621.365 U6S5tt no.27 Cop. ^ CQNFEREKC ■•■AM ANTENNA LABORATORY Technical Report No. 27 ..L1NOIS >, ILLINOIS/ COUPLED WAVEGUIDE EXCITATION OF TRAVELING WAVE SLOT ANTENNAS CONFERENCE ROOM ^ by WALTER L. WEEKS 1 December 1957 Contract No. AF33(61 61-3220 Project No. 6(7-4600) Task 40572 WRIGHT AIR DEVELOPMENT CENTER ELECTRICAL ENGINEERING RESEARCH LABORATORY ENGINEERING EXPERIMENT STATION UNIVERSITY OF ILLINOIS URBANA, ILLINOIS ANTENNA LABORATORY Technical Report No„ 27 COUPLED WAVEGUIDE EXCITATION OF TRAVELING WAVE SLOT ANTENNAS by Walter L„ Weeks 1 December 1957 Contract AF33 (616)-3220 Project No. 6(7-4600) Task 40572 WRIGHT AIR DEVELOPMENT CENTER Electrical Engineering Research Laboratory Engineering Experiment Station University of Illinois Urbana. Illinois COUPLED WAVEGUIDE EXCITATION OF TRAVELING WAVE SLOT ANTENNAS IP'** ABSTRACT The analogy of coupled waveguides to a pair of coupled transmission lines is employed to obtain a design procedure for the establishment (approximately) of a certain class of traveling wave field distributions over an aperture in a conducting plane. The aperture is the opening to free space in the broad' wall of a rectangular waveguide (dielectric loaded). This waveguide is coupled to a second waveguide through a series of slots or holes. The coupled waveguides permit the simultaneous excitation of two modes whose propagation constants can be designed to have a convenient difference. The major features in the radiation patterns can be predicted by the superposition of the patterns of two line sources which are equivalent to the traveling wave field distributions of the two modes. Advantage is taken of the degree of adjustment possible in the propagation constants of these modes to obtain a variety of radiation patterns. In particular, it is found that directive radiation patterns with low side lobes (lower than those of a uniform distribution) can be synthesized. Experimental results in the form of radiation patterns, aperture distributions, and normal mode propagation constants are included. In Appendix D, some consideration is given to a simple means of scanning an antenna of this type. iii CONTENTS Page Abstract ii List of Symbols v 1. Introduction 1 2. Coupled Transmission Line Analogy and the Normal Modes 4 3. The Aperture Field Distribution and the Radiated Field 6 4. Design Procedure 12 5. Difficulties and Disadvantages 17 6. Experimental Results 20 7. Design Data 28 8. Acknowledgements 28 References 31 Appendix A. Coupled Transmission Line Equation 32 Appendix B. Normal Mode Solutions to the General Coupled Transmission Line Equations 34 Appendix C. Composite Antennas 36 Appendix D. Scanning a Coupled Waveguide Antenna 37 Distribution List iv ILLUSTRATIONS Figure Number Page 1 . Antenna Structure Most Studied and Variations 3 2. Conventions for the Geometry 7 3. Amplitude Distribution, Sin ^/r" Curves to be Added in Phase, and Space Factor for A(z) in Figure 3a by adding Sin ^A 1 Curves of Figure 3b 9 4. Amplitude Distribution, Sin ^/r* Curves to be Added, and Space Factor by Adding Curves. 10 5. Phase Velocity of Dominant Mode in Waveguide Partially Filled with Polystyrene 13 6. Amplitude as a Function of Propagation Direction 14 7 . Apparatus for Probing Aperture 15 8. Half Sinusoidal Amplitude Distribution and Space Factor for Amplitude Distribution of Figure 8a. 18 9. Aperture Distribution on Single Dielectric Loaded Guide. 18 10. Aperture Distribution 21 11 . Comparison of Aperture Distribution in One Guide with Power Variation in the Other Guide 21 12. Aperture Distributions and Radiation Pattern 22 13. Aperture Distributions and Radiation Pattern 22 14. Waveguide Cross Section for Antenna of Figures 12 and 13 23 15. Pattern of Antenna of Figure 11 23 16. Radiation Patterns, Aperture Distributions, and Geometry of the Waveguide Cross Section 25 17. Experimental Radiation Pattern and Geometry of the Waveguide Cross Section 26 18. Pattern and Aperture Distribution of Antenna of Figure 14, Except with Slot Coupling 27 19. Experimental Values of Phase Velocity in Dielectric Loaded Radiating Waveguides . 29 20 Experimental Values of Phase Velocities and Beat Wavelengths for the Waveguide Geometry Indicated 30 l*-l Schematic Diagram of Coupled Waveguide Phase Controlled Scanner38 I>-2. Space i of Beam in Scanning Cycle 39 I>- i Universal Scan Function as Function of Coupled Guide Phase Dj f f < j'-nce 40 Jj-4 . Scan Angle vs. Phase Difference 40 LIST OF SYMBOLS A(z) distribution of source (complex) amplitude along its length E (0) space factor (or array factor) S L length of radiating aperture V , V transverse voltages on a pair of coupled transmission lines a width of rectangular waveguide b height of rectangular waveguide c velocity of light in free space c ,c constants in coupled transmission line equation, defined in 12 21 A ^- A Appendix A„ d thickness of dielectric filling f ratio of normal mode amplitudes p aperture length in wavelengths (p ~ ^-) v "average" phase velocity (v = f X ) a a a v phase velocity of the faster of the normal modes v phase velocity of the slower of the normal modes S z propagation direction z distance of the first null in the envelope from the start of the radiating aperture (see Fig* 6). f} free space propagation constant (rr~) A difference in normal mode propagation constants Y_ ,v constants in coupled transmission, line equations, defined in Appendix A ■y fast normal mode propagation constant •y slow normal mode propagation constant X free space wavelength 27T F "t" S X "average" guide wavelength. Or— = — — ), see Fig. 6 a A. 2 X beat 'wavelength" - distance between nulls in envelope of distribution. (See Fig, 6) 7TL c v|/ parameter in space factor, i\> — t-(cos - — ) $ angle from the end fire direction measured In plane of conducting sheet (f) relative phase of the normal modes at start of