L I B RAHY 
 
 OF THE. 
 
 U N IVLRSITY 
 
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 no. 2- 14 
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Digitized by the Internet Archive 
 in 2013 
 
 http://archive.org/details/techniqueforcont11dunc 
 
Antenna Laboratory 
 Technical Report No. 11 
 
 A TECHNIQUE FOR CONTROLLING THE RADIATION 
 FROM DIELECTRIC ROD WAVEGUIDES 
 
 by 
 
 J„ W. Duncan 
 R. H„ DuHamel 
 
 15 July 1956 
 
 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 
 
ABSTRACT 
 
 This paper describes a technique for controlling the radiation from 
 a dielectric rod waveguide by placing obstacles or antenna elements at 
 appropriate points along the waveguide. The HEn mode on a dielectric 
 rod was used to excite concentric rings and slots, and radial wires. The 
 coupling of the obstacles to the HE-, i mode was determined by constructing 
 an image line with a slotted section for impedance measurements. This 
 information was used to design several antenna arrays with different 
 types of patterns. The measured patterns were very satisfactory. 
 
 1 1 
 
CONTENTS 
 
 Page 
 
 Abstract ii 
 
 1. Introduction 1 
 
 2. The Dielectric Rod Waveguide 3 
 
 3. Measurement of the Obstacle Admittance 5 
 
 4. Array Designs and Results 19 
 
 5. Surface Wave Exciters 29 
 
 6. Conclusions 32 
 Bibliography 33 
 Distribution List 
 
 ill 
 
ILLUSTRATIONS 
 
 Figure 
 
 Number Page 
 
 1. Approximate Electric Field Configuration of the HEn Mode 
 
 on a Dielectric Rod Waveguide 3 
 
 2. Characteristic Curves for Symmetrical and Unsymmetrical or 
 Hybrid Modes on a Dielectric Rod 4 
 
 3. Diagram of the Equipment Used to Measure Obstacle Admittance 6 
 
 4. Apparatus for Measuring the Coupling of Obstacles to the 
 Dielectric Rod Waveguide 7 
 
 5. The Slotted Section 7 
 
 6. Slots and Rings for the Image Line 8 
 
 7. Shunt Admittance of a Ring as a Function of the Mean Ring 
 Radius 9 
 
 8„ Shunt Admittance of a Slot as a Function of the Mean Slot 
 
 Radius 11 
 
 9o Shunt Admittance of a Vertical Wire as a Function of the 
 
 Wire Length 12 
 
 10. Shunt Admittance of a Wire as a Function of the Wire Length 13 
 
 11. Normalized Shunt Conductance of Resonant Wires as a Function 
 
 of the Spacing from the Ground Plane 14 
 
 12. Shunt Admittance of an Inclined Wire as a Function of the 
 
 Wire Length 15 
 
 13 . Normalized Shunt Conductance of a Resonant Wire as a 
 
 Function of the Angle of Inclination 16 
 
 14. Length of Resonant Wire as a Function of the Angle of 
 Inclination 18 
 
 15. The Dolph -Tchebycheff and Cosecant, Arrays 19 
 
 16. Radiation Pattern of a Uniform Broadside Array with 12 
 Elements at Guide Wavelength Spacing 21 
 
 17. Transverse Radiation Patterns for Uniform Arrays 22 
 
 18. Radiation Pattern of a 20 db Dolph Tchebycheff Broadside 
 
 Array for 12 Elements with Guide Wavelength Spacing 23 
 
 19. An End View of the Doiph -Tchebycheff Array 24 
 
 20. Radiation Pattern of a Nonresonant Uniform Array with 12 
 Elements with an Element Spacing of 0.75 A 25 
 
 21. Design Curves for a Cosecant Pattern 27 
 
 IV 
 
ILLUSTRATIONS (Cont. ) 
 
