8905-1-F THEORETICAL AND EXPERIMENTAL INVESTIGATION OF PARASITIC LOOP COUNTERPOISE ANTENNAS Final Report (16 June 1967 - 16 June 1968) Scientific Report No. 3 September...1.98 Contract No. FA67WA-1753 Project 330-004-05N SRiS RepotH:'t6 RD-688-0 This report has been prepared by The University of Michigan Radiation Laboratory of the Department of Electrical Engineering for the Systems Research and Development Service, Federal Aviation Administration, under Contract FA67WA-1753. The contents of this report reflect the views of the contractor, who is responsible for the facts and the accuracy of the data presented herein, and do not necessarily reflect the official views or policy of the FAA Prepared by D. L. Sengupta, J. E. Ferris and V. H. Weston The University of Michigan Radiation Laboratory Department of Electrical Engineering Ann Arbor, Michigan 48108 For Systems Research and Development Service Federal Aviation Administration, Washington, DC 20590 8905-1-F = RL-2189

8905-1-F ABSTRACT The radiation field produced by a single parasitic loop counterpoise antenna has been investigated both theoretically and experimentally. Geometrical theory of diffraction is applied to obtain theoretical expressions for the far field produced by such an antenna. Within the range of approximation the agreement between theory and experiment has been found to be very good. In the absence of mutual coupling between the parasitic elements, the present theory can be applied to double- and multiple-parasitic loop counterpoise antennas. The parasitic loops in general reduce the counterpoise edge diffraction effects on the far field patterns. The behavior of the parasitic loop counterpoise antenna pattern near the principal maximum is not appreciably different than the Alford loop counterpoise pattern near its maximum. Parasitic loops increase the response of the antenna in regions of space near the Ienith 0 = 0~, Detailed results of numerical and experimental investigations of various aspects of the parasitic loop counterpoise antenna have been given. These results bring out the effects of the different parameters of this new antenna system on the radiation patterns. The parasitic loop concept has been found to be capable of shaping the pattern pro duced by an Alford loop counterpoise antenna pattern in regions of space below the plane of the counterpoise. On the basis of our investigation we conclude that when suitably designed, the parasitic loop counterpoise antenna is potentially capable of minimizing the siting; errors ikssoiate'd Withexisting VOR systems. We have proposed three new antenna. systems which may find possible application in a VOR system. ii

TABLE OF CONTENTS I INTRODUCTION 1 1. 1 Preliminary Remarks 1 1.2 Simple VOR Antenna 1 1. 3 Previous Work Done 2 1. 4 The Parasitic Loop Counterpoise Antenna 2 1. 5 Outline of the Report 2 II RADIATION CHARACTERISTICS OF AN ALFORD LOOP ABOVE A COUNTERPOISE 4 2.1 Introduction 4 2. 2 Radiation Field of an Alford Loop Above a Counterpoise 4 2. 3 Description of Experimental Arrangement 6 2. 4 Experimental Results and Comparison with Theory 9 2. 5 Omnidirectionality of the Pattern in Azimuth 9 2. 6 Numerical Investigation 9 2. 7 Discussion 16 III RADIATION FIELD OF A SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA 17 3. 1 Introduction 17 3.2 Far Field Expression 17 3. 3 Description of Experimental Arrangement 31 3.4 Comparison Between Theory and Experiment 34 3. 5 General Effects of the Parasitic Loop on the Radiation Pattern 38 3. 6 The Effects of Variation of the Parasitic Loop Parameters 38 3.7 Discussion 39 IV RADIATION CHARACTERISTICS OF A SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA 40 4. 1 Introduction 40 4. 2 Experimental Results 40 4. 3 Numerical Results 45 4. 4 Discussion 57 V INVESTIGATION OF A DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 59 5. 1 Introduction 59 5. 2 Double Parasitic Loop Counterpoise System 59 5. 3 Theoretical Expression for the Radiation Field 59 5. 4 An Example 61 iii

TABLE OF CONTENTS (continued) 5. 5 Optimum Double-Parasitic Loop Counterpoise Antenna 62 5. 6 Pattern Variation with H2 66 5. 7 Impedance Characteristics 66 5. 8 Double Coplanar Parasitic Loop System 72 5. 9 Comparison with Single Parasitic Loop System 72 5.10 Discussion 75 VI MULTIPLE PARASITIC LOOP COUNTERPOISE ANTENNA 76 6. 1 Introduction 76 6. 2 Description of a Multiple Parasitic Loop Antenna 76 6. 3 Radiation Patterns 76 6. 4 Discussion 76 VII PROPOSED VOR ANTENNA MODELS 80 7.1 Introduction 80 7. 2 VOR Antenna Requirements 80 7. 3 Proposed Parasitic Loop Counterpoise Systems 81 7.4 Comparison Between the Basic and Proposed Antenna Systems 83 7. 5 Discussion 83 VIII CONCLUSIONS AND RECOMMENDATIONS 87 8. 1 Conclusions 87i 8.2 Recommendations for Further Work 88 ACKNOWLEDGEMENT 88 REFERENCES 89 APPENDIX A: FAR FIELD OF A LARGE CIRCULAR LOOP ABOVE A COUNTERPOISE 90 APPENDIX B: COMPUTER PROGRAM FOR EVALUATING SA(0), S(0) 97 APPENDIX C: THEORETICAL ELEVATION PATTERNS OF ALFORD LOOP 'COUNTERPOISE ANTENNA 103 APPENDIX D: RADIATION CHARACTERISTICS OF A SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA NEAR THE HORIZON 110 iv

LIST OF ILLUSTRATIONS Figure No. 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 Caption Page No. Alford loop above counterpoise showing coordinate system. 5 Photograph of the Alford loop model. 7 Photograph of the Alford loop counterpoise antenna model. 8 Elevation radiation pattern of Alford loop counterpoise antenna.. kh=2.75, kA=17.92. 10 Elevation radiation pattern of Alford loop counterpoise antenna. kh=2. 75, kA= 6.893 11 Measured azimuthal patterns of Alford loop counterpoise antenna. 12 Theoretical elevation pattern characteristics of Alford loop counterpoise antenna below horizon...13 Theoretical variation of Alford loop counterpoise radiation characteristics as a function of counterpoise size. 15 Geometric representation of parasitic loop counterpoise antenna and coordinate system. 18 Diagram of different rays contributing to parasitic current. 20 Coordinate system for determining the edge diffracted fields. 22 Coordinate system used to determine fields due to rays 5 and 6. 25 Coordinate system used to determine the far field of large loop above counterpoise. 29 Schematic diagram of experimental parasitic loop counterpoise antenna. 32 Photograph of parasitic loop counterpoise antenna. 33 Free space far field elevation pattern produced by single parasitic loop counterpoise antenna. kh=2.75, kH=3.75, kA-17.92, kb=0.15, kB=47. 35 Free space far field elevation pattern produced by single parasitic loop counterpoise antenna. kh=2.75, kH=.3. 75, kA=17.92, kb=0.287, kB=2.57r. 36 v

3-10 Free space far field elevation pattern produced by single parasitic loop counterpoise antenna. kh=2.75, kH=l1. 78, kA=17.92, kb=0. 15, kB=37r. 37 4-1 Measured far field elevation patterns of single parasitic loop counterpoise antenna, w=0. 092 X. 41 4-2 Measured far field elevation patterns of single parasitic loop counterpoise antenna. w=0.183 X. 42 4-3 Measured far field elevation patterns showing the effects of parameter w. 44 4-4 Theoretical field gradient near horizon of single parasitic loop counterpoise antenna elevation pattern. 47 4-5a Theoretical variation of parasitic loop counterpoise antenna elevation pattern I S(0)t below horizon. kB=37r. 48 4-5b Theoretical variation of parasitic loop counterpoise antenna elevation pattern S(0)t below horizon. kB= 3. 1Ir. 49 4-5c Theoretical variation of parasitic loop counterpoise antenna elevation pattern I S(0)I below horizon, kB=47r. 50 4-6 Theoretical variation of parasitic far field SP(0) below horizon. 51 4-7a Theoretical far field S(0) of parasitic loop counterpoise antenna in direction 0=920. 53 4-7b Theoretical far field S(0) of parasitic loop counterpoise antenna in direction 0=94~. 54 4-7c Theoretical far field S(0) of parasitic loop counterpoise antenna in direction 0=960. 55 4-7d Theoretical far field S(0) of parasitic loop counterpoise antenna in direction 0=980~ 56 5-1 Diagranmfdoutbleparasitic loop counterpoise antenna. 60 5-2 Far field elevation pattern produced by double parasitic loop counterpoise antenna. 63 5-3 Measured far field elevation pattern of optimum double parasitic loop counterpoise antenna. kh=2.75, kA=17,92, kb=O. 15, kB1=4?r, kH1 3. 7, kb2-0. 15, kB2 10.27, kH1210.63. 65 vi

5-4 Measured far field elevation pattern of optimum double parasitic loop counterpoise antenna. w1iw2=0.183X, 2B1=2B2=2.5X, Hf=0.64X, H2=2. 29X. 66 5-5a-d Measured far field elevation patterns of optimum double parasitic loop counterpoise antenna. 1060 - 1120 MHz. 67 5-5e-g Measured far field elevation patterns of optimum double parasitic loop counterpoise antenna. 1140 - 1180 MHz. 68 5-6 Measured elevation patterns of double parasitic loop counterpoise antenna. 2Bl=2B2=2. 5X, Hi=0. 64X, H2 variable. 1080 MHz. 70 5-7 Impedance characteristics of Alford loop counterpoise antenna. 71 5-8 Measured elevation patterns of double coplanar parasitic loop counterpoise antenna. kh=2.75, kA=17.92. 73 5-9 Measured elevation patterns of double coplanar parasitic loop counterpoise antenna. h=0.44X, 2A=5.7X, H1=H2H. 74 6-1 Multiple parasitic loop counterpoise antenna. 77 6-2 Measured elevation patterns of multiple parasitic loop counterpoise antenna. H variable. 78 6-3 Measured elevation patterns of multiple loop counterpoise antenna. H= 1. 88X, 0. 6X and. 23X. 79 7-1 Measured far field elevation patterns of VOR,antennas at 1080 MHz. Basic System vs Antenna System No. 1 84 7-2 Measured far field elevation patterns of VOR antennas at 1080 MHz. Basic System vs Antenna SystemNo. 2. 85 7-3 Measured far field elevation patterns of VOR antennas at 1080 MHz. Basic system vs Antenna System No. 3. 86 vii

I INTRODUCTION 1. 1 Preliminary Remarks This is the Final Report on Contract FA67WA-1753, Project 330-004-05N, "VOR Parasitic Loop Counterpoise System" and covers the period 16 June 1967 to 16 June 1968. The primary purpose of the contract has been to investigate the possibility of using parasitic loops to improve the performance of the antennas used in existing VHF Omni Range systems. The concept of using parasitic loops gave rise to a new antenna configuration named the parasitic loop counterpoise antenna. A major part of the investigation has been devoted to the theoretical and experimental study of the radiation properties of such an antenna. The possible application of the antenna to VOR systems is then explored. In the following sections we discuss briefly the genesis of the parasitic loop concept and give a brief outline of the report. 1.2 Simple VOR Antenna A detailed description of the VOR antenna system has been given by Anderson(1) and will not be repeated here. For the purpose of the present investigation a simple VOR antenna is assumed to consist of a single Alford loop placed above and parallel to a circular and conducting ground plane or counterpoise. It operates in the frequency range 108 - 118 MHz. In most installations the diameter of the counterpoise used is about 5.7 X at the frequency of 108 MHz. The antenna is oriented with the counterpoise lying in the horizontal plane. It is generally elevated above the ground level to a height depending on the site chosen and its environment. The free space radiation pattern of such an antenna is omnidirectional in azimuth. It should be noted that the actual VOR antenna employs two pair of loops and has a figure-of-eight pattern(l) in azimuth. The elevation plane pattern has a maximum around 50~-60~ away from the vertical depending on the- height of the Alford loop and the size of the counterpoise. Due to the counterpoise edge diffraction effects the Alford loop counterpoise antenna has considerable response in directions below the plane of the counterpoise. Because of this, scattering objects such as trees, buildings, etc., in the vicinity of the present VOR antenna systems and also the ground reflection effects, produce errors in the VOR indicationsl). To avoid the errors in the bearing indications of the existing VOR systems the ideal requirements on the antenna radiation pattern are such that in the upper half plane of the counterpoise the elevation field pattern should resemble the Alford loop counterpoise radiation pattern and in directions below the counterpoise plane the field should be zero or negligible. Such a pattern is possible only with an infinitely large counterpoise. However, to increase the counterpoise diameters well beyond the values used in the existing systems is impractical. 1

1. 3 Previous Work Done Weston et al(2) proposed a new VOR system which uses a stacked array of two or more Alford loops above the counterpoise. They have shown that by properly choosing the amplitude amplitude and phase of excitation of the loops the field gradient at the horizon (i. e. the rate of decrease of field lo the horizon) can be increased considerably. This was achieved by producing a minimum in the elevation pattern in a direction just below the horizon. Successful operation of this antenna system requires proper phasing and feed network for the Alford loops. Although the theoretical value of the field gradient produced by this antenna was large, the average response of the antenna b the antenna below the horizon was found to be quite high. It can be shown theoretically that both the horn and lens antennas may provide partial solutions to the problems associated with the existing VOR antenna systems. However, because the operating wavelength is of the order of 10 feet, the ostructures associated with these systems will be immense. Additional difficulties will arise in adapting the present feed (i. e the Alford loop) to a lens or horn antenna. Because of these reasons the idea of using horn or lens antennas in VOR systems has not been pursued. 1. 4 The Parasitic Loop Counterpoise Antenna The basic objective of reducing the field in directions below the plane of the counterpoise may be achieved by using as large parasitic loop placed above and parallel to the Alford loop counterpoise antenna. Such an antenna will be called the parasitic loop counterpoise antenna. The parasitic loop receives its excitation from the Alford loop. It is then conceivable that by proper choice of the physical parameters of the parasitic loop, the field produced by the parasitic current in the presence of the counterpoise may be of such a phase as to reduce the field produced by the Alford loop counterpoise antenna in the directions below the horizon. The current carried by the parasitic loop being small compared to that of the Alford loop, the parasitic loop will not appreciably alter the field near the principal maximum. However, it is expected that fields near the vertical will be altered appreciably. Thus it appears that one or more parasitic loops may be used advantageously to reduce the siting errors caused by the antennas in the existing VOR systems. 1. 5 Outline of the Report The parasitic loop counterpoise configuration is a new antenna. Hence the major portion of our investigation has been devoted to the study of its radiating properties under various conditions. Throughout the report we shall refer to the Alford loop above the bounterpoise as the basic antenna. The entire study is 2

directed towards shaping the patterns of the basic antenna in certain regions of space with the help of the parasitic loops. The outline of the report is as follows. The radiation properties of the Alford loop above the counterpoise are discussed in Chapter II. The effects of changing the counterpoise size on the patterns are given. The radiation field produced by a single parasitic loop counterpoise antenna is investigated theoretically in Chapter III. The theory is then verified by experiment. The general effects of the parasitic loop parameters on the far field pattern are discussed. Chapter IV presents in detail the results of numerical and experimental investigations of the radiation properties of a single parasitic loop counterpoise antenna as the different parameters of the system are varied. The radiation characteristics of a double parasitic loop counterpoise antenna are discussed in Chapter V. The properties of an optimum antenna with best field gradient characteristics are discussed. A brief comparison between the single and double parasitic loop counterpoise antenna is also given. Multiple parasitic loop counterpoise antennas are discussed in Chapter VI. Three models of parasitic loop counterpoise antennas are proposed in Chapter VII. All of them may have possible application for the purpose of improving the performance of the existing VOR system. Chapter VIII gives our general conclusions and recommendations for further work. The Fortran IV Computer Program used for numerical analysis and some numerical results are given in the Appendices. 3

