, it shows
secondary lobes for both types of elevation patterns, as is evident
in Fig. 14.
Chapter 69
The patterns not only show secondary lobes along both axes, but
as the 3-dimensional view of the pattern reveals, the secondary
lobes are separate. An elevation pattern along an axis at 45° to the
broadside and endwise directions would show virtually no
secondary lobe structure. The strongest secondary lobe is about 12
dB lower in strength than the main lobe and would normally not
constitute a problem for NVIS operation. However, strong
atmospheric noise at medium elevation angles in certain (mostly
endwise) directions may raise the overall background noise level.
Perhaps a more interesting problem is the fact that, at the endwise
half-power beamwidth angle, the communications radius is less
than about 150 miles, rather than the 200-300 mile range we
expect of more basic antennas. (Broadside, the radius is over 200
miles.) The situation reveals that, so long as NVIS gain comes at
the expense of radiation pattern beamwidth, there are limits to the
gain that we should expect from NVIS arrays.
Chapter 69
As shown in Fig. 15, we may place a ground level screen below the
extended lazy-H. The increased element length and spacing
distance of the array requires a screen that is 2 λ endwise and 1.5 λ
broadside. As in all of the screen tests in this section, the antenna
is 0.2-λ above ground. Table 10 provides the test results.
Chapter 69
The consequences of adding an adequate ground screen below the

lazy-H parallel previous results for the Shirley and Jamaica arrays.
Gain improvement over very good ground is negligible, while over
very poor ground, we improve gain by just over 2 dB. The gain
figures are almost uniform over the range of soil qualities, with very
poor soil showing its now typical numerical edge. The beamwidth
values and the ratio between them show virtually no change.
The extended lazy-H has an additional potential. It provides usable

gain over a 2:1 frequency ratio, counting downward from the
frequency at which the elements are about 1.25 λ long. The gain,
however, is not constant as we reduce the operating frequency. At
lower frequencies, the elements are shorter as a fraction of a
wavelength. On 60 meters, the 40meter extended lazy-H elements
are about 0.9-λ long, while on 75 meters, the length shrinks to
about 0.7-λ. In addition, the space between the elements
undergoes an equally proportional reduction. (For example, on 60
meters, the antenna is close to the Jamaica array proportions.)
Both decreases in effective array size combine to reduce gain on
the lower bands. The user question is whether the remaining gain is
adequate to the mission assigned to the antenna.
Table 11 provides data for all three bands over the surveyed soil
types. As the best compromise among the bands, the antenna is
set 40’ above ground, which is somewhat high for 40 meters,
somewhat low for 75 meters, and nearly optimal for 60 meters.
However, element and spacing reductions yield lower gain on the
60-meter band than on the 40-meter band.
Chapter 69
As we lower the operating frequency, the broadside and endwise

bandwidth values both increase, as suggested by the tabular
entries. However, the rates of increase are not identical in both
directions, as the beamwidth ratio values show. We may glean a
further understanding of the changes by examining the broadside
and endwise elevation patterns in Fig. 16. With the shortening of
the elements and of the space between elements, the patterns for
bands below 40 meters show no secondary lobes.
Chapter 69
Of the bands covered, 75 meters shows the lowest gain. Before

discounting the performance on this band, compare the values with
those for a rectangle. The 40-meter extended lazy-H on 75 meters
still provides an added full dB of gain.
A more significant problem perhaps is the range of feedpoint

impedance values offered by the 3-band extended lazy-H. The
numbers cited in the table only show the possible range and are not
actual values. The actual values would depend upon the
characteristic impedance, velocity factor, and length of the two
phasing lines. In most cases, a 3-band extended lazy-H would
employ lines running to near-ground level with a remote antenna
tuner installed at that point. A parallel transmission line from the
feedpoint to the equipment room may well suffer significant loss on
one or more bands, especially where the reactance at the feedpoint
is very high relative to the resistance.
Chapter 69
Despite its limitations, the extended lazy-H—either as a monoband

or a multi-band array— offers high gain for NVIS operations. It
requires only 4 corner tall supports and possibly a short center
support for the remote antenna tuner. The smaller versions of the
lazy-H might also serve as monoband antennas with slightly lower
gain but generally wider beamwidth values for a larger calculated
communication radius. If we expect effective NVIS communications
with a prescribed radius, the family of lazy-H configurations may
approach the practical gain limits for NVIS work.
Tilting the NVIS Radiation Pattern
Thus far, we have presumed that the zenith angle is best for
virtually all missions. However, some stations have indicated a
need for tilted NVIS patterns. The primary examples both come
from near-shore locations. In one case, the goal was for maximum
inland coverage; in the other instance, the aim was for over-water
coverage. The design question that emerges is whether we can not
only tilt the NVIS pattern, but also maintain gain directly upward at
least at dipole levels.
One method that suggests itself to many is to use a dipole and

reflector wire. In the third set of notes, we examined this
arrangement in perfect vertical alignment to find the combination of
antenna height and reflector height that provided the best
performance. To tilt the radiation pattern, perhaps we need only
displace the reflector wire to some position behind the driven dipole
without materially altering the wire relationships relative to ground.
Fig. 17 shows the general outline of what we might do. The driver
Chapter 69
remains fixed while we offset the reflector to various positions.

Theoretically, the pattern should tilt to the right relative to the
sketch.
Unfortunately, the plan fails to account for an important fact about

NVIS antennas with single element parasitic reflectors. The
reflector element is only one of two major sources of radiation
reflection. The ground itself is the other major reflective element,
and in many ways, it can override the effects of a parasitic element.
Table 12 provides comparative results between a vertically aligned
pair of elements and a driver with the reflector offset to the rear by
0.2-λ. (Intermediate positions for the reflector show intermediate
results between the two parts of the table.)
Chapter 69
Although the offset reflector versions of the array show a take-off

angle that is less than 90°, the amount of overall pattern offset is
disappointingly small. Operationally, the difference would not be
noticeable. Fig. 18 compares patterns for the two cases over
average ground. In effect, the reflector element cannot overcome
the greater influence of the ground itself in reflecting signals straight
upward.
Chapter 69
The goal of having a tilted radiation pattern is significantly to reduce

signal strength to a defined rearward area while preserving signal
strength overhead and in the defined forward direction. One way to
achieve this goal is reorient the 2-element array into a horizontal
position and to place it in a relatively low position over the ground.
We shall employ 0.175-λ as the beam height as a reasonable
compromise height among the precisely optimum heights over each
of the soil types.
Before we model a beam under these conditions, we may wish to

consider which beam to use. The beam should be basic, perhaps
limited to 2 elements. We might construct larger beams, but the net
effect would be greater gain at lower angles, a feature that falls
outside of the project specifications. We need only enough gain to
Chapter 69
provide good signal reduction to the rear while maintaining the

highest possible gain in the zenith and high-angle forward
directions.
Fig. 19 presents 3 candidate beams for the role. All happen to be

parasitic beams, but one might as easily employ a 2-element
phased horizontal array. The outlines are in proper proportions to
each other. The driver-reflector array uses wide element spacing,
while the driver-director version uses much closer spacing. The
Moxon rectangle requires the least endwise space of the three
beams. Table 13 provides the 75-meter and 40-meter dimensions
of each modeled beam in feet.
Chapter 69
Prior to any practical modeling, we may estimate the relative

probabilities among the candidates of fulfilling the radiation pattern
specification. Free-space E-plane patterns, such as those shown in
Fig. 20, provide excellent guidance in selecting a beam for the task.
These patterns approximate—with the correct interpretation—the
shape of the final pattern above ground, with adjustments for
ground reflections.
Chapter 69
The driver-reflector Yagi shows a narrower beamwidth than the

other beams. As well, its shape shows less width along the plot’s
vertical axis. In contrast, the driver-director Yagi and the Moxon
rectangle have wider beamwidths and more gain along the plot’s
vertical axis. These rapidly read comparisons will translate into
distinctive features in patterns over real ground. Fig. 21 presents
samples of the broadside and endwise patterns of each beam at a
height of 0.175-λ above average ground.
Chapter 69
The upper row of patterns provides broadside views of the radiation

patterns. The two more promising beam designs show less
medium-angle gain to the defined rearward side of the antenna. In
contrast, the driver-reflector Yagi has a considerable rearward
elevation lobe. The lower row of patterns are the endwise plots at
the zenith angle, with the limit of the plot scaled to the overall
maximum gain of each beam. In all cases, the maximum gain is
greater than the zenith gain. Of the three candidates, the driver-
reflector Yagi has the weakest zenith gain compared to its
maximum gain. The driver-director Yagi and the Moxon rectangle
show only small differences in the relative strength of zenith gain.
The remaining step is to compare numerical data to determine if

there is a clear winner among the three candidate beams. Table 14
supplies the values for both 75 and 40 meters.
Chapter 69
The maximum gain varies by only a small amount among the three
beams for any given frequency and soil quality. Where we find
more important differences is in the zenith gain columns, with the
Chapter 69
Moxon providing the strongest values. (However, the margin is not

so great as to rule out use of the driver-director Yagi.) As well, the
wider free-space beamwidth of the Moxon translates into rearward
half-power points that extend over most soils just to the rear of the
zenith angle, thereby assuring adequate radiation in the immediate
vicinity of the antenna location. (Negative values in the rearward
column indicate radiation to the rear within 3 dB of maximum gain
within the specified angular distance. A positive value in this
column indicates that the –3-dB point occurs forward of the zenith
angle.)
In fact, all three candidate beams (and many other basic arrays that
we might select for the task) tilt the pattern in the defined forward
direction. The driver-director Yagi and the Moxon rectangle provide
better reduction of signal strength to the rearward areas. The
numbers and the pattern shapes that we have so far observed do
not quite complete the information that we need in order to make a
decision.
The wide spacing of the elements in the driver-reflector Yagi

assures a broad SWR bandwidth (relative to the resonant
impedance). The Moxon rectangle also has a relatively wide SWR
bandwidth. However, on 75 meters, as shown by the superimposed
SWR curves in Fig. 22, the driver-director Yagi reveals its typically
narrow operating bandwidth. Unlike 2-element arrays with
reflectors, the presence of the director reverses the SWR trend so
that it rises more steeply above the resonant frequency than below
it. Nevertheless, the region with an SWR of less than 2:1 is scarcely
60 kHz wide.
Chapter 69
On 40 meters, we find a similar situation, as revealed by Fig. 23.

The wide-spaced driver-reflector Yagi and the Moxon rectangle
have relatively wide operating bands. The values are not as great
as would be the case for a single linear dipole, but they are wide
enough to allow easy tuning of the arrays to the SSB portions of the
band. On both bands, the Moxon bandwidth is slightly greater than
the driver-reflector Yagi bandwidth. In contrast, the driver-director
Yagi SWR bandwidth is not wholly adequate to cover the upper half
of the 40-meter band. Adjusting the narrow-spaced Yagi for both
the correct frequency and optimum performance might be a
somewhat daunting task.
Chapter 69
If we add up the total information provided by the models, then the

Moxon rectangle might be the best candidate for pattern tilting
among the three candidates. However, our samples have covered
only some of the possible directional antennas that we might
consider in this regard. Nevertheless, the goals definitely rule out
tilting vertically aligned arrays. Low horizontal directional arrays of
the types considered hold the most promise of performing well in
this specialized task.
Before we close the book on the Moxon rectangle, let’s add one
more test by placing a 1-λby-1-λ near-ground screen below it,
similar to tests that we have performed with other antennas in this
overall collection of notes. Since the dimensions of the Moxon
rectangle are modest, when measured in terms of wavelengths, the
smaller screen—outlined in Fig. 24—will suffice.
Chapter 69
The results of our test appear in Table 15, which may hold a
surprise for the unwary. In all other tests, we found that the gain
over very poor soil exceeded the gain over other soils with the
screen in place. While this trend holds true for the zenith gain
values, it does not hold true for the maximum gain values.
Maximum gain at the take-off angle involves ground reflection not
only in the immediate vicinity of the antenna, but also well beyond
the screen limits in the forward direction. As a result, some major
components of the reflected rays that combine with the incident
rays are reflected from bare soil and hence show heavier losses.
The amounts are not operationally significant, but are just enough
to show up in the lack of parallelism between the progressions of
maximum gain and zenith gain values.
Chapter 69
Apart from the small surprise in numbers, the Moxon’s performance

over a sufficiently large ground screen is remarkably consistent
across the entire span of soil qualities. As in virtually all other trials,
the screen has negligible effect over very good soil, makes a
marginal improvement over average soil, and improves
performance noticeably over very poor soil. As always, its
implementation depends not only upon soil quality, but as well upon
the time, energy, and monetary resources available for the antenna
installation.
Conclusion
In our exploration of some special purpose NVIS antennas, we

have had occasion to suggest the use of some antenna types not
usually considered by radio amateurs (or many others): rectangles,
extended lazy-Hs, and horizontal beams. The special needs that
we have explored may not match the special needs of your
Chapter 69
particular installation. However, they do illustrate that fact that the

possible antennas for NVIS operations go well beyond the basic
dipole, inverted-V, and square or diamond loop. For every need,
there likely is an antenna type that we can adapt to the application.
These notes have not covered all possible special needs. One fairly
obvious omission is the need for rapid frequency changes, such as
those demanded by automatic link establishment (ALE) techniques.
Antennas to meet these needs, such as terminated antennas with
relatively constant feedpoint impedance values over a very large
frequency range, are the subject extensive notes elsewhere at this
site. The gain deficits that are inherent in these antennas have
spurred investigation in two directions. One is the development of
an antenna without the loss of gain but with the uniform feedpoint
impedance. The other is the employment of high-speed antenna
tuner switching to allow the use of common antennas with higher
gain to do the job. In addition, for non-military, non-governmental
applications, such as the wide range of type of emergency
communications, the situation has raised the question of whether
we need frequency change times in the microsecond range or
whether we might ably use change times in milliseconds, of which
many ATUs are capable.
Moreover, we have not addressed the special needs of mobile and

field antennas. Many new commercial offerings are appearing in
this arena, and a few of them actually offer some incremental
improvements. Obviously then, these scant closing notes only
function to say that the subject of NVIS antennas is far from
Chapter 69
concluded with this set of observations on special purpose NVIS

antennas.
Chapter 69
Chapter 70: All-Band Horizontal-Plane Loops
T
o set a contrast with the vertical-plane (VP) loops (covered in
another note in this series on vertical-plane deltas), I made a
couple of models of 80- meter 4-sided horizontal-plane (HP)
loops, each 70' per side to bring them close to resonance in the 80-
meter band. One I fed at a corner; the other a fed mid-side. The
loops are at 35' up over medium earth and are #12 copper wire.
The general summary is this: on 80, either loop is a cloud burner,

but with pretty good gain at 45 degrees elevation. In general,
except for 40 meters, the corner-fed loop shows more bi-directional
patterns (with minor side lobes), mostly through the corners where
Chapter 70
the feedpoint is the backside. On bands from 20 meters, there is up

a slight (3-4 dB) front-to-back ratio.
Fed on one side (rather than at a corner), there is a tendency for

the antenna to exhibit more lobes per band, with those to the far
side from the feedpoint being slightly stronger--again by no more
than 2-4 dB.
Both the corner-fed and the side-fed antennas, as the charts will
show, represent easy work on an antenna tuner, with very
reasonable values of R and X. Indeed, a 300- ohm line will likely
show the smallest excursions of R and X along the line length,
although 450-ohm line is perfectly good as well. From the values in
the chart, line length should not be critical.
In the charts below, all maximum gain figures use the TO angle
(elevation angle of maximum radiation) except for 80 meters,
whether the gain is at a 45-degree TO angle.
1 wl loop (70'/side), corner-fed: #12 copper 35' up over medium earth:
Freq. TO angle Max Gain Feed Z Pattern notes
MHz degrees dBi R+/-jX
3.58 90 5.16@45 67 +j 4 oval thru corners
7.1 48 5.69 84 -j150 oval across corners
10.1 41 9.32 370 -j575 narrow oval thru corners
14.1 27 10.51 305 -j105 clover leaves thru corners
18.1 20 13.75 350 +j240 EDZ-like thru corners
21.1 17 13.63 245 -j105 clover
24.95 14 14.09 320 +j110 thru crnrs w/side lobes
28.1 12 12.92 225 -j145 12 lobes
Chapter 70
1 wl loop (70'/side, side-fed:) #12 copper 35' up over medium earth:

Freq. TO angle Max Gain Feed Z Pattern notes
MHz degrees dBi R+/-jX
3.58 90 5.09@45 65 +j 4 oval thru sides
7.1 44 6.73 275 +j130 oval thru sides
10.1 35 6.86 285 -j535 lobes at corners
14.1 27 9.69 265 -j165 4 lobes at corners
18.1 21 11.65 400 +j180 6 lobes, strong=far side
21.1 18 10.61 400 -j120 many lobes, strng=far side
24.95 15 11.08 370 +j 45 many lobes, strng=far side
28.1 11 11.83 250 -j180 many lobes, strng=far side
The side-fed shows slightly less max gain on the upper bands, but
has more stronger lobes other than the corner-fed version. If the
pattern notes can be deciphered, you can choose whichever suits
your operating desires most.
To assist in interpreting the brief pattern notes, the following

azimuth patterns of corner-fed and side-fed HP loops at 10.1, 21.1,
and 28.1 MHz may be useful. For each pattern, the antenna is a
square aligned with the graphic borders. The corner-fed model is
fed at the lower left corner of the graphic. The side-fed model is fed
at the middle of the left side.
Chapter 70
Chapter 70
The 10.1 MHz patterns show the most unique differences, with the
corner-fed model having a beam-like pattern, while the side-fed
model pattern is somewhat non-descript but more omni-directional.
Chapter 70
Chapter 70
At 21.1 MHz, the side-fed model shows much broader lobes, while
the energy from the corner-fed model is concentrated in 4 fairly
narrow lobes.
Chapter 70
Chapter 70
By the 10-meter band, there is little to choose from between the two
antennas.
As a general rule, the horizontal loop offers more directions,

especially in the side-fed version, than the single wire, which
concentrates its energy more toward the ends as the frequency
goes up. A compendium of patterns for 135' doublets and for 102'
doublets appears in notes taken from the series done for Low
Chapter 70
Down. The loop has fewer bands with problematical impedances

than any of the doublets.
For all-band use, the HP loop seems to offer more than the VP
loop. The HP loop elevation angles are close to those of a single
wire doublet, which places them lower and stronger than those for a
VP loop. In general, with either mode of feeding, expect strongest
results in the quadrants across the way from the feedpoint.
Chapter 70
Chapter 71: A 40-Meter Star-Shape Loop
T
he horizontally oriented 1-wavelength square loop is a fairly
standard low-HF amateur antenna. It lends itself to use with
parallel feedline for multi-band application. However, a 1-
wavelength loop tends to radiate broadside to the loop. Therefore,
the antenna tends to provide better performance on bands above
the lowest.
The Standard Square and the 4-Pointed Star Loops
The need for a longer circumference is often at odds with amateurs

who have only limited space for wire antennas on the lower HF
bands. However, one way to increase the circumference of a loop
without increasing its footprint is to draw in the 4 sides of the loop
toward the center. The result is a 4-pointed star configuration. Fig.
1 shows the difference between the standard and star loops, as
viewed from above (or below, as the case may be).
Chapter 71
Fig. 1 also provides us with a key to the main dimensions of the

loop and the star. The length of a side for a square horizontally
oriented loop is also the length of one side of its footprint. For the
40-meter (7.15 MHz) test case, each side of the loop is about 36.2'
long for a near resonant loop. This provides an antenna and a
footprint circumference of 144.8' or about 1.05 wavelengths at 7.15
MHz for a near-resonant loop. On the right side of Fig. 1 is the star.
Here, we must distinguish between the wire length and the
footprint. For a near resonant loop, we require a footprint side
dimension of about 31.9', which results in a footprint circumference
Chapter 71
of 127.6'. This dimension set is actually smaller than for the square
loop. However, as shown in the sketch, each wire is stretched
inward toward the center. We cannot make the wire touch at the
center, but we can come in rather close. The most radically inset
case that I have so far explored positions the apex of each angle
formed from the side wires at 1.75' from the antenna center. This
yields a distance of about 3.5' between opposing points. The
resulting wire length for each side of each point in the star is about
21.35'. The total wire circumference thus becomes about 170.8' or
close to 1.25 wavelengths.
We can compare the potential performance of the two

configurations on 40 meters via the following table of modeled
results.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Square and Star Loop Performance at 7.15 MHz
Antenna Height 50'. Antenna Wire AWG #12 copper. "Insets" refers to the
distance of the limit of the star side inset point from the exact center
of the array.
Gain El. Angle Feed Z

dBi Degrees R +/-jX Ohms
Square 5.54 47 157.5 - j 6.3
Star: 1.75' insets 5.50 39 65.7 + j 9.0
Star: 2.0' insets 5.50 39 66.8 + j12.0
Star: 3.0' insets 5.50 40 71.1 - j 0.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Several aspects of the tabular data are significant. First, the 40-
meter gain of the two versions of the loop is virtually the same.
However, the elevation angle of maximum radiation is considerably
Chapter 71
lower in the star version. Fig. 2 graphically illustrates these matters

by showing the two azimuth patterns, each at its respective TO
angle, to exactly overlay each other. However, the elevation pattern
of the star along the axis of maximum radiation has a noticeably
lower angle of maximum radiation (take-off or TO angle).
Second, if operation is contemplated only on 40 meters, then the

impedance of the star configuration is suitable for a coaxial cable
as the feedline Either 50-Ohm or 75-Ohm cable will do. For similar
operation, the square configuration would require either the use of
a parallel feedline or the use of a 4:1 balun with a 50-Ohm coaxial
cable feedline.
Third, the star configuration is not especially sensitive to just how

far toward the array center we push the insets. The distances from
Chapter 71
center shown may be doubled to see how far apart we may place
the inner points of the star. There is considerable room for variation
before we lose our advantage over the square loop in terms of TO
angle. However, note that the 3.0' inset has bumped the TO angle
upward one notch. As we further move the inner start points away
from center, the antenna slowly returns to the characteristics of a
simple square loop.
The principle behind the star is an attempt to increase its wire

circumference length without increasing its footprint. The 0.2-
wavelength increase, while not giving us the almost pure edge-wise
radiation of a 2-wavelength loop, does raise the entire wire length in
the star loop to 1.25 wavelengths. That much length is sufficient to
lower the 40-meter radiation angle by a noticeable amount.
The Square Loop as a Multi-Band Wire Antenna
The square loop allows us to feed the antenna on higher bands,

relative to the base-line 40-meter band to which we have cut it. We
can summarize the performance with the following tabulated
samples for the HF bands.
Chapter 71
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40-Meter Square Loop Performance
Antenna Height: 50'. Antenna Wire AWG #12 copper.
Freq. Gain TO angle Feed Z Pattern Shape

