See "The Wavelength Factor" - Part III
August 1952 QST

Part 3 of this three-part "The Wavelength Factor" series is titled "Choice of Frequency Bands for Civil Defense and U.H.F." It appeared in the August 1952 issue of the American Radio Relay League (ARRL) QST magazine. Part 1 (Influence of the Antenna of the Choice of Wavelength for Best Communication) debuted the series in the February edition and Part 2 (Propagation, Modulation, and Receivers) in the May edition. Author Yardley Beers provides a comprehensive review of transmitter and receiver powers, antenna gain, and system range that can be expected based on the presented equations.

Choice of Frequency Bands for Civil Defense and U.H.F.

By Yardley Beers.* W2AWH

In this final article of the series the author draws some interesting conclusions, based on the antenna and equipment considerations outlined earlier, as to the optimum frequencies for civil defense work. Suggestions also are made for a logical way of approaching the problems of .h.f. development in the am amateur field.

The various instrumental factors that influence the choice of a wavelength for a particular purpose have been considered in some detail in the two preceding articles.¹ We now come to the conclusions to be drawn from consideration of these factors. There are two principal objectives: The selection of optimum frequencies for civil defense work, and the stimulation of development of the u.h.f. bands.

Selection of a Frequency for Civil Defense

Civil defense utilizes primarily portable stations which probably would use dipole antennas, or certainly antennas of low gain. By reference to the discussion on antennas and with negative inference from most of what followed, one may conclude that large local civil defense nets should be placed on the lowest available frequencies, except perhaps for ionospheric considerations. The choice, then, is between the following three bands: 28 Mc., 50 Mc., and 144 Mc. The wavelength factor of the antenna favors the 28-Mc. band over 50 Mc. by a ratio of 3.2 (5 db.), and over the 144-Mc. band by a ratio of 26 (14 db.), while the 50-Mc. band is favored over 144 Mc. by a ratio of 8.1 (9 db.). Mobile antennas of high efficiency may be built on all three bands. On the other hand, the more favorable antenna factors at the lower frequencies may be compensated by increased atmospheric noise,² especially at 28 Mc. where ionospheric propagation is prevalent. To render a decision on atmospheric noise would require extensive data not now available.

The ionospheric propagation at 28 Mc. is a security risk in that it may aid an enemy to overhear information. Also, it results in QRM which hampers at least the training of nets. However, in an actual emergency it is presumed one net could gain exclusive use of its channel. If two nets in different parts of the country used the same channel it would be very unlikely that disaster would strike both regions at once. Ionospheric and tropospheric propagation at 50 Mc. are sufficiently rare as not to be an important disadvantage on this band for local operation.

A usable crystal-controlled signal derived from fundamental-type crystals may be obtained from two triodes at both 28 and 50 Mc., while at 144 Mc. at least three triodes must be used with fundamental crystals, or else special harmonic crystals - often hard to get - must be used. Reasonably good receiver noise figures can be obtained at 28 and 50 Mc. with conventional circuits, while at 144 Mc. special circuits, usually requiring one more tube, must be used. Band-switching equipment of reasonable efficiency can be made to operate at 50 Mc. and lower, but it is very difficult to design band-switching circuits that include 144 Mc.

TThese considerations conspire to give a strong indictment against the 144 Mc. band. The choice between the 28- and 50-Mc. bands is not so clear, but in the opinion of this writer the advantage seems to be in favor of 50 Mc., especially if one also remembers that the total frequency space available there is larger. These conclusions are not likely to be popular, because the 50-Mc. band has not been as widely used for mobile and civil defense purposes as either of the other two bands. Furthermore, most of the existing operation on 50 Mc. is with horizontally polarized antennas, while for mobile use vertical polarization is to be preferred. Unpopular as they may be, the conclusions are in the opinion of this writer technically sound. Unfortunately, it may be too late in most cases to change nets that have already been established, but new ones are still in a position to consider these remarks.