 Figure 
 Number 
 
 Page 
 
 22. Radiation Pattern of a 13-Element Array Designed to Produce 
 
 a Cosecant Pattern 28 
 
 23. Equivalent Transmission Line Representation of a Transverse 
 
 Ring or Wire Acting as a Source on the Rod Waveguide 29 
 
 24. Launching Efficiency of a Ring, Annular Slot and Vertical Wire 31 
 
1 . INTRODUCTION 
 
 During recent years, increasing use has been made of surface wave 
 antennas. Examples are corrugated surfaces, dielectric rods and tubes, 
 dielectric coated conductors, dielectric slabs, etc Most surface wave 
 antennas have been designed for endfire or near endfire radiation. Only 
 minor success has been obtained in controlling the radiation from sur- 
 face wave antennas in directions other than endfire. The objective of 
 this work has been to devise methods of modifying surface waveguides in 
 such a manner that accurate control of the radiation can be obtained. 
 
 Mueller 1 succeeded in obtaining broadside radiation from a dielec- 
 tric rod antenna by means of placing dielectric disks on the rod with 
 approximately half -wavelength spacing between the disks. Although his 
 simple array theory predicted the direction and width of the main beam 
 with fair accuracy, control of the side lobe level could be obtained 
 only on an empirical basis. A disadvantage of the dielectric disks was 
 that the polarization was a function of the circumferential angle. 
 
 It is believed that the technique described in this paper will allow 
 accurate designs of modified surface wave antennas. The method is simi» 
 lar to Mueller's in that obstacles or discontinuities are placed at 
 appropriate points along the waveguide in order to force and control the 
 radiation. If an obstacle, such as a piece of metal, is placed near an 
 excited surface waveguide, it will radiate and will also excite surface 
 waves. By choosing the proper waveguide dimensions and/or choosing 
 obstacles with a certain symmetry, all surface wave modes except one may 
 be made negligible* The antenna system may then be represented by a 
 single transmission line loaded at the appropriate point by the equivalent 
 obstacle four pole network. If the axial length of the obstacle is 
 small, its equivalent, admittance is a simple shunt element. Knowledge 
 of the radiation pattern and the equivalent admittance of the obstacle 
 would allow a simple, straightforward design of arrays of the obstacles 
 to produce specified patterns. In some cases it may also be necessary 
 to take into account the effect of the mutual admittance between the 
 obstacles. 
 
 Briefly, the work to be described is the following: The coupling 
 of wires, rings, and slots to the HE^* mode on a dielectric rod waveguide 
 was measured. This information was then used to design several arrays to 
 produce various types of patterns. The arrays were constructed and 
 
 -1. 
 
tested. Good agreement between the predicted and measured patterns was 
 obtained. Finally, the excitation efficiencies of several types of sur- 
 face wave exciters were compared. 
 
2. THE DIELECTRIC ROD WAVEGUIDE 
 
 The dominant HE X1 (or dipole) mode on a dielectric rod is a hybrid 
 mode which has axial components of both the electric and magnetic field 
 intensities, and is unsymmetrical in that all field components vary as 
 the sine or cosine of the circumferential angle, 0. The electric field 
 configuration of the HEn mode on a dielectric rod is shown in Fig. 1. 
 The cutoff wavelength of a particular mode on the dielectric rod is a 
 function of the rod radius, b, and the operating frequency or wavelength, 
 X. Characteristic curves showing the variation of \-/\, the ratio of the 
 
 Figure L Approximate Electric Field Configuration of the HE | 
 Mode on a Dielectric Rod Waveguide (From Reference 
 
guide wavelength to the operating wavelength as a function of the param- 
 eter b/X are plotted in Fig. 2. The curves are for the symmetrical E i, 
 Hoi, Eo2» and H02 modes, and the unsymmetrical HEn, HEi 2 , and EH12 
 modes. The symmetrical modes on a dielectric rod are either transverse 
 electric or transverse magnetic and the field intensities are independ- 
 ent of the angle 9. 
 
