May 1952 QST
Table of Contents
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At long last, I finally acquired the February
1952 issue of QST magazine, which contains Part 1 of the threepart "The Wavelength
Factor" article series. Author Yardley Beers covers a lot of ground (pun
intended) regarding selection of the best transmitter, receiver, and antenna
type for the intended purpose, including fixedtofixed and/or fixedtomobile
communications. Part 2 focuses on propagation, modulation, and receivers.
Finally, Part 3 covers choice of frequency bands for civil defense and UHF.
See "The Wavelength Factor"
Part 1,
Part II,
Part III
The Wavelength Factor  Part 1
Influence of the Antenna of the Choice of
Wavelength for Best Communication
By Yardley Beers, * W2AWH
Good radio operating always requires detailed knowledge of the properties of
all wavelengths available and the intelligent choice of the one best suites for
a particular purpose. At the present time two general problems facing the amateur
fraternity require particular consideration of this subject: (a) selection of the
best band for Civil Defense nets, and (b) the development of the microwave bands,
which is stimulated by the recent establishment of Technician Class licenses.
Superficially, the selection of a baud for Civil Defense and the development
of the microwave bands appear unrelated questions. However, the same reasoning may
be applied to both, although with completely opposite conclusions. It will be shown
partly in this article and partly in others to follow that, except for ionospheric
communication, there is every advantage in placing mobile operation on the longest
possible wavelength, while the u.h.f. and microwave bands are suited for fixedstation
operation partly because of the necessity for using highgain antennas with narrow
beam widths and partly because of the complexity of the apparatus required to exploit
the chief advantages of these very short waves.
The choice of the optimum wavelength for a given type of communication  fixed
station to mobile, fixed to fixed, etc. is considered objectively, based
on known principles of antenna operation. The conclusions that logically follow
may be surprising to many amateurs, especially those not familiar with the "effective
area" concept.
Although the discussion here and in subsequent articles principally deals with
v.h.f.. and u.h.f., the lowfrequency man will find it of considerable interest,
too.
At the lower frequencies the choice is based
primarily on the ionospheric properties of the various bands, as these are by far
the most important. However, at frequencies greater than 50 Mc.  as well as in
groundwave operation at lower frequencies, where the ionosphere plays no part 
the principal factors governing the choice of a band are instrumental: that is,
the characteristics of the transmitter, receiver, and especially the antennas, although
there are also some effects produced by the lower atmosphere. For skywave operation
at the lower frequencies the instrumental effects are also present, of course, but
to a large extent are obscured by the ionospheric ones. The purpose of this article
is to review these instrumental effects in the hope of aiding the solution of the
problems mentioned above. Ionospheric effects at the lower frequencies will not
be discussed: those readers whose main interest is in skywave communication may
nevertheless find some of the topics to be of value.
Most of the instrumental factors are very familiar by name. A list of the more
important ones follows:
 Transmitter power.
 Type of modulation.
 Gain and efficiency of the transmitting antenna.
 Gain and efficiency of the receiving antenna.
 Noise figure of the receiver.
 Bandwidths of the r.f., i.f., and a.f. portions of the receiver.
 Gain of the receiver.
 Overload properties of the receiver.
 Type of demodulation.
 Relative frequency stability of the transmitter and receiver.
There remains one more item, which although familiar to engineers and physicists
who have worked on microwaves, is not, widely known in amateur circles: the equivalent
area of the receiving antenna, which is a measure of the effectiveness of the receiving
antenna in intercepting radiation. As one would expect, the equivalent area is related
to the gain, and whenever anything is done to increase the gain, the equivalent
area increases in proportion. However, gain is not the only consideration. The equivalent
area also depends, as we shall see, on the wavelength. The gain of the transmitting
antenna and the equivalent area of the receiving antenna are the two most important
instrumental factors in the selection of an optimum wavelength, and therefore these
will receive special attention.
The Antenna Factors
Before going any further let us define a few terms to prevent confusion. Not
all of the power supplied to a transmitting antenna is radiated. Some of it heats
up the metal conductors of the antenna. The ratio of the total power radiated to
the total power supplied is the efficiency of the antenna. The radiated power, however,
is distributed over many different directions. The ability of the antenna to concentrate
its radiated power in a preferred direction or directions is called the gain of
the antenna. More quantitatively, the gain of an antenna is specified with reference
to a standard antenna. It is the ratio of the power radiated (per unit solid angle)
in the preferred direction, by the antenna in question, to the power radiated in
the preferred direction by the standard antenna. It is assumed, of course, that
the total power radiated in all directions is the same for both antennas.