Development of the U.H.F. and Microwave Bands

Below 30 Mc. there are seven frequency bands, containing the major portion of all amateur activity. Above 30 Mc. there are eleven bands which, except for 50 and 144 Mc., are largely unused. (For convenience the amateur bands, except for the five lowest ones, are listed in the accompanying table.) It seems desirable to formulate plans for the use of this large assignment of frequency rather than to leave it for haphazard development without benefit of all the knowledge now available concerning these frequencies.

Generally speaking, in the development of the lower frequency bands there was a tendency to proceed, as a band became occupied, to the one next higher in frequency. At that time, techniques were not known and it was necessary to proceed gradually. Also, the nature of ionospheric propagation is such as to cause the properties of adjacent bands to be radically different. However, in the present situation a great deal of information is available concerning techniques, and it is known that there is no such rapid change in the manner of propagation with frequency. Therefore, it would seem desirable to select a few widely separated bands on which to concentrate the efforts of those interested, leaving the intervening bands for later occupancy. Such a selection involves consideration of many aspects and cannot be made by one person. However, it is in order to point out some of the important topics and likely choices.

As stated, the 50-Mc. band seems to be the optimum choice for mobile use. It is also of interest to fixed stations because of occasional ionospheric propagation to large distances, although such stations do not profit from as favorable antenna factors as they might obtain at higher frequencies with antennas of the same size.

Earlier it was indicated that in practice the best antenna factors for general coverage fixed-station operation probably can be obtained in the 420-Mc. band. This alone is an important reason for selecting this band. In addition the frequency is high enough to have a moderate probability of long distance propagation by "trapping" in a duct. It is the highest frequency band at which (a) tank circuits employing lumped LC circuits or open-wire lines may be used; (b) it is practical to employ high-stability narrow-band modulation techniques; (c) common receiving tubes may be used; and (d) where tubes with directly heated filaments (the 957 and 958 acorns) are rated for operation. On the other hand, anyone with an interest in r.f, "plumbing" and accurate machine work will find it to his advantage to follow his interest. Some war surplus equipment is in use on this band, and other such equipment now in use at 144 Mc. - e.g., the SCR-522 - may be modified for use at 420 Mc. by making the last stage of the transmitter a tripler or by adding a tripler to the present 144-Mc. amplifier. The expected development of the commercial u.h.f, television bands should make improved tubes available at low cost. The 420-Mc. band is wider, on a percentage basis, than any of the lower frequency bands except 1.75 and 3.5 Mc., and it is the lowest at which television is permitted. In spite of a disadvantageous antenna factor of 70 (18 db.) in comparison with the 50-Mc. band, portable operation employing dipole antennas may still be effected. At present there is a legal limit of 50 watts peak antenna power, but that should not be a serious handicap.

On the other hand, the 220-Mc. band has certain advantages over 420-Mc. Under practical conditions, one probably cannot quite obtain the optimum antenna factors. Nevertheless, higher transmitter powers can be obtained, partly by greater efficiency and partly by the absence of the 50-watt legal limit, and probably one less multiplier stage is required in a crystal controlled transmitter. At the same time receiver noise figures may be a bit better. Finally, this band, in contrast to the 420-Mc. band, has been reserved for civil defense so that any equipment for use on it may be of value in time of emergency.

The 144-Mc, band, which has the greatest occupancy of any of the v.h.f. bands, suffers by being "neither fish nor fowl." The antenna factors are inferior to those at 50 Mc. for portable operation, and to those at 220 and 420 Mc. for fixed stations. Also, ionospheric or atmospheric effects tending to give extended range are more probable at both lower and higher frequencies.