MHz dBi Degrees R+/-jX Ohms
7.15 5.5 47 160 - j 6
Oval
10.125 4.8 32 3060 + j 3140*
Almost square
14.1 8.5 19 275 + j 1204-leaf clover
18.1 7.2 16 1035 + j 1480*
wobbly oval
21.1 8.7 13 255 + j 55
4 main lobes, 60
degrees off axis
24.95 8.0 11 1230 - j 1380* 6 near-equal lobes
28.1 10.8 10 265 + j 115 4 lobes 45 degrees
off axis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
With exceptions, the patterns generally are strongest in a line

through the feedpoint and the corresponding center point of the
wire opposite. We may call this the main axis of the antenna. On
two bands of high interest, however, the patterns depart from the
noted tendency.
Chapter 71
Fig. 3 shows the azimuth patterns of the square loop on 15 and 10

meters, with the axis presumed to run vertically on the page. The
15-meter pattern forms a sort of butterfly, with small lobes along the
antenna axis. However, the strongest lobes are angled to the sides
by about 60 degrees. The 10-meter pattern has only 4 notable
lobes, each about 45 degrees off axis.
We may also note in passing the starred entries in the feedpoint

impedance (Feed Z) column. Each of the non-harmonic bands
presents an impedance where the resistance and the reactive
components are both above 1000 Ohms. Without careful attention
to the characteristic impedance and length of the parallel feedline
used, the impedance at the antenna tuner terminals may fall
outside the range of values that it can match.
Chapter 71
The 4-Pointed Star Loop as a Multi-Band Antenna
We may perform the same modeling experiment with the 4-pointed

star loop to evaluate its potential as a multi-band antenna for 40-10
meters. The results appear in the following table.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40-Meter Star Loop Performance
Antenna Height: 50'. Antenna Wire AWG #12 copper.
Freq. Gain TO angle Feed Z Pattern Shape

MHz dBi Degrees R+/-jX Ohms
7.15 5.5 39 65 + j 10 Oval
10.125 6.7 26 6820 - j 7650* Diamond
14.1 9.3 19 540 + j 1850* 4-leaf clover
18.1 6.9 16 925 + j 75 Broad beam: F-B 5.2 dB
21.1 6.2 13 945 - j 1270* Broad beam: F-B 1.3 dB
24.95 6.8 11 55 + j 340 Broad beam: F-B 2.5 dB
28.1 6.9 10 715 - j 670 Triple forward lobes
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
For the entries called "Broad beam," the direction of maximum gain
is toward the side of the star containing the feedpoints. If we
overlay the outline of the antenna on top of the azimuth patterns in
Fig. 4, the feedpoint will be above the plot center line across the
page.
Chapter 71
The patterns show one potential advantage of the star as a multi-

band antenna. On all bands, there is a main lobe along the antenna
axis through the feedpoint. Hence, the user is always aware of the
direction of strongest signal. (30 meters is the one exception, but
the main lobe to the reverse of the feedpoint side is only 0.7 dB
stronger than on the feedpoint side, a difference that will not be
detectable in operation.) Although the beam action--that is, having
a small front-to-back ratio--is small, the reliability of having the main
lobe along the same axis on every band used is a distinct plus.
Chapter 71
There are three bands on which the reactance rises above 1000
Ohms. However, only on 30 meters are the values for both
resistance and reactance so high as to create a very distinct
problem for matching the feedline termination to the transceiver 50-
Ohm system.
Why?
The distinctness of the square loop and the star loop patterns
should arouse some curiosity as to the reason for the differences.
Fig 5 provides a partial answer.
Chapter 71
The upper diagrams compare the relative current magnitude

distribution of the two loops on 40 meters. The current on the star
remains higher further outward toward the array corners than on
the square loop, and this phenomenon plays a role in lowering the
elevation angle of maximum radiation (the take-off or TO angle).
Chapter 71
Otherwise, the gain and pattern shape of the 2 versions of the loop
are the same.
The 15-meter case is especially interesting. For the star loop, the
current magnitude peaks and valleys appear in close proximity
along the outward star-point wires. Hence, the currents (or, more
properly, the fields that result) tend to simply add to or subtract from
each other-- with due place given to the phase of each current
magnitude sampled. However, in the square loop, we have current
magnitude peaks more linearly separated from each other, with
distinct peaks at the four corners of the array. The result is the 6-
lobes pattern, with the largest lobes at a considerable angle from
the axis of the antenna.
These brief notes suggest that for some users of square loops,
modification to a star design may be useful. The array dimensions
for 40 meters will easily scale to 80 and 160 meters, although most
users will have difficulty in scaling the height as well as the wire
length. Since we are only approximating resonance on the lowest
band of use and presuming parallel feedline to an antenna tuner,
fussiness with dimensions seems out of place. Since the wire of the
antenna has a small diameter relative to a wave length, any 50-
Ohm resonance on the lowest band of use is likely to be a very
narrow-band phenomenon.
Nonetheless, for the loop-user who wishes a lower TO angle on the

lowest band of use and a pattern that has a maximum along the
axis of the antenna on every band used, the 4-point star is viable
alternative to the standard square loop. The cost is less than 20%
Chapter 71
more wire, which is likely to be the cheapest part of the antenna

anyway. The star loop is not an answer to every loop problem.
However, it does show that it pays to explore different wire
geometries to see whether they have any potential for use.
Chapter 71
Chapter 72: Horizontally Oriented & Polarized Big Wire Loops
L
arge wire antennas are deservedly popular among QRP
operators who have room for them. They are cheap and
effective: the two favorite words among hams.
Among the more usable of the large wire antennas is the loop that
is at least 1 wl long at the lowest frequency of operation. However,
large loops belong to three different families, each with distinct
characteristics.
Chapter 72
Fig. 1 shows the three families of antennas. VOVPLs are vertically

oriented, vertically polarized wire loops, such as the delta and the
rectangle when we feed them along the side. They stand upright
and vertically polarized radiation is broadside to the antenna plane.
Ordinarily, VOVPLs are monoband antennas and perform less well
than their relatives when pressed into service on other bands.
VOHPLs are vertically oriented, horizontally polarized wire loops.

The quad loop fed along a horizontal wire is the most popular
member of this group, although horizontally polarized triangular
antennas are also common. VOHPLs show significant superiority
over VOVPLs in all band use. However, they have two limitations.
First, if we can place a wire doublet at the top height of the VOHPL,
it will usually show a lower angle of maximum radiation, because
the VOHPL's radiation is a combination of the upper and lower
wires. Second, to be a truly large loop of 1 wl or greater, the
VOHPL requires exceptionally tall supports.
For the ham with more area than height in his yard or field, a more
frequent selection is the HOHPL: the horizontally oriented,
horizontally polarized large wire loop antenna. The standard
installation is to place the loop as high as one can, with only the
placement of supports and the overall yard size as restrictions on
the loop length. Loops up to several wavelengths long around their
perimeter are in use on 80 meters--and on all of the bands above.
(We should note in passing that there is no known HOVPL, that is,
a horizontally oriented, vertically polarized large loop antenna.)
Chapter 72
HOHPLs can be strung around the edge of a yard, meaning that

even a city lot whose perimeter is at least 280' long can support a 1
wl version at 80 meters. Such a lot is about 70' by 70' if square. If
the yard width is only 50', then the yard need only extend 90' back
to hold the antenna. With allowance for sidewalks, flower beds,
trees, and the like, there is still room for a HOHPL in many more
ham homesteads than we might think. Therefore, the entire class of
HOHPLs deserves a longer look to discover their strengths and
their weaknesses.
Let's develop a plan of attack for understanding HOHPLs. The first

part of our work will include some answers to the most pressing
questions about HOHPLs:
• 1. How big should we make HOHPLs?

• 2. What shape should we make them?
• 3. Where and how should we feed a HOHPL?
• 4. At what height should we place the antenna?
• 5. On what frequencies can we use the HOHPL?
• 6. How does the HOHPL compare to other all-band
antennas?
The second part of our effort will be devoted to a compendium of

modeled antenna patterns to give you some idea of what to expect
from HOHPLs. Some of the answers we give to questions just
outlined will become graphically clear when we peak at a number of
antenna patterns.
Chapter 72
1. How big should we make HOHPLs?
Ideally, a HOHPL should include at least 1 wl of wire at its lowest

frequency of operation. For 80 meters, that means about 280'
defines the antenna perimeter. In a pinch, we can make the
antenna shorter and still effect a match using parallel feeders and
an antenna tuner. However, let 3/4 wl be about the absolute
minimum for the antenna.
Chapter 72
The circular HOHPL outlines in Fig. 2 show my best suggestion:

make the loop larger than 1 wl. A 1 wl horizontal loop that is less
than 1/2 wl above ground tends to be a cloud burner. NVIS (near
vertical incidence skywave) antennas are certainly useful--and
desirable to certain types of operation. But they have very poor DX
potential.
By the time a loop is at least 2 wl long at its fundamental frequency

of operation, it loses its ability to warm the clouds and becomes an
antenna with some potential for longer distance communications.
So, the general rule for HOHPLs is this: make them as long as you
can support in your yard.
These notes apply to the use of a HOHPL at the lowest desired

operating frequency. However, longer is not always better if our
main interests are at the upper end of the HF spectrum. As we shall
see, a desire to operate on both 80 and 10 meters with a HOHPL
may provide us with a bit of a dilemma.
Although I shall be speaking in terms of 1 wl and 2 wl HOHPLs,

there are no rules against making them even larger or against
making them some non- integral multiple of a wavelength. In some
respects, we can say with assurance that performance of a 1.5 wl
HOHPL will be intermediate between a 1 wl and a 2 wl version.
However, as we shall discover, there are enough variations in the
performance of a 1 wl HOHPL to make my claim fall among the
world's most vague statements.
Chapter 72
2. What shape should we make a HOHPL?
Ideally, a circular HOHPL would likely be best from a theoretical

perspective. However, a circular at 80 or 160 meters is usually
impractical for most ham installations. Therefore we must turn to
polygons, that is, shapes with straight lines that compose the
perimeter.
Before we speak in geometric terms, let's note a mechanical issue

that will be involved in the shape decision. Besides the position of
the supports for corners, we must also take into account the length
of each side vs. the strength of the wire used to form the HOHPL.
Assuming the availability of supports, we would normally place
supports at distances to protect the antenna from undue stress,
especially stress due to weather. Wind and ice are the major
enemies of large loop antennas with long wire runs.
Copperweld is a good material for a long wire loop and may call for
fewer supports than soft-drawn copper wire. Although heavier than
pure copper, quality copperweld wire has many times the strength.
However, another reality of HOHPL construction is that hams tend
to use whatever bargain wire they can find at hamfests, close-outs,
and other inexpensive sources. If you choose the economic route,
be prepared to splice breaks during the life of the antenna.
Realities of ham antenna farms usually breed irregular shapes for

HOHPLs. These shapes are not only usable, but as well they can
be modeled and analyzed. However, we can only do this on a case-
Chapter 72
by-case basis. For our work today we must confine ourselves to

regular polygons. You may think of any regular polygon as a
greater or lesser approximation of a circle: the more sides to the
polygon, the closer the approximation to a perfect circle.
Fig. 3 Illustrates some of the typical geometries used in

constructing making HOHPLs of both regular and irregular shape.
We shall from here on confine ourselves to the regular shapes. Our
reason is a matter of both the general application of the ideas and
the ease of making calculations.
Chapter 72
Regular polygons have some dimensions that are especially useful

in planning and calculating the various antenna dimensions. Fig. 4
shows them in outline form for the triangle through the octagon.
Note the Side (S), radial to a peak (A), and radial to a side (H).
Chapter 72
Table 1 lists some of the relationships among S, A, H, and C (the

overall circumference or total wire length of the loop. Note that the
more numerous the sides, the closer the lengths of A and H to each
other. A circle with an infinite number of sides from a geometric
perspective finds A and H to be equal.
Table 1. Figuring a Regular HOHPL
A. Deciding the Wire Length
L = wire length = 300 / Fl (meters) = 984 / Fl (feet) Fl = lowest frequency used in MHz
L (1.8 MHz) = 167 m = 547' L (3.5 MHz) = 86 m = 281'
B. Figuring the Layout (See fig. 4)
C = length of circumference S = length of side A = length of radial from center

H = length of X or Y from center of loop
I. Triangle III. Hexagon

S = C / 3 S = C / 6
H = 0.29 S (= 0.10 C) H = 0.87 S (= 0.14 C)
A = 0.58 S (= 0.19 C) A = S (= 0.17 C)
A + H = 0.87 S (= 0.29 C)
II. Square IV. Octagon

S = C / 4 (= 0.25 C) S = C / 8
H = 0.5 S (= 0.13 C) H = 1.2 S (= 0.15 C)
A = 0.7 S (= 0.18 C) A = 1.3 S (= 0.16 C)
V. Circle VI. "Irregular"

A = H = 0.16 C String wire along ground and adjust
The table of relationships is especially handy when you begin the

process of planning a HOHPL with a paper sketch of your yard
space. They are also handy if you wish to calculate the wire end
coordinates on an antenna modeling program. The main shapes
that we shall focus on in generating patterns for possible HOHPLs
will be the square, the hexagon, and the octagon--the last because
it most closely approximates a circle.
Chapter 72
3. Where and how should we feed a HOHPL?
Since the HOHPL is a multiband antenna, the feedpoint impedance

will vary from band-to-band. Therefore, the only practical feed
system is a parallel transmission line to an antenna tuner. The line
can be anything from TV lead to commercial or home brew bare
wires spaced every so often with almost any weather- resistant
insulating rod. Even segments of plastic coat hangers will do for
insulators, since the spacing will keep the rods from undergoing
undue electrical stress.
You may locate the feedpoint of a HOHPL at any point along its
length. Mechanically, this usually means intersecting the antenna at
the position that allows the straightest line from the antenna to the
shack entry point. For some installations, the feedpoint may be at a
corner (or junction of sides); for others, the feedpoint may be
centered on a side--or even off- center on a side.
One of the surprises that modeling the HOHPL produced is this: at

what point you feed the antenna does make some difference in the
resulting pattern on at least some of the bands in the HF region. As
we shall see, when we explore the antenna over many ham bands
with several geometric configurations, even the octagon fails to act
like a circle on some of the upper HF bands. When we look at the
patterns of the various antenna versions, keep in mind where you
want the lobes and nulls to be relative to your own possible
installation. A less direct feedline might yield a superior pattern
relative to your operating desires.
Chapter 72
At this point I shall make a brief pitch for every serious antenna buff
to acquire at least one of the antenna modeling programs. There is
no reason for us to simply accept what a roughly constructed
antenna might give us. We can plan and tame the beast-- whether
by relocating wires or relocating the feedpoint--to give us the best
compromise of lobes going just where we want them.
4. At what height should we place a HOHPL?
Like all of the questions surrounding large loops, this question has
two dimensions: the mechanical and the electrical. Therefore, the
simple answer ("As high as possible") does not tell us everything
we need to know or think about in constructing an antenna that
consists of hundreds of feet of wire and a system of at least 3 and
up to 8 support structures.
Chapter 72
The most ideal and yet practical arrangement for supporting a

HOHPL corner appears in Fig. 5. Note that the system includes a
pulley and rope for raising and lowering the wire. A cleat near the
ground is useful for tying off the rope. I have also used rope loops
and clip rings at the cleat level. I disconnect the extra rope used
Chapter 72
only when lowering the antenna and store it out of the weather. I
clip the upper rope to a hook instead of a cleat. When I need to
lower the antenna, I add the extra section, which is long enough to
reach but not pass through the pulley.
A slip ring can be made from almost any plastic, although I tend to
prefer Schedule 40 PVC Tee fittings for their durability. Their
smooth interiors also tend to minimize wire kinking and rubbing,
thus prolonging the life of the antenna. I do not offer these
mechanical notes as a final and best answer to every situation.
Instead, I hope that they get you to think about the mechanical
details of your antenna as being just as important to its successful
performance as the electrical details.
Electrically, the question of HOHPL height is a matter of the

elevation angle of the radiation. We can best picture what height
means to use if we select an antenna design, a set of heights, and
a few test frequencies. So let us take a square HOHPL that is 1 wl
long at 80 meters and place it 35' up, 50' up, and 75' up--all typical
ham installations. Now let's see, with the aid of computer modeling,
what happens. But first, be sure to understand that antenna
modeling presumes flat terrain with no ground clutter. Hence, the
results will be very general.
Chapter 72
Fig. 6 demonstrates the difficulty of using a HOHPL at its lowest

frequency (where it is 1 wl long). The 1 wl loop radiates
predominantly broadside to the plane of the wire, which is straight
up and down. Even at 75' up, the antenna is a "cloud-burner," or a
suitable candidate for NVIS (Near Vertical Incidence Skywave)
service.
Chapter 72
On 40 meters, as the patterns in Fig. 7 show, the antenna begins to

form patterns that are suited to normal sky wave communications.
However, the antenna is still a bit low when under 75' up, so the
angles of maximum radiation are 37° at 50' up and 44° for 35' up.
Longer distance effectiveness is enhanced by raising the antenna
to 75' up, where the angle is about 26°.
Chapter 72
On 20 meters, as illustrated in Fig. 8, the same antenna begins to

show excellent DX potential. At 35' up, the elevation angle of
maximum radiation is 26°, with angles of 19° and 14° appearing at
heights of 50' and 75', respectively. The emergence of higher angle
secondary lobes becomes apparent, but these lobes are generally
not as large as those that form with doublets at the same height.
Chapter 72
On 10 meters, as revealed by the patterns in Fig. 9, the HOHPL

become an excellent DX antenna, with very low elevation angles of
radiation: 12°, 9°, and 6° for heights of 35', 50', and 75'
respectively. (Remember that the lobes have a vertical beamwidth
so that the angles cited represent the center points of reasonably
broad angular spreads that can handle propagation angles
somewhat distant from the center line.)
If the HOHPL has a significant weakness, it lies in the operation of

the antenna at its fundamental frequency. To some extent, this
weakness can be ameliorated by further elevating the antenna. A
better solution, if land area is available, is to build a longer antenna,
so that the fundamental frequency is lower. When the antenna is
operated at its 2nd harmonic (when it is 2 wl long), the primary
radiation is mostly in the same plane as the wire loop. Elevation
angles at 80 meters will still be high, but not nearly as high.
Chapter 72
Compare Fig. 10 to Fig. 6. Although the elevation angle on 80

meters for the 2 wl loop is not ideal, it is considerably better than
the elevation angle of the 1 wl version.
5. On what frequencies can we use the HOHPL?
The answer to this question is simple: on any HF frequency. With

parallel feedlines and an antenna tuner--hopefully a link-coupled
tuner--we can load the antenna and produce useful signals on
every band, whether traditional or WARC. What we get for
radiation, however, depends on many factors, including the shape
of the antenna, the length of the wire, and where we feed the
antenna.
Therefore, let's look at a compendium of azimuth patterns for the

HOHPL using a variety of configurations to sample the territory.
(Remember that a full set of patterns would use up a book, so we
Chapter 72
must restrict ourselves to a relevant sample.) We shall look at 1 wl

antennas in the square and the octagon configurations, each fed at
the center of a side and at a corner. Then we shall repeat the
process with a 2 wl long hexagon as a sample of a longer HOHPL.
From these examples, you can likely extrapolate what might
happen with a large loop placed in your own yard.
In all cases, the feedpoint of the antenna is placed at the left-most

point on the antenna relative to the pattern shown. This procedures
gives you a fair comparison, especially of patterns that are too
complex to place in a single figure by laying one pattern on top of
the other. In some cases, it would be impossible to keep track of
which lobe belonged to which antenna. Therefore, we shall use
separate figures and devote one page to each of the amateur
bands for the 80-meter antennas--and a column to each band for
the 160-meter model.
Chapter 72
80 Meters
Any differences of performance among the loops shown here are

too small to detect in operation, amounting to only 0.07 dB. The
basic pattern of the loop at its fundamental frequency is a broad
oval, stretched in the direction through an axis running from the
feedpoint to a point on the opposite side of the loop. The loop
"sides" are only a little over 2 dB down from the gain maxima.
Chapter 72
All of the loops in this long sequence of azimuth patterns have been
modeled so that the feedpoint is to the far right, whether that point
is in the middle of a side or the point where the wire takes a new
direction. The orientation of the loop is shown only for the 80-meter
azimuth patterns. However, the loop and feedpoint positions do not
change as the modeling runs increase in frequency on succeeding
pages. You can draw your own North line on each pattern.
Chapter 72
For all of the loops shown here, the 3.5 MHz azimuth patterns have
been taken at an arbitrary 45° elevation angle. The actual elevation
angle of maximum radiation on 80 meters is 90° or straight up for
these loops, which are 1þ long. If you compare these patterns with
Fig. 6, you will see that there is very little low elevation angle
radiation on 80 meters, since the basic radiation pattern is
broadside to a 1 wl loop.
Chapter 72
On 80 meters, an 80-meter loop arranged as a HOHPL makes a

very good NVIS (near vertical incidence sky wave) or cloud burner
antenna. Long- distance contacts will likely be rare on 80 meters,
although contacts within a 300-500 mile radius may be stronger
than with some other types of antennas, such as verticals and
inverted Vees. See the 80-meter patterns of Fig. 15 and Fig. 16 for
an alternative, composed of 2 wl loops at 80 meters.
Chapter 72
40 Meters
Both the loop shape and the feed position begin to make
themselves evident on the 40-meter azimuth patterns. Elevation
angles of maximum radiation run from 37° to 43° for these 1 wl
loops at 7 MHz, which allows direct comparisons among the
azimuth patterns. Beginning with the square loops, we can examine
them a pair at a time.
Chapter 72
The square loops show a very distinct difference in shape and gain
that depends upon the feed point. The side-fed model shows
stronger lobes (by almost 0.8 dB) and deeper nulls. In contrast, the
corner-fed model is a round-cornered diamond, with a bit less gain
in the direction of the feedpoint. Moreover, the points of maximum
gain for the corner-fed model are to the sides; that is, at right
angles to the axis passing through the antenna feedpoint and the
point opposite it on the antenna loop.
Chapter 72
In contrast to the differences between patterns depending on the

feedpoint for the square loops, the octagon loops show an almost
insignificant difference in pattern, whether the antenna is fed at a
corner or in the middle of one side. The smaller differences also
show up in the feedpoint impedances, with the squares showing a
large difference as the feedpoint is moved.
Chapter 72
The simultaneous change in both pattern and feedpoint impedance

in the square models indicates that the diamond and square
configurations make a difference in the current distribution and
interaction as the turned with the change in feedpoint. At 40 meters,
the effect is much less for the octagon, since the difference in
length between a radial to a corner and a radial to a side is much
smaller. Whatever the differences, all four of these loops would
make very good omni-directional antenna for 40 meters.
Chapter 72
30 Meters
On 80 and 40 meters, the loops are close to resonance.