II RADIATION CHARACTERISTICS OF AN ALFORD LOOP ABOVE A COUNTERPOISE 2. 1 Introduction In this chapter, properties of an Alford loop located above and oriented parallel to a counterpoise are discussed. The complete expression for the radiation field produced by such an antenna system has been obtained by Weston et al (2) They also have reported satisfatory agreement between theoretical and measured radiation patterns. The Alford loop above a counterpoise being the basic antenna system, its radiating properties are of fundamental importance for our investigation. The radiation characteristics of the antenna are therefore investigated in more detail both numerically and experimentally. The results are discussed critically and are represented in a form suitable for later use. 2.2 Radiation Field of an Alford Loop Above a Counterpoise The cross sectional view of the Alford loop above the circular ground plane along with the coordinate system used is shown schematically in Fig. 2-1. For theoretical analysis the Alford loop is approximated by a small circular loop (ka<l) carrying a constant amplitude current. In practice the Alford loop used is square in shape with each side approximately of the order X/5 so that the above approximation is reasonable. Since the development of the theoretical expression for the radiation field of the antenna has been discussed elsewhere (2), it will not be repeated here. Only the final result is quoted here. Assuming that the loop carries a current of the form -t T -ist I I e, 0 it can be shown that the complete expression for the far field produced at a point P(R, 0) and in the range 0 < 0< is given by A ka 2 e ikR- /4)( E= - (0e), (2.1) p 0o o 2 R where A SF~(0)sinO -ikAsinO cos sin(2) ikro (22) S ( /Trkro sine ' i( -kAsint. 3/2 3/2 0 2e / cs -sin 3/2 e0ikAsin cos 3/2 o 1-L (= cos0o-sinO clsin cos iosin (2. 3) \/l-si'n \ 0 'o / l+sin0 '0 4

z A I ^ P(R,e) R \ a v — Alford Loop Counterpoise FIG. 2-1: ALFORD LOOP ABOVE COUNTERPOISE SHOWING COORDINATE SYSTEM. 5

ikr sin(0-) o)2/ ikr sin(0+) fp 2 Fo (e)=e 0 0 I ei7rt2/2 dt-e 2 dt, (2.) -00 -00 kro/2 P0-0- 2/ Pi=2 (-r )/cos(,. 2, (2. 5) 7r 2 kr 1/2 +0+ /2 2=2 (-) cos ( 2 (2.6) r2= A2h2 (2.7) 0 o tano = h (2.8) o A 27T k =- is the free space propagation constant, no is the intrinsic impedance of free space and the other parameters are as explained in Fig. 2-1. The implied time dependence in Eq. (2.1) is e-iwt. The far field produced is polarized in the 0-direction and is independent of the azimuthal angle 0. The term SA(0) in (2.1) may be looked upon as the complex far field pattern. Thus lsA(o) is the conventional far field radiation pattern and arg JSA(O)I gives the variation as a function of 0 of the phase of the radiation field at a constant distance R from the origin. To determine the accuracy of Eq. (2,2) the radiation pattern of the antenna has been measured and compared with the theoretical pattern obtained numerically from (2.2), The expression is then studied numerically by varying the different parameters, These are explained in the following sections, 2.3 Description of Experimental Arrangement Experimental investigations have been carried out at the frequency of 1080 MHz which is about ten times the operating VOR frequency. The Alford loop used is a tenth scale model of a typical loop used in the existing VOR antenna system, the 'design of which is discussed by Anderson('. A phbtographQ.of the. Alford loop model is shown in Fig. 2-2. The loop is made of brass strips and fed by a coaxial line with the help of a balance-to-unbalance transformer. The loop is square shaped with each side equal to 0.21", which is about X/5 at the frequency of 1080 MHz. The counterpoise has been cut from aluminum sheet 0.125" thick and backed with a wooden frame to ensure rigidity. It has a diameter of 5.2?. The loop is mounted 4,8"? above the counterpoise with its axis coincident with that of the counterpoise. The experimental Alford loop counterpoise antenna is shown in Fig. 2-3. The present configuration studied corresponds to a full scale simple VOR antenna system consisting of a standard Alford loop above a 521 diameter counterpoise. In all the measurements to be discussed below the above 6

FIG. 2-2: PHOTOGRAPH OF THE ALFORD LOOP MODEL 7

FIG. 2-3: PHOTOGRAPH OF THE ALFORD LOOP COUNTERPOISE ANTENNA MODEL.

model has been used as a receiving antenna. It is of some interest to mention here the following normalized physical parameters of the antenna used (see Fig. 2-1): 2A" 5.7X, h^0.44X, and a.#X/10. 2. 4 Experimental Results and Comparison with Theory. The measured elevation pattern of the Alford loop in the presence of a 5.2' diameter counterpoise is shown in Fig. 2-4. For comparison, the theoretical values of SA(o) as obtained from numerical computation of Eq.(2.2) are shown in the range 0 < 0 <,r in Fig. 2-4. The general agreement between theory and experiment is considered to be excellent for this case. Elevation patterns of the same Alford antenna have been measured for 2A=4', 3' and 2' respectively and the agreement with theory has been found to be very good in all cases. The measured and theoretical patterns for the case with a 2' diameter counterpoise (kA=6.893) are shown in Fig. 2-5. It may thus be concluded that for AZ X, Eq. (2.2) should predict quite accurately the radiation pattern produced by the Alford Loop counterpoise antenna. It is anticipated that the theory may give the pattern with reasonable accuracy even for A < X. However, we have not tested the theory experimentally for such cases. 2. 5 Omnidirectionality of the Pattern in Azimuth As can be seen from Eq. (2 1) the far field is independent of the azimuthal angle 0. This is consistent with the physical symmetry of the theoretical model shown in Fig. 2-1. To test the omnidirectionality of the azimuthal pattern of the experimental model, elevation patterns have been measured in various meridian planes of the antenna (i.e. for different values of 0). The variation of the pattern as a function of 0 is shown in Figs. 2-6a - c for three selected values of 0. As can be seen from Figs. 2-6a, b, the omnidirectionality of the pattern in azimuth may be considered to be very good in the horizontal plane and in the direction of the pattern maximum. The omnidirectionality for the case 0=10~(Fig. 2-6c) is found to be worse compared to the previous two directions. 2. 6 Numerical Investigation By using a high speed computer Eq.(2.2) has been computed for different values of A with constant kh=2.75. The computer program and numerical results are given in Appendices B and C. The computer used was the IBM 360/67. In the present section we discuss a few of the important radiation characteristics of the Alford loop counterpoise antenna on the basis of the numerical investigation. Pertinent information obtained from our experimental study will also be given for comparison. 2. 6.1 Amplitude and Phase of the Radiation Field As mentioned in Chapter I, the primary purpose of the investigation has been to shape the Alford loop counterpoise pattern near and below the horizon. For this purpose it is important to know both the variations of I SA(0) I and arg SA(0) for 0 > 7r/2. Here we discuss the amplitude and phase variation of the field within the region 90~ < 0 < 120~ which is the most important region from the VOR point of view. Figure 2-7 shows the amplitude and phase of the radiation field as a function of 0. In general 9

0 0 FIG. 2-4: ELEVATION RADIATION PATTERN OF ALFORD LOOP COUNTERPOISE ANTENNA, kh=2.75, kA=17.92, f=1080 MHz ( ---) Measured (e e) Theoretical. 10

FIG. 2-5: ELEVATION RADIATION PATTERN OF ALFORD LOOP COUNTERPOISE ANTENNA. kh=2.75, kA=6.893, f=1080 MHz, (-)Measured, ( * ) Theoretical. 11

(b) 0=55~ (c) 0=10~ FIG. 2-6: MEASURED AZIMUTHAL PATTERNS OF ALFORD LOOP COUNTERPOISE ANTENNA. kh=2.75, kA=17.92, f=1080 MH7. 12

Arg SA(O)-3600 90~ 180 270~ 360~ 90 o10 (a) Relative Amplitude o(o). 110 (b) Phase Angle 120.1.2 IsA(0).3 4.6 FIG. 2-7: THEORETICAL ELEVATION PATTERN CHARACTRISTICS OF ALFORD LOOP COUNTERPOISE ANTENNA BELOW HORIZON. kh=2.75, kA=17.92, f=lunu0 lvis. 7 13

it may be said that the phase varies quite rapidly around the horizontal direction 0=90~. It can be seen from Fig. 2-7 that for a change of 30~ in 0 below the horizon the phase of the radiation field changes by about 212~. The curves shown in Fig. 2-7 will be used later for the purpose of modifying the pattern below the horizon. 2. 6. 2 Pattern Characteristics as a function of the Counterpoise Size In this section we discuss briefly the radiation pattern characteristics of the Alford loop counterpoise antenna as the counterpoise radius A is changed. The normalized radius kA of the counterpoise is varied from 6.893 to 51.69Batthe frequency 1080 MHz, which corresponds to a variation of A from 1' to 7.5'. The results obtained from the numerical investigation are shown in graphical form in Fig. 2-8. Curve (a) shows the variation of the direction of principal maximum 0max as A is varied. It may be concluded from curve (a) that as A is changed from about X to 8X, 0 increases from 55~ to 60~. Curve (b) shows the field gradient at the horizon as afunction of the counter poise size. The field gradient is defined to be the negative of the ratio field at 0=96~/ field at 0=90~, expressed in db. As expected, the field gradient at first increases substantially as A is increased, but for larger values of A, it increases very slowly. Curve (c) in Fig. 2-8 shows the variation of the field in the direction 0=90~ relative to that in the direction 0=0max as A is increased. As the counterpoise size is increased the field in the direction 0=90~ decreases more and more relative to the field in the maximum direction. For a quick comparison, the theoretical and experimental values of the different quantities are shown in Table II-1. On the basis of the results discussed above we single out the following information regarding the pattern characteristics of an Alford loop above a 5.2' diameter counterpoise at the frequency of 1080 MHz: emax = 55. 30 field gradient = ag = -20 logl0 E(90) = 3. 09 db/60 field reduction = aF= -20 log10 E(900) = 10. 38 db. I E(6max) The above information will be found useful for later work. TABLE II-1: ALFORD LOOP COUNTERPOISE ANTENNA PATTERN CHARACTERISTICS AT f=1080 MHz, kh=2.75 AND VARIABLE A. 2A kA 0max(ino) ag(in db) aF(in db) (ft) ___ Theory Exp. Theory Exp. Theory Exp. 2 6.89 55 56 1.63 1.8 5.15 4.4 3 10.30 55 55.5 2.18 2.1 7.45 7.2 4 13.74 55 54.5 2.62 3.0 9.03 10.2 5.2 17.92 55 55.2 3.09 3.15 10.38 12.5 10 34.47 60 - 4.49 - 13.35 - 15 51.69 65 - 5.56 - 14.86 - 14

10 (c) aF ^~ ~F 90 (a) 0max -—.Abmmmw - db - - * - 50- 0 (^) QMax - aO 0 2 20 20 10_ 3 - 3 0 4~ 0 FIG. 2-8: THEOBETICAL VABIAT~ ON OP AL- Loop C C CTERSTIAS FUNCTIONOF C g~c aF s FVkcA. - 15

2. 7 Discussion The radiation pattern characteristics of an Alford loop above a counterpoise have been discussed here both theoretically-and experimentally. The results presented will be used later in evaluating and also improving the performance characteristics of the existing VOR antenna systems. 16

