January 1967 QST
articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list
of the QST articles I have already posted. All copyrights are hereby acknowledged.
Computer modeling of antenna radiation patterns has evolved
from a relatively simple electric field equation that diminishes
as the inverse of the distance from the source, to exotic, highly
sophisticated numerical methods that account for conducting
and dielectric surfaces and volumes. A spreadsheet can be built
rather quickly to calculate and graph the free-space azimuth
and elevation e-field patterns for a 1/4-wave whip or a dipole
antenna using textbook formulas, but building a model for displaying
the 3D radiation patterns of a cellphone placed next to a human
head, or a UHF radio antenna on top of an aircraft takes some
pretty serious computing power. In large part we owe a debt
of gratitude to the Ph.D. types who have labored hard to make
such tools available to us commoners. As with PCB layout software
and circuit simulators, chances of success with a first pass
prototype has increased significantly as software has improved.
Even with the advent of near-miraculous software, there is still
a need to verify empirically that the design matches the predicted
results. That's where taking physical measurements comes in.
Fortunately, there is a lot of great software for automating
testing as well, but occasionally, especially for the less well
funded amongst us, measuring points manually is required. Even
with automated systems at your disposal a few quick "sanity
check" points are measured prior to submitting the design to
a full barrage of tests. This article describes how the author
first calculated the expected pattern for a 1/4-wave vertical
whip antenna mounted on a car, and then went about validating
Modeling Radiation Patterns of Whip Antennas
By Dale W. Covington, K4GSX
The rapid development of efficient transceivers and power
supplies has solved many of the problems of going mobile. Furthermore,
old Sol is playing a strong supporting role by improving propagation
conditions on the very bands for which the mobile antenna is
most efficient. While the bandwidth and efficiency of the whip
antenna have been extensively studied and improved, any description
of the resulting radiation patterns has received only light
treatment. Such patterns would be useful guides, for example,
in calling DX or in beginning to conclude a contact before making
a major change of route direction. Therefore the intent of the
following note is to call on stage yet another actor portraying
a simplified picture of mobile whip radiation.
Scale-model car used for obtaining data plotted
in Fig. 3B.
Actually it is a complicated matter to describe this radiation
precisely as a function of the total elliptical polarization
of the radiated E-field, the distorted currents flowing on sculptured
car bodies and loaded whips, the frequency dependence of the
ground conductivity, and so on. On the other hand, the principal
features can be exhibited by using a model of a vertical element
over an incomplete ground plane.
Employing a model for a complicated analysis usually implies
a certain degree of approximation. The case in point is no exception.
Cars are about 1/4 wavelength long at 20 meters and almost 1/4
wavelength wide at 10 meters. As the whip itself is a 1/4 wavelength
at 10 meters, it seemed appropriate to restrict the analysis
primarily to this 10- to 20-meter range. Fig. 1 shows the general
shape and the coordinate position of the model, which had ten
1/4-wave ground radials from 0 to 90 degrees beneath a vertical
1/4-wave element fixed in the normal-180-degree plane. The ground
plane was spaced 1/10 wave above ground. Crudely speaking, the
model thus represented a car with a whip mounted on the left
rear deck. The driver's side is along the 0-degree direction,
and the rear bumper is along the 90-degree direction.
Fig. 1 - Coordinate system for the model.
Ground-plane radials and vertical element are 1/4 wavelength
The actual calculation of the patterns consisted of computing
the far E-field from cosinusoidal currents flowing on 1/4 wave
elements1 as arranged in Fig. 1. All of the resulting
vector fields were then added to yield a polar plot of the radiation
patterns as a function of the angle of elevation. Since an actual
whip does not remain truly vertical once the car starts moving,
the equations for the model were solved for the vertical element
normal to and tilted away from the ground radials.