 Figure 2. Characteristic Curves for Symmetrica 
 and Unsymmetrical or Hybrid Modes on 
 a Dielectric Rod (From Reference 2) 
 
3, MEASUREMENT OF THE OBSTACLE ADMITTANCE 
 
 The dielectric rod waveguide was utilized to investigate modified 
 surface wave antennas for two reasons.. First, the rod has a simple 
 geometry for which theoretical solutions are available. Second, by 
 using an image system,, accurate standing wave measurements may be made 
 along the rod by means of a slotted section in the ground plane.. 
 Figure 3 illustrates the arrangement of equipment which was used to 
 measure the equivalent shunt admittance of the various types of ob- 
 stacles.. Figure 4 is a photograph of the microwave equipment and di- 
 electric image line. Shown from left to right are the signal oscillator 
 and associated rectangular waveguide test equipment, the horn exciter, 
 the dielectric rod image line, a ring type of obstacle, and a short 
 circuit plate The^ launching horn is a half conical horn approximately 
 25=4 centimeters long with a mouth diameter of 17,8 centimeters. It is 
 fed by a 16.2 centimeter length of half cylindrical waveguide. The 
 launching horn and dielectric rod are mounted on a 0.64 centimeter brass 
 plate which is 206 centimeters long and 25.4 centimeters wide Utiliz 
 ing the image principle, the polystyrene rod has been halved along its 
 length and fastened to the brass plane by polystyrene pins, The total 
 length of the dielectric image line was approximately 168 centimeters 
 for most of the admittance measurements The polystyrene pins are 
 0,32 centimeter in diameter and two pins are used for each 28 centimeter 
 section of rod. The rod sections were machined to accurate length to 
 realize a very tight fit between the interface of two sections and 
 thereby minimize reflections from the discontinuity of the interface. 
 Measurements indicated that reflections from such discontinuities were 
 negligible The polystyrene rod has a diameter of 2.22 cm and the 
 operating wavelength was maintained near 4*5 cm, This results in a 
 b/X ratio of about 0.25 and reference to Fig 2 shows that the guide 
 wavelength of the HE ; -. mode was approximately 86% of the operating or 
 free space wavelength. The rod diameter and operating wavelength were 
 purposely selected so that only the dominant HE^ mode was present on 
 the rod waveguide; all higher order modes were cut off, as may be seen 
 from Fig, 2, The short circuit plate is silver plated brass and has a 
 radius of 4.45 centimeters. 
 
 The slotted section of the ground plane, which is located to the 
 left of the ring obstacle, is shown in Fig, 5. The tapered slot is 
 approximately 0.32 centimeter wide and 22.9 centimeters long. The probe 
 
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 Figure 5. The Slotted Section 
 
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is supported by a Hewlett-Packard Universal Probe Carriage which was 
 modified and mounted on the underside of the brass plate. An inclined 
 wire obstacle may be seen on the right side of the picture. The opera- 
 tion of the slotted section was quite satisfactory. The residual VSWR 
 was less than 0.2 db and VSWR's of 40 db were obtained for the line 
 terminated with the short circuit plate. 
 
 Concentric rings and slots were placed on the image line by means 
 of the plates shown in Fig. 6. The obstacles were fabricated from 
 0.08 centimeter brass plate. These plates were inserted at a break in 
 the ground plane (see Fig. 4) and the two sections of the ground plane 
 were then clamped to make good electrical contact. The slots were in- 
 vestigated to determine their usefulness as surface wave exciters. 
 
 Figure 6. Slots and Rings for the Image Line 
 
 Since the existence of only a single mode was demonstrated, the 
 Hrjrr,i ttance measurements were made in the same manner as that for a 
 conventional waveguide and slotted section. The short circuit plate 
 was alway. placed an odd number of quarter-wavelengths past the ob- 
 stacle. The neaaured normalized shunt admittance of a ring as a 
 function of the mean ring radius is presented in Fig. 7. Since the 
 i mum VSWR that could be <>l,t 1 1 ned with a short circuit termination 
 II' for the ring measurements, the points at the top of the 
 
 8- 
 
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 Figure 7 Shjnt Admittance of a Ring as a Function of the Mean 
 Ring Radius 
 
admittance chart are not very accurate. Figure 8 shows the normalized 
 shunt admittance of a slot as a function of the mean slot radius Figure 
 9 shows the normalized shunt admittance of a vertical wire or monopole as 
 a function of the wire length. For this series of measurements a VSWR 
 of 40 db could be attained for short circuit termination of the line 
 It may be seen from Figs 7 and 9 that the resonant ring and wire are 
 strongly coupled to the line (conductances of 5.3 and 3.3. respectively). 
 