III RADIATION FIELD OF A SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA 3. 1 Introduction In the present chapter we investigate the radiation field produced by an Alford loop counterpoise antenna system as modified by the presence of a parasitic loop. The latter system is referred to as the parasitic loop counterpoise system and is shown schematically in Fig. 3-1. For theoretical analysis the Alford loop is represented by a small circular loop of radius a (ka << 1). The parasitic loop has a radius B and is placed at a height H above and parallel to the counterpoise. It is assumed to be made of conducting wire of radius b. In the following sections we shall first develop a theoretical expression for the radiation field produced by the above antenna system. An experiment is then designed to obtain results so that the accuracy of the theory may be determined. Finally the various radiation properties of the antenna are discussed in general. 3.2 Far Field Expression The parasitic loop receives its excitation from the Alford loop. The first step in the analysis is to obtain the current induced in the parasitic loop by the field produced by the excited loop. The radiation field produced by the parasitic current in the presence of the counterpoise is then determined. Finally this field is combined vectorially with the Alford loop counterpoise field given by Eq. (2.1) to obtain the far field produced by the parasitic loop counterpoise antenna. 3.2. 1 Current Induced in the Parasitic Loop From the symmetry of the system and the nature of the field produced by the excited loop, the current in the parasitic loop may be assumed to be of the form p epo (3.1) where 0 is the unit vector in the 0-direction and Ipo is a constant to be determined. In determining Ipo it is assumed that the current at any point on the parasitic loop is equal to that induced by a longitudinally polarized (the electric field parallel to the axis) plane electromagnetic wave incident normally on a conducting cylinder of radius b and of infinite length (for example the cylinder is oriented parallel to the y-axis in Fig. 3-1). This is a basic assumption of geometrical optics and should be a reasonable approximation for the present problem as long as kB > 1. Using the 17

z Field Point B P(R, 0, O Parasitic i Tb — --— 7 71 R H a Alford Loop h A --- - Counterpoise FIG. 3-1: GEOMETRIC REPRESENTATION OF PARASITIC LOOP COUNTERPOISE ANTENNA AND COORDINATE SYSTEM. 18

well-known results of the scattering of plane electromagnetic waves by ma conducting cylinder of infinite length (3), it can be shown that 0,4 in in inc r - k __ _ E (P) (3.2) Po rlok n=-o H(l)(kb) n where inc E (P) is the incident field at the position of the parasitic loop produced by the current Ioe-iJt in the small-excited loop, H) is the Hankel function of the first kind and order n, n is the azimuthal angle measured along the circumference of the cylinder, and the other parameters are as explained before. It is now assumed that kb < 1, so that it is sufficient to retain only the n=O term in (3.2). After making the small argument approximation for the Hankel function we obtain the following from (3.2) 2 inc (33) Po ir lkM E where kb 7( M = 0. 577 + n( )-i. (3.4) Thus the evaluation of the parasitic current Ipo is reduced to the determination of the incident field at the position of the parasitic loop. 3. 2. 2 Incident Field at the Parasitic Element inc The incident field E (P) at the point P on the parasitic loop is obtained from ray optics considerations. It is assumed that Etc (P) is due to the following rays originating from the phase center Q of the excited loop and reaching the point P (Fig. 3-2): (i) direct and reflected rays 1 and 2 respectively originating from Q, (ii) the rays 3 and 4 originating from Q and singly diffracted by the n-ear and far edges of the counterpoise respectively, (iii) a ray 5 from Q and singly diffracted by the diametrically opposite region P' of the parasitic loop before reaching P, (iv) a ray 6 single diffracted by the parasitic loop at P and reflected back to P by the counterpoise. 19

z P' 5 Int on Loop. I r ar rage o1 Near Edge Counterpoise. of Counterpoise FIG. 3-2: DIAGRAM OF DIFFERENT RAYS CONTRIBUTING TO PARASITIC CURRENT. 20

There are other rays that may contribute to the field at P but they will be higher order diffracted and hence are neglected for the present purpose. It is clear from physical considerations that the contributions due to the direct and reflected rays will be predominant. It is also anticipated that for kH >> 1 the contribution due to the diffracted rays will be of less importance. However, for small and moderate values of kH the diffracted ray contributions can no longer be neglected. Thus the incident field at the point P on the parasitic loop may be formally written as: inc 12 34 56 E (P) - E (P)+ + E (P) P), (3.5) where the superscripts on the right hand side refer to the rays contributing to the field. 3.2, 3 Evaluation of the Incident Field at the Parasitic Element 12 It is quite easy to obtain the field component E4 (P) due to the direct and reflected rays. It can be shown to be given byfield at P due to the lkr ikr2 E1 P) =I (ka 2B ee] (3.6) where r = B+(H-h) 2 2 2 r2 = B +(H+h) 34 The evaluation of the field Eo (P) due to the near and far edge diffracted rays is not straightforward and hence we discuss the key steps involved in obtaining it. The near and far edge diffracted fields at P are determined separately and then combined to obtain E34(p). The coordinate system used in obtaining these fields is shown in Fig. 3-3. In obtaining these fields the results of Sommerfeld's theory of diffraction of plane waves by a half-plane(4) are used. The application of Sommerfeld's theory to the present type of problem has been discussed elsewhere (1) and will not be repeated here. It can be shown that the incident field at P due to the near-edge diffraction of the field originating from the phase center Q of the excited loop is given by 21

z I I I I I Q ------- I I I I I 1 4 (1ro a i, i — r FIG. 3-3: COORDINATE SYSTEM FOR DETERMINING EDGE DIFFRACTED FIELDS. 22

1 ikr E [(P) = H P3 - p3 ikr ka 2 e 0 X [I (o) sino g r i for kA >>, kr >>1. (3.8) where kro 1/2 0o-3 P=2(-) cos ( ), (3.9) 3 7r 2 p=2 ) os ( O 3) (3.10) and the other parameters are as explained in Fig. 3-3. In Eq. (3.8), the first factor (A/A-r3sinO3)V2 is the near edge divergence factor which takes into account the circular geometry of the counterpoise. From the geometry shown in Fig. 3-3 it can be seen that A 2 A 1/2: A?/2 A/ (3.11) A-r3sinO3 B The last factor in (3.8) is the incident field at the near edge produced by the circular loop of radius a and carrying a current Io. After introducing (3.11) into (3.8) and some algebraic manipulation, the following is obtained for the contribution of the incident field at P due to the near edge diffracted ray 3: E3(P) i2 A A) /2 1/2 -i37r/4 E (P)=tK'rO( ) - - e02 2 B 7rzkr3 0 ik(r +r3) r Oo3 Oo-03 ~ e sec ( 3) -sec( ) (3.12) Similarly it can be shown that the field produced at P due to the far-edge diffracted ray 4 is given by 4( ) -i/2 A /2 A )12 -i, ( 1) ( r4sinO4-A 4 i2sr P4 P4 eikr4 a 2n ePPo4) K e -%o 2) sineo,,forkAl >> 1, kr4>> 1, (3.13) ~:hq ro 23

where all the parameters are as defined in Fig. 3-3 and kro 1/ 2 Ooi4 co/s( o4) (3.145) 4 7r 2 The interpretation of the different factors in (3.13) is similar to those in (3.8). The factor e-i /2 in front of (3.13) is due to the fact that the diffracted rays pass through the focal line (z-axis); the negative sign in the last factor is due to the reversal of the incident field polarization at the far edge of the counterpoise with respect to the near edge. After some rearrangement, (3.13) may be written as follows: E0P) - k (r)2 A) /2 I /2 e i/4 7/2 r2 B kr4 2 e ik(ro+r 4) 0 -0 4+0 xe ) ec( 2 )-sec( 024. (3.16) After combining (3.12) and (3.16) we obtain the following as the contribution to the incident field at P due to the near and far edge diffracted rays 3 and 4: 34 ka2 A ikr o e A 1/2 E (P)=roI() -e. _ 0 oo2 r2 m2 T2 B 0 )L 1 1/e3/2 eikrc3 o0-3)_sec( ~+ 3 1 /2 ikr4 +0 rkr4 e sec( 2 -sec 2. (3.17) The contributions to the incident field at P due to the rays 5 and 6 are found in the following manner The geometry involved is as shown in Fig. 3-4, where PI is the cross section of the parasitic loop situated in a region diametrically opposite to P. To obtain the field at the point P due to the ray 5 we at first obtain the field at the point P due to the scattering of a plane electromagnetic wave of proper amplitude incident normally at an y-directed conducting and infinite cylinder of radius b located 24

z p' A FIG. 3-4: COORDINATE SYSTEM USED TO DETERMINE FIELD DUE TO RAYS 5 AND 6. 25

at P'. It is assumed that kb << 1 so that the low frequency approximation to the. wellknown results(3) of the scattering of electromagnetic waves by an infinite cylinder may be used for this purpose. The incident field at P' is that produced by the circular loop located at Q and its field is assumed to be locally a plane wave in the vicinity of P'. Thus it can be shown that the scattered field at P is E I(P) 2' n I (ekr 7r 1 Y2 i(2kB-T/4) E 002 r r j jk e2 B ik318] -- -M ( nkB) r where M is as given by (3.4) and the other parameters are as explained before. The field at P due to the ray 5 is now assumed to be given by (3.18) multiplied by the proper divergence factor which takes into account the circular nature of the parasitic loop. The appropriate divergence factor in this case can be obtained from the divergence factor in front of (3.13) with A replaced by B and r4=2B and 04=7r/2. Thus the field at P due to the ray 5 is obtained as: E5() - Ika 2 7r B ikr1 1 1/2 i(2kB-t/4)1 E (P)= -I(- 2M - e k e (3.19) 02) -o-M 2Mr2 n The approximation involved in deriving (3.19) is valid for kB > 1. Following a similar procedure the field at P due to the ray 6 can be obtained. It can be shown that it is given by: E +I (ka)2 7r B ikr 1 1/2 i(2kH-/4) (320) E (P) +ri2 ( e (3.20) oo2 i2M r- (jkH) e 1 Thus the combined field at P due to the rays 5 and 6 is obtained by the addition of (3.19) and (3.20) and is given by: 56 ka 2 r B ikrx F 1 1 /2 i(2kB+7/4) 1k i(2kH- /4) E (P) oo2 2iM r21 Le x kB) e ) e (3.21) This completes the evaluation of the component incident fields in volved in Eq. (3.5). 3. 2. 4 Evaluation of the Parasitic Current We are now in a position to evaluate the current Ipo induced in the parasitic loop.. After introducing Eq. (3.5) into (3.3), Ipo is obtained in terms of the current 26

Io and other physical parameters of the system. Following the same convention used in (3.5) we can write 12 34 56 Ipo'= o Po I o ' (3.22) Using (3.3), (3.4), (3.6), (3.7), (3.17) and (3.21) it can be shown that the component currents in (3.22) are given by the following set of equations. ikrl ikr2 p2 Iko 2 2) ikM r2 r2 (3.23) Ipo I( ikM r2 r2 1 2 22 2 2 2 2 rl=B +(H-h), r =B +(H+h) (3.24) M=0.577 +tn(kb/2)-ir/2 34 ka 2 7r A ikro e-i3/4 A 1 po= 2) ikM 2e - BO 1% iI kr3 { 0-03 0+03 x ( )2 e3 sec( 0 )-sec( 2 ) 1 kr3)2 2 +i1 ( ) ikr4 sc( -04 044( +i kr4 /2e s ec( )-sec( 2, (3.25) 2 222 2222 r2=(A-B)2+H2; r2=(A+B)2+H; rA+h2 (3 tan 3=H/(A-B); tan04 H/(A+B); tan =h/A(36) I6 =I- 2 a 2(kB) eikrl 1/2 i(2kB+7/4) 1 1/2 i(2kH-/4) 5po 2 M2 (kr 12 7rkB TkH (3.27) This completes the evaluation of the current induced in the parasitic loop element. As mentioned before the approximations involved in the derivation makes the above set of equations valid for the cases when kB >> 1 and kA > 1, i. e. when both the parasitic loop and the counterpoise diameters are large compared to the wavelength. For 0o sufficiently small and the present polarization of the field produced by the excited loop, it can be seen that the contribution due to the I4 term is much less than the other terms. More will be discussed about this later. 27

3.2.5 Far Field of a Large Circular Loop Above a Counterpoise In this section we give the theoretical expression for the radiation field produced by a large circular loop of radius B(i. e. kB >> 1) and carrying a current of the form IP= Ipo e and placed at a height H above a counterpoise of radius A. The method of analysis is similar to the one used by Weston et al (2) to obtain the radiation field produced by a small circular loop above a counterpoise. The derivation of the expression is discussed in Appendix A. With reference to Fig. 3-5, it can be shown that the far field at the point P(7r, 0, 0) is given by the following expression, valid in the region <0 <<T: kB R-'/4) I (kB e F(0) (3.28) where p J (kBsin&) p -ikAsin cos0sin(-) ikrP L F()= FP()e + e L P(0), (3.29) 7- cos krpSin2 i(7/2-kAsinO) 7 cosl2 0 J1(kBcos0) -sin/20 J 1(kBsin0) 1-sin ' cos p -sin ikAsin0 J 1(kBcosp)cos/2 (3.30) ir p+sinOe L f p5 ' 2 ikr s-in(0- P) 5 i7rt2/2 ikrpS-n(e+0p) 6 irt2/2 FP(O)=e n e dt-e P' e dt, -oo -oo (3.31) kr 1/2 -e-7r/2 p5=2( -P) cos (, (3.32) kr.l/2 ~p+7+lr/2 P6=2( /2 cos ( ) (3.33) r2=A2+H2 ( P (3.34) tan p=H/A 28

z Far Field Point P(R, 0, 1) / Loop carrying current - ------ -- -; b I eI pr 0 - A - - Counterpoise FIG. 3-5: COORDINATE SYSTEM USED TO DETERMINE FAR FIELD OF LARGE LOOP ABOVE COUNTERPOISE. 29

and J1 is the usual notation for the Bessel function of the first kind and first order. 3.2. 6 The Radiation Field of a Parasitic Loop Counterpoise Antenna The radiation field produced by the parasitic loop counterpoise antenna shown in Fig. 3-1 can now be obtained by superposing the fields given by (2.1) and (3.28) with the parasitic loop current Ipo in (3. 28) being given by (3. 22) - (3.27). Thus it can be shown that in the range 0 < 0 < r the far field may be expressed in the form ka 2 ei(kR- 4) E0= lo( R s(e), (3.35) where S(0)=sA(0)+s ) (0 )+s34(0) (0) (3.36) 12 34 56 In (3.35), S(0) is identified as the complex far field pattern produced by the parasitic loop counterpoise antenna. In (3.36) the terms SA(0) is the free space complex far field pattern produced by the small loop only above the counterpoise and is given by Eq. (2.2). The last three terms in (3.36) constitute the complex far field pattern produced by the parasitic loop only in the presence of the counterpoise. The subscripts in the terms on the right hand side of (3.36) refer to the approximation used in evaluating the corresponding parasitic current. The conventional radiation pattern of the loop counterpoise antenna is given by IS(0)|. Explicit expressions for the terms in (3.36) are given below for future reference. A(0) F~(0)sinO -ikA+sin Icos0 sin( o ) ikr ) ( e___ o(0)1, (3.37) [\ >/4rkr~sin0 F~(0), L~(0) are as defined by (2.3) - (2.8). M 2](0) (3.38) r(k ikrl 1 1kr2 12 k-ir4 i kro A ikr2) 4 e(84 SP4(0) 7r(kA)(kB) e /4 e 1 2 4sec( 0)-sec( 0 34 iM 2 e kr0 B kr4 1 ikr3 __ 0 11 (rkr3 2 F 30