Sometimes, differences show up most graphically when an antenna
is operated at a frequency for which it is not resonant. For all of the
loops, the feedpoint reactance is in the vicinity of 600 Ohms at 10.1
MHz. Once again, the squares show a stronger pattern difference
that depends solely on the feedpoint selection.
Chapter 72
When fed at the corner, the 30-meter square pattern becomes very
bi-directional, with about a 2 dB front-to-back ratio and about 8 dB
or more front-to-side ratio. The distance from the feedpoint to the
opposite peak is about 3/8 wl. In contrast, the side-fed square
feedpoint is only about 1/4 wl from the opposite point across the
square. Radiation remains strongest off the corner peaks, and the
gain along the feedpoint axis is nearly 7 dB down from the forward
gain of the corner-fed model.
Chapter 72
Once more, the octagon-shaped models show much less difference

that can be attributed to the selection of the feedpoint position.
Although there is little operational difference between the two
octagons, it is interesting to note minor pattern tendencies. For
example, absolute gain maxima do not appear in corresponding
positions.
Chapter 72
In addition, the nulls of the side-fed octagon are slightly deeper

than those of the corner-fed model. This feature shows a kinship
between the side-fed square and octagon models.
In all, three of the four arrangements make very respectable omni-

directional antennas. Only the corner-fed square arrangement is
less suited to this service and better suited to bi-directional
operation that requires careful antenna orientation for effective use.
Chapter 72
20 Meters
On 20 meters, the elevation angle for the loop, whatever its shape
or feedpoint position, has decreased to about 20°. This angle (a
product of the 50' height for all of the models) places the antenna
radiation into the DX range, although signals would be stronger with
the antenna even higher. On 20 meters, the antenna planner is
faced with further decisions.
Chapter 72
The square loop shows major lobes near or above 10 dBi off each
of the four corners. The lobes of the side-fed model are broader,
which would lessen the problem of orienting the antenna toward
desired areas of the world. In contrast, the narrower but stronger
lobes of the corner-fed square would provide a gain advantage,
especially in three of the four directions that the antenna favors.
The cost of the added gain is a collection of very wide and deep
Chapter 72
nulls in the pattern, which would effectively limit communications in

many directions.
In contrast, the octagons seem once more to have very similar

patterns to each other, regardless of the feedpoint position.
However, note the fact that the lobes are a function of feedpoint
position and not of whether there is a side or a corner at the lobe
Chapter 72
location. This factor shows up in the differential in the feedpoint

impedances for the two octagon models.
What the octagons lack in maximum gain, they make up for in

omni- directional potential. Although nulls can be as deep as 10 dB
below the lobes, they cover less territory and are shallower than
most of the nulls in the patterns for the square models. The lesson
here is simple: if 20 meters is a desired band for operation of a
Chapter 72
HOHPL and if one wishes to work in every possible direction, then

the HOHPL should be as round as one's terrain permits. The
squarer the shape, the larger and deeper the pattern nulls.
17 Meters
The patterns for 17 meters appear to have no rhyme or reason--

indeed, they seem to suggest an error in modeling. However, they
Chapter 72
are as correct as NEC-4 can make them. Once more, nonresonant

operation of the loop permits the current distribution to change
radically with small changes of configuration. The result is a diverse
set of patterns.
The corner-fed square shows a high-gain bi-directional pattern that

is similar to and in line with the 30-meter pattern for the same
model. Maximum gain is off the corners that are in line with the
Chapter 72
feedpoint. The side-fed square also shows its maximum gain off the
corners. However, since the feedpoint is between corners, the gain
is more evenly distributed among all four corners. Hence, the
apparent major difference in the operation of the loops turns out to
be smaller than at first sight, but very significant for planning.
The corner-fed octagon pattern shows its affinity to the corner-fed

square with a noticeable but less extreme bi-directional pattern.
Chapter 72
The greater "side" gain results in a lower gain along the major axis
of the antenna, compared to the square. However, the "side" gain is
not sufficient to qualify this arrangement as having good omni-
directional potential.
The pattern for the side-fed octagon may seem initially mysterious.
Twisting the antenna and moving the feedpoint by only 22.5° alters
the axis of highest gain by 90°. Part of the mystery begins to clear
Chapter 72
up when we note that the antenna is attempting to produce 10

lobes from 8 sides and 8 corners. Since the antenna is over 5 wl
long at 18.1 MHz, current distribution and resultant gain distribution
can change rapidly with small changes in antenna configuration.
Since 17 meters is less widely used, these difficulties are usually
minor.
15 Meters
Chapter 72
The tendency of a square loop to radiate with maximum gain from

its corners continues on 15 meters. The elevation angle is in the
13-14° regions, which gives the antenna significant DX potential.
The strongest lobe of the corner-fed square has a gain rivaling a 3-
element Yagi, but over a much narrower beamwidth. (We should
especially note this fact, because wire antenna makers often
advertise their wares as equal to beams. The illusion only persists if
we ignore beamwidth.)
Chapter 72
With corner feed, current magnitude and phase combine to yield 4

strong, narrow lobes with corner feed. With side feed, the major
lobes become many (12, to be exact), well spread around the
horizon, but at loss of over 3 dB of maximum gain. (Note that the
corner-fed version also has 12 lobes, but 8 are very minor.) The
side-fed square becomes the configuration of choice if we desire
maximum coverage on 15.
Chapter 72
Like the 17-meter model, the 15-meter models of the octagon show
far greater similarity than do the square models. The corner-fed
version retains a bit of the 4-lobe dominance found in its square
counterpart, but the minor lobes have grown into major ones, giving
the antenna better potential for omni-directional contacts. However,
the side-fed octagon has the most even pattern of all, with only a
small tilt of the pattern away from the feedpoint.
Chapter 72
As has been the case on other bands, the feedpoint impedance

differs most widely between the two square models, with
considerable less difference between the two octagon models. The
corner-fed square has a lobe with the highest gain of the four
models. In contrast, the highest gain of the very even-lobed side-
fed octagon is about 4 dB lower than the corner-fed square. Even
lobes usually mean lower maximum gain.
12 Meters
Chapter 72
The 12-meter corner-fed square continues the pattern of bi-

directionalness on this model on the non-harmonically related
bands. As was the case with lower band models, the highest gain is
along the axis from the corner feedpoint through the corner
opposite. When side fed, the square once more shows maximum
gain from the four corners of the loop.
Chapter 72
The loop which is 1 wl long on 80 meters has 14 lobes, or 7 per half

loop on 12 meters. This is no accident, since the length of the loop
at 24.9 MHz is a little over 7 wl. (On 80 meters, the loop showed
only two lobes in the oval pattern, 1 per half wavelength.) As the
side-fed pattern shows, some lobes may be very small. In other
cases, lobes may merge to become almost indistinguishable from a
single lobe. However, you can always count on them being present
as a function of the length of the wire at one lobe per half
wavelength.
Chapter 72
The 14 lobes of the 12-meter octagons are clear and distinct in both
the corner and side fed versions of the antenna. In the octagons,
the lobes are functions of the feedpoint in terms of direction.
However, the difference between the two feed positions shows up
in the minor differences in the relative strengths of the individual
lobes, except for the one directly opposite the feedpoint.
Chapter 72
Interestingly, the 12-meter models are as a group closer to

resonance than any other group. The bi-directional corner-fed
square shows the highest reactance. The other models, with their
more even collection of lobes, show between 20 and 75 Ohms
reactance. You may track the feedpoint impedances in the
reference table that immediately follows this compendium of
azimuth patterns. You may find it useful to correlate the pattern
descriptions, the maximum gains, and the feedpoint impedances of
the models.
10 Meters
Chapter 72
28 MHz is exactly 8 times 3.5 MHz. since the loops at 80 meters

had two lobes, we should be able to count 16 lobes in the 10-meter
models. In fact, the square models only show 12 lobes. What has
happened to 4 lobes? In principle, two things can occur. One is that
the lobes merge. In most instances, merges lobes show some
aberration of the normal cigar shape of a lobe. No such odd shape
appears in the square models.
Chapter 72
The other possibility is that lobes cancel each other due to the
presence of equal but opposite radiation from symmetrical points
across a loop. In the corner-fed model, notice the wide and very
deep nulls at the 45° angles, and in the side-fed model, notice
similar nulls at the 90° points. Both sets of nulls correspond to the
middle points along the sides of the squares. In effect, the lobes for
these positions have cancelled each other out across the antenna
loop.
Chapter 72
The relative positions in the octagon that might correspond to those

in the squares are not quite right for complete cancellation of any
lobes. Hence, the full complement of 16 lobes appears in each of
these models. The corner-fed octagon shows its strongest lobes on
either side of the position where the corner-fed square has its
strongest lobe. The side-fed octagon positions its strongest lobes
like those of the corner-fed square.
Chapter 72
The side-fed octagon also illustrates lobe merging and the

consequent distortion of lobe shape as two or more lobes come
together. The "mittens" at 135° and 225° are good examples of
merging lobes.
It is clear from this compendium that loop shape can make a

difference in how the loop performs on various bands. If you plan to
build an irregular loop, by all means, anticipate its performance
through modeling.
Azimuth Patterns of Hexagon 160-Meter Loops, Corner and

Side Fed
Chapter 72
80 Meters
Because the 160-meter loop is about 2 wl long at 3.5 MHz, the

pattern resembles that of the 80-meter loop when used on 40
meters. However, the antenna height is proportionately lower
(about 0.18 wl for the 160-meter loop on 3.5 MHz vs. 0.35 wl for the
80-meter loop on 7 MHz), so the elevation angles of maximum
radiation are higher: in the 48° to 49° range. Nevertheless, there is
far more radiation at lower elevation angles than with the 1 wl loop
Chapter 72
on 80 meters. The additional low angle gain holds the promise (but
not the guarantee) of more regular longer distance contacts on 80
meters. Although the radiation pattern is fairly even all the way
round the loop, it is slightly stronger at 90° to the feedpoint axis.
There is virtually no difference between the patterns for the version
using a corner feedpoint or for the one using a side feedpoint.
Chapter 72
40 Meters
On 40 meters, the 160-meter loop becomes quite bi-directional with

either corner or side feeding. Maximum gain occurs off opposite
points of the hexagon. With corner feeding, the axis of maximum
gain is through the feedpoint to the opposite corner. However, if we
side-feed the hexagon, the axis of maximum gain is at right angles
to the feedpoint-to-opposite side axis.
Chapter 72
Both of the 40-meter patterns of the 160-meter loop are exercises

in finding hidden lobes. We expect 8 lobes. In the corner-fed model,
we can almost count them in terms of small bumps in the pattern.
The side-fed model appears to be missing a lobe--the one to the
rear of the feedpoint. In fact, this lobe is highly suppressed and
would appear only if there were deeper nulls on each side of it.
Chapter 72
30 Meters
The patterns for the 160-meter hexagon at 10.1 MHz are roughly
bi-directional along the axis from the feedpoint to the opposite
position on the loop. However, the side-fed version achieves an
almost rectangular pattern, which is somewhat of an oddity.
Chapter 72
Of equal significance with the pattern shape are the high values of
resistance and reactance at the feedpoint of either version of the
160-meter hex. The 80-meter loop showed only a few values of
reactance above 500 Ohms, and no resistance values reached that
level. In contrast, the 160-meter loop will show values in excess of
that level for many bands. The length of the feedline used may
require careful selection with the larger loop to ensure that the
values presented to the antenna tuner are within the range of
available adjustment. Some feedline length-switching may be
required as one moves from one band to another.
Chapter 72
20 Meters
The 20-meter patterns for the larger loop show a combination of

most of the pattern characteristics we have already seen: bi-
directionalness, merged lobes, and a number of others. Primary
radiation is off opposing sides, as with the 40-meter patterns, but
with a greater complexity of lobe structure. As well, the feedpoint
resistance and reactance values are fairly high.
Chapter 72
Of interest is the fact that maximum gain values fall only in the
middle of the span of those exhibited by the 80-meter loop when
run at 14 MHz. On this band--and on others as well, the antenna
offers little to justify the added complexity of running a wire twice as
long as the 80-meter loop. One might well argue for some
installations that the benefits derived on 80 meters from the larger
loop are offset by the disadvantages on some of the higher bands.
Indeed, the shorter loop and a separate 80-meter antenna might be
easier to use.
Chapter 72
17 Meters
The 17-meter patterns for the 160-meter loop bear a striking

resemblance to those for 40-meter operation if we do two things.
First, we have to smooth the peaks of the narrower and more
numerous 17 meter lobes. Second, we have to notice the
movement of the peak gain regions a small angular distance away
Chapter 72
from their axes on 40 meters so that a narrow weak area develops

along the precise axes of 40 meter peak gain.
As curious as the patterns are, the 17-meter impedance values are

also interesting because they come closer to resonance than the
values on any other band. However, there will still be considerable
excursions of voltage and current on the feedline, because the high
values of feedpoint impedance on other bands almost dictate the
use of 600-Ohm open parallel feeders as the best compromise
among all the impedance levels encountered.
Chapter 72
15 Meters
At a certain level of lobe multiplication, azimuth patterns tend to

lose their identity as guides to antenna radiation and become more
like Rorschach ink blot tests. With the 15-meter patterns of our
large loop, we may have reached that stage. Local ground clutter,
terrain irregularities, and simple blowing of the antenna wire in the
Chapter 72
wind may lessen the utility of following out each pencil-thin lobe of
the azimuth pattern.
Nonetheless, we can gain something from observing the azimuth

patterns, if only by gaining a general impression of regions of
strength and weakness. For example, between the corner-fed and
the side-fed patterns, the former seems to have more lobes of
higher strength in more directions, thus promising contacts in both
the morning and the evening hours of the daily skip cycle
(assuming that the antenna is set up on a rough East-West axis).
Chapter 72
12 Meters
The patterns for both 12 meters and 10 meters share some

interesting characteristics. Regardless of the feedpoint, there are
very few lobes that are less than 8 to 10 dB down from the peak
gain lobes, and almost all of them have very narrow beamwidths.
Therefore, the effective gain of the antenna is not given by the
maximum gain figures, which happen to range in the vicinity of 14
Chapter 72
to 15 dBi. Rather, the average gain over the 360° horizon is more
like 5 to 8 dBi. These are gain values more akin to a multiband
quarter-wavelength vertical with a ground plane mounted on a roof
top than they are to typical gain antennas.
There is a strong possibility that, if your interests are in upper HF

operations, the large 160-meter loop will prove to be a
disappointment. Its true virtue lies in the lower HF region, especially
on 80 meters, with reasonable good performance through 20
meters.
Chapter 72
10 Meters
Although the 80-meter loop shows poor performance on 80 meters

for every application other than NVIS, the smaller loop has distinct
advantages over the larger loop on almost every other band. The
patterns are smoother, with reasonable gain in most directions. The
feedpoint impedances are moderate and amenable to the use of
inexpensive and readily available 300-Ohm or 450-Ohm parallel
Chapter 72
feedlines. The values of impedance presented to antenna tuners

are more likely to be within the adjustment range of inexpensive
units.
Size alone then, is not the sole determinant of HOHPL

performance. Smaller size can be better for some operational
purposes. As important as size is the antenna shape and the
feedpoint position in the determination of the antenna patterns that
will most benefit our operational needs. A HOHPL that best fits our
needs is a blend of many factors.
Chapter 72
Chapter 72
Reference Tables of Modeled Antenna Performance for

Antenna Azimuth Patterns Shown
80-Meter Square Loop, Corner-Fed: Fig. 11
Freq. Gain TO Feedpoint Z

MHz dBi Deg R +/- jX Ohms
3.5 4.4 45* 120 - j 100
7 6.0 43 95 - j 230
10.1 10.4 29 280 - j 650
14 11.3 20 245 - j 240
18.1 14.1 15 375 + j 245
21 14.2 13 250 - j 170
24.9 14.7 10 345 + j 125
28 13.7 9 260 - j 220
80-Meter Square Loop, Side-Fed: Fig. 12

3.5 4.3 45* 120 - j 100
7 6.7 37 290 - j 105
10.1 8.0 27 280 - j 610
14 10.7 19 215 - j 265
18.1 11.7 15 415 + j 210
21 10.8 13 410 - j 215
24.9 11.7 11 380 + j 20
28 12.2 9 280 - j 250
80-Meter Octagon Loop, Corner-Fed: Fig. 13

MHz Bi Deg R +/- jX Ohms
3.5 4.3 45* 135 - j 55
7 6.3 41 205 - j 150
10.1 7.9 29 250 - j 580
14 9.3 21 155 - j 250
18.1 11.6 15 310 + j 250
21 11.9 13 275 - j 230
24.9 10.5 11 300 + j 40
28 11.4 10 310 - j 310
Chapter 72
80-Meter Octagon Loop, Side-Fed: Fig. 14

3.5 4.3 45* 135 - j 70
7 6.3 41 200 - j 180
10.1 7.7 25 250 - j 610
14 9.8 19 270 - j 230
18.1 9.8 16 295 + j 150
21 10.0 14 275 - j 335
24.9 10.8 11 265 - j 70
28 11.8 10 300 - j 415
160-Meter Hexagon Loop, Corner-Fed: Fig. 15

3.5 5.4 49 145 - j 265
7 10.5 36 350 - j 505
10.1 10.9 23 2810- j 1140
14 10.8 21 815 - j 1010
18.1 13.2 15 415 - j 90
21 13.0 14 1830- j 370
24.9 14.8 11 870 - j 540
28 14.9 10 1300+ j 635
160-Meter Hexagon Loop, Side-Fed: Fig. 16

3.5 5.5 48 145 - j 260
7 9.2 33 285 - j 495
10.1 8.9 25 2205- j 1105
14 10.3 18 655 - j 920
18.1 11.7 15 385 - j 130
21 12.5 14 1570- j 687
24.9 15.0 11 735 - j 585
28 14.6 9 1455+ j 125
Chapter 72
Notes:
1. * beside a TO entry means that the angle used is arbitrary.

