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Theory and Application of U.H.F. (Part 7)
October 1944 Radio News

October 1944 Radio News
October 1944 Radio News Cover - RF Cafe[Table of Contents]

Wax nostalgic about and learn from the history of early electronics. See articles from Radio & Television News, published 1919-1959. All copyrights hereby acknowledged.

Special Insert: Radio-Electronic Engineering Department

This seventh installment in an eleven-part series on "Theory and Application of U.H.F." appeared in the October 1944 issue of Radio News magazine. Author Milton Kiver covered a wide range of topics including basic and advanced circuits, tube types, modulation, resonant cavities, oscillators, transmission lines, waveguides, antennas, electromagnetic fields, and Maxwell's equations. Part 7 continued the discussion of how waveguides, both rectangular and circular, support the conduction of electromagnetic waves. Methods for injecting and extracting signals is covered as well. Interestingly, the Smith chart never appeared even though Phillip H. Smith had introduced it around 1936. In fact, the first mention of the Smith Chart in Radio News, per a WWW search, was in 1950.

Eleven installments appeared in the following issues: Part 1: December 1943 (p35), 2: January 1944 (p32), 3: March 1944 (p41), 4: April 1944 (p46), 5: May 1944 (p50), 6: August 1944 (p53), 7: October 1944 (p58), 8: December 1944 (56), 8: February 1945 (p58), 10: April 1945 (p57), 11: June 1945 (p57). I hope to eventually procure those editions and post the articles.

Part 7. Additional properties of wave guides used as a means of transmitting energy at the ultra-high frequencies.

Illustrating the variation between transverse and longitudinal waves - RF Cafe

Fig. 1 - Illustrating the variation between transverse and longitudinal waves. (A) No wave motion. particles are at rest. (B) Transverse wave, particles vibrate up and down while the wave energy moves forward. (C) Longitudinal wave particles move back and forth while wave energy moves forward. Length of arrows in (C) indicates relative distance of particle movements.

By Milton S. Kiver

In the August issue of Radio News the fundamental ideas concerning wave guides and the electromagnetic waves that flow along these guides were presented. As stated, a wave guide merely confines the radio waves that ordinarily would flow uncontrolled in three-dimensional space. The method of starting these waves off is very much like our ordinary every-day processes with which all are so familiar. An antenna, in this case the inner conductor of a coaxial cable, is placed inside a guide and from this emanates the electromagnetic energy. By a series of reflections off the restricting walls of the guide, the energy is propagated down the guide to whatever use may be made of it. The end may be open, in which case the energy flows out into free space, or the receiving antenna may be placed here to pick up this energy.

The final property of a guide, mentioned in the last article, concerns the action of this wave guide in allowing waves of certain frequencies to be propagated down the guide, while others of a lower frequency are stopped, so to speak, at the very mouth of the guide. This selective effect, or filtering action, may be useful if only certain waves are desired to the exclusion of others of lower frequency. Note that this action is comparable to that of a high-pass filter in ordinary radio or electrical circuits. Keep in mind throughout this entire wave guide discussion that these guides are used for the very simple reason that they attenuate the high frequencies less than any coaxial cable devised so far. It is entirely permissible to think of these guides as transmission lines specifically designed for the ultra-highs, and, indeed many writers do.

Up to this time the types of waves merely have been mentioned without taking time out to explain the system used in arriving at these peculiar looking symbols. It might be best to start at the beginning and explain the difference between a transverse and a longitudinal wave which will lead more directly to the desired results. To demonstrate longitudinal wave motion take an ordinary tuning fork and hit it sharply, causing it to vibrate back and forth. This motion will force the molecules nearest the tuning fork to vibrate back and forth, and the resultant waves will travel outward in all directions. The vibration of the molecules, in this case, is in the same direction as the propagation of the sound waves thus causing their paths to be parallel. This is the defining characteristic of a longitudinal wave. It should, of course, be remembered that the molecules vibrate about a mean point while only the energy is expanding outward. It is somewhat analogous to a situation where a straight row of billiard balls is tapped at one end. The energy is transmitted forward by the balls while the balls themselves remain fixed.

For the case of a transverse wave, consider the motion set up by water waves that is caused by a small pebble dropped into a pond. The waves travel outward while the small water molecules move up and down or at right angles to the direction of propagation of the wave. Another example of this type of wave motion is illustrated by the action of a rope, one end being secured and the other end moved up and down by hand. Fig. 1 emphasizes the difference between the two types of waves pictorially.

Rectangular wave guide showing the three separate axes - RF Cafe

Fig. 2 - Rectangular wave guide showing the three separate axes, x, y. and z.

Electromagnetic wave in a plane propagated along axis X - RF Cafe

Fig. 3 - An electromagnetic wave in a plane propagated along axis X. Arrowed lines E signify electric lines of force, while those of H signify magnetic lines of force.