The definitions of efficiency and gain of
receiving antennas are similar. The efficiency is the ratio of the power supplied
to the input terminals of the receiver to the total power extracted from the radiation.
The gain is the ability of the antenna to discriminate in favor of signals coming
from a desired direction or directions over signals coming from other directions
and is usually specified numerically with respect to a standard antenna. As a result
of the socalled "reciprocity theorem," the directional properties of a given antenna
are the same when it is used as a receiving antenna as when it is used as transmitting
antenna. Therefore, the numerical values of the gain are the same for both applications.
Two types of antennas are used as a standard for the specification of gain. One
of these is an imaginary antenna which would radiate equally well in all directions,
called an "isotropic" antenna. The other is a halfwave dipole, which has zero radiation
along its axis and a maximum in the plane at right angles to the axis. The power
radiated (per unit solid angle) in the directions of maximum radiation of a halfwave
dipole is 1.64 times (2.1 db.) that radiated in any direction by an isotropic antenna
radiating the same total power. Therefore, gains expressed in terms of the isotropic
antenna may be expressed with respect to a halfwave dipole by dividing by 1.64
(or subtracting 2.1 db.). In the present article the isotropic antenna will be used
as a standard.
With these definitions in mind we shall explain why the equivalent area of a
receiving antenna depends upon the wavelength. Let us suppose that we have a receiving
antenna of some definite type  for example, a threeelement broadside array  pointed
at a transmitter. Then suppose that the wavelength of the transmitter is doubled,
keeping the efficiency and gain of the transmitting antenna and the power of the
transmitter the same. No longer will our receiving broadside array operate correctly.
We must double both the element length and the spacing. In doing this we do not
change the directive properties nor the gain. Nevertheless, the array "looks bigger"
to the transmitting antenna and therefore is more effective in intercepting the
radiation, just as a large pan will collect more water in a rainstorm than a small
pan.
We shall defer a precise definition of equivalent area to a later article. When
this is done, there is a very simple formula^{1} relating the gain, G, the
equivalent area, Α, and the wavelength, λ:
A = Gλ^{2}/4π (1)
This formula is general and applies to antennas of all types. It shows, as we
expected, that A is proportional to the gain and also that A increases with the
square of the wavelength. If, as in our example, we double the wavelength and keep
the gain constant, the equivalent area and therefore the strength of the signal
would increase by a factor of 4 (or 6 db.); or if we increase the wavelength by
a facto of 3, the received signal increases by a factor of 9 (or 9.5 db.). Equation
(1) shows also, since G is a pure ratio, that A has the same units as λ^{2},
which are square meters, square centimeters, or possibly square feet. These are,
of course, units of geometrical area. This gives still further significance to the
concept of equivalent area.
Finally, in the case of large broadside arrays, horns, and parabolicmirror antennas,
the effective area is between 40 and 100 per cent of the actual geometrical area
of crosssection of the antenna. Therefore, the effectiveness of these antennas
for receiving depends primarily on their geometrical areas. For example, if we replace
a large broadside array by another one having the same area but operating at twice
the wavelength, to operate correctly the new array requires elements of twice the
length and twice the spacing, and therefore will have approximately one quarter
the number of elements. Because of the smaller number of elements the gain will
be reduced and the beam width will be greater. In order that Equation (1) will be
satisfied we conclude that the gain must have been reduced by a factor of 4, and
in general we may conclude that for antennas of the types mentioned having constant
area the gain varies inversely with the square of the wavelength. It can be inferred
that much of this reasoning also applies to endfire and linear arrays, except for
the fact that with them there is no related geometrical area that may be so clearly
identified with the equivalent area.
It may be concluded that the effectiveness of a receiving antenna  that is,
its equivalent area  (a) increases with the square of the wavelength if the antenna
has constant gain, and therefore the wavelength from this point of view should be
as long as possible, while (b) it is independent of the wavelength if the antenna
is a directional array of constant geometrical area.