r2(kB)2 r 1/2 kB+ r/4) S (O)= (k ) 1 ) e + 56 2M2 (kr2 kB 1 1/2 i(2kH-/4) F) 3.40) where F(O) is as given by (3.29) - (3.34) and all the other parameters are as defined before. It is appropriate at this stage to list the following approximations involved in the derivation of (3.37) i (3.40): kSA ~> 1, kB >, 1, kH >> 1, kib << 1 and kA > kB @ (3141) The influence of each of the parameters, A, B, H and b on the pattern as well as the relative importance of each of the terms in (3.36) will be discussed later. This completes the derivation of the theoretical expression for the radiation field produced by the parasitic loop counterpoise antenna. 3. 3 Description of the Experimental Arrangement For experimental investigations a parasitic loop was positioned coaxially with the axis of an active Alford loop antenna. Both the parasitic element and Alford loop were mounted above a counterpoise having 2A^, 5.7 X at an operating frequency of 1080 MHz and is shown in Fig. 3-6. All pattern measurements were carried out in the 0-variable plane of Fig. 3-6. The basic Alford loop counterpoise antenna is similar to the one described in Section 2. 3 and was not varied during the experiment. The parasitic loops were held in position by a polystyrene foam structure as shown in Fig. 3-7. As can be seen from both figures, the parasitic loops are made of conducting strips rather than conducting wires as assumed in the. theory. This has been done for mechanical simplicity. In comparing the experimental results with theory it is assumed(5) that a conducting strip of width w is electrically equivalent to a conducting cylinder of radius b, which is a reasonable assumption provided w 4b ad w, wb < X. The parasitic elements were fabricated from brass strips 9.15x 103 X thick at 1080 MHz and oriented as shown in Fig. 3-6. Two basic parasitic elements having w = 1" and w = 2" were used during the experiment. These two widths correspond to 9.15x 10-2 X and 1. 83x 10-1 X respectively at the frequency 1080 MHz. Employing each of these basic parasitic loop configurations in the Alford loop counterpoise system, the effects of the variation of H and B (Fig. 3-6) on the patterns were studied. All the patterns were measured in an anechoic chamber. It should be noted that the height H of the parasitic loop is measured from the top surface of the counterpoise to. the center (w/2) of the parasitic element. 31

z l 5.7X x X FIG. 3-6: SCHEMATIC DIAGRAM OF THE EXPERIMENTAL PARASITIC LOOP COUNTERPOISE ANTENNA. 32

Co3 FIG. 3-7: PHOTOGRAPH OF THE PARASITIC LOOP COUNTERPOISE ANTENNA.

3. 4 Comparison Between Theory and Experiment A typical measured elevation pattern of the loop counterpoise antenna system with one parasitic loop is shown in Fig. 3-8. This particular value of H was chosen here because it was anticipated that the disagreement between theory and experiment would be more for smaller values of H. Theoretical points as obtained from numerical computation of IAs(0) SP (0)1 of Eq. (3.36) are shown as dots in Fig. 3-8. It can be seen that with this first order approximate theory, the agreement between theory and experiment is fairly good over most of the range of 0 despite the fact that the pattern has been computed by neglecting all diffraction effects in the determination of the parasitic current. Diffraction effects on the parasitic current are taken into account by numerically computing ISA() +SP (0) +SP (0)1 of Eq. (3.36). These computed points are shown as crosses in Fig. 3-8, which shows a slight improvement in the agreement between the theory and experiment due to the inclusion of the term SP (0). The improvement is found to be more than 3 db for values of 0 near 0~ and for 0 > r/2. Numerical computations indicated that the term SP4(0) in (3.36) is negligible compared to the other terms. For this reason, in the theoretical calculations discussed below, this term was not considered and was also neglected for all subsequent calculations. Figure 3-9 shows the measured and theoretical elevation patterns produced by an antenna system with a parasitic element having a larger value of b. The agreement between theory and experiment here may be considered to be satisfactory in. the range 0 < 0 < 80~. For 0 > 80~ the disagreement between the two is found to be worse than that considered in Fig. 3-8. This is attributed to the fact that the values of b, B and H used in obtaining the theoretical pattern in Fig. 3-9 lie in the extreme end of the range of validity of the approximation mentioned in (3.41). For larger values of B and H the agreement will be better. The present theory may be further improved by taking into account higher order diffraction terms in obtaining the induced current in the parasitic loop. However it is anticipated that for larger values of H and B the present theory should agree better with experiment. This is borne out in Fig. 3-10 where the agreement between the two may be considered to be excellent. On the basis of our comparative study of numerical and experimental patterns it may be said that the theory given in Section 3. 2 can be used with satisfactory 34

180~ FIG. 3-8: FREE SPACE FAR FIELD ELEVATION PATTERN PRODUCED BY SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA. ka=2.75, kH=3.75, kA=17.92, kb=0.15, kB=47r, f=1080 MHz ( —)Experimental, (,,*)SA(0)+SS1P(0) Theoretical, (xY) 12 IS\)P (e) + ) + SP (0)1 Theoretical. 2 35 35

FIG. 3-9: FREE SPACE FAR FIELD ELEVATION PATTERN PRODUCED BY SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kH=3.75, kA=17.92, kb=0.287, kB=2.5ir, f=1080 MHz (-)Experimental, (., ) Theoretical. 36

FIG. 3-10: FREE SPACE FAR FIELD ELEVATION PATTERN PRODUCED BY SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kH=11.78, kA=17.92, kb=0.15, kB=2.57r, f=1080 MHz (-) Experimental, (.o) Theoretical. 37

accuracy for kb < 0. 25 and kB, 2.57r and kH > 3.75. The accuracy will be better for larger values of B and H and smaller values of b. 3. 5 General Effects of the Parasitic Loop on the Radiation Pattern The elevation pattern of the basic Alford loop counterpoise antenna was discussed in Chapter II. The considerable response of the antenna for 0 > r/2 as shown in Fig. 2-4 is due to the effects produced by the counterpoise edge diffraction. After comparing the patterns given in Figs. 3-8 through 3-10 with that given in Fig. 2-4, it can be said that, in general, the parasitic loop reduces the effects of counterpoise edge diffraction considerably. This is evident from the fact that the parasitic loop counterpoise antenna patterns discussed in Section 3.4 show much reduced response in directions 0 r/2 than that shown in Fig. 2-4. This effect is particularly true for small values of H and all values of B. In addition to this the introduction of a parasitic loop increases the average response of the antenna near the axial directions. This observation has also been reported by us elsewhere(6). The parasitic loop can thus be utilized to shape the loop counterpoise antenna patterns in the regions near 0=0~ and also 0 > 90~. We shall discuss this in more detail in a later section. 3. 6 The Effects of Variation of the Parasitic Loop Parameters r. ' ~.... -,......'.....;.. /; - ' " In this sectionwwe'discuss qualitatively the' general effects of the variation of the parasitic loop parameters b, H and B on the parasitic loop counterpoise radiation patterns. Quantitative discussions of these effects will be given in later sections. The following observations are made from a general study of the numerical and experimental results. The parameter b (or w) has been found to be quite critical. For kb < 0.15, (i. e. w < 0.09X) the parasitic loop does not receive enough excitation to affect the pattern appreciably (Eq. 3.3). As kb is increased beyond 0.15, the amount of reduction in field response in directions 0 > 90~ at first increases, but for kb > 0.3 the overall pattern becomes too much distorted as compared with Fig. 2-4. It was mentioned in Section 3.5 that for small values of H the parasitic loop produces strong effects on the overall pattern. This is due to the fact that as H is increased the magnitude of the parasitic current IIpol decreases. A study of (3.23) - (3.27) reveals the fact that |Ip I becomes maximum near H - h, i. e. the parasitic loop lying near the plane of the Alford loop. With kb = 0.15 it has been found both theoretically and experimentally that for H > 2 X the effect of the parasitic loop on the radiation pattern near the direction 0 > 90~ is negligible. 38

The effects of the parameter B has been found to be quite strong whenever 2B is of the same order of some multiple of a wavelength. The position and amplitude of the minor lobes in the parasitic loop counterpoise antenna pattern near the axial region is found to depend in a complicated manner on both B and H. 3. 7 Discussion In the present chapter we have developed a theory for the radiation field produced by a parasitic loop counterpoise antenna. Within the range of approximation the theory has been found to agree satisfactorily with experimental results. It may thus be concluded that the theory can be used for theoretical investigation of the various radiating properties of the present antenna configuration as the different parameters are varied. 39

IV RADIATION CHARACTERISTICS OF A SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA 4. 1 Introduction In the present chapter we investigate in more detail various aspects of the radiation characteristics of a single parasitic loop counterpoise antenna. The parasitic loop counterpoise radiation patterns are compared with the pattern produced by the basic Alford loop above the counterpoise. The effects of the different parasitic loop parameters on the patterns are also discussed. The investigation is divided into two main parts. The first part presents and discusses the results of an experimental investigation of the radiation properties of the antenna. as the parasitic loop parameters are varied. The second part gives the results obtained from numerical computation of the theoretical expressions given by Eqs. (3.37) - (3.40). These contain information about the amplitude and phase variation of the far field as functions of the different parameters of the parasitic loop. 4. 2 Experimental Results The experimental arrangement has been described in Section 3.3. The basic system was the Alford loop placed at a height 0.44X above the 5.7X diameter counterpoise as described in Sections 2.3 and 3.3. Two sets of parasitic loops having w=0.0915X and w=0.183X and variable B and H (Fig. 3-6) were used during the experiment. With the first type of parasitic elements (w=0.0915X) the elevation patterns of the system were measured at 1080 MHz by varying the height H from 0.23 X to 1.88 X in steps of 0.18X increments and the diameter 2B from 1.0X to 5.0X in 0.5X increments. Similar measurements were carried out for the antenna with the second type of parasitic elements (w=0. 183 X) with the corresponding variations of H from 0.46 X to 0.82X and of 2B from 1.0 X to 5.O0X. All the measurements were carried out at 1080 MHz. 4. 2. 1 General Behavior of the Patterns The radiation patterns obtained for single parasitic loop counterpoise antenna as a function of the parasitic loop parameters are presented in Figs. 4-1 and 4-2. Although the details are lost these figures may be found useful in ascertaining the general behavior of the patterns with the variation of H and B. Figures 4-1 and 4-2 should be compared with the pattern produced by the basic Alford loop counterpoise antenna as given in Fig. 2-4. It should be noted that the Alford loop is located at a 40

-- Parasitic Element Diameter 2B/X 1.88 CO J 1.70 CD ) CD C C' CQD C CD 9 cD c<D C-,C)c2Z Cl) 0 0 a2) 0 a1) C.) -4-a Cl) 1.52 QO QC D mQDjI227 1.35 CD Qcl~D 1.15QD CD c KI1 0.96 QC IC C c2DK2 0.78 D D dj Kh 0.60 Cr Kf) c Q f ) CD3 C Q 9 0.41 ci CD (Q5 Q ~SW CK cW Z i1T 0.23 D (Q 1D cD cz D ( ) CD C9 FIG. 4-1:MEASURED FAR FIELD ELEVATION PATTERNS OF SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA. h=0.44X, w=0.092X, A=5.7k, f=1080 MHz, 2B and H variable. 41

Q ca 0 - l -o 03 0o *-4-l a) -* Parasitic Element Diameter, 2B/X 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.82 C fi2 2 2 1Q K221 0.64 ( 0.46 ) Q C -P) Q K Ci ec 5 D CI I3 KC U CD 9 Ct C FIG. 4-2: MEASURED FAR FIELD ELEVATION PATTERNS OF SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA. h=0.44X, w=0.183X, A=5.7X, f=1080 MHz, 2B and H variable. 42

height h=0.44X above the counterpoise. After comparing Figs. 4-1 and 4-2 with Fig. 2-4 it is found that in general the behavior of the pattern near the principal maximum is not altered appreciably due to the introduction of the parasitic loop. The principal maximum of the basic Alford loop counterpoise antenna is in the direction 0=550 (Fig. 2-4). The direction of principal maximum in the pattern of the parasitic system varied between 50~ to 60~ over most of the range of variations of H and B shown in Figs. 4-1 and 4-2. The main effects of the parasitic loop are observed in the two regions of space. New lobes appear in the pattern in the region near 0=-0. The position of maximum of this lobe has been found to lie within 100 to 200 off the axial direction. In general the amplitude of this lobe has been found to be of the order of the main maximum but it may become larger than the main maximum for larger values of B. For large values of B there appeared more than two secondary maxima near the region 0=00. In the second region of space defined as 0 > 900 the general effects of the parasitic loop has been found to reduce the average level of response of the antenna, i. e. the counterpoise edge diffraction effects are reduced by the parasitic loop. The above effects depend, in a complicated manner, on the parameters w, B and H, so that it is not possible to give any rule for the effects produced by the variation of these parameters. In the following sections we give a few quantitative observations obtained from more careful study of the experimental patterns. 4. 2. 2 A Few Observations (1) For H < 0.44X, i. e. when the parasitic loop lies below the Alford loop the direction of the principal maximum moves towards the direction 0 = 00, for values of 2B in the range 1 - 2 X. This has been found more pronounced for the case w-O. 183 X where the principal maximum occurred near the direction 0=35~. (2) For H < 0.44X and all the values of B the parasitic loop is found to be ineffective in modifying the pattern shape in the directions 0 > 90~. (3) For HN0.6 X the parasitic loop is found to be most effective in reducing the field in directions 0 > 90~. This effect has been observed for all values of B. The amount of reduction is found to increase with increasing w. For example the maximum field reduction in the direction 0=900 is found to be about 24db for H=0.64X, 2B=2.5X and w=0.183X and 20db for H E 0.6X, 2B=2.5X and w=0.092X. For the basic system this factor was 10.3db. (4) The effect of the generation of the secondary maxima near 0=0~ and the reduction of field in directions 0 > 90~ increase with increasing w. This can be seen from the typical patterns shown in Fig. 4-3 43

(a) w=l", H= 6.5" (b) w=2", H=711 FIG. 4-3: MEASURED FAR FIELD ELEVATION PATTERNS SHOWING EFFECTS OF PARAMETER w. h=4.8", A=5'2", f=1080 MHz. 44