Three wave guides, all of the same dimensions - RF Cafe

Fig. 4 - Three wave guides, all of the same dimensions showing the changes in electric and magnetic field strengths as a result of increasing frequency. Solid lines indicate electric field while dotted lines indicate magnetic field. (A) TE0,1 wave. (B) TE0,2 wave. (C) TE0,3 wave.

Methods of exciting wave guides - RF Cafe

Fig. 5 - Methods of exciting wave guides to obtain the wave patterns illustrated.

Changing from water waves and sound waves to electromagnetic vibrations, it can now be shown how the preceding information can be used to label the various types of waves in rectangular guides. As mentioned before, every electromagnetic wave may have electric and magnetic fields with components along any of the three conventional directions, namely, x, y and z (see Fig. 2). Suppose a wave had a magnetic field along the z axis (Fig. 2) but no electric field in this direction. The electric components could be either in the x or the y direction or both. Since the direction of propagation of the wave is in the z direction, it can readily be seen that as far as the magnetic field is concerned, since it has a component in the z direction, this is a longitudinal wave. The necessary conditions as just defined at the beginning of this paragraph are satisfied. However, since the electric field has no components in the z direction, but only in the x or y directions, it can be called a transverse wave. This also follows from the definition of transverse waves. Thus, there is a choice. With regard to the magnetic field it is a longitudinal wave whereas with respect to the electric field it is a transverse wave. The custom has been to label the wave after the transverse component, so in this case the notation would be T E, standing, of course, for transverse electric. Another notation sometimes used is H waves.

To reverse the situation, let there be an electric field component along the direction of propagation, the z axis, but no component of the magnetic field. The latter will be confined to either the x direction, the y direction or both. .(It has not been mentioned recently, but it will be recalled that the electric and magnetic fields must be at right angles to each other so that it is not possible to have a magnetic and an electric field along the same direction.) In this case there would be a longitudinal wave with respect to the electric field and a transverse vibration with respect to the magnetic field. Retaining the usual notation of labeling the wave after the transverse component, will give, for this wave, the name T M wave. The T M is an abbreviation for transverse magnetic. Another name that is sometimes used is E waves. Having taken care of the two main cases a third and final type of wave might be mentioned, which is in reality a plane wave (see Fig. 3). Here the electric and magnetic fields are at right angles to each other and at the same time are perpendicular to the direction of propagation. This can truly be called a transverse wave for here there are no longitudinal components. The name given this type of wave is a combination of the former two types and is TEM.

So far the nomenclature has been general, indicating only the class of waves in operation but we still lack a specific notation that would point out which particular wave in any group is being dealt with. In order to bring this out more clearly refer to Fig. 4 where three types of waves in the TE class are shown. The simplest wave in this group is shown in Fig. 4(A), where it can be seen that the dimension x is just wide enough to accommodate a half wave of the electric field. In Fig. 4(B) the frequency of the wave has been raised, so that now the same dimension x can accommodate a full wave. In Fig. 4(C) the frequency has again been increased and now we have three half waves. This process can be kept up as high as the frequencies can be generated and each wave is differentiated from the other by a small subscript n. Thus the lowest frequency waves, Fig. 4(A), would be represented by having n equal to 1, Fig. 4(B) would have an n of 2, Fig. 4(C) would have an n of 3, etc. The nomenclature is now more specific than it was before and is written as TEn.

But there is no reason why the dimension in the y direction should be ignored since it is possible to have a variation in the electric field in that direction also. In this case, use the subscript m and call each half wave of variation in this direction 1. So finally the general notation is TEm, n and specifically the wave in Fig. 4(A) is TE0,1 that in Fig. 4(B) is TE0,2 etc. Zero is used for m because there is no variation in the electric field in the y dimension, but let it not be forgotten that waves like TE1,1, TE2,1 etc. are perfectly possible. They are not frequently mentioned because of the extremely high frequencies involved, which for the present at least, are not easily generated. And whatever has been said about the subscripts m and n are equally applicable to the TM type of waves.

Filtering action of a cylindrical (or rectangular) waveguide - RF Cafe

Fig. 6 - Filtering action of a cylindrical (or rectangular) waveguide to separate two frequencies. The lower freq. is lost as the wave enters the smaller portion of the guide.