The Transmitting Antenna
While the strength of the received signal depends on the equivalent area, of
the receiving antenna, its dependence upon the properties of a highefficiency transmitting
antenna is through the gain. Therefore, many of our previous arguments have to be
reversed when applied to transmitting antennas. As long as the transmittingantenna
gain is constant, there is no advantage of any wavelength over another so far as
the transmitting antenna is concerned. But, if we are limited to a definite size
 or, more exactly, a definite area  we see that the wavelength should be as short
as possible because the gain varies inversely with the square of the wavelength.
However, if we attempt to operate with antennas of very high gain we must expect
that as the gain increases the beam width will become narrower, and for certain
purposes it may become so narrow as to give difficulty. For example, a parabolic
mirror antenna 3 feet in diameter operating in the 3300Mc. band (9 cm. wavelength)
would have a gain of approximately 800 (or 29 db.) and a beam width of approximately
7 degrees between the extreme directions at which the power gain is onehalf maximum.
The difficulties in general coverage operation without prearranged schedules, using
an antenna with a beam width of only 7 degrees, may be seen by comparison with the
following angles: The New York City limits (not including suburbs) would subtend
an angle of 15 degrees from Philadelphia (75 miles away) and 7 degrees from Boston
(180 miles away). Also, Los Angeles and San Francisco differ in direction as "viewed"
from New York by 7 degrees.
Some alleviation could be obtained by using an antenna with greater vertical
directivity than horizontal. However, there is a practical limit to usable vertical
directivity because of errors in alignment, unevenness of the ground, and atmospheric
effects. This writer would guess that a vertical beam width of 10 degrees and a
horizontal width of 45 degrees would be the most narrow beam that could be tolerated
in operation without prearranged schedules. In the case of parabolic mirrors and
horns., the beam width, θ, in degrees, is given approximately by a simple
formula:
θ = 2.3λ/d, (2)
where the wavelength, λ, is expressed in centimeters, This formula applies
to antennas of circular crosssection, strictly speaking.^{2} In this cased
is the diameter expressed in feet. However, little additional error is introduced
if the formula is applied to antennas of rectangular crosssection. In this case
d represents the dimension in feet corresponding to the plane in which θ is measured.
Thus for the horizontal beam width, d would represent the width of the antenna.
Probably the error in this formula is not greater than 25 per cent for antennas
which are adjusted correctly. More accurate formulas would take into consideration
the exact shape as well as other details neglected in the present article.
Table I gives the approximate dimensions of parabolic mirror or horn type antennas
which according to Equation (2) would have a horizontal beam width of 45 degrees
and a vertical beam width of 10 degrees for three amateur bands of interest. In
all three eases the gain is about 135 (or 21 db.).
The upper limit on the size of an antenna
depends upon the financial resources and mechanical skill of the builder. Undoubtedly,
the following figures can be or have been exceeded, but it is unlikely that antennas
larger than those indicated would be built often. A mirror or horn 5.7 feet by 1.7
feet is of practical size, but ones 16 feet, by 3.6 feet would be too large for
convenience. Therefore, the 1215Mc. band is probably the lowest frequency where
antennas of this type and beam width would be used. However, because of its open
construction a broadside antenna 16 feet by 3.6 feet and having about 4.0 halfwave
elements for the 420Mc. band is within the possibility of practical construction.
Such an antenna would have approximately the same equivalent area and gain, but
it would be bidirectional and therefore it is to be presumed that the major lobes
would be somewhat narrower than 45 X 10 degrees. By adding a group of elements to
act as reflectors the array could be made unidirectional, but then the gain would
be somewhat greater and the beam width somewhat smaller than 45 X 10 degrees. This
could be corrected by reducing the crosssection of the antenna slightly. The adjustment
of an antenna with 40 elements is, of course, a problem but not an insurmountable
one. These arguments tend to indicate that an antenna of the minimum usable beam
width and maximum gain for general coverage operation is within the realm of practical
possibility for the 420Mc. band. At the same time it may be inferred that such
an antenna for 220 Mc. would be too large for the resources generally available.
Of course, it is the combined performance of the transmitting and receiving antennas
which is significant in the choice of a wavelength. This subject will be summarized
a little farther on. For the moment, however, we shall consider some antennas of
types that are of principal interest at the longer wavelengths.
Dipoles, "SuperGain" Antennas, and Unorthodox Antennas
As mentioned previously, the gain of a halfwave dipole is 1.64 relative to an
isotropic antenna. Its equivalent area then may be calculated by substituting this
value into Equation (1). Since by definition the length is onehalf wavelength,
we may conclude that the equivalent area depends upon the geometrical size of the
antenna. Thus the properties of the halfwave dipole are not in contradiction with
any of the ideas we have considered.