(5) The gradient of the field at the horizon is not much improved for small values of H. The improvement is found to take place for longer values of H and B. This is because for these values of H and B there appears a minimum in the pattern a few degrees below the direction 0=900. With a single parasitic loop system the best theoretical field gradient obtained was 8.4 db/60 with the system shown in Fig. 3-10. 4. 3 Numerical Results In this section we discuss the theoretical behavior of the patterns produced by the parasitic loop counterpoise antenna system in the region below the horizon defined as 90~ < 0 < 1200. The reason for choosing this region of space is that it is in this region the existing VOR antenna patterns need to be improved. The experimental investigation discussed above indicated that for largers values. of H and B the parasitic loop can improve the horizontal field gradient considerably. The pattern behavior is discussed for the parasitic loop counterpoise system having kb=0.15, and kH > 10.00 and kB > 3r. As discussed in Section 3.4 within this range of parameters the theory predicts the pattern with satisfactory accuracy. The results discussed below have been obtained by numerically computing Eq. (3.36) without the term SP (0). In the sections below the following notations are used to represent the various pattern functions. SA(O) = complex far field pattern produced by the basic Alford loop above the counterpoise, S(0)=S (e)+SP2(0)+ sP (0)= complex far field pattern produced by the parasitic loop counterpoise antenna, SP()=SP (0)+sSP (0)= complex far field pattern produced by the parasitic loop 6 only above the counterpoise, o= field gradient at the horizon = -20 log 10 E (90) EO(90~) ] aF= field reduction at the horizon= -20 log 10 E0(900m) ~ 4. 3. 1 Field Gradient Characteristics As mentioned in Section 2.6.2 the field gradient at the horizon obtained from the basic Alford loop counterpoise antenna is 3,09 db, Experimental results discussed in Section 4.2 and numerical investigations indicate that for small values of H (i.e. H < 1.5 X) although the parasitic loop considerably reduces the response of the parasitic loop antenna in the directions 0 > 90~, it only improves slightly (1 or 2db) the 45

field gradient compared to that obtained in the basic system. Usually ag takes on large values whenever B is some multiple of X. This can be seen from Fig. 4-4 which shows the theoretical variation of ag as a function of kH with kB as the parameter. It is found that significant improvement in the field gradient can be obtained only for some specific values of B and H. Within the ranges of variables shown in Fig. 4-4 a parasitic loop with kB=3rT and kH=11.7 is found to be the optimum and it yields a maximum value, of a g=8.43 db. This is confirmed by the experimental pattern shown in Fig. 3-10, which is also found to be the optimum pattern from this point of view. The curves given in Fig. 4-4 can thus be used to obtain the best field gradient characteristics from a single parasitic loop counterpoise system. 4. 3. 2 Pattern Behavior Near the Horizon - 45 The behavior of the parasitic loop counterpoise antenna radiation pattern in the region near and below the horizon (900 < 0 < 1200) is shown in Figs. 4-5a - 4-5c for various values of B and H. The range of values of B and H are chosen to be the same as considered in Section 4.3.1 so that direct comparison of results may be possible. It is found that for each value of kB considered a minimum in the pattern appears inlS(0)l for some value of kH. As kH is increased the position of this minimum moves towards the horizontal direction; at the same time the amplitude of the minimum assumes a largest value for some intermediate value of kH. On comparing Figs. 4-4 and 4-5a-c, it can be seen that an optimum parasitic system producing the best field gradient may not necessarily yield the deepest minimum in the far field pattern below the horizon. Using the curves given in Figs. 4-4 and 4-5a-c, a best compromise can be made under a given practical situation. 4. 3. 3 Parasitic Field Near the Horizon In a practical situation it may be desirable to control the position and amplitude of the minimum in IS(0) below the horizon. For the system considered here this can be done, in principle, by adjusting the phase of the parasitic field SP(0) to be 180~ out of phase from that of SA(0). The variation of the amplitude and phase of SA(0) has been discussed in Section 2.6.1. In this section the behavior of the complex field SP(0) near the horizon is discussed. Figure 4-6 shows the complex parasitic field SP(O)= Re SP(0)+ i Im SP(0) as a function of H for some selected values of 0 below the horizon. Note that the curves in Fig. 4-6 are given for constant B and that the values of kH are marked on the individual curves. It is important to note that the phase of the parasitic field, as shown here, lies in the fourth quadrant. These curves combined vithtthose given in Fig. 2-7 may be found convenient in the design of single parasitic counterpoise antennas having a required field characteristic near the horizon. 46

9 kB=47r 8 7 6 5 Gradient ag (db) 10.0 11.0 kH - 12.0 12.6 FIG. 4-4: THEORETICAL FIELD GRADIENT NEAR HORIZON OF SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA ELEVATION PATTERN. kh=2.75, kA=17.92, kb=0.15, kB and kH variable.

0 kH= I s(o)l -20 (db) = co -30 -40 90 100 0o 110 1 20 FIG. 4-5a: THEORETICAL VARIATION OF PARASITIC LOOP COUNTERPOISE ANTENNA ELEVATION PATTERN [S(0)| BELOW HORIZON. kh=2.75, kA=17.92, kb=0.15, kB=3r, kH variable..78

0 I Is(0)I (db) I I Co I FIG. 4-5b: THEORETICAL VARIATION OF PARASITIC LOOP COUNTERPOISE ANTENN ELEVATION PATTERN IS(0)[ BELOW HORIZON. kh=2.75, kA=17.92, kb=0.15, kB=3.1r, kH variable.

0 kH = s(O) (db) 01 0 *-20 ~-30 -40 90 e FIG. 4-5c: THEORETICAL VARIATION OF PARASITIC LOOP COUNTERPOISE ANTENNA ELEVATION PATTERN S(0) BELOW HORIZON. kh=2.75, kA=17.92, kb=0.15, kB=47r, kH variable.

Re SP(0) kH=11.4 1.04 6.24\A.2 2.20.18.16.14.12.10.08.06 kH=11.6 ~ 06 0=940 0=96 \. 11.6 12.08 \.10 12 2 t;4 \1i. \. 12 2.0 12.6.1.20 22.2.22 -.24-.26 FIG. 4-6: THEORETICAL VARIATION OF PARASITIC FAR FIELD SP(0) BELOW HORIZON. kh=2.75, kA=17.92, kB=37r, kb=0.15. 51

4. 3. 4 Far Field of the Parasitic System Near the Horizon As discussed in the previous sections, a parasitic loop counterpoise antenna with H^- 0.6 X and B > 1.5 X reduces the overall response of the antenna in directions 0 > 90~. However, the field gradient characteristics of such an antenna is not much superior to that of the basic Alford loop counterpoise antenna. As will be discussed later, it may be necessary to use such a single parasitic loop system as the basic antenna and to use another parasitic loop above it so that the pattern produced by the complete system will yield a very large value of ag. For this purpose it would be convenient to have information about S(0) near the horizon. Figures 4-7a - d show the variation of -S(0) as functions of kB and kH for selected values of 0 below the horizon. Each curve is for a constant kH and the variable kB values are marked on each. Note that the curves show the negative of S(0), the reason for doing this will be discussed later. It is interesting to note the regions A and B of Fig. 4-7c for 0=96~. It can be seen that in these two regions S(0) is insensitive to small variations in B and H. Thus an antenna system designed to operate in this region will not change its field characteristics near the horizon for small changes in B and H. This observation may be found convenient in some practical situations. The curve SP(96~) shown in Fig. 4-7c is superposed here for future reference and will be discussed in a later section. 4. 3. 5 Some Useful Results In this section a few useful quantities pertaining to the radiation pattern produced by a single parasitic loop counterpoise antenna are given in tabular form in Table IV-1. These tables are meant to provide quick estimates of the variation of the various quantities as the parasitic loop parameters are changed. The variation of the following quantities will be tabulated: 00 = the direction of the principal maximum, aF = the field reduction factor, ag = the field gradient/6~ at the horizon in db, p = the field ratio = 20 loglo E(100), 001 = the directions of the maximum of the minor lobes near the regioni 0=0~, aO1 = the minor lobe amplitude relative to the maxima at 0=00, in db, E(00)= amplitude of the field in the direction 0=0., in db. 52

Re S(O) (negative real axis) I I I I I I I 9 I N I 5 I I I I I I I I.32.30.28.26.24.22 4.1r 41r6-0 s-* N- -~~ mt t I I I I. I I I I.20.18.16.14.12.10.08t.06 N 40,000015M,100 4M 4 a* 4101WAMOWab -,% 0 0 "%% N\ C." CA. 'I 'I I I ) 3.8wr I 0\3.97r.06-.08-.10...12......14-.16-.18_ 04 00 -0 I U, /.2 0 -.22 -~.24 - FIG. 4-7a: THEORETICAL FAR FIELD 5(0) OF PARASITIC LOOP COUNTERPOISE ANTENNA IN DIRECTION 0=920. kh=2.75., kA=17. 92,, kb=0.15 ( —)kH=3.8., (-)kH=3.7)( ---)kH=3.6.

^ A I I I I 7 -i I- II I II 1.20.26.24.22.20.18.16 ~-.14.12.10.08..06.06 -.0o8 - - 041 47' 00 m m0 -WWItf * -0wp % 0.10 I N 0 00 0 'I 7.97r * 3.87r I I I.12.14.16.77r.18.20.22 _.24-.26 - FIG. 4-7b;P THEORETICAL FAR FIELD S(O) OF PARASITIC LOOP COUNTERPOISE ANTENN IN DIRECTION 0=940. kh=2.'75,9 kA=17.92, kb=0. 15 (- -)kH=3.8 (-)kH=3.7 (- - -)kH=3.6.

FIG. 4-7c: THEORETICAL FAR FIELD S(0) OF PARASITIC LOOP COUNTERPOISE ANTENNA IN DIRECTION 0=90~. kh=2.75, kA=17.92, kb=0.15, ( ---)kH=3.8, (-)kH=3.7, ( — — )kH=3.6. 55

.04 I I I I I I I I.20.18.16.14.12.10.08.06.0.08.10.12 - C,, 3.7fr 41.2 2 J FIG. 4-7d: THEORETICAL FAR FIELD s(e) OF PARASITIC LOOP COUNTERPOISE ANTENNA IN DIRECTION e=980.' kh=2.75, kA=17.92., k~b=0.15., ( —)kH=3.8)., (-)kH=3. 7, ( — -)kH=3.6

4. 4 Discussion The results given here indicate that a single parasitic loop placed suitably above an Alford loop counterpoise antenna is capable of improving the field characteristics of such an antenna in the region below the horizon. The field pattern near the principal maximum direction is not altered much. Near the region 0=00 the antenna response increases considerably and new lobes appear in the pattern. Numerical results given here should be found useful for the purpose of shaping the radiation pattern of an Alford loop counterpoise antenna with the help of one or more parasitic loops. TABLE IV-1: RADIATIOX PATTERN CHIARACTEiSTICS OQFA SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA (a):kh=2.73, kH=4.00, kb=0.15, kA=17. 92, kB is variable kB Oo (7) (~) E(0o) F 0 F a 001 g (0) 2.50 2.75 3. 00 3.25 3.50 3.75 4. 00 4.25 4.50 4.75 5.00 55 50 45 60 55 55 50 60 60 55 50 5.87 4.80 3.33 5. 15 5.83 5.74 5.08 4.18 5.42 6.19 5.70 15. 31 19. 46 14. 74 12.55 13. 64 16. 60 16. 14 11. 52 12. 49 15. 27 15. 62 3.97 3.65 3.53 3.89 3.85 3.58 3.01 3.71 3.74 3.56 2.95 15 10 10 10 10 10 10 10 5 5 5 -3. 38 -0. 93 +1. 58 -1. 98 -4.84 -3. 73 -2. 55 -3. 07 -5. 33 -5. 90 -2. 88 p -6. 37 -6.29 -5. 87 -6. 51 -6. 51 -6. 21 -5. 31 -6. 24 6. 33 -6. 21 -5. 10 -6. 85 -6.28 -5. 89 -6. 69 -6. 48 -6. 14 -4. 65 -6. 19 -6.24 -6. 18 -4. 89 (b): kh=2.75, kH=4. 00, kb=0.287, kA=17. 92, kB is variable 2.50 2.75 3.00 3.25 3.50 3. 75 4.00 4.25 4.50 4. 75 5.00 55 50 45 60 55 50 50 50 60 55 50 5.95 4.84 3.58 4.82 5.76 5.68 5.41 3.80 5.23 6.20 6. 15 15. 13 17, 72 19. 20 12. 70 13. 18 15. 17 18. 78 11. 57 11.98 14. 26 17. 20 4.05 3. 62 3.37 3.99 3.83 3.53 2.55 3.69 3.68 3.53 2.56 15 10 10 10 10 10 10 10 5 5 5 -2. 17 +0. 34 +3. 27 +0. 57 -3. 09 -1. 80 -0. 71 -0. 77 -4. 03 -2. 45 -1. 30 57

TABLE IV-1 (continued (c): kh=2. 75, kb-0. 15, kH o0 (0) kB=37r, kA=17. 92, Kh is variable E(0o) aF a 001 0 g (O). 10.63 10.90 11.20 11.50 11. 78 12.00 12.30 12.50 50 50 50 50 50 50 50 50 3.67 3.83 3.98 4.11 4.18 4.21 4.20 4.16 8.81 9.96 11.20 12.30 13. 00 13.29 13.27 14.05 3.94 4.83 6.26 7.92 8.40 7.29 5.07 3.80 10 10 10 10 10 15 15 20 01 -3. 70 -2. 93 -2. 86 -3. 52 -4. 75 -6. 15 -7. 99 -9. 18 p -6.89 -8. 69 -12. 30 -17. 95 -13. 52 -8. 91 -5. 30 -3. 77 The corresponding quantities for the basic Alford loop counterpoise antenna are: kh=2.75, kA=17.92, 0o=550.3, E(0o)=+4.59, aF=10.38, ag=3.09, p= -5. 15. 58

v INVESTIGATION OF A DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 5. 1 IntrQduction.-; From the results discussed in the previous chapters it is found that a single parasitic loop counterpoise antenna is capable of producing good field gradient characteristics near the horizon while maintaining the characteristics in the regions near the principal maximum similar to those of an Alford loop counterpoise antenna. The largest value of a obtained for such an optimum system was found to be 8.4db. It is conceivable that by using another parasitic system it may be possible to obtain larger values of ag. In the present chapter we investigate the feasibility of using two parasitic loops in conjunction with the basic Alford loop counterpoise antenna in order to achieve better field gradient characteristics. 5. 2 Double Parasitic Loop Counterpoise System A double-parasitic loop counterpoise antenna system is shown in Fig. 5-10 ft consists of two parasitic loops placed parallel to each other and to the plane of the counterpoise. Sometime this will be referred to as a colinear system in contrast to the coplanar system where the parasitic loops are placed in the same plane. It is assumed that the two parasitic loops have the same b (or w in the experimental model). Additional control may be obtained by using different values of b. The principle of the design is to choose the parameters H1, B1 and H2, B2 such that the combined field produced by the parasitic loops in a certain direction below the horizon be such that when it is superposed with the Alford loop field in that a direction a deep minimum is produced in the pattern. The choice of the H1, B1 and H2, B2 may be facilitated by using the results of the previous chapter. 5. 3 Theoretical Expression for the Radiation Field If the distance between the two parasitic loops are small, then the mutual coupling effects between them must be taken into account and the theoretical analysis of the radiation field becomes complicated. However, after studying the phase of the parasitic field (arg SP(0) ) below the horizon (as discussed before), it is found that the phase of the parasitic field in this region opposes that of the basic Alford loop field for values of H near 0. 6 X and 2 X. It is thus anticipated that for the present purpose the two parasitic loops should be separated by a distance at least of the order of X or more. in such cases the mutual effects may be neglected. hi a coplanar parasitic loop system mutual coupling effects may be neglected if B2-B1 > X. 59