the radiating aperture. angle of the observer with the line of the array (see Fig. 2). Digitized by the Internet Archive in 2013 http://archive.org/details/coupledwaveguide27week 1 . INTRODUCTION This paper considers certain aspects of the traveling wave antennas which have been described as "leaky pipes," especially those whose radiating apertures are set flush in a conducting plane. The main features in the radiation pattern of an antenna of this type can be calculated from linear array theory, in which the array elements are the source distributions which are equivalent to the tangential components of the traveling wave field distribution over the aperture (s) in the leaky waveguide. Examination of the space factor of such an array discloses that if the array is continuous (as in a traveling wave slot) or nearly so (as with closely spaced slots or holes) the main lobe makes an angle 9 with the line of the array such that cos 9=e/v, where v is the phase velocity of the mode in the waveguide. If v is less than c, while the slot has appreciable length, the main lobe may not appear in the visible region. If the array is discrete, (element spacing about ,4} or greater), other major lobes may appear in the pattern, but, in any case, the pattern is very nearly that of a linear array, with all of its advantages and limitations. This means, for example, that if the slot length in wavelengths is appreciable, the array of sources which are equivalent to the fields of a pure waveguide mode gives a space factor whose main lobe width is determined by the array length, and whose first side lobe is about 13,5 db down, independent of length (if c/v - 2V ( ^1 "^2 } + 4C 12 C 21 1/2 2. I /. 2 22 . 2 2 1 2 ( \ ^2 ) + 2V (Y 1 -Y 2 > + 4C 12 C 21 ,ll (3) The coefficients in (2) are determined by the boundary conditions over transverse planes. Unfortunately, at the present time there appears to be no convenient way to determine (theoretically) the constants in (3) applicable to waveguides. We will therefore use (1) and (3) only to make plausible the idea that the coupling of a pair of waveguides results in modes of propagation whose propagation constants can be controlled by: 1) adjusting the phase velocities in the uncoupled guides (for example, by changing the size or extent of dielectric filling); 2) adjusting the geometry of the coupling apertures, in the manner indicated by (3). 3, THE APERTURE FIELD DISTRIBUTION AND THE RADIATED FIELD The radiated field can be calculated in terms of the tangential components of the fields in an aperture. These tangential field components can be expected to have the same z-variation (propagation direction is z) as the symbols in (2), which, we assume, represent the mode voltages of the propagating modes. If we ignore the polarization and unit pattern effects, we can employ linear array theory to calculate the space factor E (9) of the array of sources equivalent to the o tangential field variation (for example, the array of magnetic dipoles equivalent to E X n in the aperture) . (We ignore here the field variation in the x direction.) The geometry is indicated in Fig. 2. Following linear array theory, one finds the space factor for a continuous array is given by the equation (4) where A(z) is the distribution and |3 is the free space propagation constant In our problem, A(z) is one or the other of equations (2), except for an unimportant multiplicative constant. For example, if we let subscript 1 refer to the radiating guide, and put V 1 = f V e J r(i.e., V. has some lo IF IS phase and amplitude relationship to V at z = o) 7 we find the equation 1 F for the space factor, E s (9) = vi ( e j( P C ° S 9 " ^F> z dz + f e j M e ^ cos e " V S > z dz A (5 ) We now introduce some algebraic rearrangements which lead to a rather use- ful representation. Introducing substitutions as follows: I = P cos - v F , A = y s _ v F , |L IL, C , } (6) + = - . T (cos e - -) o B O o w o o w o l-H fa V where X is the free space wavelength, we find the result AL r *. ■% E f9) = V,„ e J L r^*W**J«'*-*£f-*- " The interpretation of (7) leads to a graphic representation of the types of radiation patterns which can be synthesized by a coupled waveguide excitation. According to (7), the space factors which can be generated can be found by the point-by-point phasor addition of a pair of universal sin Wt curves, with one of the curves displaced from the other by an amount -5- and adjusted in relative amplitude by the factor f . (We have assumed negligible attenuation) . The visible region is that part of the space factor which lies in the range 4, = - &£. + d to - &f - 1) ^v F X v F 27T _ A AL For example, if f = 1, = -IT and L = so that — = IT, we find a familiar situation. The aperture amplitude varies sinusoidally as indicated in Fig. 3a, the sin W4 1 curves are displaced and added in phase as indicated in Fig. 3b, to give a net result as shown in Fig. 3c. As another example, if f = 1, p= -TT, L = 47t/(y - v ) so that ~4 = 27T, the amplitude distribution is as indicated in Fig. 4a. The sin WH* curves o are displaced and added 180 out of phase as in Fig. 4b to give the result indicated in Fig. 4c. Figure 4c also indicates the additional requirement necessary to obtain a single main lobe in the pattern — namely, the visible region must be positioned (by the selection of v ) so that the main lobe F of the displaced sin ^/r curve (the slow wave) is placed outside the visible range. An inspection of Fig. 4b also shows that if the amplitude of the slow mode is somewhat greater than that of the fast mode (namely f~2) , the amplitude of the side lobes in the visible range can be further decreased without broadening the main lobe (at the expense of efficiency, however). = TT O L Z FIGURE 3a AMPLITUDE DISTRIBUTION -4-TT -3TT -2T1 3TT ^TT 5TT FIGURE 3c SPACE FACTOR FOR A(z) IN FIGURE 