In the 1215-Mc. band and above the antenna factors tend to favor point-to-point operation on a prearranged schedule. In other respects the techniques change. Because of radiation losses it is no longer possible to use open-wire transmission lines as tank circuits. Coaxial lines and, finally, hollow cavities must be used, and as the frequency is raised greater accuracy must be employed in the machining of parts. Yet this situation presents a challenge to enterprising individuals with a mind to mechanical precision. A lathe is almost a necessity. Perhaps some radio clubs having a number of members with interest in u.h.f. might consider owning a lathe, although if one is obtained its use should be closely supervised to prevent damage to it and injury to inexperienced users. On the other hand, if cavities or other r.f. "plumbing" line components are purchased at other than war surplus prices the cost is fantastically high, since these items have never been mass-produced for the retail market. At current prices, for example, a wave-guide crystal mount costs $125, while the cavity for a 2K28 "McNally" reflex klystron costs $300 (although the latter is somewhat more elaborate than would be necessary for amateur use).

Above 3750 Mc. all tubes in general use are of the "integral cavity" type: that is, their tuned circuits are largely, and usually completely, contained within the vacuum envelope, and they can cover a frequency range of ten per cent or less. In fact, many of the traveling-wave mag-netrons have no tuning adjustment at all, and the only way one may change frequency is to use another tube. Integral-cavity klystrons and magnetrons have appeared on the surplus market for frequencies up to 30,000 Mc., but practically none of these lies within the assigned amateur bands. However, there are a few integral-cavity types which lie within the 3300-Mc. band. In addition. the 707B or 2K28 "McNally" klystron using an external cavity can be made to operate in this band. Also, it is possible that lighthouse tubes, especially if selected and if used in pulsed operation, may be persuaded to operate here. In the 2300-Mc. band and below, integral-cavity tubes are not generally available. The McNally tube and lighthouse tubes will operate in the 2300-Mc. band, and in the 1215-Mc. band they will be joined by "pencil" triodes and possibly selected 6F4 and 6L4 acorn tubes, whose rated upper limit is 1200 Mc. The machining of a McNally tube cavity for 3300 or 2300 Mc. may be somewhat easier than a cavity for 1215 Mc. because tuning at the higher frequency is accomplished by simple screws penetrating the cavity, while at 1215 Mc. tuned circuits involve coaxial lines which must be tuned by a plunger with sliding contacts. External-cavity klystrons that can be made to operate at frequencies above 3750 Me. have recently been developed, but probably these cannot be obtained without a priority and then only at a high price.

From the preceding discussion it may be concluded that widespread use of bands higher than 3300 Mc. appears impractical because of the lack of inexpensive tubes. Of the bands above 420 Mc. left for consideration, the 3300-Mc. one appears to hold more interest partly because it is the highest frequency practical with present components and partly because of the variety of tube types which might be employed. However, it is to be noted that the 1215-Mc. band is the lowest one at which pulsed operation is permitted. For general coverage with this type of modulation this band might be preferred. Should tubes and other components become readily available for the higher frequency bands, the 10,000-Mc. band might have some appeal since here waveguide techniques become very convenient.³ The propagation properties differ appreciably from 3300 Mc., and the frequency is low enough not to suffer appreciable absorption by water vapor.

To summarize, if one may forget present usage and select three bands for concentrated development there would be considerable argument in favor of: (1) the 50-Mc. band for portable use and occasional ionospheric and tropospheric propagation; (2) 420 Mc. for fixed-station general coverage, with the possibility of television and wide-band f.m. as well as high-stability narrow-band a.m. and occasional propagation by ducts; (3) 3300 Mc. preferably for pulsed operation and also preferably for point-to-point work on prearranged schedules, with considerable probability of propagation by ducts.

While no one can deny the very great advantages to be obtained by the use of the best available techniques, modulated oscillators and super-regenerative receivers have a certain amount of appeal especially among beginners or those whose interest in the higher frequencies is casual. When there are so many virtually unoccupied bands it would seem a little too bad not to reserve one region where such techniques might be employed. Because of its large width the 420-Mc. band offers an advantage. Perhaps the portion 420 to 432 Mc., which is not in harmonic relation to the 144- and 220-Mc. bands, could be used for this purpose. On the other hand, the needs of civilian defense might well be served by such techniques if nothing else were available, and it might be preferable to reserve the 220-Mc. band for this use.