2-,2B2 Parasitic - -Loop No.2 Parasitic Parasitic A. T Ae ao~w T.,' I - H1 1 I A JLU p NO.1 2B1 ('-Phase center of Alford Loop I 1 I ' -q I --,,/ / /// / / / // / / // /,. /// // IF -- A —....! FIG. 5-1: DIAGRAM OF DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA. 60

In the absence of mutual coupling between the parasitic loops the theoretical expression for the radiation field produced by a double-parasitic loop system can be obtained by a simple modification of the theory given in Section 3. 2 for the single parasitic loop system. Thus the far field produced by the system consisting of the Alford loop, the parasitic loop No. 1 and the counterpoise can be written as ka 2 ei(kR-7/4) S1 =18 2), (5.1) where S ()=A(0)+P (0)+ (0)+P (0) (5.2) 1 12 34 56 and all the other notations are as explained in Section 3.2.6. All the parameters involved in the detailed expressions of (5.2) (see Eqs. 3.37 - 3.40) should pertain to the parasitic loop No. 1. Similarly, the far field produced by the parasitic loop No. 2 only above the counterpoise can be written as 2 i(kR-r/) (0) E02= Io) R S2 ( (5.3) where S2() S12(0) +S34 (0)+S56(0) (5.4) In (5.4) the terms on the right hand side are given by (3.38) - (3.40) with the understanding that the different parameters involved pertain to the parasitic loop No. 2. Thus the far field produced by the double-parasitic loop counterpoise system in the range 0 < 0 < ir is given by the following expression: ka)2 ei(kR-r/4) ()+s) 0=0oio( 2 R ()+S() The approximations involved in (5.5) are same as discussed in Section 3.2.6. Thus, Si(0)+S2(0) gives the complex far field of the double parasitic loop counterpoise antenna. 5.4 An Example In the present section we outline the method of designing a double-parasitic loop counterpoise antenna so that there may be a deep null in the radiation pattern in a direction 0=96~. Let us choose the normalized height of the first parasitic 61

loop to be kH1=3. 70. This particular value of H is chosen because a single parasitic loop system with this value of H yields maximum field reduction factor aF1. The negative of the complex far field S1(0) in the direction 0=96~ as a function of kB1 is then given by the curve marked with a: cross in, Fig. 4-7c. In the same figure we have also given SN(0) for 0=96~ as a function of kH2 for the second parasitic loop with kB2=37r. The points of intersection of the curves S(960) and S~(96~) in Fig. 4-7c will give the undetermined parameters kB1 and kH2. It is thus anticipated from Fig. 4-7c that for kB1=47r, kH1=3.70 and kB2=37r, kH2=11.9 a sharp minimum will be produced in the pattern in the direction 0=96~. The complete far field pattern produced by the system may be obtained from Eq. (5.5). The measured elevation pattern produced by such an antenna is shown in Fig. 5-2. The theoretical points obtained by numerical computation of Eq. (5.5) are also shown in Fig. 5-2 in the range 0<0<7r. The agreement between the two may be considered to be satisfactory. 5. 5 Optimum Double-Parasitic Loop Counterpoise Antenna In the example given above and with reference to Fig. 4-7c, it can be seen that for the particular parameters chosen S1(0) and SP2(0) do not completely cancel each other in the direction 0=960. It may thus be possible to obtain a larger value of ag from the antenna by slight adjustments of the parameters H1, B1 and H2, B2. This was done experimentally as follows. The parameters B1 and H1 were fixed at kB1=47r, kHl=3.70. Then H2 and B2 were adjusted slightly and for each setting of H2, B2 a complete pattern of the system was measured. During this adjustment it was found that the setting of the parameter H2 was more critical. In this way an optimum system was obtained which yielded the maximum value a The optimum pattern obtained is shown in Fig. 5-3. The field gradient obtained is 1 db/50~ 5 and the field reduction factor caF=23db. In order to observe the effects of the parameter w on the pattern a parasitic system was fabricated with strips of wl=w2=0.183X (i.e. kbl=kh2=0.3) and the system pattern was optimized experimentally by adjusting the parameters. The measured elevation pattern of this second optimum double-parasitic loop counterpoise antenna is shown in Fig. 5-4. This pattern has a -12 db and aF= 16 db. On comparing Figs. 5-3 and 5-4 it is found that the field gradient is better in the former but the response of the antenna beyond the minimum below the horizon is much less in the second antenna. This may be found useful in some practical situations. The basic principle by which high field gradient is obtained is the cancellation of the Alford loop counterpoise field in a certain direction by the parasitic fields in that direction. It is therefore anticipated that the performance of any optimum system thus designed will be highly frequency sensitive. The radiation pattern produced by the first optimum antenna system was measured over the frequency range 62

FIG. 5-2: FAR FIELD ELEVATION PATTERN PRODUCED BY DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kHl=3.70, kB1=4z, kH2=11. 78, kB2=0.15, f=1080 MHz. (-)Experimental (a *)Theoretical 63

FIG. 5-3: MEASURED FAR FIELD ELEVATION PATTERN OF OPTIMUM DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kA=17.92, kb =0. 15, kB1=4v, kH1=3.7, kb2=0. 15, kB2=10.27, kH2=10.63, f=1080 MHz.

0 H 0 H 0 z H 0 rx4 10 101 CL Cl Cl II cII 00 H) 01 0q 01 0 -H 00 Cl C) (0 c0 II 0 H 65

of 1080 - 1180 MHz. The overall shape of the pattern near the principal maximum did not change appreciably as the frequency was varied. However, the field characteristics below the horizon changed considerably as can be seen from Figs. 5-5a - g. The variation of the different quantities with frequency is shown in Table V-1. These values ar4 obtained from the measured patterns. 5. 6 Pattern Variation with H2 During the optimization of the antenna to obtain large field gradients it was found that the parameter H2 influences the pattern behavior considerably. In order to study this effect more carefully the patterns produced by a two-loop system, having 2B1=2B2=2.5X, H1=0.65X, w1=w2=0.183X and H2 variable, were measured. The results of this investigation are shown in Fig. 5-6 5. 7 Impedance Characteristics The impedance characteristics of the double loop antenna have been measured in the frequency range 1080 - 1180 MHz in 20 MHz increments. The objective of this investigation was to determine the influence of the parasitic loops on the impedance of the basic Alford Iloop above the counterpoise. In the experimental arrangement there was a 4.8" long section of 50 ohm coaxial transmission line between the impedance measuring point and the terminals of the Alford loop. Because of the high input VSWR associated with the Alford loop, efforts were, made to match the Alford loop (employing a double stub tuner) to have a VSWR of less than 1. 2: 1. The measured impedances referred to by the input connector, of the Alford loop above the counterpoise are shown in Fig. 5-7. The corresponding VSWR obtained are shown in Table V-2. As can be seen from the table, the values of VSWR at 1160 and 1180 MHz are somewhat higher and are probably caused by the double stub tuner needing to be positioned differently along the line. The two colinear parasitic rings were constructed from 2" wide strips each having a diameter of 27" (i. e. 2B ' 2.5X at 1080 MHz). They were positioned so that the lower loop was 7" (- 0.6Xat 1080 MHz) and the upper loop was 22" (a 2 X at 1080 MHz) above the counterpoise. The VSWR characteristics obtained at the input terminals of the two parasitic loop antenna are shown in Table V-2. As can be seen from the table, the parasitic loops have very little effect on the VSWR characteristics. 66

(a) f = 1060 MHz (b) f = 1080 MHz (c) f = 1110 MHz (d) f = 1120 MHz FIG. 5-5 a-d: MEASURED FAR FIELD ELEVATION PATTERNS OF OPTIMUM DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kA=17. 92, kbl=0.15, kBl=4r, kHl=3. 7, kb2=0.15, kB2=10. 27, kH2=10. 63. 67

(e) f = 1140 MHz (f) f = 1160 MHz (g) f = 1180 MHz FIG. 5-5e-g: MEASURED FAR FIELD ELEVATION PATTERN OF OPTIMUM DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kA=17.92, kbl=0.15, kB1=47r, kH1=3.7, kb2=0.15, kB2=10.27, kH2=10.63. 68

TABLE V-1: PATTERN CHARACTERISTICS FOR THE OPTIMUM DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA f (MHz) 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 min E. min max Emax ag 0min (0) 2 2 2. 5. 8 11 14 16 19 20 5 5 Emin (db) -0.2 -0.3 -7.0 -21.0 -24. 6 -26.4 -27. 8 -26. 6 -30. 0 -32. 0 0 max (0) 15 21 24 25 27 28.5 29 37 40 41 E max (db) +0.7 +8.2 +9.5 +0.5 -4.9 -8. 8 -11. 1 -13. 4 -15. 2 -16. 7 a! g (db) 21/5. 5 14. 6 12.3 7. 9 6.5 6.4 5.8 aF (db) 20. 7 26.4 29. 0 23. 0 18.9 12. 3 13.8 12. 7 12. 8 12. 6 = position of the first minimum in degrees below 0=90~, = amplitude of the field at 0=0min relative to the field at 0=90~, = position of the first maximum in degrees below 0=90~, = amplitude of the field at 0=0max relative to the field at 0=90~, = field gradient = -20 log0 E(960) glog E (900)1 aF = field reduction = -20 log10 IE(90~) 1 E (main max) I Note that in the column for ag, the values are not given for the first three frequencies because at these frequencies the gradient per 60 cannot be defined. The field gradient for f = 1080 MHz is defined to be for 50 5 instead of 60~. 69

-- F.- -. A ~-ll 11 ilH 11FHT I-iI~i, I~~TIIIII 1F I MFIITTIT I 1[~iit hT~=llj[llJtI - T 7 r f/lK} Tl t r t1~.il!Iit itt4HH Hqlwf ttI HHltft~li-IlflH 'H!S!I~Eli~ i 1|ttrT L; - T '! H2 1M.6I 3 MI ~!-HH-HH. -H+-ti rt-t-HHlit~tlI HtH-H.HHH-IIH~! T-HilII{i-[E:[IH! tl1!1d H~ I:~_ 1 lillHili~H-~.~~~~~~~~~~~~~~i +H-tJ F111111tH-H:-+~~t '~-l~H-tI!qH~H~~~;:~ tF H2= 1.63X H2 (not present) 2 H2=1.85X H2= 1.20X H2=2.08k Hu'::,.T[ i] i, ]:1- i lt E! i t1 Jt[l1 ii - 4~I ~I'llllt11 Utt I l i. L ] I tU t.~ t,- I tltt.1H --- ldI~ H! Hti-HI-it 1- -lilll Itrl II;FI i~Ttl FT'I II 4 I I+H H ~ H Ht HI.... 4+!IItHHitlliI!!: H2=1.42X H2=2.29X FIG. 5-6: MEASURED ELEVATION PATTERNS OF DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA. 2Bl=2B2=2.5X, HI=0.64X, f=1080 MHz, H2 Variable. 70

FIG. 5-7: IMPEDANCE CHARACTERISTICS OF ALFORD LOOP COUNTERPOISE ANTENNA ( Freq. = MHz). 71

TABLE V-2: VSWR CHARACTERISTICS OF DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA Frequency VSWR without VSWR with (MHz) two 2" rings two 2" rings 1080 1.14 1.18 1100 1.12 1.16 1120 1.14 1.14 1140 1.16 1.16 1160 1.40 1.50 1180 1.80 2.00 5. 8 Double Coplanar Parasitic Loop System It may be convenient in many situations to use two parasitic loops in the same plane instead of different planes as considered above. Such a system is referred to as the double coplanar parasitic loop system. The measured patterns produced by such an antenna are shown in Fig. 5-8. The average values obtained for ag and aF are indicated on the patterns. The general features of the patterns here are that the response of the antenna in directions 0 > 900 are considerably reduced and the response near the region 0=0~ is increased substantially. The general behavior of the patterns of such an antenna as the different parameters are varied, is shown in Fig. 5-9. 5. 9 Comparison with Single Parasitic Loop System The general pattern characteristics of single and double parasitic loop counterpoise antenna systems are found to be similar. The double-loop system offers additional parameters to shape the pattern near the horizon. From the results discussed above it can be seen that with the addition of the second parasitic loop it is possible to achieve a much deeper minimum in the pattern below the horizon. It is because of this, the double parasitic loop system produced a field gradient much better than that obtained from a single parasitic loop antenna. 72

(a) 2B2=3.5X, H1=H2=0.06X (b) 2B2=1.5X, H1=H2=1.7X (c) 2B2=2.5X, H1=H2=1.7X FIG. 5-8: MEASURED ELEVATION PATTERNS OF DOUBLE COPLANAR PARASITIC LOOP COUNTERPOISE ANTENNA. kh=2.75, kA=17. 92, w=0.09X, 2B1=2X, f=1080 MHz. (a) g(avg)23. db, aF(avg)=5db. (b)g(avg)=7 8db, aF(avg)=161 db () g(avg) =8 5db, F(avg)= 16db. 73