Maximum gain is straight up (elevation angle = 90°).
2. Feedpoint impedance figures are representative and will vary

with the exact length and layout of the antenna loop. The
impedance presented to the antenna tuner will also be a function of
the exact length, characteristic impedance (Zo), and velocity factor
(VF) of the transmission line used for each particular installation.
3. Gain figures represent the maximum gain of the strongest lobe in

the azimuth pattern and should not be interpreted as the sole basis
for deciding among HOHPL designs. Equally important are the
distribution of the lobes, the depth of the nulls, access to all desired
communications directions, and other factors.
4. TO angles are the elevation angles of maximum radiation from

the strongest lobe. The vertical structure of lobes may vary.
6. How does the HOHPL compare to other all-band

antennas?
Although it would be impossible to do a detailed comparison with

every possible contender against the HOHPL, we can sample one
case: the standard 135' center-fed doublet. For fairness, we shall
place both antennas at 50 feet and overlay azimuth patterns for 80,
40, 20, and 10 meters, as representative of a fuller comparison.
Chapter 72
On 80 meters, there is no major difference between the doublet and

the square HOHPL. The HOHPL shows a higher radiation angle,
giving the doublet about 1.2 dB more gain (5.6 vs. 4.3 dBi at the
arbitrary 45° elevation angle).
Chapter 72
There is a distinct difference between the HOHPL and doublet 40-

meter patterns. The doublet is 1þ long and shows a bi-directional
pattern. The HOHPL loop is 2 wl long and displays major lobes in
four directions, although at lesser gain (8.1 vs. 6.7 dBi at about 36°
elevation). Which antennas have the advantage depends on one's
operating needs.
Chapter 72
On 20 meters, the 1wl HOHPL shows enough tilt in the pattern

away from the feedpoint to give it a small gain advantage at similar
elevation angles. Although the patterns seem otherwise fairly
similar, with only small offsets in the lobes, the doublet shows some
deep nulls broadside to the antenna, nulls that can adversely affect
communications in certain quadrants. Although the "side" nulls of
the HOHPL are deep, they do not differ as much from the doublet
wire-end nulls.
Chapter 72
The 10-meter patterns, while a bit confusing at first sight, also show
that the HOHPL has somewhat fewer nulls of great depth than the
doublet. Moreover, especially in the direction away from the
feedpoint, the HOHPL lobes are stronger (by about 1.5 dB) and
more even in gain. In contrast, the doublet is beginning to show
greater strength in lobes that are further from the broadside
direction and more towards the antenna ends.
Chapter 72
Conclusion
Summing up all of the patterns for the HOHPL shows it to be a

somewhat better performer over a full azimuth circle than the 135'
doublet. A 2 wl HOHPL would show an even greater evenness in
the lobe structures, since its 80-meter pattern is already like the 4-
lobe pattern we saw above for 40 meters. In this summary
comparison, I have not stressed matters of raw gain, but instead, I
have placed emphasis upon the nature and position of the lobes
and nulls. For nation-wide and world-wide communications,
evenness of pattern may often be more important than the gain of
one or more individual lobes.
As a consequence of this behavior, the advantage of the HOHPL

will not show itself in any one contact or in a short period.
Satisfaction with the antenna grows with time and changes in the
propagation paths, a successful communications almost
everywhere shows up in the log.
Still, the HOHPL, even in its smaller 1 wl form, requires a

considerable investment in real estate, supports, wire, and
accessories compared to the simpler doublet. Only the potential
user can decide if it is the right antenna for his or her installation.
Chapter 72
Chapter 73: Configuring Horizontal Wire Loops
I
n the previous Chapter 72, I provided some extensive notes on
horizontally oriented, horizontally polarized wire loop antennas
(HOHPLs). In those notes, the most common practice with
horizontal loops was using a 1-wavelength circumference at the
lowest operating frequency. Since writing that Chapter, I have
changed the recommendation that I usually make, depending on
the space available to the loop builder.
So let's begin again and work with a different plan. My plan of

attack is based on the 3 most asked questions:
• How Big?
• How High?
• What Shape?
Since we shall defer the question of shape until last, we shall need
a paradigm model with which to begin. Let's use a nearly perfectly
circular loop as our starting point, as outlined in Fig. 1. The loop
uses 40 wires to form the circle, so the approximation is quite good.
For our first 2 questions, the feedpoint will be on the right, in the +X
direction. (We shall alter that for our last question for reasons that
will become apparent when we arrive at questions of shape.) Note
the orientation of the X, Y, and Z axes in the outline drawing. These
axes lines will be important to orienting ourselves to some of the
patterns in upcoming figures.
Chapter 73
A circular loop as a starting point has some advantages over

beginning with other shapes. With both regular and irregular
polygons, we tend to find performance differences depending on
whether we feed the antenna at a corner or somewhere within a
side. Since a circle has no sides (or infinitesimal ones, at best), we
can avoid those differences until we reach our last question.
How Big?
The question of how big to make a horizontal loop antenna is a

function of frequency, specifically, the lowest frequency of intended
use. Virtually any size will work to some degree, but some sizes are
better than others. Remember that here we are speaking of
relatively large loops, not mini- or micro-loops used as table-top
antennas. Since I cannot know the lowest frequency of intended
Chapter 73
use, let's express dimensions as a function of a wavelength at the

lowest operating frequency. Since a horizontal loop is usually used
as a multi-band antenna, we shall likely feed it with parallel
transmission line and an antenna tuner. Hence, ultra precision of
dimension is not necessary (as it might be for an antenna that must
have some particular feedpoint impedance). So if I suggest a
length, such as 3 wavelengths, for a loop size, anything relatively
close to that size will do fine. "Relatively close" means about +/-
15% of the suggested size.
The basic dimension of loop size is normally its circumference, that

is, the total length of wire making up the loop. Of course, being a
loop implies that there is relative parity of cross dimensions,
although distended rectangles, rhombics, etc. will work. However,
we have to confine our work to what we can handle, so we shall
stay with regular polygons throughout these notes.
For our work, if you wish to translate a length in wavelengths into

an English measure, you may use a very simple equation: L(feet) =
(984 / F(MHz)) * n, where n is the number of wavelengths specified. If
you wish to go metric, then use this equation: L(meters) = (300 /
F(MHz)) * n. These equations are not precise, but they are within the
limits that we need to convert a horizontal loop into a length of wire.
To see how big to make our loop at the lowest operating frequency,
let's put the loop into free-space and examine some 3-dimensional
radiation patterns. These patterns will tell us something about why I
have changed my recommended length for a horizontal loop. The
following table provides the key dimensions of the loops whose
Chapter 73
patterns appear in Fig. 2. The basic loop size is the circumference,

but the diameter gives you an idea of the backyard space needed
to hold the loop.
Some Possible Circular Loop Sizes

(All dimensions in Wavelengths)
Circumference Diameter
0.5 WL 0.159 WL
1.0 0.318
1.5 0.476
2.0 0.636
3.0 0.955
4.0 1.273
Chapter 73
The 3-D patterns may seem a bit confusing, but let's align
ourselves with Fig. 1 and its axes lines. The X-axis and the Y-axis
indicate horizontal directions relative to the orientation of the loop,
presumed to be horizontal, even if we are working in free space
with no real "ups" and "downs." The Z-axis is the vertical direction
at right angles to the plane formed by the loop.
Since each 3-D pattern has about the same total volume, relative to
the axis lines, we can see a few trends. First, the 1/2-wavelength
loop forms an oval with slightly stronger radiation in the X direction
than in the Z-direction. The next two loops (1.0-wavelength and 1.5-
wavelength) have stronger radiation along the Z-axis than along
either the X- or Y-axes. Not until we reach a circumference of 2
wavelengths does radiation strength occur predominantly in the X-Y
plane. Another way of expressing this is to say that when a loop
reaches a circumference of 2 wavelengths, it radiates more strongly
off the loop edge than it does broadside to the loop.
This conclusion tallies well with our practice of using 1-wavelength

loops in quad beams that rely on radiation broadside to the plane of
the loop. If we want a 2-wavelength loop to radiate more strongly in
the broadside direction, we must break the connection across from
the feedpoint. However, our job is not to make a quad beam, but to
see what a wire horizontal loop can do for our signals. So we may
omit any consideration of broken loops.
The longer loops also show stronger radiation in the X-Y plane than
in the +/-Z direction. However, their patterns are so convoluted that
it is almost impossible to see exactly where the radiation is going.
Chapter 73
To get a better handhold on the radiation of all of the loop sizes,

let's return almost to earth. We shall place each loop 1 wavelength
above average soil. (With horizontal antennas, the actual soil
quality makes little difference to the signal, so using average soil
will not distort the conclusions that we reach.) Fig. 3 presents the
modeled elevation and azimuth patterns for the loops sizes
surveyed in Fig. 2. Each pattern indicates the strongest lobe, and
the small inset of the loop shows how that lobe is oriented relative
to the loop's feedpoint.
Chapter 73
The primary feature to note is that for loops with a 1.0- or 1.5-
wavelength circumference, the upper elevation lobes are stronger
Chapter 73
that the lower lobe. Given the high elevation angle (about 35
degrees) of the upper lobe, the lower lobe is obviously that one that
we rely upon for most communication (NVIS excepted, of course).
When we reach a circumference of about 2 wavelengths, the lower
lobe begins to dominate once more. Hence, for skip
communications, the smallest advisable circumference for a
horizontal loop is about 2 wavelengths at the lowest operating
frequency. Smaller loops will work, but at reduced signal strengths.
The second notable feature is the fact that horizontal loops above a
helf-wavelength over ground answer to the standard lobe
development angles that apply to virtually all horizontal antennas
and arrays. All of the lower lobes, regardless of loop length, have a
14-degree elevation angle. The length of a loop does not change
the elevation angle.
For a given power from the transmitter, all of the loops radiate the
same power over the hemisphere above ground. Hence, they differ
only in the maximum gain created by the formation of lobes and
nulls in the pattern (both horizontal and vertical). The following table
summarizes the gain of the strongest lower lobe and gives an
indication of the impedance at the feedpoint. That impedance may
vary considerably with variations in the actual wire length used to
make a loop.
Chapter 73
General Performance Values for Circular Loops

Height: 1 wavelength above Average Ground
Elevation Angle: 14 degrees
Circumference Gain Impedance
wavelengths dBi R+/-jX Ohms
0.5 7.03 >100k - j85k
1.0 6.09 125 - j110
1.5 5.56 9200 + j6500
2.0 7.23 180 - j125
3.0 8.16 215 - j130
4.0 9.26 235 - j135
Loops that are integral multiples of 1-wavelength tend to have lower

impedances, while those in the n.5-wavelength caregory tend to
have very high impedances. Although the gain value for the 1/2-
wavelength loop looks quite usable--when compared to the other
values--the feedpoint impedance is not especially promising. As
well, a 1/2-wavelength loop becomes a 1-wavelength loop on the
next band upward in frequency, and we lose a lot of gain in the
lower lobe on that band.
You may relate the improving signal strength maximum values that
accompany longer loops with the width of the lobes for those larger
loops in Fig. 3. Hence, as we make a loop longer, the beamwidth of
the individual lobes grows narrower. As we increase the number of
lobes, we also increase the number of nulls, where signal strength
decreases to a level that may prevent communications.
Finally, for a circular loop (but not necessarily for other shapes), the
number of lobes follows a regular pattern. The number of lobes is
twice the loop circumference in wavelengths. Hence, a 4-
Chapter 73
wavelength loop shows 8 distinct lobes. When we disturb the

circular shape of the loop, the flat sides that we produce will alter
this pattern of lobes and nulls, and we shall sample those
alterations before we finish.
To obtain an estimate on how good a loop may be in our own

backyard, let's pause to make a comparison. We shall place a 1/2-
wavelength dipole at 1 wavelength above average ground. For that
antenna, we obtain the following performance report.
General Performance Values for 1/2-Wavelength Dipole

Height: 1 wavelength above Average Ground
Elevation Angle: 14 degrees
Dipole Length Gain Impedance
wavelengths dBi R+/-jX Ohms
0.5 7.98 72 + j2
Fig. 4 shows the dipole, its 3-D free-space pattern, and its elevation
and azimuth patterns at the specified height. The dipole has as
many lobes as a 1-wavelength circular loop, but they are stronger
at the prime 14-degree elevation angle.
Chapter 73
The loop does not catch up to the dipole until we reach a

circumference of 2 wavelengths, where we also have the loop's 4
lobes.
How High?
Those who do not seem to have much luck with loops--even when
at least 2 wavelengths long--very often have neglected the role of
height in the performance of any horizontally polarized antenna.
Most of these antennas are aimed at improving performance on the
lower HF bands. However, the average height (from my e-mail
reports) seems to be between 35' and 50' above ground. This
height range covers about 0.06 to 0.11 wavelength on 160 and 0.12
to 0.18 wavelength on 80 meters (low end figures).
So far, we have looked at the circular loop when it is 1 wavelength

above average ground. We do not know what the patterns might
look like at other heights. Therefore, let's take a 2-wavelength
Chapter 73
circumference loop and place it at a number of different heights,

from a high and improbable 2 wavelengths up to a low value of
0.15-wavelength above ground. The shape of the azimuth pattern
will not change significantly from the view at 1 wavelength.
However, the elevation patterns will change considerably.
For contrast, let's also look at the numbers for a dipole at the same
height. As always, we shall list the maximum gain of the strongest
lobe or lobes. More important than gain will be the TO angle, that
is, the elevation angle of maximum radiation. The following table
summarizes the loop and dipole results. Since the data should be
applicable to any lowest frequency of use, the heights are functions
of a wavelength.
Comparative Performance of a Circular 2-wavelength Loop and a Dipole at
Various Heights
Circular Loop Dipole
Height Max. Gain TO Angle Max. Gain TO Angle
wavelengths dBi degrees dBi degrees
2.0 7.36 7 8.05 7
1.0 7.27 14 7.98 14
0.75 7.75 19 7.57 19
0.5 7.43 29 7.91 28
0.25 5.94 47 6.33 60
0.15 4.76 52 6.59 90
Both types of antenna show the same or nearly the same TO

angles down to 1/2-wavelength above ground. As well, they both
show the same pattern of maximum gain levels. The slight
depression of the maximum gain value that the dipole shows at a
height of 0.75-wavelength appears in the loop at a height of 1
wavelength.
Chapter 73
However, the loop shows a faster reduction in gain as it gets close

to the ground, but it sustains a lower TO angle with height
reductions. If you re-examine the patterns in Fig. 4, you can clearly
understand why the dipole TO angle climbs rapidly as we reduce
the height below 1/2 wavelength. The dipole in free space shows as
much radiation vertically as it shows horizontally. Close to ground,
the radiation directed upward dominates. At heights from about
0.15 to 0.25 wavelength, the dipole makes a quite good simple
NVIS antenna.
In contrast, if you return to Fig. 2, you will see that the 2-

wavelength circular loop has stronger radiation off its edges than it
has perpendicular to the plane of the loop. As a result, the loop (at
a closed circumference of 2 wavelengths) does not make a
particularly good NVIS antenna. If you examine Fig. 5, you will see
that the loop lacks radiation straight up. Hence, its TO angle is
lower than that of the dipole when close to the ground.
Chapter 73
The comparison between the dipole and the circular 2-wavelength

loop does not mean that the loop is a stellar performer when close
to the ground. For general propagation conditions, angles of 47 and
52 degrees are still too high for strong communications. However, if
you look also at the half-power angles in the diagrams (the red line
on either side of the main-lobe center line), you will see that the
lower of these angles does tend to fall within the set of angles that
provide relatively reliable communications in the lower HF region.
(See a recent edition of The ARRL Antenna Book for further
information on typical propagation angles on the various amateur
bands.)
So the reputation of the loop for improved communications relative

to a dipole at the same height has some truth to it for antenna
heights below 1/2 wavelength. However, examine the gain values
Chapter 73
for these heights and then subtract another 2-3 dB for working near
the half-power angles. Raising the antenna higher not only yields a
higher maximum gain value, but also places the TO angle nearer
to--if not within--the range of angles providing stronger
communications.
For any horizontal wire antenna, there is no substitution for height.

This rule of thumb applies up to at least 1.25 wavelengths above
ground, if not higher. On the lowest amateur bands (160 and 80
meters), there is always room for height improvement before
reaching the limits of the rule of thumb. What we lack normally are
the means to support the antenna at the most desirable height.
What Shape?
We have so far confined our examination of loops to a circular

shape--mostly to ensure that all comparative figures are fair.
However, few of us have the means to set up a truly circular
horizontal loop on the lowest amateur bands. In most cases, we are
lucky to approximate a regular polygon. Hence, it is not possible
here to cover all of the possible loop shapes that your
circumstances might dictate. In fact, we shall confine ourselves to
the circle, the triangle, and the square.
There are two reasons for the confinement. First, polygons with
limited numbers of sides have two general feedpoint positions. One
is at a corner, where the wire changes direction. The other is the
midpoint of a side. Of course, we can feed a loop anywhere along a
Chapter 73
side, but, again, that would give us too many variables to cover. So
we shall look at 1 circle, but 2 triangles and 2 squares.
Second, most horizontal loops are intended for multi-band use. So

for each option, we need to look at several options. If a 2-wave-
length loop is cut for 160 meters, then 80, 40, and 20 meters
constitute a progression of frequencies (F) that include 2F, 4F, and
8F. If we cut the original antenna to be 2 wavelengths at 80 meters,
then the corresponding harmonically related bands are 40, 20, and
10 meters for the same F, 2F, 4F, and 8F progression. Space does
not permit us to include non-harmonically related bands in the
progressions.
As we increase the operating frequency, the height of the antenna

also changes when related to a wavelength. Hence, if we start 1
wavelength above ground, the upper bands will see the antenna at
2, 4, and 8 wavelengths above ground. The 14-degree TO angle at
a 1-wavelenght height becomes progressively 7, 4, and 2 degrees
(with the angle confined to integer values).
Under these conditions, the 2-wavelength circular loop shows the

azimuth patterns in Fig. 6. I have moved the feedpoint to the "left"
on the antenna so that its position corresponds to the feedpoint
position of the remaining shapes that we shall explore. Although the
lobes increase in number as earlier noted, we might think of them
as having equal strength. However, the 8F pattern makes clear the
fact that the lobes have slight variations in strength despite the fact
that all of the models use lossless wire. The interaction among the
Chapter 73
sections of the circle is sufficient to create the small differences.

These differences will not be small with other shapes.
We might be tempted to mentally draw a line connecting the

outermost tips of the lobes and think that the antenna has the
resulting near circle as its pattern. However, every pair of lobes has
an intervening null. The practical effect of having a large number of
narrow lobes and nulls tends to be a rapid fluctuation in signal
strength, especially on windy days, that can slightly alter the exact
orientation of the wire antenna. At lower frequencies, where the
lobes are broad, the antenna is nearly immune to this effect.
One popular arrangement for a 2-wavelength loop is a triangle,

since that shape needs the fewest support posts or trees. We shall
first look at a triangle fed at a corner, specifically, the left-most
corner relative to the orientation of the patterns. Of course, we shall
retain the 2-wavelength circumference and the 1-wavelength
antenna height.
Chapter 73
Fig. 7 shows the patterns that result for each frequency when using
a corner-fed triangle. The nearly equal strength of the lobes
disappears, even at the lowest frequency. The antenna has a slight
beaming effect along a line that runs from the feedpoint to the
middle of the side opposite the feedpoint. In all cases, the strongest
radiation is in the direction of that far side of the triangle. Therefore,
if you use an equilateral triangle for a loop, it pays to orient the
antenna toward a primary communications target region.
Chapter 73
If we feed a triangle in the middle of a side, as shown in Fig. 8, we

obtain patterns that in general terms are not very different from the
ones for a corner feedpoint. However, note that the patterns for 2F
and 4F are strongest across the antenna and away from the
feedpoint side, while the patterns for F and 8F are strongest to the
side containing the feedpoint.
When we move to square shapes, a side-fed loop looks square,

while a corner-fed square looks like a diamond in terms of the
orientation to the patterns. We shall look at the side-fed square first.
The patterns are in Fig. 9.
The square has a pattern at F that is very similar to the one for the
circle. However, from that frequency upward, everything changes.
Each pattern has fewer lobes than the corresponding pattern for a
triangle. As well, the strongest lobes are not aligned with the
feedpoint and the opposite side of the square. Instead, the
strongest lobes occur at oblique angles to the square for 2F
through 4F. Since that angle changes with the operating frequency,
Chapter 73
finding a good orientation for all intended frequencies may be

difficulty.
When we feed the square at a corner, we once more align the

patterns along a line from the feedpoint corner to the opposite
corner of the diamond, at least through 4F. Fig. 10 provides the
patterns. At 8F, the strongest lobes are at an angle to the array.
The following table provides a summary of the modeled maximum
gain values. However, above about 2F (a circumference of 4
wavelengths), the lobes become so narrow that a maximum gain
value can be quite misleading as a guide to the general
communications capabilities of each antenna.
Chapter 73
Maximum Gain Values for Each Antenna at Each Sampled Frequency

All loops are 2-wavelengths at F.
Frequency F 2F 4F 8F
TO angle (degrees) 14 7 4 2
Antenna
Circle 7.27 9.22 10.71 11.57
Triangle, corner-fed 8.34 9.95 14.38 8.41
Triangle, Side-fed 8.34 10.45 13.24 8.94
Square, side-fed 8.42 11.29 13.59 14.29
Square, corner-fed 6.95 11.51 14.28 14.92
Reference Dipole/Doublet 7.99 9.66 9.64 11.16
The gain data is only useful in comparing the outer rings of each
pattern. Note the reduction in gain for the two triangles when
operated at 8 times the lowest frequency. I have included the data
for a 1/2-wavelength dipole at F to allow comparisons on the
various harmonics when using that antenna as a multi-band
doublet. The patterns for the doublet appear in Fig. 11. Only up to
2F (or 1-wavelength) does the doublet show its strongest lobes
broadside to the wire. Above that frequency, the strongest lobes
depart at oblique angles that change with frequency.
Chapter 73
These small demonstrations show that a loop's shape can make a

great deal of difference to the azimuth patterns of radiation from it. I
shall select no version as better than the others, since I cannot
know the lay of the land for each installation. However, it does
appear that operating a 2-wavelength loop much above twice the
design frequency does yield narrow lobes that may or may not be
useful to communications. The remaining body of radiation in the
pattern is considerably weaker than the main lobes. For patterns
associated with other loop shapes, see the article mentioned at the
beginning of this one.
Conclusions
Based on what we have explored in the realm of wire horizontal

loops, we can draw a few conclusions. These recommendations
are based on the idea of using the loop for more than one band.
1. How Big? The loop should be at least 2 wavelengths in

circumference, regardless of the final shape. For most purposes,
the antenna should be considered for use over a 2:1 frequency
range, even though it will load on other bands well above the
design frequency. The exception to this recommendation is the
case in which the antenna is for NVIS use on the lower band and
for normal skip communications above that band. In that case, a 1-
wavelength loop at the lower frequency will provide the best
compromise.
1. How High? Because the antenna is used mostly on the lower HF

bands, it is safe to suggest that the antenna should be as high as
Chapter 73
feasible. A height of 1 wavelength above ground is certainly not too

high, although in most circumstances the antenna will be restricted
to lower heights. The exception is the case in which the antenna
serves for NVIS communications on the lower band. In that case,
the 1-wavelength loop should be between 0.15 and 0.25
wavelength above ground for the strongest upward pattern. On the
second harmonic, the antenna will be 2 wavelengths long and
between 0.3 and 0.5 wavelength above ground for better, if not
ideal, longer-range communications.
3. What Shape? Of the sampled shapes, the circular version

produces the most even set of lobes on all frequencies. Hence, a
polygon that approaches circularity is more likely to have fewer
interactions among the sections of the antenna to produce a pattern
with only a few spiky lobes. However, even a circular design will
produce 4 main lobes when it is 2 wavelengths in circumference.
None of these recommendations is absolute, since the loop will

work at many lengths, heights, and shapes. It is not possible to
cover all eventualities in a single set of notes or even many sets of
notes. Hence, the prospective loop builder should strongly consider
obtaining at least a rudimentary antenna modeling software
package to test any possible design. In that way, you can predict
more accurately the performance of a loop designed to fit a given
yard.
Chapter 73
Chapter 74: Closed & Interrupted Loops for 40 Meters
In the next Chapter 75 "The IL-ZX Antenna for 40 Meters", I present