Appendix on Line-of-Sight Range

With two important and mathematically simple exceptions, no formulas have been used since it is assumed that many readers will not care to follow extensive calculations. However, for those readers who have more mathematical minds, it is desirable to put some of the preceding arguments on a more rigorous basis by repeating here the derivation of the well-known "one-way transmission equation." At the same time it can be shown that the theoretical line-of-sight range obtainable with small amounts of power is much larger than one might otherwise expect. Therefore, for local communication it is practical to employ very low power.

With reference to Fig. 1, let us suppose that at T there is a transmitter of power P_t. In the case of pulsed transmitters of low duty cycle, there is a question as to whether P_t should represent the average power, the peak power, or an intermediate value. If the receiver bandwidth is adequate to pass the pulses with little distortion, to a good approximation P_t should represent the peak power. With the types of modulation conventional at lower frequencies P_t would represent the carrier power. Let us suppose atmospheric absorption may be neglected.

For the moment it will also be assumed that the transmitting antenna is "isotropic." Therefore, the fields produced at one instant at the transmitter travel outward and at a later time will be evenly distributed over the surface of a sphere. The receiving antenna is at a distance R. When it is connected to a load equal to its radiation resistance and given optimum orientation, its ability to absorb radiation is characterized by an equivalent area A_r. The received power P_r will be P_t multiplied by the ratio of A_r to the area of a sphere of radius R or

In practice, the transmitting antenna is not isotropic but has a gain G_t when oriented in the optimum manner. Therefore, we may write

Equation (3A) is given in terms of the gain of the transmitting antenna and the equivalent area of the receiving antenna and therefore corresponds to special case (3) discussed in the first article of this series. In confirmation of the remarks in that article it is observed that the wavelength does not appear in Equation (3A).

By use of Equation (1) of the first article, A_r may be expressed in terms of the gain of the receiving antenna G_r:

Then Equation (3A) is transformed into a form corresponding to Case (1):

It is to be noted that, in accord with the first article, the received power is proportional to the square of the wavelength.

Finally, Equation (3A) may be put in a form corresponding to Case (2) by expressing G_t in terms of the equivalent area A_t:

The wavelength dependence is again in accord with the first article.

The theoretical limiting range for line-of-sight operation with no atmospheric absorption will occur when P_r is approximately equal to the equivalent noise of the receiver

P_r = FkTB,                            (4)

where F = noise figure of receiver expressed as a ratio,

B = noise bandwidth, which may be taken approximately as the half-power bandwidth of the i.f. amplifier in most practical cases,

k = Boltzmann's constant,

T = Absolute "room" temperature.

If B is expressed in kilocycles per second, KT may be taken as 4 X 10^-18 watts per kilocycle.

The range may be found by equating the values for P_r in Equations (3B) and (4) and solving for R:

This is the so-called one-way transmission equation.⁴ In this form, R has the same units as A. The gains of the antennas may be expressed in terms of the equivalent areas by use of Equation (1).

A form of Equation (5) more convenient for numerical computation may be obtained by expressing the wavelength λ in terms of the frequency, changing some of the units and lumping all of the numerical constants into a single factor:

wherein R = range in miles,

f = frequency in Mc. per sec.,

B = noise bandwidth of receiver in kc. per sec.,

P_t = transmitter power in watts,

F = noise figure of receiver expressed as a ratio,

and G_t and G_r are respectively the gains of the transmitting and receiving antennas expressed as ratios with respect to an isotropic antenna.

It is of interest to substitute some conservative values into this equation. For example, if the following values are used:

P_t = 1 watt,

f = 30 Mc. per sec.,

B = 10 kc. per sec.,

F = 5 (7 db.),

G_t = G_r = 1.64 (corresponding to half-wave dipoles),

the computed value of R has the fantastic value of about 57,000 miles, approximately twice the circumference of the earth! Of course, such line-of-sight ranges have no practical direct meaning. However, it is to be expected that under extremely good ionospheric conditions absorption should be small and the observed range should approach the theoretical line-of-sight range. Therefore, it is no wonder that since the very start of international DX amateurs have frequently reported contacts of several thousands of miles while using powers of the order of only one watt.