Diameter (2B 2i~nX) 1.5 2.0 o Cv 2.5 Qz Qc2D 3.0 Q2 3.5i Q i) Q22) C2D H=O. 78X 0 Qf!~1 H=0. 6X 1.5 2.0 2.5 -~3.0 m 3.5 a)Q C:) C Z" ) C.(Z-1 p-E 1.5 C ) 2.0o C 2.5 3.0Qf c~1 H=0. 96X ci~ H=1.33X H= 1.70X CID 1.5 c22 S2s22 1ic22 2iI%7 c-4j — 1.0 H= 1. 15X c~o QI~~ H=1.52X H=1.88X QQ 1.5 cIVz 0 Qc7 1.5 C!239 2.0 I 2.5 1D 3.0 1.0 2.0 c: 9 2.5 KQ 2.0 CD FIG. 5-9: MEASURED ELEVATION PATTERNS OF DOUBLE COPLANAR PARASITIC LOOP COUNTERPOISE ANTENNA. h=0.44X, 2A=5.7X, Hl=H2=H and f= 1080 MHz. 74

5. 10 Discussion The radiation properties of a double parasitic loop counterpoise antenna have been discussed above in detail. For the case of large separation between the two parasitic elements the patterns can be analyzed theoretically. The choice of the specific parameters for a particular antenna will depend on the requirements on the pattern behavior. The influence of the different parameters on the patterns produced can be obtained from the results given above. 75

VI MULTIPLE PARASITIC LOOP COUNTERPOISE ANTENNA 6. 1 Introduction In this chapter the results of a limited experimental investigation of the radiation patterns produced by a multiple parasitic loop counterpoise antenna are discussed. This study was undertaken in order to determine whether it is possible to obtain increased response from the antenna along and above the horizon by using more than two parasitic loops. 6. 2 Description of a Multiple Parasitic Loop Antenna A multiple parasitic loop antenna is. shown schematically in Fig. 6-1. It consists of the basic Alford loop located at a height h above the counterpoise of radius A. Four coplanar parasitic loops of variable diameters were placed at a height H above and parallel to the counterpoise. During the experiment the diameters of the parasitic loops were fixed at 1, 2, 3 and 4X respectively and the height H was varied from 0.23X to 1.88 X in steps of 0.18 X. All the patterns were measured at 1080 MHz. 6. 3 Radiation Patterns The measured elevation patterns of the four parasitic loops antennas of Fig. 6-1 are shown in Fig. 6-2 as a function of the height H. The general behavior of the pattern appears to be similar to the single and double parasitic loop antennas discussed earlier in the report. However, it can be seen from Fig. 6-2 that the use of four parasitic loops gives rise to more lobes in the pattern near the region 0=00. Three of the patterns given in Fig. 6-2 are shown separately in Figs. 6-3a-c so that the details may be studied more carefully. 6. 4 Discussion It can be seen from Fig. 6-2 and 6-3 that the response in the direction of the horizon does not increase due to the increased number of parasitic elements. For some values of H the increased number of elements produced more uniform coverage in the half plane above the counterpoise. Although a multiple loop system offers more adjustable parameters for pattern shaping, further study is needed to determine its usefulness as compared to the single and double loop systems. 76

F L_ 0 0 4X - - 1-I 3X - I 2X -A -I Parasitic 1X — n Loops 0 00 T~ H - A=5.7X -- - F -I FIG. 6-1: MULTIPLE PARASITIC LOOP COUNTERPOISE ANTENNA. 77

1.88 1.70 1.52 1.35 5- CD 0.60 ^ 0.96 Q4I 0.60 KQ 0.41 CD 0.23 C FIG. 6-2: MEASURED ELEVATION PATTERNS OF MULTIPLE PARASITIC LOOP COUNTERPOISE ANTENNA. W1lw2=w3=w4=0.092X, f=1080 MHz, H variable. 78

(a) H=1.88X oD) (C) H=0.6X H=.23X FIG. 6-3: MEASURED ELEVATION PATTERNS OF MULTIPLE LOOP COUNTERPOISE ANTENNA. f=1080 MHz, wl=w2=w3=w4=0. 092X. 79

VII PROPOSED VOR ANTENNA MODELS 7. 1 Introduction In the previous chapters we have discussed both theoretically and experimentally the radiation properties of parasitic loop counterpoise antennas. As mentioned in Chapter I, the purpose of the investigation has been to determine the feasibility of using parasitic loops to shape the patterns produced by the Alford loop counterpoise antenna. From the results given earlier it is evident that by suitably placing one or more parasitic loops it is possible to shape the Alford loop counterpoise antenna patterns in the regions of space which is of interest to the VOR systems. In the present chapter we propose a few parasitic loop counterpoise antenna systems obtained on the basis of our investigation. All the proposed systems appear to be capable of improving the existing VOR antenna performances in one way or another. The choice of a particular system will depend on the specific VOR requirements. The antennas proposed here have omnidirectional patterns in azimuth. Hence, further study will be needed to establish their usefulness in the existing VOR systems which have figure-of-eight radiation patterns in azimuth. 7. 2 VOR Antenna Requirements The general requirements on the antenna radiation patterns for satisfactory operation of the VOR systems have been discussed in Chapter I. From the discussion given there it is found that the following criteria can be used for considering an antenna to be ideally suited for a VOR system. i) the radiation pattern characteristics near the principal maximum should not be too different than that produced by an Alford loop above a counterpoise. ii) the field gradient produced at the horizon should be as large as possible. An arbitrary limit is imposed such that ag > 7 db. iii) the average level of the field produced in the directions 0 > 900 should be as small as possible. Arbitrarily we set the restriction such that the minimum value of the field ratio defined as.0(0) Et (900) i in the range 1000 < 0 < 1200 is -10 db or less. 80

iv) the field reduction factor aF should be as small as possible. acF for an Alford loop above a 5.7 X diameter counterpoise is about 10 db. Almost any parasitic loop counterpoise antenna satisfies condition (i). Condition (iii) can be satisfied by placing single and double parasitic loops of proper diameters near the plane of the Alford loop. Condition (ii) is the most important and also the most difficult to achieve. As expected, it is very difficult, if not impossible, to satisfy all the four conditions simultaneously. In a practical system a compromise must be made. 7. 3 Proposed Parasitic Loop Counterpoise Systems On the basis of the criteria discussed in Section 7.2 we propose three parasitic loop counterpoise antennas which may be found useful in a VOR system. Because of their improved pattern characteristics, all three models appear to be capable of reducing the siting errors in the bearing indications of the present-day VOR system. Each of the three systems proposed uses a standard Alford loop antenna above a 5.7X diameter counterpoise. All the dimensions are at first given for a full scale frequency 108 MHz. The normalized dimensions are then given so that their.design at any frequency may be facilitated. 7. 3. 1 Basic Alford Loop Counterpoise Antenna The radiation characteristics of the standard Alford loop counterpoise antenna have been discussed in Chapter II. The important design parameters of the antenna are A=521, h=4' at the full scale frequency, 108 MHz; the corresponding normalized values for these parameters are kA=17. 92 and klh=2. 75. The far field elevation pattern produced by the 1/10th scale model of the antenna at the frequenc 1080 MHz is shown in Fig. 2-4. The measured pattern shown in Fig. 2-4 has the following average characteristics: agg= 3. 09 db/6~, aF = 10. 38 db and p = -6. 15 db. Antenna System No. 1. It consists of a single parasitic loop placed above and parallel to a counterpoise. The design parameters of the antenna are: Full Scale Freq. 108 MHz Normalized Values A = 52' kA=17. 92 h=4' kh=2.75 2B= 27' 31 kB = 37r H = 17 1" kH 11.78 W 10" kb = 0.15 81

The far field pattern produced by the 1/10th- scale model of the antenna at the frequency 1080 MHz is as shown in Fig. 3-10. The measured pattern produced by the model has the following average characteristics; ag=7 db/60, aF=13.00 db and p = -8.5 db. This model appears to satisfy all the conditions reasonably well. However, it is desirable that a and p should be improved. Further study is needed to determine whether better vafues for a and p can be obtained from this antenna. The performance of the antenna over the frequency band of the VOR system should also be investigated. Antenna System No. 2. It consists of a single parasitic loop placed above and parallel to a counterpoise. The design parameters are: Full Scale Freq. 108 MHz Normalized Values A=52' kA= 17.92 h=4' kh=2.75 2B=22' 9" kB=2. 5r H=5' 10" kH=4.02 W=1' 8" kb=0.287 The far field elevation pattern produced by the 1/lOth scale model of the antenna at 1080 MHz is given by Fig. 3-9 and was also discussed in our Quarterly Report(7). The measured pattern shown in Fig. 3-9 has the following average characteristics; that there is 10 db minimum in the pattern in the direction 0=30~. This may not be serious in some practical situations. The field along the horizon is considerably reduced. However, the pattern in the directions 0> 900 does not have any strong minor lobe. The field gradient obtained here is the same as that of the previous antenna. Antenna System No. 3. It consists of two parasitic loops placed above and parallel to a counterpoise. This has been repeated by us elsewhere(8). The design parameters of the double parasitic loop antenna are: Full Scale Freq.108 MHz Normalized Values A=52' kA=17.92 h=4' kh=2.75 2B1=36' 3" kBl=47r H 15' 5" kH1=3. 73 W1= 10" kb1= 0.15 2B2=29' 10" kB2=10. 26 H2= 15' 5" kH2= 10. 62 W2= 10" kb2= 0. 15 82

The measured far field radiation pattern produced by the 1/10th scale model of the double parasitic loop antenna system is given in Fig. 5-3. The pattern shown in Fig. 5-3 has the following average characteristics; a =21db/5~. 5, aF= 23 db and p = +2.6 db. This system is highly frequency sensitive. The antenna produces the largest field gradient at the horizon at a considerable sacrifice of aF and p. However, as mentioned in Section 5. 5, both aF and p can be improved by designing the system so that ag is less than the optimum value (see Fig. 5-4 and Table V-1). 7.4 Comparison Betwe-en the Basic and Proposed Antenna Systems The measured far field elevation patterns produced by the VOR parasitic loop counterpoise antenna systems proposed in the previous section are shown in Figs. 7-1, 7-2 and 7-3. The measured pattern, produced by a basic VOR Alford loop counterpoise antenna, is superposed on each of the above figures for comparison. The two patterns in each of the Figs. 7-1 through 7-3 are normalized so that they have the same response along the directions of their principal maxima in the patterns. In all these patterns the details in the region near the backward direction are omitted. It can be seen from these figures that each of the proposed parasitic loop counterpoise antennas are capable of superior performance when compared with the basic VOR Alford loop counterpoise system. 7. 5 Discussion We have proposed the above three antenna systems, each of which is capable of improving the existing VOR system performance. From viewpoint of the field gradient characteristics, Antenna System No. 3 seems to be the best. We do not give here our preference for any one of the three systems. Depending on the particular system requirements, and from mechanical considerations, any one of them may be found advantageous in a practical situation. 83

1800 FIG. 7-1:MEASURED FAR FIELD ELEVATION PATTERNS OF VOR ANTENNAS AT 1080 MHz (- )Basic Alford Loop Counterpoise Antenna ( —) Parasitic Loop Counterpoise Antenna System No. 1. Average Performance Characteristics Basic System Proposed System No. 1 ag=3. 09 db/6 ag =7 db/6~ aF=10. 38db -aF=13. 00 db Pmin= -6. 2db Pmin= -8.5 db 84

150 30~ 1800 IG. 7-2:MEASURED FAR FIELD ELEVATION PATTERNS OF VOR ANTENNAS AT 1080 MHz(-)Basic Alford Loop Counterpoise Antenna ( —)Parasitic Loop Counterpoise Antenna System No. 2. Average Performance Characteristics Basic System Proposed System No. 2 g=3. 09 db/6~ ag=8. 5 db/6~ aF=10. 38 db aF= 29. 7 db pmin -6. 2 db Pmin= -8 db 85

15~ 300 FIG. 7-3:MEASURED FAR FIELD ELEVATION PATTERNS OF VOR ANTENNAS AT 1080 MHz (-) Basic Alford Loop Counterpoise Antenna ( —) Parasitic Loop Counterpoise Antenna System No. 3. Average Performance Characteristics Basic System Proposed System No. 3 ag=3.09 db/6~ ag=21 db/5~ 5 aF= 10. 38db aF= 23db Pmin= -6.2 db Pmin 2. 6 db 86

VIII CONCLUSIONS AND RECOMMENDATIONS 8. 1 Conclusions The radiation field produced by a single parasitic loop counterpoise antenna has been investigated both theoretically and experimentally. Theoretical expressions for the radiation patterns produced by a single parasitic loop counterpoise antenna have been obtained by applying geometrical theory of diffraction. Within the range of approximation the agreement between theory and experiment has been found to be very good. The present investigation demonstrates an excellent application of geometrical theory of diffraction to antenna problems. In a multiple parasitic loop counterpoise antenna system where the mutual coupling between the parasitic loop is negligible, the present theory can be extended to analyze the radiation field produced. For a double parasitic loop counterpoise antenna we have obtained good correlation between theory and experiment. In general, it has been found that by introducing one or more parasitic loops the counterpoise edge diffraction effects in the patterns can be reduced considerably. The behavior of the pattern near the principal maximum is not appreciably changed compared to that produced by an Alford loop only above the counterpoise. Parasitic loops in general increase the response of the antenna in regions of space near 0=00. Extensive numerical and experimental investigations of various aspects of the parasitic loop counterpoise antenna have been carried out. These results being out the detailed effects of the different parameters of the system on the radiation patterns. As expected the antenna is found to be essentially narrow band. The parasitic loop concept has been found to be capable of shaping the patterns produced by an Alford loop above a counterpoise in the regions of space below the plane of the counterpoise. In particular a double parasitic antenna system yielded a field gradient of 21 db/50. 5 at the horizon. We thus conclude that the primary purpose of the present investigation has been fulfilled. On the basis of our investigation we arrived at the conclusion that when suitably designed, the parasitic loop counterpoise antenna is potentially capable of minimizing the siting errors inherent in the existing VOR systems. We have proposed three antenna systems which may find possible application in VOR systems. All three of the antennas appear to be capable of yielding improved performance compared to the present day VOR antenna. One or all of these proposed antennas should be investigated more carefully with the specific VOR application as the goal. 87