The discussion of wave guides has progressed far enough so that it is now possible to investigate the various methods used to excite these guides and get the different types of waves mentioned. Excitation was only vaguely referred to previously when it was merely stated that an antenna was placed in the guide and the electromagnetic waves radiated from it. Each general type of wave (both TE and TM) and each specific wave requires a different setup to produce the desired field patterns. However, the similarity between the various waves of the TE group will be readily evident and the same holds for the TM group. The generator will be omitted in each case showing only the concentric cable placement in the wave guide but the obvious connection of the cable to the generator should be understood. The simplest wave of the TE group, namely TE0,1 can be generated by the type of arrangement shown in Fig. 5 (A). The electric field pattern is shown underneath so that a mental connection between the two can be formed. The TE0,2 wave can be produced by the arrangement shown in Fig. 5(B). Since the exciting rods are 180° out of phase, the electric fields are shown as being in opposite directions. The closer the lines of force are, the stronger the electric field. As stated before, the intensity at the sides of the wave guide must be zero and this condition is adhered to here. The case of the TE0,3 wave is also shown and follows quite naturally, Fig. 5(C). Note that it is the inner conductor that is connected from the generator.

Two methods of exciting wave guides - RF Cafe

Fig. 7 - Two methods of exciting wave guides. (A) TM type wave. (B) TE type wave.

To produce the fields for the TM type of wave, a setup similar to that shown in Fig. 7(B) for the TE wave is used except for the position of the antenna in the wave guide. For comparison, methods of producing both the TE and TM fields are shown together in Fig. 7. In general, for the TEm,n type of wave, the antenna will be at right angles to the direction of propagation while- in the TMm,n case, these antennas are parallel to the direction of propagation. This is logical since as previously pointed out, the TE wave has no electric field in the forward direction while the TM wave has. It is only natural, then, that the placement of the radiators should also differ by 90°. Provision is also usually made whereby the length of the antenna in the wave guide can be adjusted to give best results. This is an important adjustment since the measured intensity of the transmitted wave may vary quite a bit between the best condition and the worst. Another adjustment that is important is the distance between the antenna and the end of the wave guide nearest it which acts as a reflector or backboard. The correct alignment can greatly improve the transmitting efficiency. And while only the transmission has been discussed here, every radio man knows that a good transmitting antenna is also an excellent receiving antenna and so the results work both ways. In the case of reception, however, the coaxial cable from the antenna is connected to a crystal detector which rectifies the received current and thus makes it available for further use. Incident-ally, these antennas when used for reception are pretty selective and will pick out one type of wave almost to the exclusion of all others. By having several types of transmitting antennas placed in various positions and at the other end of the guide receiving rods in similar positions, the guide can be used for multiple channel transmission. This is a point that will probably be of good use in days to come.

The reader may be a little confused by all the different types of waves that have been explained. A question might naturally arise in his mind as to the reason for having so many different modes of operation. The answer lies in the frequency that is to be transmitted down the guide. For low frequencies, where there is only one standing half wave across the mouth of the guide, a simple type of electromagnetic wave may be used, such as the TE0,1. As the frequency is raised, the number of half waves likewise increase and so the wave becomes more and more complex.

Cylindrical wave guide showing direction of wave and various coordinates - RF Cafe

Fig. 8 - Cylindrical wave guide showing direction of wave and various coordinates.

Method of exciting a cylindrical wave guide to obtain a TM0,1 type of wave - RF Cafe

Fig. 9 - (A) Method of exciting a cylindrical wave guide to obtain a TM0,1 type of wave. (B) Electric and magnetic lines of force set up for this type of wave.

Method of exciting a cylindrical wave guide to obtain a TE1,1 type of wave - RF Cafe

Fig. 10 - Method of exciting a cylindrical wave guide to obtain a TE1,1 type of wave. Compare this with Fig. 9 and note the 90° change in antenna position.

Electromagnetic horn - RF Cafe

Fig. 11 - An electromagnetic horn.

Each of these complex waves may be looked upon as combinations of simple types and they must observe the same general rules that apply to all electromagnetic radiations. Another reason for studying these different type waves lies in the fact that some have properties that may be of more use to us than those of other waves. Some may be easier to generate and send, while others may not suffer attenuation as they travel down the wave guides. Then, of course, there is the question of size. Higher frequency waves require smaller guides than those of the lower frequencies. However; the lower frequencies are easier to generate. Hence we arrive at a situation that is not unlike what we have today. Some people prefer one type of circuit over another and for each the reasons advanced are the best solution to the problem. As more and more uses of the ultra-high frequencies are found there probably will be greater simplicity and only a few types of waves will be used. But for a field that is just in its first stages, everything connected with it comes under the engineer's microscope. It is only by this process of experimentation that better and easier working models are achieved.

The only wave guide discussed so far has been the rectangular wave guide, and this was used because it is easier to visualize the actions of the electromagnetic wave. However, there are other forms that these guides can assume, most of them being of little practical importance, except the cylindrical wave guides. As with the rectangular forms, it is possible to use the two notations (TEm,n and TMm,n) to label the various types of waves that can be propagated down the length of the tube, provided the frequencies used are not too low for a particular diameter of the guide. The same conditions pertaining to electric and magnetic fields still hold true even if the shape of these fields has changed. In fact, the change is due to the difference in shape of the guide.