 In the design of an array it is certainly desirable, although not 
 essential to use resonant obstacles., In addition, the elements should 
 be loosely coupled to the line, i.e., the conductance should be consider- 
 ably less than one. It is readily seen that the ring and protruding wire 
 do not satisfy these requirements, A study of the field distribution of 
 the HE Ll mode makes apparent two methods of controlling the coupling of 
 resonant obstacles to the rod First, since the fields decay exponen- 
 tially away from the rod, a resonant obstacle could be displaced from the 
 rod to reduce the coupling. Second, since the fields vary sinusoidally 
 with the circumferential angle, certain types of resonant obstacles, such 
 as wires could be oriented or rotated about the axis of the guide to 
 control the coupling The work to be described below illustrates these 
 methods 
 
 In Fig 10 there is plotted the normalized shunt admittance of a 
 wire normal to and displaced 3 mm from the slab as a function of the 
 wire length For these and the following measurements the VSWR on the 
 line with the short circuit plate was at least 37 db, Thus the points 
 near the top of the chart are more accurate than some of those shown 
 previously The wire passed through the first and second resonances 
 when its length was 0.38A and 0.72X, respectively. This measurement 
 was repeated for two other displacements from which the curves of 
 Fig 11 were constructed These curves show the normalized shunt con 
 ductance of the resonant wires as a function of the spacing from the 
 ground plane Although control of the conductance has been obtained, 
 it is apparent that the wire would have to be placed completely outside 
 of the rod in order to obtain conductances of 0.1 or less, Additional 
 pporf of the wire would then have to be provided. 
 
 • Lgure L2 shows the normalized admittance loci of an inclined wire 
 •< ;i f urift.i on of the wire length for several angles of inclination 
 Dn s data wa.s used to construct the curves of Fig.. 13, which show the 
 normalized shunt "inductance of a resonant wire as a function of the 
 
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Figure 8 Shunt Admittance of a Slot as a Function of the Mean 
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 11 
 
Figure 9 Shunt Admittance of a Vertical Wire as a Function of the 
 Wire Length 
 
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d= 3 mm 
 
 Figure 10. Shunt Admittance of a Wire as a Function of the Wire 
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angle of inclination. It may be seen from the curve for the second reso- 
 nance that a wide range of small conductances may be obtained 
 
 Since only a single element was used, the measurements are not accu- 
 rate for the second resonance curve for angles of 30° or less.. For accu- 
 rate results, several elements in tandem should be measured, as is done 
 for loosely coupled slots in rectangular waveguides. This technique has 
 the added advantage that it takes into account the incremental conductance 
 due to the mutual coupling of the elements. It was found that the reso- 
 nant length of the wire changed slightly with the angle of inclination, 
 as is illustrated in Fig. 14. 
 
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 18- 
 
4. ARRAY DESIGNS AND RESULTS 
 
 Since the inclined wire had the most desirable properties of the 
 obstacles tested, it was used in the design of the arrays to be de- 
 scribed. Now, given a prescribed pattern, the conventional linear 
 array synthesis methods may be used to determine the array length, 
 element spacings, and the equivalent shunt conductance of the antenna 
 elements. Then, using Figs. 13 and 14, the angle 9 and the wire 
 length may be determined for each element. Two arrays which were de- 
 signed by this procedure are shown in the photograph of Fig. 15. The 
 
 Figure 15. The Dol ph-Tchebycheff and Cosecant Arrays 
 
 upper array is a 20 db Dolph-Tchebychef f broadside array and the lower 
 is designed to produce a cosecant pattern. Notice that for the com- 
 plete rod the image wire has been added so that each element consists 
 of two wires with an included angle of 29. The horn feed wire is 
 oriented so that the electric field of the HEn mode is normal to the 
 plane bisecting the angle between the wires. For the Tchebycheff 
 array a two inch diameter short circuit plate proved quite satisfactory, 
 For the lower non-resonant array a resistance card was inserted in the 
 rod to form a matched load. 
 