If we now consider what happens if we replace a halfwave dipole by one considerably
shorter, we shall encounter a situation which is very different in several respects.
The radiation pattern of a "short" dipole in free space is similar in general to
that of the halfwave dipole, having a zero along the axis and a maximum in the
plane at right angles to the axis. However, in detail the pattern is slightly different,
resulting in a gain of 1.5 (or 1.7 db.) instead of 1.64 (or 2.1 db.). Thus the gain
of the short dipole is 0.91 (or minus 0.4 db.) relative to the halfwave dipole.
If we substitute the value G = 1.5 into Equation (1), we find for the equivalent
area 1.5λ^{2}/4π
while for the halfwave dipole we would have the factor 1.5 replaced by 1.64.
However, we are no longer required by definition to change the length of the dipole
every time we change the wavelength, and therefore we conclude, that with the short
dipole both the gain and equivalent area are independent of the geometrical size.
Furthermore, it would appear that by replacing a halfwave dipole by one very much
shorter we still have an antenna that is 91 per cent as effective in both transmitting
and receiving! This conclusion is difficult to believe; although to a large extent
it is true. However, this situation requires us to consider a matter that we have
been able to overlook up to now: the efficiency.
A transmitting antenna is characterized
by a quantity called the radiation resistance, referred to a point which is usually
taken at the center of a dipole or, in the case of longwire antennas, at it current
loop. The radiation resistance is defined in such a way that when its value is multiplied
by the square of the current flowing at that point one obtains the radiated power.
This impedance is quite real in the sense that it may be measured by an impedance
bridge connected to the antenna. The value of the radiation resistance and the measured
current will vary with the choice of reference point, although the changes in the
resistance and current are interrelated in such a way as to keep the power constant.
Therefore, by itself the value of radiation resistance has little meaning; only
when it may be compared with other resistances in the output circuit does its value
have significance. These other resistances include the plate resistance of the final
amplifier, losses in the final tank, antenna coupler, transmission line, and the
radiator itself. By consideration of the impedance stepup properties of the intervening
circuit, the equivalent series resistance at the reference point due to each of
these may be determined. If the radiation resistance is high compared with the total
of these other equivalent resistances, the efficiency is large; if it is low in
comparison, the efficiency is poor. If the antenna is used for receiving, the efficiency
(and also the noise figure) will depend in a similar fashion upon the comparison
of the radiation resistance with the total equivalent resistance resulting from
portions of the input circuit as far as the grid of the first tube.
It, is true that the voltage developed across the terminals of a perfect voltmeter
connected to a short dipole will increase in proportion to the length of the dipole.
However, the radiation resistance also varies with the square of the length in order
to keep the available power and therefore the equivalent area independent, of the
length, as required by our formula. Therefore, as we decrease the length of an already
"short" dipole while keeping the wavelength constant, the radiation resistance will
drop until it becomes comparable with or even smaller than the equivalent resistance
of the rest of the circuit, with a deterioration of efficiency.
Some countermeasures may be taken against this loss in efficiency·. On the one
hand, we may load the antenna in various ways to raise the radiation resistance.
On the other hand, losses may be reduced by using heavy conductors in the antenna
and elsewhere, and components of high quality. From the widespread success of 4Mc.
mobile stations· with 10foot antennas operating against the car body as ground
it may be concluded that dipoles of a twentyfifth and possibly onefiftieth of
a wavelength can be made of sufficiently great efficiency to be practical.
The effect of low antenna resistance and these countermeasures combine to make
the circuit very selective, necessitating retuning for very slight changes in frequency.
In itself this is not always a disadvantage, since it may result in the suppression
of unwanted signals in receiving and suppression of unwanted harmonics in transmitting.
However, the design of the coupling circuit may depend in an important way upon
parasitic capacities and the L/C ratio in the antenna coupler, factors that ordinarily
have little effect. Also, in transmitters very high voltages may be developed across
the variable condensers with the result that these may have to have higher voltage
ratings than usual with transmitters of the same power. The coils must be of lowloss
construction, and changing inductance by shorting turns will result in a serious
loss of efficiency. Finally, the performance will be affected by rain and swaying
in the wind.