3a BY ADDING Sl " - CURVES OF FIGURE 3b T L Z FIGURE 4a AMPLITUDE DISTRIBUTION =)TT -4* -3tt -2t 'isible range, for 117T to +7T, by making BE 4c SPACE FACTOR BY ADDING CURVES JN MOURE 4b 11 Other examples are readily prepared. It should be pointed out, however, that the foregoing analysis applies strictly only to propagation without loss, and to continuous apertures. If the fast mode, for example, suffers a small amount of attenuation, the curves to be superposed are slightly different; however, the qualitative aspects of the argument are unchanged. If the radiating aperture is made up of discrete openings sin nx (slots or holes), the curves to be superposed are of the type — 7Tri sin x (neglecting attenuation) where x = -r— (cos 6 - — ), where d is the * v_ F element spacing and n is the number of elements. Thus with discrete arrays there is the possibility of more than one major lobe in the space factor of each mode, so that the visible range must be more judiciously selected. Also, the relative phase in the phasor addition of the curves is influenced by the number of elements, especially if the number of elements is small ( — ■ not close to 1). UNIVERSITY OF ILLINOIS LIBRARY 12 4. DESIGN PROCEDURE In this sec + :on we shall illustrate the design procedure by giving a simple example. Unfortunately, the quantities of interest (the prop- agation constants of the normal modes of the coupled system) are not known from Theory, even approximately, except, for one or two special cases. Consequently, we shall also indicate a procedure for an orderly development program. We shall suppose that the designer has made the following decisions: 1) pattern type (of this class) , 2) angle of the main lobe with respect to the line of the array, and 3) the aperture length in wavelengths. As an example of a specific design, we shall suppose that a space factor of the + ype indicated in Fig„ 3c is desired, that the main lobe is to make an angle 9 with the line of the array, and that the length of the radiating slot is to be p wavelengths (L = pX) . Thus we know that the ampli- tudes of the modes are to be the same (f = 1) and that they are to be 180 oat of phase at the start of the radiating slot. A relatively easy way to accomplish the foregoing is to couple a pair of identical guides by a series of slots or holes in the common broad wall, connect one of the guides to the oscillator, and radiate from the other guide with the radiating slot begin- ning and ending with the coupling section. Next we note from Fig. 3c that to pu + the main lobe at , we must have 4 1 = 7T/2 when 6 = as follows: o o ,l, IT TTL , _ c x di = - a «-- ( cos - — ) 2 A, o v„ F or - = cos - -i- (8) v p o 2p and c « 1 = COS + - - (q) V c O 2p VB ' With coupling geometry as mentioned above, it is found that c/v is not too F different from trie c/v calculated for a closed waveguide of the same type. F Hence, the value of c/v r obtained from (8) can be entered into a graph of 9 type shown in Fig. 5 to determine the waveguide geometry. 13 V FIGURE 5 PHASE VELOCITY OF DOMINANT MODE IN WAVEGUIDE PARTIALLY FILLED WITH POLYSTYRENE 14 Next, we face the most difficult part of the design, namely, the production of the required c/v (or rather, the production of the desired difference in normal mode propagation constants) . Data are presented in Section 6 which can be used as a rough guide in the design of antennas of some particular types. But, in practice, if and p are rigidly specified at a given frequency, it is usually necessary to develop the details of the coupled waveguide geometry on a cut and try basis. Consequently, we shall indicate here some further algebraic rearrangements which suggest a procedure for an orderly development program. Note that the equation V = v e"^F z + f V e j( ^' YS *> 1 IF IF can be put into "the form V l = 2f V 1F 6 ^ I i-j ( W z p\(-f \c-\\\ator S^lsyn Trans Mo+or JDriv<£ FIGURE 7 APPARATUS FOR PROBING APERTURE 16 in the design can be found in terms of the foregoing experimentally determined quantities as follows; 277 7T c X X , , , . v s " IT + I - or 7" = X" + 2XT (11) a b S a b 211 IT c X X ,. n v Vf = T ~ XT or 7" = IT " 2~T (12) a D Fab 2z = -, 77 (1 - -j— ) (13) AL _ 7TL 2z AL _,. o , L (14) b b The quantity f can be found from the ratio of minimum to maximum V . In practice, if only one of the guides is connected directly to an oscillator, the amplitudes are nearly equal if the two guides have the same propagation constants. Finally, we present a few points which are important enough in practice to deserve special mention. 1) The quantity — depends somewhat on the coupling and radiating geometry. 2) The amplitudes of the propagating modes can be made unequal, either by making the guides dissimilar and exciting one guide as usual (over a transverse dross section) or alternatively by exciting both guides simultaneously with appropriate phase and amplitude differences. 3) The beat wavelength can be decreased (Y_ - "Y e increased) by F S making the guide geometries differ (as, for example, with a differ- ent percentage of dielectric loading) or by increasing the coupling coefficients with "tighter" coupling. These possibilities are suggested by Eq . (3). 