 19- 
 
The radiation patterns which are presented below represent a first 
 attempt. That is, the array was designed from Figs. 13 and 14, con- 
 structed, and tested without any adjustments being made. Since conven- 
 tional methods have been used, little will be said about the method of 
 design for the various types of arrays. 
 
 First consider the pattern in Fig. 16 of the uniform array with 12 
 identical elements at guide wavelength spacing. The pattern was measured 
 in the longitudinal plane which bisects the angle between the wires. The 
 beam width and sidelobe levels are very close to the theoretical values. 
 The small lobe pointing towards the top of the figure represents the 
 stray radiation from the horn exciter. A similar pattern was obtained 
 with a similar array for which the half angle between the wires was 60° 
 instead of 40°. The transverse radiation patterns for the two arrays are 
 shown in Fig. 17. It will be noticed that the patterns for the two cases 
 are considerably different. Theoretically, the patterns should be 
 symmetrical about a vertical line. The discrepancy is due to a misalign- 
 ment of the feed horn and slight variations in the wire length and in- 
 clination Aside from the asymmetry the transverse patterns are probably 
 not suitable for practical applications. However, it is felt that 
 further experimentation would lead to antenna elements with various 
 types of useful transverse patterns. 
 
 The design data and radiation pattern for the 20 db Dolph Tchebycheff 
 broadside array for 12 elements with guide wavelength spacing are shown 
 in Fig 18. The element conductances were made proportional to the 
 square of the calculated excitation coefficients of the array. Note the 
 excellent agreement between the predicted and measured side lobe level. 
 The variation of the angle between the wires is readily apparent in the 
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 Similar data are presented in Fig. 20 for a non-resonant uniform 
 array of 12 elements with an element spacing of 0.75 A_. Since the 
 purpose of this work has been to illustrate the method of design 
 rather than to develop a practical antenna, the array was designed so 
 that 40% of the input power to the array was absorbed in the matched 
 resistance card termination on the dielectric rod. This simplifies 
 the design calculations considerably for a short array since the VSWR 
 along the line may be considered to be unity for design purposes. 
 Larger array efficiencies could be obtained by a more refined design 
 procedure. The direction of the beam and the beam width are in 
 excellent agreement with the theoretical values. However the first 
 lide \<>\>i- is only 10 db down instead of 13 db down and the stray 
 radiation from the horn La at a higher level than before. This 
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 [he line] example La for a non- resonant array designed to produce 
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Fig, 21 was determined by Woodward's Method. The parameter z represents 
 distance along the array. The element locations were determined from 
 the intersection of the curve for the desired aperture phase and the 
 curve of the phase on the dielectric rod. The relative power to be 
 radiated from each element was then determined from the curve of the 
 desired power distribution in the aperture. Although this is an approxi- 
 mate design procedure, previous work had indicated that it was accurate 
 when the element spacing was less than one wavelength. The above infor- 
 mation was then used to determine the design data given in Fig. 22. It 
 will be noticed that there is poor agreement between the predicted and 
 experimental patterns. This difference is probably due to the wide 
 variation of the angle (from 19° to 60°) between the wires. That is, it 
 has been assumed in the design method that all the element patterns are 
 identical. This is certainly not true for this case. In fact, it is 
 rather surprising that the agreement for the two previous designs was so 
 good since there was considerable variation of the angle between the 
 wires for those cases. 
 
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 Figure 21 Design Curves for a Cosecant Pattern 
 
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5. SURFACE WAVE EXCITERS 
 
 There has been considerable interest recently in the surface wave 
 excitation efficiency of various types of sources, The launching effi- 
 ciency, T\» of a source is defined as the ratio of the power converted to 
 the desired surface wave to the sum of the radiated power and the sur- 
 face wave power. The sources usually consist of large horns which have 
 fairly high efficiencies. However, the usefulness of surface waveguides 
 would be increased many times if simple and small, but efficient, ex 
 citers were available. Recent theoretical results have predicted effi 
 ciencies of 95% for a uniform current loop around a dielectric rod and 
 for a line source above a grounded dielectric slab. However, experi- 
 mental verification of these predictions is lacking. 
 