(or resurrect, depending upon one's point of view) a compact
interrupted loop antenna for 40 meters. By using folded element
wire construction, it provided a coax-compatible feedpoint
impedance with no compensating or loading components. Since the
overall circumference of the interrupted loop was about 1/2
wavelength, the antenna was very compact, fitting within a 20' wide
by 20' High (plus ground clearance) footprint. Fig. 1 on the right
shows the essential outline of the ILZX when used vertically. Single
wire horizontal versions of the antenna exist. Indeed, in Britain, you
may obtain a multi-band version of the antenna.
Chapter 74
On the left in Fig. 1 is an antenna that is similar in size and that

also uses a vertical orientation. It is a closed loop with a diameter of
about 0.127 wavelength, with a resulting 0.4-wavelength
circumference. As we move from the region of very small loops with
feedpoint resistive components in the 1-Ohm range up to the
medium-loop range (circumferences between about 0.25 and 0.75
wavelength), we find some interesting properties. First, the resistive
component of the feedpoint impedance climbs so that we no longer
need worry as much about the losses of compensating and
matching components or the losses of construction joints. Second,
the reactance of the closed loop becomes increasingly inductive.
When the loop is electrically about 1/2 wavelength in circumference
(which for a closed loop is physically larger than 1/2 wavelength),
the reactance reaches a peak inductive value only to suddenly
reverse to a peak capacitive reactance value with only a slight
further increase in circumference. (This phenomenon is familiar to
those who have center-fed linear wire antennas that are about 1
wavelength long.) At the same time, the performance of the loop
improves with increasing size. The result is a compromise. When
the loop is about 0.4 wavelength in circumference, The feedpoint
resistance approaches 100 Ohms while the inductive reactance has
a high but manageable value for which we can compensate with a
small (low-pF) series capacitor. By tradition--derived from very
small loop construction more than from necessity--most closed
loops in this arena use fat elements--often copper pipe.
Both antennas are interesting, if for no other reason than the

similarity of their sizes. One can square the closed-loop circle or
circularize the square shape of the ILZX. However the shapes have
Chapter 74
little bearing on performance. The closed-loop's circle is convenient

for the most commonly used materials, while the wire structure of
the ILZX lends itself to the used of non-conductive side supports
with rope ties to the corners of the square. Therefore, in the
discussion to follow, I shall use the modeled construction shown in
Fig. 2, which gives the dimensions for both subject antennas.
In a situation calling for a very compact 40-meter antenna, the

structure is likely to be close to the ground. I selected a 5-meter
(16.4') bottom height to have a rounded number that accords
reasonably well with amateur practice. In both cases, the top height
of the antenna is less than 11 meters (or 35') above ground. The
radius of the closed loop is 0.0635 wavelength at 7.15 MHz, the
selected common test frequency for both antennas. The loop
Chapter 74
material is 1" copper, a diameter that results in a 98.5% power

efficiency according to NEC model reports. (The NEC report does
not include losses incurred from the average ground over which I
placed both antennas). For an important reason that we shall
consider shortly, the dimensional outline of the closed loop does
not show the position of the feedpoint or of the required series
capacitor.
The ILZX has several notable features. It uses AWG #12 wire
(0.0808" diameter). Although the wire is thin compared to the value
used in the closed loop, the power efficiency is over 96%. Instead
of viewing the antenna as an interrupted loop, let's think of it as a
folded dipole with 3" spacing between wires and with the linear
elements bent into a square that is 5.5 meters (18.04') on a side.
Like a folded dipole, the equal-diameter elements create a 4:1
impedance transformation (regardless of spacing--within limits).
Hence, a single wire version of the antenna might show a feedpoint
impedance in the 12- to 16-Ohm range. The folded version shows
an impedance in the 50- to 65-Ohm range, depending on
orientation and height above ground. With the side feedpoint
shown, the impedance is about 64 Ohms.
The difference between a linear folded dipole and the bent version
in the ILZX is the proximity of the element ends, added to the
parallel sections of the "top" and "bottom" sections. The element
tips exhibit strong coupling. Therefore, the gap between them
becomes an important means of setting the reactance at the
operating frequency. Note that the tips come to a point on each
side of the gap. If we leave the tips blunt--as we might in a regular
Chapter 74
folded dipole--the gap dimension becomes very finicky. By bringing

the tips to a point, we reduce the amount of reactance change with
each unit of physical change in the size of the gap. Such antennas
actually go back to the 1930s and sometimes used copper pipe
construction (on unbelievably heavy wood frames) with gap
extensions that consisted of small plates soldered to screw threads
for fine tuning.
The sketches show the ILZX at a relatively low height, vertically

oriented, with a side feedpoint and a side-gap position. This
orientation yields the best low angle patterns that we can obtain
from the antenna. In contrast, most common implementations of the
closed loop have chosen a bottom position for the feedpoint and
reactance-compensating capacitor. In fact, the closed loop has
properties sufficiently like a very small loop to allow us to position
the feedpoint and the required capacitor almost anywhere along the
circumference, and not necessarily at the same place. Each
selection has consequences that we may accept or reject according
to our needs. For example, a very small loop has a current
magnitude and phase that remain virtually constant along the
length of the loop. In the 0.4-wavelength circumference loop, the
current magnitude changes by no more than a 3:1 ratio of
maximum to minimum. This change is small compared to the
current levels that we find along a linear element. As well, it is small
compared to the ratio of maximum to minimum current in a full 1-
wavelength loop.
Let's assume that the terms "top," "bottom," and "side" have
conventional meanings relative to the ground. We may place the
Chapter 74
feedpoint at any one of these positions. Likewise, we may place the

series capacitor at any one of these positions. The following table
shows what happens to the maximum gain, the elevation angle of
maximum radiation, and the feedpoint impedance for various
combinations. In all cases, the compensating series capacitor value
remains constant and represents a reactance of -j2417 Ohms at
7.15 MHz. As well, the closed loop remains physically constant.
With the feedpoint and capacitor both positioned at either the top or
bottom, the pattern for the relatively low and vertically oriented loop
is mostly straight up. The dominant polarization is horizontal. Fig. 3
shows the broadside and edgewise elevation patterns for some of
the cases. The left pair of elevation plots yield the most NVIS-like
upward patterns at a reasonably good gain level. The right side of
Fig. 3 shows the elevation patterns for the use of a bottom
feedpoint and a top-positioned capacitor. However, the patterns
also apply to the case in which the feedpoint is on the side and the
capacitor is at the top. The top-mounted series capacitor pattern
has a significant lower angle component, but only edgewise to the
Chapter 74
plane of the loop. These cases appear to illustrate the fact that the
position of the series capacitor has a stronger bearing on the
pattern shape than the feedpoint position. For example, the table
suggests that the feedpoint at the bottom with the capacitor on a
side yields patterns very much like those where both the source
and the capacitor are positioned on a side.
Only two of the options present a highly workable feedpoint

resistance: bottom-bottom and side-side. The side-side position
combination does require adjustment to the capacitor value to 9.31
pF to null the remaining loop reactance. The very small amount of
required change (0.1 pF) suggests that tuning the loop can be very
finicky without either special components or excellent ingenuity.
Fig. 4 compares the elevation plots of the side-side closed loop and
the ILZX. In the configuration shown in Fig. 2, the ILZX shows a
maximum edgewise gain of 0.05 dBi at 24 degrees. The maximum
edgewise gain is -0.26 dBi at 25 degrees. The average gain of the
two antennas is almost identical, while the ILZX exhibits a slightly
Chapter 74
more circular azimuth pattern. (With the ILZX fed at the bottom and
the gap at the top, the resulting patterns are similar to those for the
closed loop in the bottom-bottom configuration.)
When oriented at relatively low heights, both the closed loop and
the ILZX benefit from side feeding to yield low angle patterns that
benefit HF communications. Indeed, their patterns are not
sufficiently different to be detectable in ordinary operations. The
remaining question is whether there is a more decisive factor to
separate the two antennas for amateur operations. There might be,
if we assume that most amateurs prefer wider operating
bandwidths from their antennas.
Chapter 74
Fig. 5 presents the SWR sweeps for the closed-loop and the ILZX
from 7.0 to 7.3 MHz. In each case, the curve is references to the
resonant impedance of the individual antenna. For the ILZX, the
reference impedance is 64 Ohms. The 98.5-Ohm reference
impedance of the closed loop includes the use of a 9.31-pF series
capacitor at the side feedpoint. The 2:1 SWR bandwidth of the
closed loop is 60-70 kHz. In contrast, the 2:1 SWR bandwidth of the
ILZX is about 150 kHz. As well, even without 50-Ohm matching at
the feedpoint, the rate of SWR change for the ILZX is low enough
that the internal tuners that come with many current transceivers
Chapter 74
could easily handle the matching task. At 40 meters, the losses of

coaxial cables larger than RG-58 would not be troublesome for
most operations. Nevertheless, for maximum 40-meter QRN
reduction, the narrower bandwidth of the closed loop may serve a
useful purpose.
When we lay out the physical and the electrical properties of both
antenna types, each has advantages and disadvantages. The point
of these notes is not to recommend one over the other, but to make
the relative properties of each more readily apparent. Perhaps the
only general conclusion to these notes is the fact that if we
construct either antenna in a vertical plane and at relative low
heights, then side feeding is generally highly beneficial for long
distance operations, although bottom feeding can create a compact
NVIS antenna. Enjoy the interesting conundrum. . .
Chapter 74
Chapter 75: The IL-ZX Loop for 40 Meters
E
very antenna design has a niche in the overall world of
amateur radio antennas. The one described here has a quite
small niche: it is for the individual who requires operation on
40 meters at low elevation angles, but who does not have the real
estate to erect one of the SCV (self-contained vertically polarized 1
wavelength loop) antennas. The IL-ZX provides low-elevation angle
radiation within a narrow operating bandwidth at low gain with a bi-
directional pattern and reduced radiation at higher angles. It can be
fed directly with 50-ohm coaxial cable, although a network antenna
tuner will likely be useful for increasing the usable bandwidth.
IL-ZX is shorthand for Intermediate Loop-Impedance

Transformation antenna. The design has some of the properties of
a small loop, for example radiation off the edges of the loop rather
than off the face. However, it does not require the level of
mechanical care associated with small loops and replaces the
capacitor with a simple capacitive gap, the spacing of which
resonates the loop. The native feedpoint impedance of such a loop,
about 1/2 wavelength in circumference, is around 10 ohms. By
using a double-loop form of construction, the impedance is raised
to about 40 ohms.
Small Loops
The small loop is defined by some experimenters, such as W5QJR,

as a loop whose circumference is between 0.1 and 0.3
Chapter 75
wavelengths. Figure 1 shows the elevation pattern of one such

loop resonated at 7.2 MHz. The maximum gain for copper loops
and lossless capacitors is relatively constant across the range of
defined size at 0.4 to 0.45 dBi at low elevation angles. Feedpoint
impedances range from 0.5 ohms for the smaller sizes to about 1.5
ohms for the larger sizes. Below 0.1 wavelength circumference, the
loop gain drops rapidly, as does the feedpoint impedance.
Chapter 75
Small loops require extreme care in construction, since every

fraction of an ohm connection loss results in large increases in
power lost to heat. Hence, 3/4" diameter copper water pipe,
soldered at every joint, is a common material. The required
resonating capacitor demands special care of construction and
attachment. If one has the skills to build one, a small loop can be a
very effective antenna. With a stepper motor operating the
capacitor, a 2:1 frequency range of operation is easily possible with
good results.
Large Loops
In contrast, a large loop is thought of as a full wavelength in

circumference, such as the quad loop. This loop has a natural
resonant feedpoint impedance of 125 to 130 ohms. Many users
reduce this impedance with a 1/4 wavelength section of 75-ohm
coax so that it presents a reasonable match to 50-ohm coax for the
remainder of the run. The antenna offers a fairly wide operating
bandwidth without further adjustment.
The full wavelength loop is capable of higher gain than a dipole

placed at the center height of the loop. However, a large loop is
about 1/4 wavelength on a side, about 35' horizontally and vertical
on 40 meters. If fed at the bottom or top, the radiation pattern is
largely horizontally polarized and subject to the same high-angle of
maximum radiation as a dipole. Hence, low mounting heights
reduce the effectiveness of this antenna.
Chapter 75
Fed in the middle of one side, the antenna offers low angle
radiation, largely vertically polarized. However, for maximum
effectiveness, the antenna requires about 10' spacing above
ground, raising its top height to about 45' or so. Figure 2 shows the
pattern of a vertically polarized 40-meter large loop.
The full-size quad loop is but one of several SCV designs for
achieving low angle vertically polarized radiation without need for a
ground plane and without high angle radiation or reception of QRM
Chapter 75
and QRN from those upper angles. They have come into increased
use by those who have directly or indirectly read into materials
researched by ON4UN and others. Another entry in this series of
notes attempts to put into perspective the entire spectrum of SCV
antennas.
SCVs require significant real estate, either or both horizontally and

vertically. The modern city lot or rental property does not always
offer sufficient space even for a 40-meter SCV.
The Intermediate Loop
The Intermediate Loop (IL) is a small loop enlarged to approach 1/2

wavelength in circumference. Because the antenna approaches a
natural resonant point, its operating bandwidth enlarges, reducing
its gain at any single frequency. However, the antenna offers lower
construction losses because the resonance can be established
simply by adjusting the width of the gap at the top of the antenna.
Capacitance from one wire end to the other is sufficient for the task,
but the low-C high L nature of this circuit also contributes to broader
response and lower gain. Figure 3A shows the outline of the basic
IL, which has a natural resonant feedpoint impedance of about 10
ohms. Relative to a small loop with an adjustable capacitor, the IL-
ZX is a one-band antenna.
Chapter 75
The feedpoint impedance can be raised to about 40 ohms by

doubling the loop and feeding only one of the wires, as shown in
Figure 3B. (Hence, ZX = Impedance Transformation.) This method
is essentially the same impedance transforming technique used in
the folded dipole. With wires of the same diameter at any spacing,
the transformation is 4:1. This transformation applies to both
radiation and heat components of the impedance, so no magical
reduction in losses occurs--and likewise, no magical increase in
gain occurs. However, the feedpoint impedance is now more
manageable for use with 50-ohm coax.
A second benefit of the double loop is that it offers the builder

standard techniques of wire antenna construction. The loops may
Chapter 75
be spaced from 6" to 3' apart with corner CPVC spacers. Wire
joints should be carefully constructed and soldered. The antenna
benefits from the use of large wire sizes, with 1" wire showing an
additional 0.5 dB gain over #12 wire. Therefore, one may wish to
build the antenna from such materials as 450-ohm parallel line for
each loop to simulate fatter wire. If such a method is selected, it is
usually wise to solder a short across the parallel line periodically to
ensure equal currents on each wire. (Do not short the two loops
except at the top gap.)
Figure 4 shows two arrangements for the top gap. In one case, the
loops are brought together as a point; in the other they approach
each other as a bar across the loop ends. Since the gap is actually
the dielectric space for a capacitor formed by the loop ends, the
difference in construction can make a big difference in antenna size
and adjustment. Models of the point- gap required about 18' per
side for the antenna, with a gap between 0.2 and 1.0' wide,
depending on spacing of the loops. The flat-gap antenna, for loops
spaced at 2' and a gap of 0.8' required sides of only 17' each. The
flat-gap construction will make side length a much more sensitive
Chapter 75
function of the loop spacing, since the capacitance between ends

will change more radically with loop spacing and the consequential
lengthening or shortening of the wires facing each other. In all
cases, the builder should be prepared to do considerable
experimentation to achieve resonance.
Performance
The IL-ZX offers the would-be 40 meter operator a relatively small

antenna, no more than 18' per side. Its best low angle performance
occurs with the center about 15' high and its bottom wire therefore
about 6' off the ground. The high point becomes about 24' up.
The 2:1 VSWR operating bandwidth is about 100 kHz at 40 meters.

However, a network ATU in the line should expand this without
introducing significant losses on this lower HF band where a full
wavelength of coax feedline is over 90' long (accounting for velocity
factor).
Chapter 75
The primary signal direction of the IL is like that of the small loop:
off the edges of the loop, as shown in Figure 5. With a center
height of 15' or so, the elevation angle of maximum gain is 21 to 22
degrees, similar to SCV angles. Front-to-side ratio is generally
around 10 dB.
In the process of further experimenting with the IL-ZX design, I

discovered that you can easily create a virtually circular low angle
pattern--still of relatively low gain--by turning the IL-ZX "on its side."
In this orientation, we need to raise the antenna to a base height of
about 15' (for a top height of about 33') in order to eliminate
excessive influence of the ground on one side of the antenna wire
run more than on the other. At the 15' height, the impedance is
about 64 + j15 Ohms, still an easy match for coax.
Chapter 75
Figure 6 shows the circularized pattern at about the same take-off

angle as the "upright" IL-ZX. Gain is not significantly different from
one version to the other. Hence, which orientation you choose to
use is largely a matter of the pattern that you desire and the ease of
feeding the antenna at the side vs. at the bottom.
The principle disadvantage to the IL-ZX antenna is low gain. The

antenna gain at maximum is about 3 dB less than that of a full size
quad loop and about 4.5 dB less than that of a half square, when
each of these is at optimum height. The reduction is less than a full
S-unit in signal strength.
However, the antenna offers two advantages that offset the

reduction in gain. First, although not as narrow in reception
bandwidth as a small loop, the sensitivity of the antenna to
reception noise is considerably less than that of a resonant dipole
or large loop. Second, the attenuation of signals at higher angles (in
the 45-degree elevation angle range) reduces the reception
strength of QRN and QRM. Hence, the signal-to-noise ratio of the
antenna should be quite good for signals in the desired main lobes
of the antenna. Since most receivers have excess gain at 40
meters, reception of desired distant signals should be a matter of
increasing either pre-filtration or post-filtration gain.
Even if we become very conservative and estimate performance at

6 dB down (1 S-unit) from an optimized half square, the transmitting
success ratio should only go down in contest and pile-up
conditions. For QRP operation, raising power from an initial 1 watt
to a final 4 watts would restore signal strength at the reception end.
Chapter 75
The IL-ZX is not by any means a perfect antenna, designed to

outperform anything else on the market. However, neither is any
other antenna. Every set of performance figures carries with it a set
of operating specifications within which performance is measured.
We too often ignore this fact when evaluating antennas.
If vertical and horizontal space are at a premium and skills needed

to build an effective small loop are somewhere in the future, the IL-
ZX may serve as an effective low radiation angle antenna in the
interim until a perfect antenna site can be purchased. If you decide
that you do not like the antenna, you can likely put the materials to
use on other projects.
The ILZX Horizontally
Considerable interest has grown up in the last few years relative to

the intermediate or interrupted loop used in a horizontal position.
One or more such antennas--strung together for multi-band use--
have appeared on the market within the British Commonwealth;
one is called the "Cobbweb." However, a single-wire intermediate
loop shows a very low impedance and requires a matching system
for the ubiquitous coaxial cable feedlines preferred by many
amateurs.
The ILZX form of the interrupted loop is quite usable in a horizontal

position. In fact, with almost no adjustments, the vertical ILZX for 40
meters can be used horizontally. In the following notes, we shall
build the model ILZX in the same way for horizontal use that we
Chapter 75
used for vertical applications. The #12 elements will be separated

by 6" and form a square that is 18' on a side. The tips that
approach each other will form a "spear tip" pair for ease of
adjusting the gap to refine the source impedance. The tips will be 1'
apart.
Chapter 75
If we place the antenna at 50' above ground, we find a pattern

resembling the one in Fig. 7. Note that the pattern is stronger along
the axis formed by the feedpoint and the gap. The feedpoint
impedance under these conditions is about 53 Ohms, with about
the same bandwidth as the vertical version: 100-150 kHz or about
1/2 of the 40-meter band. Since the antenna is set for mid-band, a
user would have to adjust the dimensions to favor either the CW or
the SSB portion of the band.
One myth surrounding interrupted loops is that they have a circular

pattern. They do not. Due to the current distribution along the wire,
radiation from the region on each side of the feedpoint yields a
stronger pattern on the feedpoint-gap axis. In order to develop a
circular pattern, one must readjust the shape of the ILZX into a long
rectangle with shorter feed-region and gap-region dimensions. An
example of such an antenna appears in the next Chapter 76
"Experimental Omni-Directional Antennas for 6-Meters." The
general proportions would be a partial guide to developing a truly
omni-directional interrupted loop for any other band. However,
expect to make considerable adjustments for differences in the wire
spacing, the wire size as a function of a wavelength, and the shape
of the wire ends at the gap.
Chapter 75
The maximum gain of the horizontal ILZX is about 5.1 dBi at a 37-
degree TO angle. The minimum or side gain is 3 dB less.
Nevertheless, the pattern shows considerable side-pattern
development, as displayed in Fig. 8. The graphic shows both the
vertical and horizontal components of the total pattern. The vertical
components are largely a function of ground reflections, but they
still contribute to the overall useful radiation. Since 3 dB difference
between the main and cross axes amounts to about half an S-unit,
Chapter 75
the radiation might be considered to be adequate for omni-

directional operation.
Compared to a dipole, the horizontal ILZX holds its own quite well,
as demonstrated in Fig. 9. I modeled a resonant dipole at 50' above
average ground for comparison. The dipole's maximum gain is
about 1.1-dB higher than the maximum for the ILXZ. However, the
dipole shows about 7-dB difference between its maximum and
minimum gain, where the minimum is off the ends of the antenna.
Note that for dipoles well under 1-wavelength above ground, we do
not obtain a true figure-8, but only a peanut. Brought closer to
ground, the pattern becomes a broad oval.
Chapter 75
Since the ILZX has a naturally oval pattern, it better approaches the
omni-directional pattern favored by many hams who have only a
single, fixed-position antenna. Erecting an ILZX requires only an 18'
by 18' space, but does require 4 corner support posts for the 40-
meter version. A version for 20 meters would require only a 9' by 9'
space and might be supported on a single mast with fiberglass
spreaders. The higher the frequency, the easier the ILZX will be to
support. Because the antenna has a pattern that approaches the
omnidirectional, it requires no rotator. However, it does call for
Chapter 75
orienting the strongest axis in the direction(s) of the most favored

communications targets.
Although the antenna looks something like a beam, it is not. Hence,

it will not provide the QRM attenuation to the sides and/or rear of a
beam. Indeed, the gain is less than that of a dipole (and hence
considerably less than the gain of any well-designed beam). That is
the price one pays for omnidirectional coverage. About the only
way to obtain more gain from the ILZX is to extract it from the high-
angle radiation. One (impractical) scheme for doing so is to stack
and feed in-phase two ILZXs spaced 1/2-wavelength vertically. The
result is about 3-dB more gain in every direction.
The horizontal ILZX is suited to an exceptionally wide variety of

construction techniques, depending on the frequency of operation
and the exact layout of the loop and gap structures. Nested multi-
band version may use a fairly low impedance line to connect
feedpoints. The system of closed sleeve coupling sometimes works
best when the main feedpoint is the highest frequency loop. Wire
interactions will require loop adjustments, especially for the inner
loops. As well, expect significant current on the inactive band loops
and consequential modifications of the overall pattern on some
bands. Finally, if one or more bands seem hard to bring into line, try
moving the composite feedpoint to a different element relative to
the one initially used. Be certain to check the SWR bandwidth for
each trial arrangement before finalizing the selection.
For a multi-band antenna, you may have better luck separating the
bands. 20-15-10 provides less element-to-element interaction than
Chapter 75
a 5-band version of the antenna, although the harmonic relationship