Usually, when dealing with these cylindrical wave guides, the geometrical notation is changed from that used with the rectangular guides. This is illustrated in Fig, 8 for a cylindrical guide. Note that the, axis in the direction of propagation is left the same, the changes occurring where we previously used the x and y axis. Instead of these, we now deal with the radius

r and the angle B which allows us to go any distance from the central axis and also to rotate through the complete 360° about this axis. Electric or magnetic fields having components along any of these directions are differentiated from each other by subscripts. Thus Ez means an electric field component in the z direction, Er pertains to the radial direction and Eθ tells of any field in the circular path. The same, of course, holds for the magnetic field components.

For excitation of perhaps the TM0,1 wave in cylindrical guides, it is possible to use a setup as pictured in Fig. 9(A). The resulting field pattern is shown in Fig, 9(B), the view being an end one. Having only transverse components of the electric field, the TE1,1 type depicted in Fig. 10 is obtained and its method of excitation is included for those who might be curious. The critical or cut-off frequency is higher for the TM0,1 wave than it is for the TE1,1 wave, identical diameters being used in each case. This can be easily seen when the formulas are given:


for the TE1,1 wave. Note that due to the inverse relationship of the frequency to the radius, a higher cut-off frequency requires a smaller opening of the cylinder. Remember again that this frequency represents the lowest frequency (or longest wavelength) that will be propagated down the tube without too much attenuation. Practically, it is possible to transmit below this frequency but the range is rather limited. Theoretically, all higher wavelengths can be easily transmitted without much attenuation (using actual conductors), but in practice the upper frequencies begin to show excessive attenuation because of increased skin effect. In between these two extremes can usually be found a frequency that will have least attenuation. Whether or not it is used will be determined by other factors that may assume greater importance than attenuation.

It is now possible, since the action of a wave guide has been described in some detail, to study some of the uses that have been evolved for wave guides. First and foremost is its most important use, that of carrying ultra-high frequency power from one circuit to another. The wave guide is essentially a transmission line which has been modified for the very high frequencies and its extensive use is due to the low loss or small attenuation introduced. What attenuation there is results from the fact that the walls of the guide are not perfect conductors.

Some readers may resent the fact that it has been mentioned several times that imperfect conducting walls will result in power losses and yet, no explanation has been advanced which would prove or explain this. The explanation can be found quite easily, but only if the investigator is equipped with a good knowledge of electric and magnetic fields and also the differential equations developed by Maxwell. Since only an elementary knowledge of mathematics has been assumed throughout this series, all complicated. expressions have been omitted.

Continuing on, another use for the wave guide is possible, that of a high pass filter. This property is connected with the action of a guide in allowing only frequencies that are above a certain minimum value, which is known as the cut-off frequency, to pass and all lower values to be rejected. This effect does not necessarily have to take place at the opening of the guide; it may occur anywhere along its length. Fig. 6 illustrates what is meant. The first section of the pipe has a certain diameter which becomes less after the constriction. Waves that could be propagated in the first half might not continue on after the diameter has been decreased and would thus be attenuated or reflected, probably both. The point, however, is that they would not continue on in the latter portion of the pipe. In this way frequencies may be separated, an action that can only be brought about at lower frequencies by coils and condensers. In fact, the analogy to filter circuits can be extended even further by combining sections of wave guides that have different filtering characteristics.

Another use that will be mentioned briefly here (but to be described later in greater detail) is the cavity resonator which can be considered as a section of a wave guide. Just as it was possible to take a small portion of an ordinary transmission line and convert it into a resonant circuit, so is it possible to close one end of a small section of a wave guide and get the same results, only at much higher frequencies. The transition of the tuned circuit can be pictured as starting out at the low frequencies with a coil and condenser, becoming a section of a transmission line at the hyper frequencies and then finally ending as a cavity resonator at the ultra-high frequencies. The function still remains the same, the means for accomplishing this end being varied.

The final use to be considered will also be gone into in greater detail in another chapter and concerns itself with the action of a wave guide as an antenna. The wave will travel down a wave guide without reflection of any of its energy just as long as no changes occur in the guide itself. This is equally true in any transmission line. However, should any change occur, such as a solid wall or constriction in the guide, it immediately results in a reflection of energy back along the guide. For transmitting purposes, the open end is of most importance. Some of the energy hitting this open end will continue out into free space while some of it will be sent back. However, if the change is not made very abruptly, but rather is introduced gradually, then the amount of energy sent back (or reflected) will be less and the forward transmitting efficiency of the wave guide will increase appreciably.

This flared type of guide (Fig. 11) is known as an electromagnetic horn and has very definite directional properties. It will be considered in greater detail along with other types of ultra-high frequency antennas to be taken up presently. Here the flare is a gradual change in the wave guide which allows more of the wave to be sent forward and less reflected hack. (To be continued in December issue)



Posted April 8, 2021

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