 The admittance measurements which were made for the transverse 
 rings, wires, and slots may be used to calculate the efficiency of these 
 obstacles when used as sources. Considering the rings and wires as 
 sources on a semi infinite line, it may be shown that the equivalent 
 transmission line representation of the obstacle and rod waveguide is 
 that of Fig. 23 where Z is the normalized shunt impedance of the ob- 
 stacle, It has been assumed that a short circuit has been placed to the 
 
 Short 
 Circuit 
 
 Figure 23, Equivalent Transmission Line Representation of a Transverse 
 Ring or Wire Acting as a Source on the Rod Waveguide 
 
 left of the source. If the short circuit is placed a quarter wavelength 
 from the source, then a simple calculation yields 
 
 We = TTrTz X 10 ° in P ercent " 
 -29= 
 
The impedance Z is identical to the passive shunt impedance that the ob 
 stacle presents to the surface waveguide with the generator terminals 
 shorted, provided that the current distribution on the obstacle is the 
 same for the sink and source conditions. This assumption should be accu- 
 rate for obstacles which are small compared to a wavelength. In a simi 
 lar manner, the equivalent transmission line representation for a trans- 
 verse slot is a generator in parallel with the normalized shunt admit- 
 tance of the slot. Thus for a slot the efficiency relation is 
 
 TUlnt- = ^ x 100 in percent. 
 
 siot 1 +Re Y 
 
 These expressions were used to compute the efficiency curves shown in 
 Fig, 24. The ring appears to be the most efficient exciter (with an 
 efficiency of 85%) of the obstacles which were considered as sources. 
 By placing several rings at half-wavelength intervals on the line it 
 should be possible to realize efficiencies of 95% or more. A detailed 
 analysis which yields the above efficiency formulae and an experimental 
 investigation of obstacle launching efficiency will be the subject of a 
 subsequent technical report. 
 
 30- 
 
Figure 24„ Launching Efficiency of a Ring, Annular Slot, 
 and Vertical Wire. 
 
 31 
 
6. CONCLUSIONS 
 
 The measurements have proven the feasibility of obtaining accurate 
 control of the radiation from a dielectric rod waveguide in the longi- 
 tudinal plane by means of placing obstacles along the waveguide. Since 
 only a few types of obstacles have been investigated, it is likely that 
 considerable control of the pattern in the transverse plane may be ob- 
 tained by utilizing other types of obstacles such as dielectric pins, 
 holes, or slots in the rod, and more suitable arrangements of inter- 
 secting wires. It should be possible to apply the same technique to 
 other types of surface waveguides with equal success. The basic require 
 ments needed for applying the design procedure are the following: an 
 efficient surface wave exciter, the existence of only a single mode on 
 the surface waveguide, an accurate means of determining the equivalent 
 network for the coupling of the obstacle to the surface waveguide, and, 
 of course, the discovery of obstacles for which the coupling may be 
 varied over a wide range with only a moderate effect on the individual 
 obstacle pattern. Conventional array design methods may then be used to 
 obtain various types of patterns. 
 
 32- 
 
BIBLIOGRAPHY 
 
 1. Mueller, G. E. "A Broadside Dielectric Antenna," Proc , I.R.E., Vol. 40, pp. 71-75, 
 January 1952. 
 
 2. Beam, R. E. Final Report on Investigation of Multi-mode Propagation in Waveguides 
 and Microwave Optics, Army Signal Corps Contract No. W36-039 sc-38240„ Microwave 
 Laboratory, Northwestern University, Evanston, Illinois. 1 May 1949 to 30 November 
 1950. 
 
 3. Woodward, P. M. "A Method of Calculating the Field Over a Plane Aperture Required 
 to Produce a Given Polar Diagram," J.I.E.E., Part IIIA, Vol. 93, pp. 1554-1558, 
 March -May 1946. 
 
 33 
 
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