of 20 and 10 meters may show some pattern deviations. Of course,
a second smaller array for 17 and 12 meters makes a good
antenna to stack on top of the tri-band model.
The ILZX principle of raising the feedpoint impedance simplifies the

matching problem that faces single-wire interrupted loops.
However, it requires greater care in supporting the double-wire
loops. The wire problem might be resolved by using TV twinlead or
450-Ohm window line. Such insulated transmission lines will likely
require adjustment of the dimensions downward by 2 to 5 percent
to account for the antenna velocity factor of the vinyl coatings.
Every variation of the horizontal ILZX will demand ingenuity and

considerable experimentation. As well, remember that the
horizontal ILZX resembles every horizontal antenna in the
relationship of its elevation angle of maximum radiation to the
height above ground. The original vertically polarized ILZX provided
low-angle radiation, but suffered gain losses due to its proximity to
ground. The horizontal ILZX provides more gain, but at higher
elevation angles until the antenna is at least 1/2-wavelength above
ground. The higher the operating frequency, the easier it is to meet
the height requirement for long-distance communications.
Happy experimenting!
Chapter 75
Chapter 76: Experimental Omni-Directional Antennas for 6M
A
lthough our subject matter refers to the 6-meter band--more
specifically, 50.5 MHz as a design frequency--the ideas in
the following notes are applicable to any other band on
which we wish to use any of the antenna designs to obtain a
horizontally polarized omni-directional pattern.
We shall do a brief review of turnstiles and their limitations, followed

by the introduction of some different types of omni-directional
antennas.
Turnstiles
The basic idea of a turnstile is not dependent upon any one type of
antenna. Any horizontally polarized antenna is a fit subject for
turnstiling. The most common type of turnstile employs two dipoles,
as sketched in Fig. 1.
Chapter 76
The dipoles are set at right angles to each other. We then run a 90-
degree long phasing line between the two to obtain quadrature, that
is, 90-degree phasing. There are more complex systems of
achieving the required phasing, but each is subject to the same
limitations. The key requirement for the simple phasing system is
that the characteristic impedance (Zo) of the phasing line must be
very close to the natural resonant impedance of the individual
dipoles. A 70-Ohm line is a good match for the dipole turnstile. The
Chapter 76
net feedpoint impedance will be 1/2 of the impedance of the

individual dipoles, or about 35 Ohms for the antenna sketched in
Fig. 1.
A dipole has a limited -3 dB beamwidth. Therefore, the pattern that

is produces in a turnstile antenna will be less than perfectly circular.
The gain variation around the rim of the pattern is a little over 1 dB
for an ideally constructed turnstile. Fig. 2--on the left--shows the
squared but usable dipole turnstile azimuth pattern.
The azimuth pattern--whether a free-space E-plane pattern or an

azimuth pattern over real ground--does not change except for the
increase in signal strength created by ground reflects and the
elevation angle of maximum radiation over ground. All of the
Chapter 76
antennas that we shall discuss have take-off angles of 13 degrees

when mounted 1 wavelength above ground.
The H-plane pattern in free space becomes the elevation pattern

over ground. Fig. 2--to the right--shows the free space H-plane
pattern for the dipole turnstile. From it, we should draw a clue as to
one major limitation of the dipole turnstile: it radiates better
broadside to the plane of the wires than off the edges--and it is the
edge radiation which makes horizontally polarized communications
possible from point-to-point.
Fig. 3 shows the resulting elevation pattern when we place the

dipole turnstile 1 wavelength above ground. At 50.5 MHz, this is a
height of about 20'. The strongest lobe is not the lowest lobe, but
Chapter 76
the second lobe. The lowest lobe of the dipole turnstile has a gain
of only about 4.8 dBi. While adequate for many purposes,
designers have felt that we can do somewhat better. However, we
must always remember that when we create a nearly or perfectly
omni-directional pattern, we should always expect lower gain than
from a dipole. The dipole achieve between 7.5 and 8.0 dBi gain at
the same height because it has only two lobes, with deep nulls off
the ends. The dipole turnstile uses that same power evenly in all
directions, so there will be lower power in each direction than in the
bi-directional main lobes of the solitary dipole.
Low gain is not the sole limitation of the dipole turnstile. As we vary
the frequency, the turnstile gives us the illusion of being a simple
antenna, because the SWR remains almost constant for a very
wide frequency span. However, the pattern does not stand still. As
we vary the frequency off the design frequency, the pattern grows
increasingly less circular. Fig. 4 shows the dipole turnstile patterns
1 MHz off the design frequency.
Chapter 76
Chapter 76
The patterns in Fig. 4 would also be good illustrations of other

deviations from perfect construction. For example, if the phase line
is too long or too short, we shall obtain non-circular patterns. If the
line has a higher or lower Zo than the individual antennas, we shall
obtain non-circular patterns. There are a number of schemes for
obtaining a 50-Ohm feedpoint impedance by using differential
lengths of line to each dipole. However, it is not impedance that
sets the pattern. Instead, it is the current at each dipole being equal
in magnitude and different in phase angle by 90 degrees that yields
a circular pattern. Virtually all of the matching schemes result in
distorted patterns.
The dipole turnstile, then, is a somewhat precision instrument that

is not amenable to casual construction unless we can live with a
non-circular azimuth pattern. If we can achieve good precision in
our element measurements and in the construction of the phase
line, we can make some improvements over the dipole elevation
pattern and achieve a bit more gain.
Chapter 76
Chapter 76
Fig. 5 shows one direction that we might go: the quad turnstile.
Essentially, the quad turnstile is two quad loops--shown in diamond
configuration--fed at the base just as we would feed two dipoles.
However, the impedance of the resonant quad loop at 6 meters
composed of #14 copper wire is about 125 Ohms. Hence, we must
make our phasing line out of RG-63, about the only available 125-
Ohm coax. The net impedance will be about 62 Ohms, which yields
an adequate coax match, especially since the quad SWR curve will
be as flat as the dipole curve. Indeed, SWR tells us almost nothing
about the performance of a turnstile, with two exceptions. It may tell
us that we have an open circuit or a short circuit somewhere along
the line. As well, it may reveal the need for some means of
suppressing common mode currents.
Because the lobes of an individual quad loop are somewhat wider

than those of a dipole, the E-plane or azimuth pattern will be
somewhat more rounded. Fig. 6 shows the free space azimuth
pattern (on the left) for the quad turnstile. The maximum-to-
minimum gain variation is somewhat under 1 dB for the quad
turnstile.
Chapter 76
The H-plane pattern on the right reveals the advantage of the quad
over the dipole as an antenna to put into turnstile operation. The
gain in the vertical direction does not exceed the gain in the
horizontal direction. As a result, the elevation pattern of a quad
turnstile with the center hub 1 wavelength above ground will exhibit
a main lobe that is significantly stronger than the second lobe
upward. As well, the radiation directly upward drops by about 5 dB.
Fig. 7 provides a sample elevation pattern.
Chapter 76
The quad turnstile shows a gain (over ground at 13-degrees

elevation) of about 5.7 dB, almost a full dB stronger than the dipole
turnstile. However, the quad turnstile is subject to all of the same
sensitivities to imprecise construction and design as the dipole
turnstile. QEX ran an article in Mar/Apr, 2002, covering those
sensitivities in detail.
Updating a Practical 6-Meter Turnstile Quad
In May, 2002, I published in QST some notes on a practical 6-meter

turnstiled quad for omni-directional horizontally polarized
communications ("A 6-Meter Quad Turnstile," pp. 42-46). The
general outline and dimensions of the antenna appear in Fig. QT-1.
You will find details and background in the article.
Chapter 76
The key elements for these update notes are the particular
construction methods that I used, with crossed CPVC arms to
Chapter 76
spread the wires. Fig. QT-2 shows some of the details. Note
especially the use of holes in the main mast and bolts to secure the
cross arms.
Chapter 76
Fig. QT-3 shows the method that I used to join the phase-line and
main feedline, with a plate that surrounds the mast at the bottom of
the loops. The original article provides explanations for all of the
abbreviations in the sketch.
Chapter 76
Ivan Cook, K4SRB, has built an interesting variation on the turnstile

quad for 6. His version uses some ingenious twists on PVC--
literally. Fig. QT-4 shows Ivan explaining his antenna to a local
club. In terms of construction, perhaps the most notable feature is
the absence of nuts and bolts at the center junction of the support
arms with the mast. Instead, Ivan uses a set of elbows and short
PVC links to put the arms at the same level. He cements most
joints, but leaves a few using only a friction fit.
Chapter 76
The reason for the friction fit is that Ivan uses his turnstile quad in
the field. To transport it, he can twist the elements into a flat plane.
In addition, he has used soldered connections--covered by the
PVC--for the phase-line and the main feedline connections. These
moves effectively eliminate the need for a mast extending from the
ground to the base of the antenna. In lieu of a mast, Ivan has put a
hook at the top of the central arm and hangs the antenna from a
tree limb. Fig. qt-5 provides a general idea of the antenna in use.
Chapter 76
Ivan's variations show two things of importance to antenna

experimenters. The first item is the versatility of PVC as a general
support structure that is RF invisible at least through 2 meters and
for many purposes through 70 cm. The second item is the ingenuity
of the individual experimenter in adapting an antenna design to a
specific set of needs and goals. Ivan has converted a somewhat
ungainly structure into one that is field-friendly both in use and in
transport.
The quad turnstile is not necessarily an ideal antenna. It does have

a disadvantage. Its loop construction essentially places two dipoles
an average distance apart of 1/4 wavelength. It is the double or
phased dipoles that account for the stronger lower elevation lobe of
the antenna, relative to the dipole turnstile. However, it is not
usually practical to place two quad turnstiles in a vertical stack. The
practice is common with dipole turnstiles, but with a degree of usual
carelessness that results in relatively poor performance. The pair of
dipole turnstiles will interact with each other. If the stack is to have
a nearly ideal circular pattern, the individual dipoles must be re-
resonated in the stack. Only under this condition will they provide a
circular pattern.
For better control of the feedpoint impedance, some quad-turnstile

builders have turned to the vertical rectangle as the base antenna.
If we increase the vertical dimension of a square and decrease the
horizontal dimension, we can change the feedpoint impedance from
the square's 125-Ohm value to something closer to what we need.
In fact, we can arrive at 50 Ohms, but that is not our goal here.
Instead, we want an impedance of between 95 and 100 Ohms so
Chapter 76
that the turnstile phaseline will give us a direct 50-Ohm feedpoint

impedance. Fig. R1 provides an outline of such a turnstile using
AWG #14 copper wire and set for 50.5 MHz.
The vertical sides are about 1.3 times the length of the horizontal
wires. The phaseline is 49" of RG-62, which has a velocity factor of
0.84 (for a 58.33" electrical length). The feedpoint impedance is so
close to 50 Ohms that the SWR does not rise above 1.1:1 across
the first MHz of 6 meters. However, SWR is never a problem with
turnstiled elements. The SWR remain nearly constant over a
Chapter 76
bandwidth that is much wider than the bandwidth over which the
pattern holds its omni-directional shape.
Chapter 76
Fig. R2 shows the elevation and azimuth patterns of the

rectangular quad turnstile. The pattern is virtually identical to the
pattern for the diamond quad-turnstile version. Because the
rectangles are so little out of square to arrive at individual loop
impedances near 100 Ohms, the gain does not increase
significantly. In this case, the average gain is about 5.5 dBi with a
1-dB variation between maximum and minimum points.
The finickiness of turnstile antennas--as well as their relatively large

size at 6 meters and below--has led designers to look for other
options in producing a horizontally polarized omni-directional
antenna.
Unclosed Loops
It is possible to create an omni-directional horizontally polarized

antenna by employing a interrupted loop less than 1 wavelength in
total wire length. There are two sorts of these loops--which
resemble triangles or rectangles: larger loops with a total wire
length that is about 3/4 wavelength and smaller loops with a wire
length in the vicinity of 1/2 wavelength. There are interesting
differences between the larger and smaller loops, so we shall look
at them separately.
Larger Loops
In any of the open-loop designs, one key to success is to find the

right shape so that the radiation from the center-portion and the
Chapter 76
radiation from the legs balances into a circular pattern overall. For
this reason, only certain relationships between the center portion
and the end pieces will work. The current on the center and end
portions is not equal. Therefore, in general, the shaping of the
larger loops will be triangular. Bending the end portions towards
each other is one way to fine tune the balance of currents and the
resulting pattern.
Chapter 76
Fig. 8 shows two examples of larger loops: the wide-gap and the
narrow gap versions. The versions result from giving precedence to
one of the other goals of the exercise in addition to pattern shape.
The other two goals are the feedpoint impedance and the distance
between the tips of the loop ends. In general, with larger loops, the
two goals are not compatible.
The top wide-gap triangle in Fig. 8 sacrifices the convenience of

closely spaced tips for a 50-Ohm feedpoint impedance. In fact, like
all of the loops that we shall examine, there is a high inductive
reactance at the feedpoint. However, we may compensate for this
with series capacitance at the feedpoint, using methods that we
shall describe further on. The wide-gap model shows a 50-Ohm
impedance after compensation, with a 1 MHz 2:1 SWR bandwidth.
The antenna material for the initial design is 1/4" aluminum.

Dimensions will vary with the diameter of the element. The center
portion is 68" long, with 53.7" ends. The bending of the ends to
make a near triangle results in a 47" dimension from the center
section to the element tips. The tips are 16" apart. The pattern
shows a maximum azimuth pattern gain variation of well under 0.1
dB. With the antenna 1 wavelength up, the gain over average
ground at a 13-degree take-off angle is 6.0 dBi, about 0.3 dB higher
than the quad turnstile.
Chapter 76
The top of Fig. 9 shows the elevation pattern of the antenna at the
1-wavelength height. The vertical radiation (straight up) is several
dB lower than for the quad loop.
Let's return to Fig. 8 and examine the lower loop. Here the gap is
narrowed to 0.5" so that aligning the ends becomes a much simpler
mechanical process. To sustain a circular pattern, the 1/4" diameter
Chapter 76
element is 62" long in the center portion. The ends are 52.9" long,
resulting in a 43" distance between the center element section and
the tips.
The azimuth pattern for this version of the interrupted loop is

circular within 0.6 dB around the horizon. As the lower half of Fig. 9
shows, the secondary lobes are further reduced, with vertical
radiation running nearly 18 dB below the strength of the main lobes.
The gain--again at a 13-degree take-off angle with the antenna 1
wavelength up--averages about 6.3 dBi, a further increase over the
wide-space loop.
Like the wide-spaced loop, the feedpoint of the narrow-gap version

of the antenna has a high inductive reactance, calling for
compensation. The resistive component of the impedance is about
23.3 Ohms. Therefore, we require a further method of matching this
antenna--even with the reactance compensated--to a 50-Ohm
coaxial cable. The simplest method is to use a 35-Ohm 1/4
wavelength section of cable. We can construct the section from
38.5" of RG-83 (with a velocity factor of 0.66, for an electrical length
of 58.4") or from parallel sections of 70-Ohm cables (which come in
various velocity factors, depending upon the use of solid or foam
dielectrics).
The result at the design frequency is a very close match to 50-Ohm

coax. However, the 2:1 SWR bandwidth is only about 540 kHz at
the antenna terminals. Due to cable losses, SWR measured at the
transmitter end of the line would likely show a wider bandwidth.
Chapter 76
Both loops require that we place series capacitors in the line at the
feedpoint terminals. The total capacitance for the wide-gap version
is 4.98 pF, while the total for the narrow-gap version is 5.48 pF.
These numbers are unduly precise, because construction variables
will create considerable differences in the feedpoint inductive
reactance.
Perhaps the best way to arrive at the required capacitance with

maximum trimming control is to install capacitors in each side of the
line, using double the required total capacitance for this series set-
up. We can experiment with small fixed capacitors or trim the
antenna with variables and replace them with fixed values when
tune-up is complete. However, for maximum control, we might
consider running insulated wire or thin tubing snugly against the
split fed element on each side of the line. The capacitance of the
wire and the element depend upon several variables: the facing
areas of conductor, the distance between conductors, and the
dielectric constant of the insulation on the wire or thin tube. Since a
builder will likely use materials on hand, it is impossible to provide
detailed guidance. It likely pays to start with wire lengths that are
too long and to prune them--evenly on each side--until the
reactance disappears at the design frequency.
Smaller Loops
The larger loops just described will have a center-section length

between 5 and 6 feet. This size is a considerable saving over a
dipole or quad turnstile antenna. However, it is still considerable for
Chapter 76
many installations. Therefore, one may wish to explore interrupted

loops in the 1/2-wavelength total wire region.
There are on the commercial market single element broken loops of

the smaller sort. They measure about 41" at the center, with 49"
legs--approximately and use a narrow gap between ends. I do not
have all of the physical specifications of these antennas--made by
Par Electronics in North Carolina. Therefore, the following notes do
not necessarily apply to these antennas.
Most intermediate-size interrupted loops using single elements tend

to have very low resistive components to the feedpoint impedance,
while sustaining considerable inductive reactance. By
compensating for the reactance first, one can use a balun or a
broad-band toroidal transformer to raise the impedance to coaxial
cable levels. However, at the feedpoint itself, the low impedance
raises the potential of resistive losses for the home builder without
a well equipped shop. Every fraction of an Ohm in a connection
converts a higher percentage of supplied power into heat than with
a higher impedance at the feedpoint. Therefore, one might leave
such assemblies to the pros and for home construction take a
cheaper and easier-to-build approach.
In Chapter 75 I introduced as a limited-space 40-meter antenna the

IL-ZX, the intermediate or interrupted loop impedance transforming
antenna. We can apply the same approach to a 6-meter version of
the IL-ZX.
Chapter 76
Fig. 10 shows the general outline of the rectangle forming the IL-
ZX. The short portions are 25" long per side, while the longer
sections are 41". There is a gap, which is set at 1". Note that the
loop resembles a mutilated folded dipole. Only one wire of the over-
under pair is fed. The gap consists of parallel wires, each 4" long,
the spacing between the upper and lower wires.
In several design models, the spacing between wires was varied

from 1" to 4" with only minor changes in the remnant inductive
reactance at the feedpoint. As well, changing the wire from AWG
#14 to AWG #12 resulted in similar minor variations in feedpoint
reactance. In fact, one might well control the reactance by making
Chapter 76
the wires at the gap into arrow points, thus reducing the rate of
change of capacitance between ends as the gap spacing is
changed. However, changing the gap spacing with the present
arrangement also creates only slow changes in feedpoint
reactance.
The key to the design--and the reason why it is a rectangle rather

than a square--lies in the need to have a circular azimuth pattern
and a feedpoint impedance with a resistive component near 50
Ohms. The dimensions noted above result in a pattern with about
0.1 dB variation. The top portion of Fig. 11 shows how nearly
circular the pattern is with the antenna 1 wavelength over average
ground. The elevation pattern is equally well-controlled.
Chapter 76
Chapter 76
Since the antenna is smaller than the larger loops that we

discussed, the average gain of 5.8 dBi may seem surprising. The
resistive portion of the feedpoint impedance is about 58 Ohms, and
the 2:1 SWR bandwidth is about 500 kHz. Thus, the operating
bandwidth matches the narrow-gap large loop, but not the wide-gap
larger loop. The gain levels of all three are comparable.
The IL-ZX loop has a considerable inductive reactance, and

required about 4.32 pF of total capacitance--or 8.64 pF per
feedpoint terminal. The notes given earlier on methods of providing
the required series capacitance for the larger loops are equally
applicable for the IL-ZX.
One of the advantages of the loops that we have been discussing is

the ease with which we may stack them. Unfortunately, many folks
still labor under the mistaken rule of thumb that a stack nets the
user 3 dB of gain. In fact, the gain advantage that we get from a
stack depends on the spacing between antennas. For dipoles, 5/8
wavelength yields about the highest gain advantage over a single
antenna, and with practical materials, this amounts to a little over
2.5 dB.
The goal in stacking a pair of IL-ZX antennas might initially be to

further suppress vertical radiation, since that is the most useless
part of the elevation radiation pattern. A spacing of 1/2 wavelength
yields maximum vertical radiation suppression, but the gain
advantage over a single array drops to under 2.4 dB. Although this
is highly usable gain, it is simply not the theoretical 3.0 dB bandied
about by so many.
Chapter 76
Equally important is the fact that a stack will lower the overall take-
off angle of the array. If the lower antenna is at 1 wavelength height
and the upper is at 1.5 wavelengths, then the take off angle will
drop from 13 degrees to 10 degrees. For a stack of 2 IL-ZXs, the
gain will be about 8.2 dBi.
Chapter 76
Fig. 12 shows the azimuth and elevation patterns for a stack of two
IL-ZX antennas. The circular azimuth pattern appears solely to
confirm that we may stack these types of loops without redesign, as
is required by stacked dipole turnstiles.
The elevation pattern shows the results of using the 1/2-wavelength

spacing between antennas. All lobes except the lowest have
reduced strength, a desirable effect for omni-directional horizontally
polarized local and regional communications.
The stacking harness requires careful construction. Two lengths of

70-75-Ohm coax, each electrically 3/4 wavelength long (because
1/4-wavelength sections would not meet) will transform each pre-
compensated 50-Ohm impedance to 100 Ohms. A Tee fitting
parallels the two impedances to result in a 50-Ohm match to the
main feedline.
Uniform-Current Loops
An overlooked design emerged in 1944 (Donald Foster, "Loop