Advanced antenna theory indicates that it is possible to build antennas of any
desired gain with arbitrarily small size, or at least of much smaller size than
is in accord with present practical designs. However, Chu has shown^{3}
that as the size is reduced the radiation resistance of these "supergain" antennas
falls, with the result of reduced efficiency and bandwidth. Therefore, while highgain
antennas of small size may exist in theory, the theory also predicts that they will
be of limited practicality. Although the short dipole perhaps is not included in
the definition of a "supergain'' antenna, its behavior as described above is completely
in accord with that of antennas of this type.
Incidentally, the reasoning of the previous paragraphs justifies theoretically
the success of the many unorthodox antennas put up by amateurs because of lack of
adequate space, unsympathetic landlords, or laziness. The requirement that a dipole
or a longwire antenna be cut exactly to "resonance" is to a large extent superstition.
The Antenna Factors Summarized
The combined effects of the transmitting and receiving antennas as dependent
upon the wavelength may be summarized conveniently by considering three cases which
correspond more or less exactly to most situations likely to be encountered. In
the following it is assumed that a mobile station would use a dipole, or at any
rate an antenna of very little gain. The question of efficiency will be neglected.
1) Both antennas having constant gain. This situation is likely to be encountered
at any wavelength when both stations are mobile, and almost inevitably also by fixed
stations at low frequencies. In this case the effectiveness of the transmitting
antenna will be independent of wavelength, while the equivalent area of the receiving
antenna will increase with the square of the wavelength. Hence in this case the
wavelength should be as long as possible.
2) Both antennas of constant size. This is the situation encountered normally
with fixed v.h.f. and microwave stations. The equivalent area of the receiving antenna
will be independent of the wavelength while the gain of the transmitting antenna
will increase inversely with the square of the wavelength. Therefore, the wavelength
should be as short as possible, provided that the beam widths do not become too
narrow. According to the considerations of Table I, we may conclude that the most
favorable antenna factors for general coverage operation would be realized in the
420Mc. band under practical conditions. For pointtopoint operation on prearranged
schedules, much higher frequencies would be desirable.
3) Station A having antenna of fixed gain, while Station B has antenna of fixed
size. This might be encountered with a fixed station with a rotary beam antenna
in communication with a mobile station. When Station A transmits, the gain of the
transmitting antenna and the equivalent area of the receiving antenna are both independent
of the wavelength. When Station B transmits, the gain of the transmitting antenna
varies inversely with the square of the wavelength, but this is compensated exactly
by the equivalent area of the receiving antenna, which varies directly with the
square of the wavelength. Thus in both cases there is no overall dependence upon
the wavelength. Nevertheless, if the wavelength becomes too short the beam width
of Station B will become so narrow that accurate orientation will become difficult.
By consideration of these cases we see a very definite group of conclusions:
(1) portable and mobile operation should be placed at the longest wavelength feasible;
(2) the 420Mc. band is the band best suited (not utilizing ionospheric effects)
for general coverage operation; and (3) the microwave bands are useful mainly for
pointtopoint operation on prearranged schedules. Although we have only considered
the dependence of antenna properties on wavelength so far, it happens by chance
that the other factors mentioned at the start of this article conspire almost unanimously
to confirm these conclusions.
[Editor's Note: Propagation, types of modulation, and equipment limitations will
be discussed in a subsequent article.]
1 Although this formula is simple to write and to apply, its proof involves a
lengthy application of advanced electromagnetic theory. A proof may be found in
Chapters V and VI of Microwave Transmission, by J.C.Slater, McGrawHill Book Company,
New York, 1942. However, Slater's results are not in the form of our equation, which
more recently has been widely used in other books. Slater delines a quantity "the
absorption area," which is equal to our "equivalent area" divided by the gain, and
he proves that this is equal to λ^{2}/4π for antennas of all types.
2 If θ is measured in radians and if λ and d have the same units,
the constant 2.3 is replaced by 1.22. Readers who have taken a college course in
elementary physics will then recognize this formula as that for the half angular
width of the central maximum of the diffraction pattern of a circular aperture.
3 L. J. Chu, Journal of Applied Physics, Vol. 19, page 1163 (1948).
* Associate Professor of Physics, New York University, University Heights, N.
Y. Mail address: 4 Ploughman's Bush, Riverdale 71, N. Y.
Posted February 20, 2023