17 5. DIFFICULTIES AND DISADVANTAGES Before presenting experimental data which show the extent to which the foregoing ideas can be applied, we shall list some practical difficulties and limitations on antennas of this type. One of the major disadvantages is that most of the antennas are rather inefficient,. Strictly speaking, aperture distributions involving the combination of the pair sin iV4" curves cannot be produced unless the modes are propagated without loss, Practically, this means that, with a continuous aperture, the pattern must be nearly end fire. This does not mean that good patterns cannot be produced in any except the end fire direction, but only that the aperture distribution is not sinusoidal and thus a more complicated representation is necessary. Furthermore, even with a distribution nearly like the ideal sine (Fig. 3) a very considerable portion of the input power is dissipated in a resistance card or other termination which is required to suppress a backward traveling wave. Some increase in efficiency is possible by sacrificing the pattern, as indicated with the half sine distribution shown in Fig. 8. Another practical limitation is the difficulty of avoiding the excitation of (both propagating and non-propagating) modes other than the desired pair of coupled waveguide modes. It is unfortunately true that, when the guide is opened to free space, the choice of waveguide size and aspect ratio cannot be relied upon to suppress all except the dominant mode. Experimental measurements, such as those indicated in Fig. 9, of the aperture distribution of a single uncoupled waveguide (dielectric-loaded with a long slot in the broad wall) clearly indicate the presence of at least two propagating modes. Furthermore, a surface wave mode has been noted in single 5 guides with transverse slots opening to free space. Besides this, coupled waveguides of convenient size usually have an overall dimension Which is less favorable with respect to higher order mode suppression than is standard waveguide, for example. Naturally, the presence of more than the two desired modes limits the extent to which the simple coupled waveguide ideas can be applied. Extra surface wave modes may not ruin the patterns, however. The difficulties with unwanted mode excitation seem to be more serious when the radiating guide is directly excited while the coupled guide is not. In most of the experimental work, the coupled guide is connected to CA!2^ 18 L Z FIGURE 8a HALF SINUSOIDAL AMPLITUDE DISTRIBUTION AL . TT 2 " 2 FIGURE 8b SPACE FACTOR FOR AMPLITUDE DISTRIBUTION OF FIGURE 8a, i.e., TWO ^jj — CURVES DISPLACED ~t - \ AND ADDED 90° OUT OF PHASE [A(Z\] A- ^s\ / \ / \ ' N / \ / \ / ^ / v/ v 1 -I — IOA, 30A, FIGURE 9 APERTURE DISTRIBUTION ON SINGLE DIELECTRIC "LOADED GUIDE. GUIDE IIAS LONG SLOT APPROXIMATELY X./4 IN WIDTH (Experimental) 19 the oscillator. Another limitation of the coupled waveguide radiators is their very limited bandwidth. The phase velocities of the normal modes and the beat wavelength are frequency dependent, the latter often very strongly. Finally, a constructional difficulty should be mentioned. Since it is difficult to maintain the symmetrical location of a long slot in the waveguide wall, it is correspondingly difficult to produce the expected pattern symmetry. 20 6, EXPERIMENTAL RESULTS We now present examples of measured aperture distributions and radiation patterns of structures of the types shown in Fig. 1, Figures 10 and 11 indicate the extent to which the general ideas of coupled transmission line theory represent some experimental results on open waveguide structures. Figure 10 gives the envelope of the experimental aperture distribution as recorded with the apparatus indicated in Fig. 7. The same type of information is presented in Fig. 11 in the dotted curve; Fig. 11 also indicates the correlation between the aperture distribution in one guide and the input to output attenuation in the other guide, as the length of the coupling interval is increased. (For further details, see reference 4). The geometry for the radiation patterns is shown in Fig. 2. All of the patterns presented here are taken in the plane of the conducting sheet; polarization is perpendicular to the conducting sheet. Figure 12 shows the experimental approximation to the sine tapered distribution of Fig. 3a, together with the experimental radiation pattern. The side lobes in the pattern are somewhat higher than those of an ideal sine tapered distribution, but the main features of the pattern are well predicted by the theory. Figure 13 gives experimental results for the same antenna as the frequency is increased to the point at which c/v is greater than one (slight supergain condition). The pattern is thereby narrowed appreciably, while the side lobes, although higher, are still acceptable for some applications. Figure 14 gives the geometry of the waveguide cross section at 8200 mc. Coupling is obtained by closely spaced holes. Figure 15 is the radiation pattern of the antenna whose aperture distribution is given in Fig. 11. This pattern is presented not because it is the pattern of a particularly favorable aperture distribution but because it is an example of the fact that coupled waveguide excitation provides a means of tilting the beam of a surface wave type structure, a problem which 6 is of some currant interest . The propagating mode of the radiating waveguide (Figs, la and 14) is a slow wave; hence, by itself it could give only ;m end fire beam. One of the normal modes of the coupled system can be fast, however, and hence can give radiation at a real angle. In this case 1 ow< r guide (Fig. M) was about 72% loaded with polystyrene. Solid line - ideal distribution 21 [A(zTl' Dashed line-envelope of experimental . =• 1 .07 lOA d ZOXc 50\ FIGURE 10 APERTURE DISTRIBUTION Structure of Figure 14; Frequency 9500 mc [awT oe. p(jO i.o Dashed Line - Envelope of aperture distribution of coupled guide. (Experimental) -Power measured in \0 r-a 20X Q Solid line coupled guide with varying lengths of coupling. (Experimental) 30A a FIGURE 11 COMPARISON OF APERTURE DISTRIBUTION IN ONE GUIDE WITH POWER VARIATION IN THE OTHER GUIDE. Geometry as in Figure 14, except — = .7 and Frequency = 9300 mc 22 §=0 LAfz>] .Solid Linrok<2n Lin*, li £nv<2.c c _ 20X.Z FIGURE 12a APERTURE DISTRIBUTIONS FIGURE 12b RADIATION PATTERN 6 = OUl] 8S00 tr\c/<>a.c- \ / -*— ( — i — i — i — i — i — i — i — i — i — i — i — \0\ a 20\ Q Z FIGURE 13a APERTURE