Antennas with Uniform Current, IRE, Oct, 1944). Recently, Robert
Zimmerman resurrected the idea in "Uniform Current Dipoles and
Loops," in antenneX for April, 2006. The principle is to divide the
circumference of a loop into sections such that the inductance of
each wire length is offset by a periodic capacitor and so that the
loop exhibits a 50-Ohm impedance--without need for any form of
matching. Let's divide a square of wire into 7 sections. Each section
will be 0.12-wavelength long, for a total circumference of 0.84
Chapter 76
wavelength. At each wire junction, we shall insert a capacitor. The

capacitor size will vary with the wire diameter. AWG #14 calls for
9.63-pF units, whereas AWG #10 needs 10.31 pF capacitors. The
design comes closest to an even 10 pF with AWG #12 wire.
In real terms for 50.4 MHz, each AWG #12 wire section is 28.1"
long. The square is 49.2" on a side for a circumference of 196.7".
Note that the sections (7) do not correspond to the sides (4), which
is no hindrance to effective antenna operation. One model of the
antenna looks like the outline in Fig. 13.
Note that it does not matter if the feedpoint is placed mid-side or

offset, so long as the feedpoint is in the middle of a wire section.
The figure also shows the relative current magnitude along the
circumference of the loop. The level changes by under 4% all along
the perimeter. (Initially, this phenomenon appears to have been the
Chapter 76
goal of the open-ended CCD long doublet, but the open ends
preclude obtaining that result.).
The uniform current square loop provides horizontally polarized

radiation. Although only a little larger than the triangles, the results
are equal in omni-directionality and superior in gain. At 1
wavelength above average ground, the antenna gain averages
about 6.8 dBi, with a total variation in gain of about 0.6 dB. The
gain is almost a dB better than the best triangle. Fig. 14 shows the
elevation and azimuth patterns and also reveals one significant
reason for the improved gain from the loop.
Chapter 76
Chapter 76
If you compare the elevation patterns with the one shown for the
triangle, you will see that the loop produces virtually no radiation
straight upward, leaving more energy for the lower lobes. Since the
antenna does not need to compensate for rapidly changing
reactance values, it shows a reasonable SWR bandwidth. As
shown in Fig. 15, the 2:1 50-Ohm SWR range is 50 to 50.85 MHz.
Once you arrive at a usable wire section length and employ the
most precise and well-matched set of capacitors that will handle the
anticipated power level, you can change the exact center frequency
by altering the wire length, since the same capacitance within about
0.1 pF will hold good for nearly a 400-kHz change in center
frequency.
Among the experimental designs shown, the uniform-current

square loop is perhaps the "best in show."
Conclusion
The interrupted-loop and the uniform-current square-loop designs

shown here are experimental. Any builder should expect to spend
considerable time adapting local materials to the needs of the
design of choice. As well, field adjustment will also require
considerable care and effort. In the end, the goal is to produce a
truly circular horizontally polarized pattern with a feedpoint
impedance compatible with the main feedline. Hence, much work
will be devoted to proportioning the antenna for pattern shape, and
an equal amount of work will go into compensating for the
reactance and arriving at a usable resistive impedance.
Chapter 76
In the end, it is doubtful whether the loop designs are any less
finicky than the turnstiles. Instead, they simply change the places in
construction and design that require close attention to detail.
Producing a circular pattern that is horizontally polarized is no
mean feat, whatever the design direction we take.
For frequencies above 400 MHz, the design concepts can be

applied to circuit-board construction techniques, since the elements
and capacitors are easily fabricated with these methods. The
antenna would be only a few inches per side. However, detailed
design would require FDTD or comparable techniques that are not
at my disposal.
Chapter 76
Chapter 77: Modeling the T2FD
T
he "terminated, tilted folded dipole" (T2FD) antenna has been
subject to much recent conversation, some of which has
come my way in the form of questions about modeling the
antenna. So I decided to take a systematic look at models of the
T2FD. The original T2FD was intended for use as a vertical or a
sloping antenna, often as an appendage to the tall tower. Later
(WWII), the antenna found use as a horizontal "all-band" wire
antenna used in either flat or inverted-V configurations. These
notes will deal largely with the vertical and sloping versions. For
further and deeper looks into the horizontal versions, see Chapter
28 in Volume 2 of this series on Wire Antennas.
The two models I investigated are sketched in Fig. 1 (shown

horizontally to save space). Both are similar in that they are indeed
Chapter 77
folded and dipoles, although not folded dipoles in the normal sense
of that term. The resistor placed opposite the feedpoint limits the
impedance excursions at the feedpoint relative to an unterminated
folded dipole. At the same time, the resistor also introduces losses
into the antenna in the form of converting some of the RF energy
into heat.
Both antennas are designed for use from 2 MHz through 30 MHz
as initial design criteria. We shall explore limitations in that
frequency spread along the way. The "Wide-Long" version
coincides with standard construction formulations, since the
antenna is about 300/F(MHz) long and 10/F(MHz) wide.
(Excessively fussy cutting formulas for this antenna are largely
superfluous, since strict resonance is not in question.) The "Narrow-
Short" version generally approximates or approaches the
dimensions of commercial versions of the T2FD, even if that name
is not used for the antenna. Both antennas use #12 copper wire.
Modeling the T2FD involves nothing that in any way presses the
limitations of NEC (either -2 or -4), so long as the segment length in
the long wires is not out of balance with the segment length in the
short wires and as long as sufficient segments are used per
wavelength for all frequencies to be investigated. In short, nothing
in the antenna design suggests that NEC should not give accurate
predictions of performance.
We shall look at several questions that seem to perpetually arise in

connection with the T2FD. The first involves the antenna's
feedpoint impedance across the frequency range of intended use,
Chapter 77
relative to the selected value of terminating resistor. The second

will involve antenna patterns when the antenna is oriented
vertically. Related to this second question is the matter of tilting the
antenna, as our third inquiry. Finally, we shall look at the question
of losses relative to uses to which one might put the T2FD.
Since these are notes on two models of the T2FD, they do not yield
more than suggestive results. Hence, nothing in these notes should
be construed as fixed, final, or necessarily in rebuttal of existing
claims, many of which may be based on different version of the
antenna type.
Impedance, SWR, and the Terminating Resistor
All modeling runs for the T2FD (both versions) were made with the
antenna lower end 20' above average ground and with the antenna
vertical. Check runs with the antenna tilted 45 degrees produced
no significant differences in the impedance results.
One common recommendation for the T2FD is to use a 390-Ohm

resistor for the termination and to employ 300-Ohm feedline. (The
general recommendation is to use a terminating resistor that is
about 5% to 10% higher in value than the feedline characteristic
impedance.) I performed frequency sweeps with this configuration
using both models. The technique is to obtain an SWR curve from 2
to 30 MHz using as a standard the characteristic impedance of the
desire line, with a resistive load in the model matching the desired
terminating resistor.
Chapter 77
Fig. 2 shows the results of the 390-300 Ohm combination for the
standard T2FD configuration cut for 2 MHz. (The model used is the
165' long wide version from Fig. 1. Although called a 2-MHz
antenna, the antenna is about 1.2-wavelength long at 3 MHz.) The
SWR excursions are very wide, ranging from about 1.2:1 to nearly
9:1.
I could provide a mass of similar graphics representing my search

for a combination of terminating resistor and feedpoint impedance
standard that would yield the shallowest SWR excursions. Instead,
I shall drop to the bottom line. For the standard "wide" T2FD
configuration cut for a lowest frequency of use of 2 MHz, a loading
Chapter 77
resistor of 850 Ohms combined with a feedpoint impedance

standard of 900 Ohms yields the following "best" SWR curve.
In Fig. 3, the highest value of SWR relative to 900 Ohms is about

2.1:1, with peaks in this vicinity occurring every 6 MHz from 4 to 28
MHz. This value does not coincide with any one particular feedpoint
impedance, as the following table shows.
Freq. R +/- jX
4 1435 - j 615
10 1085 - j 700
16 855 - j 665
22 690 - j 575
28 590 - j 466
Chapter 77
Although the reactive component is consistently negative at these

frequencies, the resistive component ranges from well above to
well below the 900-Ohm standard. The resistive component of the
source impedance ranged from 450 to over 1400 Ohms, while the
reactive component ranged from +j250 to -j700 Ohms across the
frequency span. These ranges must be considered tentative, since
the check points are 1 MHz apart.
Interestingly, the narrow version of the T2FD with its shorter length
(100') also required an SWR standard of 900 Ohms, with a
terminating resistor only 50 Ohms less (that is, 800 Ohms) than that
used for the optimized wide T2FD version.
Chapter 77
With these conditions, as shown in Fig. 4, one can obtain an SWR

curve between 2 and 30 MHz of under 2:1 relative to 900 Ohms.
The peak values occur at 10 MHz intervals: 7, 17, and 27 MHz. The
wire is about 1.2-wavelength long at 5.5 MHz. However, the
extreme resistive and reactive component values are not very
different from those of the standard configuration.
In principle, it would seem that some scheme to transform the

standard impedance value for both versions of the antenna (900
Ohms) down to a desired feedline value (perhaps a 50-Ohm coaxial
cable) might be necessary. For a 50-Ohm result, an 18:1
transformation would be in order, perhaps done in two steps: 9:1
followed by 2:1. However, due to the high values of reactance
present at the feedpoint at numerous frequencies within the overall
antenna design range, one would need to use great care in
selecting the means of impedance transformation. Some methods
and materials may combine to yield losses which might then show
artificially low values of SWR on the final feedline. These losses
would be in addition to those incurred via the terminating resistor.
Whether these additional losses would be acceptable might well
depend upon the application proposed for the antenna.
Patterns and Frequency Limitations of the T2FD
Although a properly designed T2FD-type antenna is capable of

providing (with suitable matching devices or networks) a low SWR
over a very wide frequency range, the utility of the antenna displays
other limitations, as some simple elevation patterns can illustrate.
Chapter 77
Fig. 5 shows the elevation pattern of the standard vertical

configuration T2FD (as cut for a 2 MHz lower limit or a length of
165') at 5 MHz. The low angle of radiation is one of the features of
the T2FD that make it appealing in certain applications. The
antenna remains 20' above average earth at the lower end. Note
that the pattern is not symmetrical when taken across the plane of
the wires (with a 5' separation), with slightly less gain in the
direction of the loaded wire. In general, the closer the wire spacing
the less the gain differential. Broadside to the plane of the wires,
the elevation pattern would be symmetrical with a gain intermediate
to the high and low values shown in this edgewise view.
Chapter 77
In Fig. 6, we find the elevation pattern for the same vertical antenna
at 10 MHz. (Note that the wider standard configuration tends to
show some pattern displacement to one side or the other, due to
the spacing of the wires. The more dominant side depends on the
frequency of operation. The narrow version shows an almost
perfectly circular pattern.)
The most noteworthy aspect of Fig. 6 is the absence of low angle

radiation, with the first main lobe peaking at greater than 30
degrees above the horizon. The high-angle of the main radiation
lobes results from the fact that at 10 MHz, the antenna is well over
1.5-wavelengths long. A linear vertical doublet would show a low
radiation angle to a length of about 1.25-wavelengths. As the
antenna becomes longer, the main lobes are no longer broadside
to the wire, but at angles to the wire. This shows up in the vertical
configuration as high-angle radiation rather than low-angle radiation
Chapter 77
that would correspond to a broadside pattern in free space (or

when used horizontally)
To establish that Fig. 6 is no fluke, Fig. 7 is the elevation pattern for

the antenna at 15 MHz.
The explanation for these less than optimal patterns is the nature of
the antenna. Although terminated, the antenna is still a folded
doublet and shows in free space all of the pattern tendencies of any
dipole. So long as the antenna is 1.25 wl long or less, then there is
in free space a single main lobe broadside to the antenna wire. (In
the range of 1.1 to 1.35 wl long, the antenna shows the side lobes
typical of the extended double Zepp.) The main lobe, when the
antenna is vertically oriented over ground, results in a low-angle
lobe of radiation or reception sensitivity.
Chapter 77
As the antenna length approaches 1.5 wl, the broadside lobes give
way to dominant angular lobes relative to the plane of the wire.
When the antenna is vertically oriented, these lobes combine to
form high angle radiation maxima, with low angle radiation either
much reduced or wholly absent.
The standard T2FD at 165' long reaches the 1.25 wl limit at about
7.5 MHz, while the shorter 100' version reaches the same limit at
about 12.3 MHz. Beyond 8 MHz for one and 13 MHz for the other,
high angle patterns become standard. When any version of a T2FD
reaches a length relative to the operating frequency of more than
1.25 MHz, its utility for low angle radiation may become less than
desired.
The solution to this problem is fairly simple: the construction of a

second T2FD. A T2FD (this time in the narrow configuration) of 40'
overall length and 0.25' width, using the same loading resistor and
feedpoint standard impedance was modeled. The SWR graph is a
single curve that does not reach 2:1 from 7 through 30 MHz when
the antenna bottom is 20' above average earth. In fact, the peak
value of SWR relative to a 900-Ohm standard is 1.72, which occurs
between 19 and 20 MHz. This new antenna is already over 0.5 wl
long at 14 MHz and does not reach a length of 1.25 wl until nearly
31 MHz.
Chapter 77
Fig. 8 shows the elevation pattern of the second T2FD at 15 MHz,

for comparison with the pattern for the long T2FD in Fig. 7.
Although the peak gain value is lower with the shorter antenna, the
radiation is at an angle of greater utility in most applications.
To Tilt or Not to Tilt: That is the Question
All of the patterns shown so far use a vertical T2FD. Tilting the
T2FD alters its pattern considerably. Modeling does not confirm
reports of omni-directional performance from a tilted T2FD. We may
illustrate this fact with a simple comparison at 5 MHz using the
standard version of the T2FD. In one pattern, the antenna is
vertical; in the other, it is tilted 45 degrees.
Chapter 77
Fig. 9 shows the two patterns. The vertically oriented T2FD shows
minimal pattern displacement from one direction to the other.
However, the tilted version shows a heavy pattern displacement,
but in neither direction is the radiation field as strong as at the peak
of the lowest lobe of the vertical version.
Chapter 77
Fig. 10 shows the orientation of the pattern displacement to the tilt

of the antenna. The patterns off the sides of the antenna are equal
and approach those of the vertically oriented antenna. Nothing in
the models shows any advantage to tilting the antenna with respect
to skip communications or reception. Perhaps the only advantage
may be mechanical, for those lacking a suitable high support from
which to hang the antenna vertically.
Chapter 77
Terminator Resistor Losses
Although transmitting uses have been made of the T2FD, its chief
use appears to be as a short wave reception antenna. In this
application, the excess available receiver gain can largely make up
for losses incurred in the terminating resistor.
The losses in the terminating resistor are considerable, ranging

from nearly half power to amounts in excess of 90% of the available
RF power. The pattern of losses is not a simple smooth curve, but
varies throughout the operating range of the antenna. The following
graph plots the losses in terms of dB. For reference, a 3 dB power
loss represents half the power being dissipated in the resistor.
Higher values indicate more of the power being dissipated rather
than being radiated (or transferred to the receiver).
Chapter 77
Fig. 11 is notable because it tracks the SWR curves for the two
versions of the T2FD in quite interesting ways. The lowest losses in
the wide or standard version of the T2FD (165' long) occur at the
same frequencies as the peaks in SWR. For the shorter (100')
version, the lowest loss points show a slight displacement (1 MHz)
but occur at the same intervals. The actual loss within the resistor is
Chapter 77
a function of the current on that segment of the antenna. Other

lengths and load resistors will show different levels and patterns of
loss from the terminating resistor.
It should not be surprising that the shorter T2FD shows much

higher losses at the lowest frequencies of operation, since the
antenna is about 0.2 wl long at 2 MHz. Basic antenna efficiency
increases rapidly as the antenna length passes the 0.3 wl mark,
which is well above 3 MHz for the shorter antenna. Indeed, we may
call the frequency at which the antenna is about 1/2-wavelength
long the "knee" frequency. Below the knee, gain frops rapidly and
losses (as well as dissipation in the terminating resistor) increase
with equal rapidity.
The losses incurred in the terminating resistor occur in the form of

heat. For reception-only applications, simple low-wattage non-
inductive resistors may be used. For transmitting purposes, heat
dissipation for the terminating resistor assembly becomes a major
factor in antenna design.
Conclusion
The purpose of these notes is not to recommend or disrecommend

the vertical or sloping T2FD. Instead, the purpose has been to
explore what modeling might tell us about the basic performance
characteristics of the T2FD. Actual use decisions must measure the
antenna performance characteristics (refined for the actual
proposed design) against the application.
Chapter 77
There are a number of questions that modeling cannot answer,

even if precise design and installation data are supplied. For
example, the standard version of the T2FD is said to be quieter
than random wires and doublets in receiving applications. The
closed loop construction with wider spacing between wires may
well account for this report, but modeling cannot itself show the
phenomenon.
Nonetheless, the models used here were constructed with sufficient

care to warrant reasonable trust in the analytical results. These
notes may provide a basis for prospective users to check out their
proposed designs prior to installation to ensure that the resulting
antenna has a good chance of meeting expectations.
Chapter 77
Chapter 78: Wire Linear-Resonator Dipoles
I
have written elsewhere about dual-band linear-resonator dipoles
for the upper HF region that used elements having a substantial
diameter. 20-meter main elements used 7/8" tubing, while 15-
meter main elements used 3/4" tubing. One major consequence of
the material selection was our ability to use a fairly wide separation
between the main element and the 1/4"-diameter linear-resonator
rod. We centered our focus on 6", but explored some narrower and
wider spacing values between 4" and 8".
In this look into the land of linear resonators, we shall reduce the
main element diameter to wire size. One consequence of the
reduction is that we shall be able to use the same diameter material
for both the main element and the linear resonator. Since all wires
in the NEC-4 models will have the same diameter, the modeling
accuracy, as indicated by the average gain test (AGT) scores,
should improve. However, there will be a second consequence for
the models (and for any physical implementation of a wire-based
linear-resonator dipole). The ability to find acceptable dimensions to
achieve a set of resonant points on 2 bands with a 50-Ohm SWR of
less than 2:1 depends in large measure on the mutual coupling
between the parallel wires within the linear-resonator section of the
antenna. Since we are wholly dependent on the wires as linear
inductors for the mutual coupling, the degree of coupling depends
upon the wire diameters and the spacing between them. As we
reduce the diameter of the wires, we must bring them closer
together to achieve the same level of coupling.
Chapter 78
Suppose that we reduce the wire size by a factor of 7:1. That is,
suppose that we reduce the diameter from 7/8" to about 1/8". The
required spacing between the wires is roughly proportional to the
element diameter. Hence, the spacing between the main element
and the linear-resonator rod will decrease from about 6" to the
vicinity of 1". As we shall see, the narrow spacing will be quite
critical in dual-band dipoles with small ratios between the upper and
lower frequencies, but will be less critical with higher frequency
ratios.
To sample both possibilities, let's explore two different wire-based

linear-resonator dipoles. The first will cover 20 and 15 meters. The
3:2 frequency ratio falls at the lower end of the scale. As well, the
combination allows us to compare the results with the model used
in Part 1 of this series. Later, we shall examine a 20-10-meter
combination. The larger 2:1 frequency ratio will show us both the
advantages and the disadvantages of the alternate design.
A 20-15-Meter Wire Linear-Resonator Dipole
The 20-15-meter combination dipole that we explored in Part 1

proved that the linear-resonator technique can be successful if we
observe its limitations. The large-diameter (0.875" diameter) model
allowed us a wide SWR bandwidth on 15 meters. However, the 20-
meter impedance dropped to the vicinity of about 35 Ohms.
Obtaining coverage of 20 meters required careful attention to the
overall length of the antenna. The 1/4"-diameter linear-resonator
rod--spaced 6" from the main element--was a little under 100" long
Chapter 78
and required a capacitor value of about 16 pF for 15-meter

resonance.
Translating that "fat-element" model to wire size requires that we

reduce both the element diameter and the rod-to-element spacing.
For reasons that will become evident a little later, I did not start with
the usual amateur AWG #12 wire 0.0808" or 2.05 mm diameter).
Instead, I used the less common AWG #8 wire (0.1285" or 3.26 mm
diameter). As well, I reduce the rod-to-element spacing down to 1".
Since the end wires of the resonator section are so short, I had to
increase the overall segmentation density of the model to preserve
some semblance of segment-length equality. Fig. 1 shows both an
overall outline of the model and an expanded view of the linear-
resonator section.
Quite likely, any implementation of a wire-based linear-resonator

dipole will require the use of parallel sections of rod to effect the
resonating capacitance. The development of a homemade
concentric capacitor that is thin enough to avoid touching the main
element is difficult at best. For our initial model, all wires are AWG
Chapter 78
#8. The proximity of the wires does not yield perfect AGT scores.
However, the values (0.985-0.988) are significantly improved
relative to earlier models that had junctions of wires with different
diameters.
The close spacing between the wires does not affect the general
radiation pattern of the dipole. As shown in Fig. 2, the 15-meter
performance includes slightly high gain and a slightly narrower
beamwidth than we obtain on 20 meters. The free-space patterns
show a 0.5-dB difference in gain. In the plane formed by the main
element and the resonator rod, the close spacing does make a
difference. In this plane, the front-to-back ratio is down to 0.1 dB, a
reduction from the 0.5-dB value we obtained from the fatter model.
As a consequence, the 15-meter pattern shows deeper side nulls
than we obtained using fatter elements: about 25 dB below the
level of maximum gain.
Chapter 78
Smaller diameter elements do produce other effects that are

noteworthy. For a linear element, a smaller diameter element
generally produces an antenna with a narrower SWR bandwidth.
We can observe this effect in a general way by looking at a typical
wide-band SWR sweep. Fig. 3 shows a 50-Ohm sweep from 13 to
22 MHz to include the bands of interest.
Chapter 78
The peak 50-Ohm SWR value between bands was between 5:1
and 6:1 for the fatter models of Part 1. For our wire versions, the
peak value will climb to the 8:1 or higher region. The actual value is
not important in operation, but it does provide a caution to
experimenters. Finding the precise values for all dimensions,
including the capacitor setting, will likely be somewhat more finicky
for a wire-base dipole than for a tube-based dipole.
By the terms of our project, we are looking for dimensions that will
produce 50-Ohm coverage on both 20 and 15 meters with less than
a 2:1 SWR. (Indeed, if we forget this project specification, we might
as well use a simple wire with a parallel feedline and an antenna
Chapter 78
tuner.) As we did for the fat-element models, we shall freeze some

dimensions and vary others to obtain a sense of the trends at work.
Varying the Resonator Rod Length
The first set of tests will use AWG #8 wire throughout. A simple
dipole for 14.175 MHz would normally require a length of about
403". One feature that we shall look for is the amount of reduction
that the use of a linear resonator forces on the overall element
length. With the tubular models, we found a usable constant main-
element length that was about 14" or 3.5% shorter than a self-
resonant 20-meter dipole. Shifting to wire does not change the level
of reduction, but it does introduce a new factor into the building
equation. Changing the length of the resonator also requires a
change in the length of the main element. For every 4" decrease in
resonator rod length, we find a 2" increase in the main element
length.
As shown by the data in Table 1, the survey covers rod lengths