The close spacing between the model and ground requires that
ground effects be included in the analysis. A review of the
interrelations between frequency, antenna height above ground,
angle of elevation, and ground constants has been given by G3HRH(note
2). Using standard techniques3 the E-field
expressions were corrected by the ground factors for 28 Mc.
and angles of elevation, Δ, of 15 and 30 degrees. Higher
wave angles are less useful for contacts from 14 to 28 Mc.4.
These ground factors revealed that, at their maximum point,
the horizontally polarized E-fields from the model over dry
soil were 11.7 and 5.9 db. below the corresponding vertically
polarized fields for Δ of 15 and 30 degrees respectively.
As the conductivity approached sea-water values, the horizontal
terms were even smaller: namely, 14.2 and 8.3 db. For simplicity
only vertical terms were retained in the patterns.
Fig. 2A - Calculated patterns of relative
E-field strength for a radiation angle of 15 degrees above the
horizon; dry soil. Solid curve, whip vertical; dashed line,
whip tilted 45 degrees.
Fig. 2B - Some for a radiation angle of 30
The patterns of the calculated E-fields are presented in Fig.
2 for the 15- and 30-degree wave angles. Solid lines show the
fields from the vertical element normal to ground while the
dotted lines denote a rather extreme element tilt of 45 degrees.
The relative field strengths can be directly compared from one
wave angle to the other; however, directly comparing field values
of the normal and tilted configurations automatically implies
a constant input current. It is immediately noted in Fig. 2
that the quadrant containing the ground plane also contains
the strongest fields. Moreover, these fields generally change
only slightly from 0 to 90 degrees.
When the vertical element is perpendicular to the radials,
the field pattern is symmetric about the 45-225 degree directions.
Here orientation is more important at the high elevation angle
where the pattern undergoes a maximum/ minimum variation of
6.4 db. compared to a 3.3-db. variation at the lower angle.
As mentioned before, the attractive increase in field strength
at the higher angle usually cannot be advantageously employed
on the higher-frequency bands.
Pattern symmetry becomes lost as the vertical element tilts
back from the normal. Not only does the direction of maximum
field shift from 45 degrees toward 20 degrees, but also the
field strength from the rear of the model is particularly reduced.
Numerically the fields in front of the model are 8.3 and 13
db. stronger at the 15 and 30 degree elevations.
Fig. 3A - Solid points, experimental data
taken on model antenna system shown in Fig. 1, at a frequency
of 430 Mc. Open points, 14-Mc. data taken on actual automobile
Fig. 3B - Solid points, experimental data
on scale-model car shown in photograph, at 430 Mc., whip vertical.
Open points, same with whip tilted 45 degrees.
Mobile operation on 40 and 80 meters is more difficult to
analyze. Even in Texas cars and whips don't come equipped with
1/4-wavelength dimensions. Instead, the sizes of both the car
body and the whip approach small fractions of a wavelength.
Also, in this range the loading coil becomes increasingly important
in relation to the current distribution on the whip. Finally,
contacts can be made on these bands by radiation at fairly high
angles of elevation, which complicates the previous polarization
argument by filling in certain parts of the pattern with a significant
combination of vertically- and horizontally-polarized fields.
The relative directivity pattern for a very small dipole
has only a slightly greater beam width than the similar figure-8
pattern for a half-wave dipole having 1/4-wave elements4.
Thus it would be reasonable to expect that the character of
the patterns of Fig. 2 would be more nearly omni-directional
because of the short length of the radiating elements. Consequently
this factor along with the increased usefulness of the higher
angles of elevation would reduce any directivity effects for
80- and 40-meter mobile contacts.
It is interesting to speculate about the patterns predicted
by the model for an incomplete ground plane installation at
a fixed station. On the lower bands, particularly, it is not
always practical to extend the long ground radials in a symmetric
shape about the base of a vertical antenna. The model should
be useful in understanding such cases if the obstruction limiting
the ground plane to less than a circle does not likewise prevent
the vertical element from being installed in the clear. For
example, the patterns for a vertical installed at one corner
of a garden would probably differ from those for a vertical
next to the corner of a house, even though both conditions might
have a 90-degree area that was unavailable for ground radials.