DISTRIBUTIONS FIGURE 13b RADIATION PATTERN 23 [ — J-jA^ NNNX^\\W \N\ \\ Air-^ •47X A FIGURE 14 WAVEGUIDE CROSS SECTION FOR ANTENNA OF FIGURES 12 AND 13 FIGURE 15 PATTERN OF ANTENNA OF FIGURE 11 Note that beam is not end fire, even though antenna is surface wave type c (; = 1.03) a 24 Figure 16 summarizes the results of an attempt to produce a distribution of a different type. The object was to create a distribution which had a 7 "pedestal" at the ends, a feature which Taylor has pointed out is one of the requisites for an optimum pattern from a line source. This type of distribution appears, in practice, to be one of the more difficult to produce by coupled waveguide excitation. In this case the waveguides were coupled by a long slot, and the radiating aperture was a long slot in the broad face. The radiating guide was connected to the oscillator and coupling was started before the radiating aperture was begun, in order to obtain the "pedestal «" Figure 17 shows a radiation pattern of a coupled waveguide system with spaced hole radiators. The details are given in the figure. The strong lobe in the generally backward direction is characteristic of such discrete arrays when the mode phase velocities are less than c. Figure 18 gives the results when the phase velocities of the modes are such as to make individual contributions to the pattern. The experimental pattern and aperture distribution correlate fairly well — the angles of the main lobes are predicted to within about a degree. Also shown in Fig. 18 is a pattern calculated by assuming that an antenna of the same length had an ideal aperture distribution of the type shown in Fig. 4a, with a c/v of F 945. The agreement of the main features is evident. In fact, at a slightly different frequency the level of the lobe at in the experimental pattern was found to be lower than that of the tilted lobes, as predicted in the calculated pattern. 25 FIGURE 16a RADIATION PATTERNS Dashed line, one half of experimental^ Solid line, one half of calculated space factor of distribution in Figure 16b, plus effect of unit pattern. FA(z)] 2 FIGURE 16b APERTURE DISTRIBUTIONS Dashed line, experimental; radiating guide fed. Solid linej idealized, from which pattern of Figure 16a is calculated. (Distribution with a pedestal at the ends) .2.&X. RadiatiMg Slot FIGURE 16c GEOMETRY OF THE WAVEGUIDE CROSS SECTION. Antenna of Figures 16a and 16 b. Frequency 10 . 6 kmc . „ 7 7-77-7"/ — .18 X .22K .2SA. • 25.K- *L1A \ Covjp*!^ ^>lcrt 26 $--o -H.io FIGURE 17a EXPERIMENTAL RADIATION PATTERN Spaced hole radiators with an amplitude distribution, as in Figure 3a. Closely spaced hole coupling. Pair of WR 62 Guides Half Wall Milled Away, FIGURE 17b GEOMETRY OF WAVEGUIDE CROSS SECTION. Frequency-11 . 6 kmc. 27 *-o 17.5° 19' Many lobes, with decreasing amplitudes Experimental Pattern Calculated pattern using ideal amplitude distribution of Figure 4a , _£_ = .945 F [Afe)]' i i t-rom probe, measurements %= r.04- % - .94.4. I / N > 10 \, \._— cTOK, FIGURE 13 PATTERN AND APERTURE DISTRIBUTION OF ANTENNA OF FIGURE 14, EXCEPT WITH SLOT COUPLING, Frequency - 8600 mc/sec 28 7. DESIGN DATA Figures 19 and 20 include a series of curves which are useful in the design of antenna structures of this type. The curves in Fig. 19 give phase velocities in uncoupled guides having the cross sections indicated. These experimental results are composites of probe measurements and radiation pattern measurements. They indicate the extent to which the theoretical results of Fig. 5 can be used in the design of waveguides with openings to free space. The data in Fig. 20 can be used to get a rough indication of the phase velocities of the important propagating modes in the open, coupled -\ Av. waveguide systems indicated. The quantities given (c/v = ■**■ and -=r-) can a A A be inserted in Eqs. (11) and (12) to get the desired information . It is interesting to observe the difference in the behavior of long slot and hole coupling (similar behavior has been indicated in closed waveguides). It is found that the beat wavelength is quite sensitive to hole size. Details of the effect of hole size can be found in reference 4. 8 . ACKNOWLEDGEMENTS It is a pleasure to acknowledge helpful discussions with P. E. Mayes and V.H. Rumsey and the invaluable assistance of J. Stafford and W. Hartley in the experimental measurements. 29 20 .10 •00 ■ 90 M> U 1 .60 0) o •70 .60 .7cm uxdujAu-Lilj -i- P I Air 4 h — 1.7cm GV^ .9 1.0 1.1 x _ 2a I.Z ,7Cfc> — I v«|.0 .9 n 1- y-.-4-Ta .slot \ coupling ^ t\y.47a hole \\ coupling ^ t EO A 10 .& .9 A, I.O i.i .7 Za r.47a slot coupling - .47a hole coupling -7 K \ / yr .e> .3 1.0 i.t ..9fc> --.47a slot T" 1.5 1.2 "" ^Vyr-^rte v > \.\ \Ij \.47a hole coupling 5o X 10 ,47a hole coupling -1 ..1 7 .& .9 I.O 1. 1 .7 .6 .9 1.0 I.I FIGURE 20 EXPERIMENTAL VALUES OF PHASE VELOCITIES AND BEAT WAVELENGTHS FOR THE WAVEGUIDE GEOMETRY INDICATED 31 REFERENCES 1. Walter, C.H. , "An End Fire Slot Antenna," Ohio State University Research Foundation, Technical Report No, 486-12. 2. Hines, J.N.,Rumsey, V.H. and Walter, C„H. "Traveling Wave Slot Antennas," Proceedings of IRE, Vol, 41, November 1953. 3. Royal, D.E., "Axially Excited Surface Wave Antennas," University of Illinois, Antenna Laboratory, Technical Report No, 7, 10 October 1955. 4. Hodges, R.R. "Distributed Coupling to Surface Wave Antennas," University of Illinois, Antenna Laboratory, Technical Report No. 15, 5 January 1957. 5. Hynemann, R.F. , "Closely-Spaced Transverse Slots in Rectangular Waveguide," University of Illinois, Antenna Laboratory, Technical Report No. 14, 10 December 1957. 6. Thomas, A.S. and Zucker, F.J. IRE National Convention Record, Vol. 5, Part 1, p. 153, 1957. 7. Taylor, T.T., Trans. IRE, Professional Group on Antennas and Propagation, Vol. AP-3, p. 16, January 1955. 