At the same time this calculation implies that at line-of-sight ranges obtainable from practical locations the signal-to-noise ratio is very large even with such conservative values of the parameters as are used in the present calculation. For example, at 15 miles the signal-to-noise ratio would be about 60 (18 db.) if the stations were "in sight" of each other, while at 5 miles the signal-to-noise ratio would be 540 (27 db.). Hence, at these closer separations one may infer there is sufficient reserve signal strength to permit one or both stations to be in partially screened locations.

Furthermore, it can be concluded that if one is primarily interested in local communication, as is the case in most civilian defense work, practical results may be achieved by the use of very low power. The present need appears to be for a large quantity of low-powered equipment rather than a small amount of high-powered equipment. Also, it is to be remembered that in an emergency gasoline for battery charging may be scarce or not available, and high-powered transmitters may be nearly useless. Under these conditions there is much to be said in favor of midget transmitters employing available receiving tubes with powers of a watt or two. Such equipment may be simplified and be made more economical by having the transmitter "borrow" its power from an automobile broadcast receiver.

During the last three years this writer has used mobile equipment of this type, at first using a 6AK5 final on 28 Mc. with 1.5 watts, and later a bandswitching affair employing a 6AQ5 doubler with 4 watts, contained in a 4 X 5 X 6-inch box along with a 6J6 converter. Most of the time the antenna was the standard Ford 54-inch b.c. whip. Ranges of 5 or 10 miles have been quite consistent on 28 Mc., and on rare occasions contacts up to 70 miles have taken place. This equipment has been used in local AREC drills and has usually effected communication from typical city locations of a few miles. While there is no doubt that the higher-powered stations have put through louder signals, only rarely has this low-powered equipment been unable to get through. The operators of stations worked have frequently expressed surprise at the strength of the signal, and a few have questioned the writer's sanity. This writer makes no general claim on the latter point, but it happens that theory has given a valid justification for the use of such low power, and all of the writer's results are in complete accord with what the theory predicts.

Author's Notes:

In the first article of this series, on pages 42 and 43 of the February, 1952, QST, it was incorrectly stated that the equivalent area of a bidirectional broadside antenna is approximately equal to the geometrical area, while a correct statement would he that equivalent area of a unidirectional broadside beam (with a reflector) is approximately equal to the geometrical area. Therefore, Table I applies to broadside antennas with reflectors. This error resulted from the author's misinterpretation of source material which was rectified by his reading page 43 of the new book Antenna Theory and Practice, by S. A. Chelkunoff and H. T. Friis, John Wiley and Sons, New York, 1952.

One cartoon contained in the second article of this series on page 32 of the May, 1952, QST, although not incorrect, did not give the best interpretation of the text. This cartoon indicates a duct with a maximum of water-vapor density at some distance above the surface of the water. Probably such ducts do exist on rare occasions, and when they exist, they can propagate as shown. However, the author had in mind something which is much more likely: a duct with maximum density at the surface of the water and decreasing with height. The author realizes the text was not as definite on this point as it should have been, and therefore the misinterpretation is quite understandable. - Y. B.

* Associate Professor of Physics, New York University, University Heights, N. Y.

1 Beers, "The Wavelength Factor," QST, Feb., 1952; "The Wavelength Factor - II," QST, May, 1952.

2 See, for example, QST, page 33, October, 1950.

3 The 1951 and 1952 editions of The Radio Amateur's Handbook contain information concerning the modification of war-surplus 723A/B or 2K25 tubes for use in the 10,000-Mc. band.

4 This name is to distinguish this equation from an analogous one giving the range of radar sets, called the "two-way transmission" equation.