from 92" to 108". At the same time, the main element changes from
390" to 382". The range of resonating capacitance for the entire
spread is about 3 pF--from 18 to 21 pF. The average value is itself
about 3-pF higher than the average value needed for the tubular
models of Part 1.
Chapter 78
We have already viewed a wide-band SWR sweep for a typical

dipole from the group. In fact, that sweep used the version with a
100" rod and a 386" main element. We may therefore confine our
examination of 50-Ohm SWR values to the specific operating
bands. The impedance values at 14.175 MHz give us an additional
reason for taking a close look at the in-band SWR values. As we
reduced the element sizes in Part 1, we saw a decrease in the 20-
meter resistive impedance. We also wondered at what rate the
impedance would continue to decrease as we reduced the element
size further. At some diameter, the impedance might slip below 25
Ohms, removing all hope of obtaining 20-meter performance with
less than a 2:1 50-Ohm SWR. As the mid-band impedance values
show, we are getting close.
Chapter 78
Using AWG #8 wire allows us to obtain a barely usable SWR curve

across 20 meters. The shorter the resonator rod (and the longer the
main element), the better SWR curve that we obtain. Unlike the
tubular elements, the wire elements required that we adjust both
the main element and the rod lengths to arrive at this result.
The corresponding SWR curves for 15 meters appear in Fig. 5. On

this band we face a different challenge created by the increasingly
narrow-banded performance of thinner elements. Between rod-
length increment changes, the mid-band impedance on 15 meters
changes more rapidly, and this factor limits our ability to obtain a
satisfactory SWR curve.
Chapter 78
The 92" resonator rod that gave us the best 20-meter SWR curve
produces the least satisfactory SWR curve on 15 meters--although
the performance is usable. As the rod length increases, the SWR
curve tends to improve, at least through the 100" length. Further
increases in rod length degrade the SWR curve. Nevertheless, all
of the 15-meter curves within the set are usable. In general, 15-
meter performance is less problematical than 20-meter
performance with a wire-based dual-band dipole.
Varying the Rod-to-Element Spacing
For further tests, I selected the model that used a 100" rod and a
386" main-element length as perhaps (but not absolutely) the best
compromise in performance on both bands. The next test involves
seeing what happens as we increase the spacing in small
increments from the 1" initial value. (I judged that a smaller spacing
is probably not feasible in most practical applications.) In these
tests, the wire diameter remains constant (AWG #8). However, all
Chapter 78
other dimensions of the antenna are allowed to change. Table 2

shows the results of these modeling tests.
As we increase spacing between the main element and the

resonator rod, the required lengths of the main element and of the
resonator rod decrease. So too does the required capacitance for
the resonator capacitor. (Otherwise expressed, the capacitive
reactance increases.) These numbers show the physical demands
of increasing the spacing.
The spacing increase also has consequences for the impedances

on each band and the resulting SWR performance. Fig. 6 provides
SWR curves for 20 meters.
Chapter 78
The mid-band impedance values for 20 meters suggest that the 50-
Ohm SWR curve may grow less satisfactory as we increase the
spacing between wires. Fig. 6 confirms the suspicion. Indeed,
although the curve for 2" spacing appears barely to meet the
standard, it might not be so easy a matter to place that curve
precisely when pruning an actual antenna. In general, 20-meter
performance depends upon using the narrowest feasible spacing
between the resonator and the main element wires.
Chapter 78
The 15-meter 50-Ohm SWR curves in Fig. 7 tell much the same
story. As the spacing increases, the SWR curves grow less
satisfactory. On 15 meters, the problem is not a decreasing
feedpoint impedance. Rather, the problem arises from an
increasing resonant impedance. The bottom line for the spacing
tests is that a wire-based linear-resonator dipole does not offer the
flexibility of fatter elements. Narrow spacing is a requisite on both
bands when the frequency ratio is fairly low.
Varying the Wire Size
Admittedly, AWG #8 wire is somewhat impractical for end-

supported antennas. In copper, its weight is excessive, and in
aluminum, the wire junctions become difficult. I selected #8
because it permitted me to find all of the dimensions required in the
model for a successful design using a 1" spacing between wires in
the assembly. Whether AWG #8 represents a limit for a practical
antenna depends on what we find if we vary the wire size. For this
test, I held the spacing constant at 1". As well, I held the rod length
to a constant 100" length. I used standard AWG wire gauges from
#6 through #12, letting the remaining physical dimensions settle at
the most optimal values. Table 3 shows the results of this test set.
Chapter 78
The table has a special section noting the most optimal settings for
the AWG #6 sample. By increasing the length of the resonator rod
8", we obtain a marginally higher 20-meter impedance. We also
obtain a superior 15-meter impedance and a capacitor value that
approximates the value used with AWG #8 wire at its optimal
resonator rod length. I did not include in the table models for AWG
#10 and #12 wire with similar adjustments to the resonator lengths.
Each of those models would have required significant resonator-rod
shortening to obtain the desired 15-meter results. However, those
rod lengths would have produced lower impedances on 20 meters,
disallowing the use of the antenna on that band within the project
terms of a maximum 2:1 SWR value.
Chapter 78
With the values shown in the table, the 20-meter SWR curves
become increasingly marginal as we reduce the wire size, as
revealed by Fig. 8. The major problem of trying to optimize the
resonator rod lengths with thinner wire is not so much the mid-band
impedance. We likely can find a satisfactory impedance with less
than a 2:1 50-Ohm SWR. The major difficulty lies at the band
edges, where every reduction in resistance provides the reactance
with a proportionately higher influence on the SWR level.
Chapter 78
The difficulty does not extend to 15 meters. The SWR curves in

Fig. 9 all fall within the highly acceptable range. The curve for AWG
#6 wire is for the model using a 100" resonator rod. With a 108"
rod, the curve largely overlaps the curve for AWG #8 wire.
Some Summary Thought for the 20-15-Meter Wire Dipole
Increasing the diameter of the wires in a linear-resonator dipole

with a frequency ratio of 1.5:1 between bands is always advisable.
The increased diameter of the elements raises the flexibility of the
antenna to accept wider spacing. Although I have not modeled
such an antenna, one might consider using wire pairs for the main
element and the resonator rod to simulate fatter conductors in a
wire structure.
The essential difficulty faced by anyone experimenting with a wire

version of the 20-15-meter dipole is the impedance on 20 meters.
As the wire grows thinner, we require narrower spacing between
rod and element wires to prevent the 20-meter impedance from
dropping below the critical 25-Ohm value. Thinner wires also
reduce the capacitance-per-inch of the rod wires that form a
capacitor at the center. Finally, the narrow-band nature of thin wires
increases the finickiness of adjustments--and their ability to hold
during extremes of weather.
Nevertheless, the intrepid experimenter may wish to see what is

possible with wire in a 20-15-meter linear-resonator dipole. To this
end, the modeling experiments may serve as a guide. As with all of
the modeling experiments, these are not design plans. Rather, they
Chapter 78
illustrate some of the trends in operation for a linear-resonator

dipole with a small frequency ratio.
A 20-10-Meter Wire Linear-Resonator Dipole
In Part 2, we examined a fat-element linear-resonator dipole for 20

and 10 meters. Using a 0.875"-diameter 20-meter dipole and a
0.25"-diameter resonator rod, with a spacing of 6", we obtain some
results that reversed the difficulties for the antenna. On 20 meters,
the antenna showed a near 50-Ohm impedance that easily yielded
excellent SWR curves. However, 10-meters proved more
problematical, since we barely obtained full-band coverage, even
reducing the band to the first MHz.
When we reduce the elements to wire size, two major questions

confront us. First, will the 20-meter operation continue to show near
50-Ohm impedance values? Second, will the narrow-band
properties of thinner wires result in reduced 10-meter coverage?
Interestingly, some of the difficulties that we experienced with the

20-15 combination do not reappear with the 20-10-meter version.
For example, as subsequent tables will show, an AWG #8 wire
settles in at 392" long for all cases. The presence of the linear
resonator section does result in a shorter 20-meter antenna than
we find with a simple 20-meter dipole (392" vs. 403"). However,
variations in the resonator rod length and the spacing have very
little affect on the overall element length, since the second
frequency is so far removed from the first. As well, the 20-10
Chapter 78
version is an average of about 3" longer than the 20-15

combination.
Like the 20-15 antenna, the 20-10 dipole requires increased

segmentation to handle the 1" spacing between the element and
the resonator rod. Fig. 10 shows both the overall structure and an
expanded view of the linear resonator area of the model used. The
segmentation detail differs slightly from the earlier model, since the
10-meter linear resonator sections are longer than those used to
cover 15 meters. Nevertheless, the AGT scores of the antennas for
both bands are very similar.
Just because we have reduced the element diameter and the

spacing between wires, we do not lose the radical difference
between the patterns for 20 and 10 meters. Fig. 11 shows overlaid
free-space E-plane patterns for 14.175 MHz and 28.5 MHz using a
typical AWG #8 wire antenna. The 10-meter pattern has a 1.6-dB
gain advantage over the 20-meter pattern, with a corresponding
reduction in beamwidth.
Chapter 78
Like the 20-15-meter antenna, the reduced spacing between wires

yields a much smaller differential in gain in the plane of the
resonator on the higher band. The difference is only 0.1 dB. As
well, the 10-meter front-to-side ratio is nearly 34 dB, a considerable
improvement over the models using fatter elements.
In concert with the 20-15-meter wire antenna, the 20-10 wire model
shows a much higher 50-Ohm SWR peak value between operating
frequencies than did the fat-element antenna for the same
Chapter 78
coverage. Fig. 12 provides a wide-frequency sweep (13-30 MHz) to

show the overall performance tendency.
The peak 50-Ohm SWR value approaches 25:1 in the middle

region of the plot, nearly twice as high as the peak value for the
antenna with a 7/8"-diameter element. The increased peak 50-Ohm
SWR value suggests that the operating bandwidth as defined by a
2:1 SWR maximum value may be reduced relative to either the wire
20-15 model or the fat-element 20-10 model.
Chapter 78
Even though some dimensions of the wire 20-10-meter dipole may

remain stable, the data to follow will have the same form as used
with the 20-15 antenna. Except for the spacing test, the models will
use a 1" uniform spacing between the main element and the
resonator rod. I shall allow all other dimensions to settle to their
near-optimum values.
Varying the Resonator Rod Length
The initial test involves finding the resonator rod length and the
corresponding capacitor value that most closely approaches
perfection on both bands, as determined by the SWR curves. In
fact, I found no significant reason to vary the main element from
392" in the entire set of test runs. The 10-meter resonator rods
average about 20" longer than the rods required by the 20-15 wire
model. Table 4 shows the results for varying the rod length from
112" up to 124".
The table shows mid-band impedances for 20 meters that are very
close to those found in fat-element models. For the larger
Chapter 78
frequency ratio in this antenna, we may obtain a nearly ideal

impedance at the middle of 20 meters. As the band-specific SWR
curve in Fig. 13 reveals, 20-meter SWR is not a significant concern,
despite the use of thin elements. The lowest SWR shifts position as
we change the length of the resonator rod, but never enough to
elevate the SWR to 1.5:1 at the band edges.
As we change the length of the resonator rod, the required

capacitance varies over a narrow range from 5.6 to 6.7 pF. This
range is very comparable to the range for the fatter model in Part 2
(4.9-6.0 pF). However, the resonator rod ranges differ: 100"-112"
for the earlier model and 112" to 124" for the current wire model.
Some of that difference results from the longer main element length
of the wire model (392") over the 7/8"-diameter model (385").
As we suspected, the use of thinner wire elements results in

narrower coverage on 10 meters. Fig. 14 shows the 50-Ohm SWR
curves for several of the rod lengths sampled.
Chapter 78
All of the curves show just above a 2:1 SWR at 28 MHz. However,
only the shorter rod lengths provide coverage as high as 28.7 MHz
with a 2:1 SWR. The mid-band impedance values in Table 4 do not
themselves reveal the more rapid change of impedance for each
small frequency increment, relative to the fat-element models that
allowed coverage of a full MHz of the band. One of the limitations of
the 20-10 thin-wire model, then, is reduced upper-band coverage.
Varying the Rod-to-Element Spacing
In concert with the 20-15-meter wire model, I varied the spacing

between the main element and the resonator rod in half-inch
increments between 1" and 2". The baseline model used a 120"
resonator rod with 1" spacing. I allowed the dimensions to settle at
the most desirable values for each spacing increment. Table 5
shows the results of this small experiment.
Chapter 78
In all cases, the main element held its length. The 20-meter mid-
band impedance does show a small decline as we increase the
spacing. However, the decrease is in no way fatal to the SWR
curves, which appear in Fig. 15. In fact, I have not identified the
curves individually, since they form too tight a group to distinguish
individual lines.
The data show that as we increase the spacing, we must reduce

the length of the resonator rod in order end up with a near-50-Ohm
impedance at 28.5 MHz. The required capacitance also goes down
Chapter 78
with increased spacing (indicating an increase in capacitive

reactance). The effects of these changes on the SWR curves for 10
meters appear in Fig. 16.
The curves do not show any significant difference of bandwidth,

although increased spacing does appear to have a small advantage
over narrow spacing. However, increased spacing does require a
lower capacitance value and may prove harder to adjust to
perfection. The displacement of the curve for a 2" space results
from my restriction of capacitance increments to 0.1 pF. Linear
adjustment of parallel or side-by-side rods used to implement the
resonator capacitor might make finer adjustment feasible, but
difficult to hold as the weather changes from summer to winter and
back again.
Due to the ever-lower value of required capacitance, I limited the

test range to a maximum spacing of 2". In terms of raw impedance
Chapter 78
values, we might in theory continue the progression, since the 20-

meter impedance changes very slowly and increased spacing may
yield wider 10-meter operating bandwidths. At a rate of about 0.4-
pF-per-inch of spacing, it is doubtful that the spacing could
reasonably approach the 6" value used for the fat-element models.
Varying the Wire Size
Despite the narrower coverage of 10 meters, the use of thinner wire

may be feasible for frequency ratios in the 2:1 range. The chief
obstacle to using thinner wire for the wire 20-15 combination was
the reduced 20-meter impedance as the wire grew thinner. The
models that we have surveyed so far for 20 and 10 meters suggest
that this problem will not occur. Therefore, I surveyed wires sizes
from AWG #6 to AWG #12 using the 1" spacing and letting all other
values settle to their optimal levels. The results appear in Table 6.
We may initially note that by letting each resonator rod settle at its
most perfect length, we obtain tuning capacitance values that vary
over a very small range.
Chapter 78
All models in the set required no alteration in overall length. With

the 392" main element length and resonator rods suited to the 10-
meter requirements, the mid-band 20-meter impedance decreases
quite slowly as we thin the wire to AWG #12. Fig. 17 shows the
resulting 20-meter 50-Ohm SWR curves for AWG #6 and AWG #12
wire. Although these curves are distinguishable, adding the other
two wire sizes would have created a fat blurry line. As the curves
make clear, the 50-Ohm SWR is always less than 1.5"1 across the
20-meter band with any of the wire sizes.
The situation differs a bit on 10 meters. Due to the use of a 0.1-pF

increment in the tuning capacitance, the SWR curves for 10-meters
do not overlay each other as neatly as they do in 20 meters. Hence,
the curves in Fig. 18 require a bit of interpretation. Essentially, at
the 2:1 SWR crossing points, the AWG #12 curve is only about
93% of the width of the curve for AWG #6 wire, despite the 2:1 ratio
of wire diameters. The difference amounts to about 50 kHz (750
kHz vs. 800 kHz--approximately).
Chapter 78
Although the use of AWG #12 wire is not fatal to the construction of
a 20-10 combination with 1" element-to-rod spacing, the narrower
operating bandwidth will make antenna adjustment more difficult.
As well, as we increase the diameter of the element, we also gain
some flexibility in selecting the rod-to-element spacing.
Nevertheless, for any size element, the most difficult adjustment to
master and to make endure through all kinds of weather will be the
capacitance.
Conclusion
In this final section of our work, we have established that wire-

based dual-band linear-resonator dipoles are feasible if we are
willing to observe some restrictions. Foremost among the
limitations is the need for close spacing of the resonator rod and
the main element. Especially for antennas with a lower frequency
ratio, such as 1.5:1, the close spacing is necessary to achieve even
Chapter 78
a usable impedance on the lower band--using 50 Ohms as the

standard. Close spacing is not quite as necessary where the
frequency ratio is higher, such as 2:1, but wider spacing does
reduce the required capacitance to a level at which stability may
become a problem.
The second restriction requires that we use the largest diameter

wire feasible. For lower frequency ratios, thin wire may reduce the
low-band impedance below the acceptable level. Again, high
frequency ratios are less of a problem on the lower band, but
thinner wire tends to reduce the upper band operating bandwidth.
Wire versions of linear-resonator dual-band antennas also suffer

from some finickiness of tuning, since virtually no dimension is
fixed. Hence, adjustments to the resonator-rod length may affect
the overall main element length. This potential difficulty is especially
apparent with lower frequency ratios.
Perhaps the most difficult challenge for linear-resonator antennas

using a higher frequency ratio involves the high capacitive
reactance and low capacitor value required for precise tuning.
Concentric and parallel capacitors formed by the resonator rods
and associated materials are subject to linear expansion and
contraction as the temperature changes. Replacing a test set-up
with a wide-temperature-range fixed capacitor may prove useful in
some cases. However, the experimenter must gauge this move
against the knowledge that the linear resonator rod itself will
change length with frequency.
Chapter 78
As we close our look at linear-resonator dipoles, I should again

remind you that all of the numbers fall far short of design plans.
Rather, they reliably indicate only the trends in values. In an
assembly as tricky as a linear-resonator dipole, field
experimentation and adjustment must take precedence over NEC
modeling results.
Nevertheless, linear resonators are a feasible means of producing

a double 50-Ohm resonance from essentially a single element. It
may be the case that frequency ratios of 1.7:1 or 1.8:1 produce the
most desirable results. The low-band impedance would be less
marginal and the high-band operating bandwidth would be more
adequate and less finicky to establish. As well, the required tuning
capacitance would likely fall around 9-10 pF, a value that might be
usable in practice. Combinations for 30 and 17 meters or for 20 and
12 meters fall in this range. In both cases, the upper band is quite
narrow, so tuning in one season would not yield an unusable SWR
6 months later.
Whether the linear resonator has applications in multi-element

arrays remains in the category of work to be done. The wider we
make the frequency ratio, the more that the radiation pattern
changes from the lower to the higher frequency. How that change
might affect the required dimensions for a multiband array remains
to be discovered. For the moment, we may be doing all that we can
by digesting the basic properties, potentials, and limitations of
linear-resonator dial-band dipoles.
Chapter 78
Wide-Band Yagi Notes - Volume 2 1
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web site shown below.
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Antennas

Simple & Effective

A Collection from the Works

Copyright © 2010 by Publisher antenneX Online Magazine. All rights reserved. No

About the Author

L. B. Cebik, W4RNL, passed away in April 2008. He had written extensively

About the Author

BROADBAND COVERAGE OF 80/75-METERS WITH AWG #12 WIRE

Chapter 51: Coverage of the 80/75-Meter Band

he chapter in The ARRL Antenna Book (9 in the 20th edition) is an

T excellent introduction to techniques for obtain full coverage of the

The premise for these notes is that we have an endless supply of

Some Ribbon and Cage Basics

We may create virtual fat wires by combining thinner wires in

Preliminary modeling consisted of checking the correlation

In each case, I adjusted the length of the dipole to resonance +/-j1-Ω

1. The minor drop in gain for each multi-wire element relative to

Table 1. Multi-wire dipoles and the equivalent single fat-wire dipoles

2-wire ribbon 130.90 2.09 3.45 to 3.76

4-wire ribbon 130.30 2.11 3.43 to 3.79

4-wire cage 129.40 2.11 3.43 to 3.80

6-wire cage 129.10 2.12 3.42 to 3.80

3. The differences across the range of multi-wire models are too

The slight differences in losses between each multi-wire dipole

Table 2 lists the remaining candidates for full-band 80-75-meter

The table has a few minor surprises. Although the spacing

Table 2. Multi-wire dipoles for full coverage of 3.5-4.0 MHz

Antenna Length Res. Fq. Impedance

Single wire 123.6’ 3.72 MHz 71.6 – j0.4 Ω (free space)

4-wire ribbon 123.4’ 3.72 MHz 72.4 + j0.4 Ω (free space)

4-wire cage 121.8’ 3.71 MHz 72.1 – j0.5 Ω (free space)

6-wire cage 122.2’ 3.73 MHz 72.1 – j0.7 Ω (free space)

4-wire ribbon structures are subject to some overgeneralization to

The models used in developing the data in Table 2 initially used a

Except for the 16”-diameter single-wire dipole, all of the antennas

Parasitic Driver Basics

The use of open-sleeve or coupled resonator dipoles (and

The most common applications of the use of coupled resonators

Fig. 4 shows one version of a 3-wire broadband dipole array for

The 3-wire system shown requires a cross-section width of only

An alternative method of achieving a similar goal is to use a folded

The folded-dipole-linear-parasitic element version of the coupled-

Back in 1997, Dave Leeson, W6NL, brought to my attention an

The broad-banding method begins by selecting the geometric mean

resonant at this frequency. Next, for the dipoles design frequency, we

Fig. 8 shows the general outline of one recommended system

The results of the technique can be modeled in a misleading way

In 1995, Frank Witt, AI1H, presented an alternative to the 50-75-Ω

an open stub across the terminals, effectively adding a shunt capacitance

Of the systems that we have examined, only the two transmission-

When we combine any antenna with a transmission line in

Arriving at a reasonably fair comparison of system losses is

Table 3. Comparative gain values of broadband 80-75-meter antennas and

Antenna Gain in dBi at 3.5 MHz 3.75 MHz 4.0 MHz

Except at mid-band, the two matching systems show about 0.5-dB

The SWR curves are satisfactory for virtually al applications.

A simple AWG #12 copper wire dipole responds to either the

equipment sensitive to 50-Ω SWR values above 1.5:1, is whether we can

Although I am aware of no actual attempt to do so, there is no rule

The 3-wire coupled resonator system shows a relatively flat SWR