8. Barkson, J. A. "Coupling of Rectangular Waveguides Having a Common Broad Wall Which Contains Uniform Transverse Slots," Ph.D. Thesis, University of Illinois, 1957. (Also available as technical report, Hughes Aircraft Company). 9. A very complete set of curves of this type will appear in a forthcoming University of Illinois Technical Report, 32 APPENDIX A COUPLED TRANSMISSION LINE EQUATIONS To the extent that we can apply the distributed circuits concepts to field problems, we can write the equations dV l dT" = " z n h + Z 12 h dI l "di " " Y ll V l + Y 12 V 2 where V and I represent the voltage and current on one line, Z, is the self impedance of the first line (in the presence of the second line), z n is the mutual impedance between the pair of coupled lines, and Y and Y XX X <-I are the corresponding admittances. A similar pair of equations with subscripts 1 and 2 interchanged holds for the second line. From these equations, we find the results ■ = (z, , Y„ + Z no Y„, ) V, -|Z, _ Y„„ + Z, , V n | V, [• 2 12 21' 12 22 " = (Z o0 Y 00 + Z 01 Y n _) V -|Z_, Y 2 v 22 22 21 12' 2 | 21 11 dz If we introduce substitutions as follows: - \ • (Z 11 Y ll ♦ Z 12 Y 21> - °12 2 = (Z 12 Y 22 + Z ll Y 12 ) [ Z 2! Y U + Z 22 Y 2l] V l " V 2 2 ' 33 we obtain the Eqs. (1). If the transmission lines are identical, Eqs. (1) take the form d \ 2 2 -2" - " "i V l + C V 2 dz d \ 2 2 — = - V v 2 + c v dz and the solution can be found in any number of textbooks. The next appendix (B) presents the detailed solution for the general case, a problem which seems to be less completely treated. 34 APPENDIX B NORMAL MODE SOLUTIONS TO THE GENERAL COUPLED TRANSMISSION LINE EQUATIONS It was shown in Appendix A that the coupled transmission line equations can be put into the form d 2 V i = -Y 2 V + c 2 V ^ 2 1 1 12 2 dz > (B-l) d V 2 a 2 dz^ * 2 21 1 J We will present here a few of the details of the normal mode solution to this problem. In this process, we look for new variables, V and V , which satisfy F S uncoupled equations, in terms of which we can write V and V . To . ': J- £* facilitate the process, we will use the matrix notation, and diagonalize the matrix. In the matrix notation (B-l) becomes dz 2 and we are looking for (J . such that and ,2 ■w (B-3) d X dz" whereby is a diagonal matrix. From (B-2) and (B-3) we find the result dz J X ^ -wiK (B-5) dz" ' ' J Then we must have the relation mn-n? m 35 These conditions result in a set of equations for the elements of J7 V which, for a solution to exist , must have the following determinant equal to zero **« " 7 kk 5 i. = = (V - Y k 2 ) '21 12 2 2 -(Y — Y ) v 2 k' so 2 Yi 2 + Y 2 2 1 2 2 ±2Y - 4 (\ x Y 2 2, 2 c 21 ~12 ' We find thereby the propagation constants of the normal (uncoupled) modes as follows Y F = + V* Yl 2 + Y 2 2 1 J 2 v 2 2 j . 2 2 2 ~ 2 V< Y 1 " Y 2 ) ♦ 4c 21 c 12 i Y 2 , Y 2 1 T 2 1_ l 2 (B-7) IV ( V-V> +4c 2i 2c i 2' 2 V The voltages on the lines are found in terms of the uncoupled voltages as follows (assuming propagation in one direction only) V = A e~ J FZ + B e V 2 = Yj _ Y F JY s z jY F z + ^ 2 2 2 2 -jY fZj _ *1 - Y S Be -jY s z > 12 12 (B-8) J The constants A and B are found from the application of conditions on V and V at z = J- £t 36 APPENDIX C COMPOSITE ANTENNAS During the course of this work, antennas in which the length of the radiating aperture was longer than the length of the coupling region were briefly investigated for two reasons: (1) as a means of increasing radiation efficiency, and (2) as a means of launching a pure mode in the uncoupled section of the radiating guide. It was found that indeed the radiation efficiency can be increased — usually with a sacrifice in desirable pattern characteristics, however,, The predominant radiating mode can also be changed by varying the length of coupling. Some typical results of such studies can be found in Figs. 16 to 20 of reference 4. This structure is fundamentally more complicated than the ones described in this report, since, at its simplest, there exist the pair of modes in the coupled region and a single mode in the uncoupled region, each with its contribution to the radiation pattern. It is also worth noting that there is, on file at the University of Illinois Antenna Laboratory, a considerable amount of radiation pattern information on the effect of (1) length of aperture, and (2) frequency on the radiation patterns of these structures. In this work, the criterion for the identification of a distinct propagating mode was that the angular position of a main lobe in the pattern be independent of aperture length and/or have the proper variation in frequency. Incidentally, no effects in the patterns were noted which unequivocally indicated the presence of higher order non-»prapagating modes. 37 APPENDIX D SCANNING A COUPLED WAVEGUIDE ANTENNA There is an interesting (but as yet untried) possibility for electrically scanning a traveling wave slot antenna with coupled waveguide excitation. The beam movement is made possible by the fact that, as pointed out in this report, the total field is made up of the fields Of two TW line sources having different phase velocities, and hence different angular positions of their main lobes. Thus, if the relative amplitudes of the normal modes could be easily controlled, the direction of the maximum could be shifted. Such control of the relative amplitude of the normal modes is possible in closed 8 i0 waveguides. For example, if we apply the conditions V = 1, V = e at z = 0, to Eqs. (B-8), and use Eqs. (B-7), we find the result for the amplitudes of the normal modes A = 2 j0 C 12 e 2 2 *1 "Y 2 - IV ( Vi 2 - Yo ) + 4c i 2 2 C 21 ^ y 2 V A 2 ' (y x - y 2 > + 4c 12 c 2i > \ "V 2 B = 1/2 22 + 2 Y ( Yi -v 2 } + 4c 2 2 12 C 21 2 J0 " C 12 e 2, 2 1 Y (Y 1 " Y 2 } + 4C 12 C 21 7 (D-l) Thus, the simultaneous excitation of both guides, as indicated, for example^ in Fig. D-l, allows a phase difference to be translated into an amplitude difference in the normal modes. This is particularly evident in the special case of coupling between identical lines (which obey the reciprocity theorem) For in that case, v = v , c = c , so that the normal mode amplitudes -L A -L £ Ax. reduce to the form < A j(f) J 2 A = 1 + e Jr = 2e cos- 3 J 2 d> B = 1 - e°^ = 2je sin ^ > (D-2) J 38 O x Variably Phasd. £jhi-ft<2.r it ■ ? 