Basically, the model suggests that a hole or depression exists
in the radiation pattern centered in the area having no radials.
Directly opposite the hole is centered a broad field maximum
over the ground radials. The hole is a function of the angle
of elevation, and its maximum depth is of the order of 6 db.
or so below the field in the opposite direction at elevations
near 40 degrees. Naturally the hole width could be greatly reduced
as the area about the base is more evenly covered with radials.
The computed patterns were subjected to several checks. One
check utilized an experimental model of Fig. 1 at 430 Mc. The
wire model was located about three wavelengths from a two-element
beam fed by a 6J6 rig from an old Handbook design. The detector
was a 1N23 crystal operating in the square-law region. The measured
E-field pattern is given in Fig. 3A for the vertical element
perpendicular to ground and an angle of elevation of 15 degrees.
There is good general agreement with the calculated pattern
of Fig. 2A. Tilting by 45 degrees produced a maximum/minimum
gain of 5 db. An increase of radiation in the forward directions
was noted at higher elevations.
Of course the primary reason for examining the incomplete
ground plane model lay in the degree that it approximated 10-20
meter mobile radiation. Included in Fig. 3A is a mirror image
(whip mounted on right rear fender) of some 20-meter E-field
data taken on the mobile installation of WA4KQO. While the receiving
antenna was higher than the whip-Hillman combination, the angle
of elevation unfortunately was not measured. It was less than
5 degrees. The experimental points are characteristic of the
low-angle radiation from the model.
To further confirm the effects of tilting the whip away from
the normal, a 1/15.4 scale model of a Toronado was constructed.
At this scale, the 430-Mc. whip was equivalent to a 1/4 wave
whip on 10 meters. An aluminum foil skin 0.00125 inches thick
covered the balsa stringer shell. Fig. 3B presents the measured
field strengths at a 15-degree wave angle. Input power remained
constant as the whip was tilted. Again comparing the experimental
data with the curves of Fig. 2A, it is apparent that the ground-plane
model does agree fairly well with the scale model. Indeed, the
standard deviation of the measured points was 1.2 db. for both
the normal and tilted conditions.
The radiation patterns of a 1/4-wave ground plane model have
been employed to approximate the patterns from a mobile whip
in the 10-20 meter range. For these bands the operating experiences
of several mobile hams indicate that the field strength over
the car body is on the average 3 to 6 db. stronger than the
field in the opposite direction. This magnitude and direction
are confirmed by the model. The model also predicts that the
patterns are more directive when the soil conductivity increases,
when the contact is by means of a short skip, or when the whip
curves back from the normal at high speeds. Low angle DX work
is less sensitive to ground-plane orientation. Large variations
from the patterns could arise from field distortions produced
by nearby objects, poor electrical contact over various parts
of the car body, and a bumper mount instead of a deck mount.
A tilted ground plane instead of a horizontal ground plane would
be a more accurate model in this latter case. The net effect
would reduce the fields over the ground plane and increase the
fields in the opposing quadrant.
In addition to the references listed, helpful ideas are gratefully
acknowledged from two other sources: first, from conversations
with K8MBV and a number of other mobile hams, and second, from
the pleasant and informative hours spent in assembling, testing,
and operating mobile equipment with W A4KQO.
1 King, Theory of Linear Antennas,
University Press, Cambridge, Massachusetts, 1956, p. 395, 421,
2 Hills, "The Ground Beneath Us," R.S.G.B. Bulletin,
June 1966, p. 375.
3 Schelkunoff and Friis, Chapter
Seven, Antennas/Theory and Practice, John Wiley and Sons, Inc.,
New York. 1952.
4 Chapter Two, The A.R.R.L. Antenna
Posted December 6, 2013