3 i>&s ilouplar jybi-id Junction, 01- Oth«.r Power Splitter .Ab. 3?aeiicl+mg Ap+a*--V o£ Coupling FIGURE D-l. SCHEMATIC DIAGRAM OF COUPLED WAVEGUIDE PHASE CONTROLLED SCANNER Also, it appears from Eqs. (B-8) that a point of maximum field in one line and a point of minimum field in the other line appear at a distance of \ — down the line from z = (start of coupling), independent of the phase , o o difference, except in the event that (p = or 180 , in which case there is a pure mode excitation of one type or the other. Therefore, if we begin a radiating aperture (of length L = X, ) at a position — down the line (at a minimum) from the start of the waveguide coupling, we can find the resultant sin 4* space factor by the superposition (in phase) of a pair of . curves displaced by an amount ^ = 77, and with relative amplitudes $ ¥ - tan *. Figure D-2 gives an indication of the manner in which the space factor could be expected to change as the phase shifter in one of the lines is varied so as to produce o o . a phase difference which varies from to 180 . Figure D-3 gives the y- value of the maximum in the space factor as a function of phase difference. Figure D-4 gives the (calculated) results in terms of angle with the line of the array for a particular design-- namely , one in which we assume L/\ a 10, — ■ .9, and — ■ 1.0. F S FIGURE D-2 SPACE FACTOR OF BEAM IN SCANNING CYCLE Phase difference (& o M FIGURE D-3 UNIVERSAL SCAN FUNCTION AS FUNCTION OF COUPLED GUIDE PHASE DIFFERENCE 30 r TT O 20 4o '-*o ic»o »©o 2>oo Ac/) FIGURE D-4 SCAN ANGLE VS. PHASE DIFFERENCE, L — = .9, — = 1.0, t- 10 F S DISTRIBUTION LIST FOR REPORTS ISSUED UNDER CONTRACT AF33 (616) -3220 One copy each unless otherwise indicated Armed Services Technical Information Agency Knott Building 4th & Main Streets 4 and 1 repro. Dayton 2, Ohio ATTN: TIC-SC (Excluding Top Secret and Restricted Data) (Reference AFR 205-43) Commander Wright Air Development Center Wright-Patterson Air Force Base Ohio 3 copies ATTN: WCLRS-6, Mr. W.J. Portune Commander Wright Air Development Center Wright-Patterson Air Force Base Ohio ATTN: WCLN, Mr, N. Draganjac Commander Wright Air Development Center Wright-Patterson Air Force Base Ohio ATTN: WCOSI, Library Director Evans Signal Laboratory Belmar, New Jersey ATTN: Technical Document Center Commander U.S. Naval Test Center ATTN: ET-315 Antenna Section Patuxent River, Maryland Chief Bureau of Aeronautics Department of the Navy ATTN: Aer-EL-931 Commander Hq, A.F., Cambridge Research Center Air Research and Development Command Laurence G„ Hanscom Field Bedford, Massachusetts ATTN: CRRD, R.E. Hiatt Commander Air Force Missile Test Center Patrick Air Force Base Florida ATTN: Technical Library Director Ballistics Research Lab. Aberdeen Proving Ground Maryland ATTN: Ballistics Measurement Lab. Office of the Chief Signal Officer ATTN: SIGNET- 5 Eng. & Technical Division Washington 25, D.C. Commander Rome Air Development Center ATTN: RCERA-1D. Mather Griffiss Air Force Base Rome, NY. Airborne Instruments Lab. , Inc. ATTN: Dr E.G. Fubini Antenna Section 160 Old Country Road Mineola, New York M/F Contract AF33 (616)-2143 Andrew Alford Consulting Engrs. ATTN. Dr. A. Alford 299 Atlantic Ave. Boston 10, Massachusetts M/F Contract AF33 (038)-23700 Chief Bureau of Ordnance Department of the Navy ATTN: Mr. C.H. Jackson, Code Re 9a Washington 25, D.C. Bell Aircraft Corporation ATTN: Mr. J D. Shantz Buffalo 5, New York M/F Contract W~33 (038)-14169 DISTIRBUTION LIST (CONTINUED) AF33 (616)-3220 One copy each unless otherwise indicated Chief Bureau of Ships Department of the Navy ATTN: Code 838D, L.E. Shoemaker Washington 25, D,C. Director Naval Research Laboratory ATTN: Dr. J.I. Bohnert Anacostia Washington 25, D.C. National Bureau of Standards Department of Commerce ATTN: Dr. A.G. McNish Washington 25, D.C. Director U.S. Navy Electronics Lab. Point Loma San Diego 52, California Commander USA White Sands Signal Agency White Sands Proving Command ATTN: SIGWS-FC-02 White Sands, N.M. Consolidated Vultee Aircraft Corp. Fort Worth Division ATTN: C.R. Curnutt Fort Worth, Texas M/F Contract AF33 (038)-21117 Textron American, Inc. Div. Dalmo Victor Company ATTN: Mr. Glen Walters 1414 El Camino Real San Carlos, California M/F Contract AF33 (038) -30525 Dome & Margolin 29 New York Ave. Westbury Long Island, New York M/F Contract AF33 (616)-2037 Raytheon Manufacturing Company ATTN: Robert Borts Wayland Laboratory, Wayland, Mass. Douglas Aircraft Company, Inc. Long Beach Plant ATTN: J.C. Buckwalter Long Beach 1, California M/F Contract AF33(600)-25669 Boeing Airplane Company ATTN: F. Bushman 7755 Marginal Way Seattle, Washington M/F Contract AF33 (038)-31096 Chance-Vought Aircraft Division United Aircraft Corporation ATTN: Mr. F.N. Kickerman THRU: BuAer Representative Dallas, Texas Consclidated-Vultee Aircraft Corp. ATTN: Mr. R.E. Honer P.O. Box 1950 San Diego 12, California M/F Contract AF33 (600)-26530 Grumman Aircraft Engineering Corp. ATTN: J.S, Erickson, Asst. Chief, Avionics Dept. Bethpage Long Island, New York M/F Contract NO(as) 51-118 Hallicraf ters Corporation ATTN. Norman Foot 440 W. 5th Avenue Chicago, Illinois M/F Contract AF33(600)-26117 Hoffman Laboratories, Inc. ATTN: S. Varian Los Angeles, California M/F Contract AF33 (600)-l7529 Hughes Aircraft Corporation Division of Hughes Tool Company ATTN: D. Ad cock Florence Avenue at Teale Culver City, California M/F Contract AF33 (600) -27615 DISTRIBUTION LIST (CONTINUED) AF33 (616) -3220 One copy each unless otherwise indicated Illinois, University of Head, Department of Elec. Eng. ATTN: Dr. E.C. Jordan Urbana, Illinois Johns Hopkins University Radiation Laboratory ATTN: Librarian 1315 St. Paul Street Baltimore 2, Maryland M/F Contract AF33(616)-68 Electronics Research, Inc. 2300 N. New York Avenue P.O. Box 327 Evansville 4, Indiana M/F Contract AF33 (616)-2113 Glenn L. Martin Company Baltimore 3, Maryland M/F Contract AF33 (600)-21703 Northrop Aircraft Incorporated ATTN: Northrop Library Dept. 2135 Hawthorne, California M/F Contract AF33 (600)-22313 Radioplane Company Van Nuys, California M/F Contract AF33 (600)-23893 Lockheed Aircraft Corporation ATTN: C.L. Johnson P.O. Box 55 Burbank, California M/F NOa(S) -52-763 Republic Aviation Corporation ATTN: Engineering Library Farmingdale Long Island, New York M/F Contract AF33 (038)14810 McDonnell Aircraft Corporation ATTN: Engineering Library Lambert Municipal Airport St. Louis 21, Missouri M/F Contract AF33 (600) -8743 Michigan, University of Aeronautical Research Center ATTN: Dr. L. Cutrona Willow Run Airport Ypsilanti, Michigan M/F contract AF33 (038)-21573 Massachusetts Institute of Tech. ATTN: Prof. H.J. Zimmermann Research Lab. of Electronics Cambridge, Massachusetts M/F Contract AF33 (616)-2107 North American Aviation, Inc. Aerophysics Laboratory ATTN: Dr. J. A. Marsh 12214 Lakewood Boulevard Downey, California M/F Contract AF33 (038)-18319 North American Aviation, Inc. Los Angeles International Airport ATTN: Mr. Dave Mason Engineering Data Section Los Angeles 45, California M/F Contract AF33 (038)18319 Sperry Gyroscope Company ATTN: Mr. B Berkowitz Great Neck Long Island, New York M/F Contract AF33 (038)-14524 Temco Aircraft Corp. ATTN: Mr, George Cramer Garland, Texas (Contract AF33 (600)-21714) Farnsworth Electronics Co. ATTN: George Giffin Ft. Wayne, Indiana Marked: For Con. AF33 (600)-25523 North American Aviation, Inc„ 4300 E. Fifth Ave. Columbus, Ohio ATTN: Mr. James D. Leonard Contract NO(as) 54-323 Stanford Research Institute Document Center Menlo Park, California ATTN: Mary Lou Fields, Acquisitions Westinghouse Electric Corporation Air Arm Division ATTN: Mr. P.D. Newhouser Development Engineering Friendship Airport, Maryland Contract AF33 (600)-27852 page 4 DISTRIBUTION LIST (CONT.) AF33(616)-3220 One copy each unless otherwise indicated Ohio State Univ. Research Foundation ATJTJ: Dr T.C Tice 310 Administration Bidg. Ohio State University Columbus 10, Ohio M/F Contract AF33(616)-3353 AlJ° Force Development Field Representative ATTN l Capt. Carl B. Ausfahl Code 1010 Naval Research Laboratory Washington 25, D.C. Chief of Naval Research Department of the Navy AJTOg Mr. Harry Harrison Code 427, Room 2604 Bldg. T-3 Washington 25, D.C. Beech Aircraft Corporation ATTN: Chief Engineer GS00 E. Central Avenue Wichita 1 , Kansas M/F Contract AF33(600)-20910 Land-Air Incorporated Cheyenne Division ATTN: Mr. R.J. Klessig Chief Engineer Cheyenne, Wyoming M/F Contract AF33(600)-22964 Director, National Security Agency RADE 1 GM, ATTN: Lt. Manning Washington 25, D.C. Melpar, Inc. 3000 Arlington Blvd. Fails Church, Virginia ATTN: K.S. Kelleher Naval Air Missile Test Center Point Mugu, California ATTN: Antenna Section Fairchild Engine & Airplane Corp. Fairchild Airplane Division ATTN; L. Fahnestock Hagerstown, Maryland M/F Contract AF33(038)-18499 Federal Telecommunications Lab. ATTN: Mr. A. Kandoian 500 Washington Avenue Nutley 10, New Jersey M/F Contract AF33(61S)-3071 Ryan Aeronautical Company Lindbergh Drive San Diego 12, California M/F Contract W-33(038)-ac-21370 Republic Aviation Corporation ATTN: Mr. Thatcher Hicksville, Long Island, New York M/F Contract AF18(600)-1602 General Electric Co. French Road Utica, New York ATTN: Mr. Grimm, LMEED M/F Contract AF33(600)-30632 page 5 DISTRIBUTION LIST (CONT„ ) AFS3(616)-3220 One copy each unless otherwise indicated Stanford Research Institute Southern California Laboratories ATTN; Document. Librarian 820 Mission Street South Pasadena, California Con tract AF19(604)~1296 Prof . J . R , Whinner y Dept. of Electrical Engineering University of California Berkel ey , Cal 2 f orni a Professor Morris Kline Mathematics Research. Group New York University 45 Astor Place New York, N.Y. Prof. A. A, Oliner Microwave Research Institute Polytechnic Institute of Brooklyn 55 Johnson Street - Third Floor Brooklyn, New York Dr. C.H. Papas Dept „ of Electrical Engineering California Institute of Technology Pasadena, California Electronics Research Laboratory Stanford University Stanford, California ATTN; Dr. F.E. Terman Radio Corporation of America R.C.A. Laboratories Division Princeton, New Jersey ATTN; Librarian Electrical Engineering Res. Lab. University of Texas Box 3026, University Station Austin, Texas Dr Robert Hansen 8356 Chase Avenue Los Angeles 45, California Technical Library Bell Telephone Laboratories 463 West St. New York 14, N.Y. Dr. R.E, Beam Microwave Laboratory Northwestern University Evanston, Illinois Department of Electrical Engineering Cornell University Ithaca, New York ATTN; Dr. H.G. Booker Applied Physics Laboratory Johns Hopkins University 8621 Georgia Avenue Silver Spring, Maryland Exchange and Gift Division The Library of Congress Washington 25, D.C Ennis Kuhlman c/o McDonnell Aircraft P.O. Box 516 Lambert Municipal Airport St Louis 21, Mo, Physical Science Lab. New Mexico College of A and MA State College, New Mexico ATTN; R„ Dressel Technical Reports Collection 303 A Pierce Kail Harvard University Cambridge 38, Mass. ATTN; Mrs. M.L. Cox, Librarian Dr. R.H. DuHamel Collins Radio Company Cedar Rapids, Iowa Dr . R . F , Hyneman 8725 Yorktown Avenue Los Angeles 45, California UNIVERSITY OF ILLINOIS URBANA Q.621 365IL655TE C002 TECHNICAL REPORT$URBANA 27 1957 3 0112 008079300