8. 2 Recommendations for Further Work Although we have discussed in detail the radiation characteristics of parasitic loop counterpoise antennas, we feel that further work is necessary before it can be established that such antennas will bring out superior performances from the existing VOR systems. Therefore, we recommend that further work be done along the following lines: i) study the performance of the single parasitic system over the full frequency band 108 - 118 MHz. Investigate the possibility of steering the minimum below the horizon by adjusting the pertinent parameters. ii) investigate the possibility of improving the field ratio p and the field reduction aF but retaining the high value of the field gradient a, of the double parasitic loop system. iii) investigate the performance of the parasitic loop counterpoise antenna when the azimuthal pattern is a figure-of-eight instead of omnidirectional. iv) study the possibility of obtaining a specified performance from the antenna with smaller counterpoise and possibly establish a minimum size for the counterpoise that can be useful. ACKNOWLEDGEMENT We wish to acknowledge the workiof Mr. Peter H. Wilcox of this Laboratory who prepared the programming for this report. 88

REFERENCES 1 Anderson, S. R. (1965), "VHF Omnirange Accuracy Improvements, " IEEE Trans., AME-12, No. 1, pp. 26-35. 2 Weston, V. H., J. E. Clark and F. M. Penar (1964), "New VOR Counterpoise System for Reduction of Siting Errors, "Conductron Corporation Final Report No. RD-64-47, FAA Contract FA-WA-4665. 3 Van Bladel, J. (1964), Electromagnetic Fields, McGraw-Hill Book Co., New York, pp. 376-382. 4 Sommerfeld, A. (1954), Optics, Academic Press, Inc., pp. 247-265. 5 Kraus, J. D. (1950), Antennas, McGraw-Hill Book Co., New York, p. 238 6 Sengupta, D. L. and J. E. Ferris (1968), "Effects of Large Parasitic Loops on Alford Loop Counterpoise Radiation Patterns, " IEE Electronic Letters (London), 4, No. 11, pp. 223-224. 7 Sengupta, D. L. and J. E. Ferris (1968), "VOR Parasitic Loop Counterpoise System, " The University of Michigan Radiation Laboratory Report No. 8905-2-Q, FAA Contract FA67WA-1753, pp. 24-25. 8 Sengupta, D. L. and V. H. Weston (1968), "A new VOR Antenna System,?" Accepted for publication in the Proceedings of the IEEE. 9 Keller, J. B. (1962), "Geometrical Theory of Diffraction, " J. Opt. Soc. Am., 52, No.2, pp. 116-130. 89

APPENDIX A FAR FIELD OF A LARGE CIRCULAR LOOP ABOVE A COUNTERPOISE It was mentioned in Section 3.2.5 that the far field produced by a large circular loop carrying constant amplitude current and placed above and parallel to a counterpoise can be obtained by generalizing the method used by Weston et al(2) to obtain the far field produced by a small current loop above a counterpoise. We will not discuss the method in detail here. Only the key mathematical steps involved in the derivation of the far field expressions will be outlined. Let the large circular loop of radius B be placed at a height H above the counterpoise of radius B (Fig. 3-5). It is assumed that the loop is carrying a current of the form Ip IpO -wt Ip=0 Ipoe where Ip is a constant. Because of the physical symmetry and the nature of the assumed current in the loop, the far field produced will be independent of 0 and polarized along the 0-direction. In obtaining the far field in the high frequency limit it is convenient to separate the entire space into the following three distinct regions: i) Region I, known as the illuminated region defined as 0 <0 ( -p) ii) Region II, known as the transition region defined as ( - p) e( + p), and iii) Region III, known as the shadow region defined as << (|+ p)<05~. The parameter p is defined in Fig. 3-5. If the field point P(7r, 0) lies in the illuminated region, then the far field at P may be written formally as: i r d d E (P) =E E(P)+E (P)+E d(P)+E2 (P), (A.1) PI ~d 90

where E (P) is the direct field produced by the loop at the point P, r E (P) is the reflected field produced by the loop at the point P, d E d(P) is the field produced at p due to the diffraction of the incident field 01 by the near edge of the counterpoise, E (P) is the field produced at p due to the diffraction of the incident field 02 by the far edge of the counterpoise. For a point P(R, 0) within the transition region the field may be well approximated by that due to the near edge diffraction effects. Thus we can write E((P) E () (A2) Equation (A.2) is a good approximation if 0 is very small, i. e. (H/A) < 1, otherwise the contribution due to the far edge diffraction should be added to (A.2). For a point P(R, 0) within the shadow region the far field can be written as d d E (P)=E (P) + E )P), (A.3) i. e. the field consists of the near and far edge diffracted components only. The proper expressions for the diffracted fields may be obtained by applying geometrical theory of diffraction(9) and the results of Sommerfeld's theory of diffraction by a conducting half-plane. Following a method discussed elsewhere (2) it can be shown that the following far field expressions may be obtained for Region I. ikR r kB ekR7 E (P)+E (p)= Ip ()2 yJ1(kBsin0) r-2isin(kHcos)], 0 < 0 < ( -p) - p O( J R 2 (A. 4) ik(R-Asin0+rp) E (P)= I (I kB )Jl(kBcosp) e 4 cos3i = 71/2 cosOsin O krin in -si <- (A.5) 7rkr sine(l-sin0) cos -sin p c- p p 91

d kB ) ik(R+AsinO+rp) i4 2 (P)=-Ip )J(kBcosp) R e cos30 1/2 x F - Lrkrpsin0(l+sin0) In the transition region the far field cosOsin P cos+sin ' <e<cosO+sinO ' 2 (A.6) E (P) E d Jl(kB cosl/) si/2 eik(R-Asin0) X - V(0), R i r7 p 7- p (A.7) where 1() i ~- ikr sin(O-p) __l P5 -ao i7t2/ dt e 'dt ikrpsin(0+0p) -e eirt2/2 -00 dt (r 22 P6=2(r1 cos (.) 6 72 2 (A.8) (A. 9) (A. 10) In the shadow region 2+0p<0 <7, Eq. (A. 7) gives the correct field due to the near ede diffraction so it can be used for E (P). The far edge diffraction contribution E02 in this region can be shown to be r^ 02 92

given by (A.6) without the negative sign in front. Thus it is found that different expressions are used to obtain the far field, depending on the region of space where the field point P lies. For computational purposes it is convenient to develop a single expression for the far field which is valid in the region 0 < 0 < 7. A single expression for the far field is obtained in the following manner: (a) Modify (A. 7) so that it gives the correct Ei (P)+E (P) + the near edge diffracted far field in Region I and the correct near edge diffracted field Ed (P) in Region III (b) Add the far edge diffracted far field expression to the modified expression derived in (a) to obtain the final expression for the far field valid in the entire region of space. If the point P is within the illuminated region, i. e. 0 is sufficiently smaller than ( _ -0p) both p5 and P6 given by (A.9) and (A.10) become large compared to unity. Under this condition the integrals in (A.8) can be split into two parts and we can rewrite (A. 7) as dos /20 ik(R-Asine) E (P)rp I (2 )Jl(kBcosp) R y (0)+2(0) 0 1 o sinl/20 R [ vl)+v2o (A. 11) where 1 i r ikr sin(O-0p) il V (-) = e -e 1-i r ikr sin(O-6) ^ —^ L kr sin(O+op)- 2, e -00 (A.12) P5 i.t2/2 ikr sin(0+0p it2u t/2 ei7t /2 dt -e P dtP P6 (A. 13) After evaluating the integral in (A. 12) and introducing V1(0) in (A.11) we obtain the following as the contribution to the far field due to V1(O): (ikR t kB ikR E (P) =r- Ip (2)J1(kBcos -) e R 0R cos )/0 c- t x -2i sin(kHcose)] sinl/2 0 (A. 14) 93

We now demand that V1(0) should contribute the correct incident and reflected field as given in(A. 4). After comparing (A.14) and (A.4) we see that (A. 7) should be multiplied by the factor J1(kBsine) (sinG 1/2 Jl(kBcospp) sin so that the contribution due to V1(0) in (A. 11) yields the correct field given by (A. 4). kB ik(R-Asin0) E (P)=r o Ip (. )Jl(kBsin0) e V(0), (A.15) 0 2 ^R where V(0)=V (0)+V (0) as before. Now consider the contribution due to V2(0). In evaluating the integrals in (A.13), we make the following approximation(4) rot2/2 _ ir2p2e i7r dt/ e for >> 1. (A.16) 17rp Using (A.16), V2(0) given by (A.13) may be expressed as follows; ikr 0p e P i/4 cossin (A.17) V2(0)= e/ — k eA.17) / (1-sine) /2(cos0 -sin0) After introducing (A.17) into (A.15) we obtain the following as the contribution to the far field at P(R,0) due to V2(0): kB ik(R-Asine+rp) 4 cos0sin p El (P)=rl7I ( 2 )Jl(kBsin0) e x - 01 Po R /rkrp (l-sin0)/2(cos0p-sin0) (A.18). After comparing (A. 18) with (A.5) we find that in order to obtain the correct near edge diffracted field from the contribution of V2(G) in (A. 15), we must add the following to (A. 15): 94

ik(R-AsinO+rp) cossin 2 EC (P) = oIP(kB e i.4. i/4 0 fVP( 2 R/7rkrp (cos-p-sinO) fos /2p J (kBcos0 )-sinl/20 J1(kBsin0 (1-sin 1/2 (sinp0 1/ (1 -sino)1/2 (s in 0)1/2 (A. 19) The composite expression obtained by adding (A.15) and (A.19) will give the correct near edge diffraction field in the shadow region if cosO in (A.19) is replaced by IcosOI. The far edge diffracted field given by (A.6) will give the corresponding field in the shadow region if cosO is replaced by IcosO. With this in mind we now add (A. 15), (A. 19) and JA.6), and after some rearrangement of the terms obtain the following for the far field valid in the region 0 < 0 < 7r, for kA >> 1, kB >1 and kA > kB: kB e i(kR-/4) E (P)= 7Ip (y) -R F(0), (A.20) Ep= 2o.2- e where 0 J (kBcossin0) ikr F(1)=1 FP- ikAsn in'2 J2 /Vnkr sinp (A. 21) i( -kAsin0) 2 LP(0) e /l-sin0' cos /20 J1(kBcos ) -sin /20J,(kBsin0) cos0 -sinO I- 'p -J2Jlk~in ikAsinO e \/i+sin0 ' J (kBcos0 )cos 0 cos0 +sin 0 Lp (A.22) ) ikrpsin(0-P) FP~e) p i rt/2 ikrpsin(0+p) I et / dt -e -a0 P6 i~rrt2/ 2 e dt, (A.23) -00 2kr- 1/2 cos ( -/2) = ) cos( (A.24) 95

krp p1/2 0+0+/4 p6=2( -) cos ( P )I r2=A2+H2 Pl H A (A.25) (A.26) (A.27) Equation (A.20) was quoted without derivation as Eq. (3.28) in Section 3.2.5. It should be noted that with proper definitions of the parameters rp.5, 5 P6, H and p Eq. (A.20) reduces to (2.1) provided we make the small argument approximation for the Bessel function J1(p) P/2 If the field is desired only within the illuminated region, for computational advantages it is better to use Eqs. (A.4) - (A.6) for the far field expression. By adding (A.4), (A.5) and (A.6) it can be shown that the far field in the illuminated region 0 < 0 < 2 - p is given by the following expression: ik [ E ( o ) e- p2isin(kHcosO)Jl(kBsin0) +J (kBcos0 )cos0sin( — ) 1 p 2 1I cosp \/2 rkrpsin&} i(krp+7/4) e G(Oe, (A.28) where -ikAsinO e cospsin) ) +i '(cos0 -sin0)(l-sin0) /2 ikAsinO e (cosp +sin0)(l+sin0)1/2 p (A.29) In some practical cases the field in the direction 0=7/2 may be of special interest. It can be shown that for a point P(R, 2 ) lying in the direction 0=7r/2, (A. 20) - (A-25) reduce to the following: E(Rj? kB e i(kR-7/4 x) J (kB) et2/2 dt 0 Jn 2 sin- i(- -kA) + ---— e x wrkrp = kr 1 2 0P p = 2( -P)1/2 sin7r. 2 cos /20 Jl(kBcos0)-J (kB) cos - 1 11 (A.30) (A.31) where 96

APPENDIX B COMPUTER PROGRAM FOR EVALUATING 8A(0). 8(0) WIT WM-360., MODEL-~67. 00011 IMPLICIT REAL*8(ABD-HK,O-Z),COMPLEX*16(C) 0002 REAL*8 CDABS i0003 COMPLEX*16 DCMPLX 0004 CEIX( XX) = DCMPLX(DCOS(XX) 9DSIN(XX)) 0005 1 LOGICAL TERM/.FALSE./ 0006f DATA SQ2/1.4142135623731/, P1/3.14159265358979/ 0001 DATA POT/1.5707963267949/1, EGAM/.577215664901533/ -occ8! DATA RCONI.01745329251992/, POF/.785398163397448/ 00091 DATA KH/2.758D0/,KCBPI/0.DO/,NTL/3/,ITS/l/ 0010 DATA KA/17.92D0/,KCR/12.566,37D0/,KCH/3.75D0/,KB/.15D0f 001.1 REAL*8 TH1(10)/5.D0,82.DO,115.DO,7*0.DO/,TH2(10)/80.009110.D00 ~170.00,7*0.D0/, THS(10)/5.DO,2.DO,5.DO,7*0.D0/ 0012 CALL FCVTHH(l) 0013 10 WRITE (6,9q9) 0014 999- FORMAT ('1') 0015 NAMELIST /IN/ TH1,TH?,THS,KHKAKBKCBKCHTERMKCBPINTL, ITTS 0016 READ (1,INEND=500) 0017 IF (KCBPI.NE.0000) KCB = KCBPI*PI 0018 KCBPI = 0.00 0019 WRITF (691000) KHKRKAKCHKCB 0020 1000 FORMAT. (e KH = 'G15.7' KB = 'G15.7' KA = 'G15.7/ ~,KCH = 'G15.71 KCB = 'G15.7/1X) Q021 IF (.NOT.TERM) WRITE (6,2000) 0022 2000 FORMAT ('-'4X'THETA'9X'RE(SP+SP2)'5X*IM(SP+SP2)14X'ARG(SP+SP2)'4X El ISP4SP21 '7X'RE(S)'1OX'IM(S)'LOX'SQ ISI'9X'IISI DB'/LX) 0023 CPLKB =DCMPLX(POTEGAM+DL0G(KB*.500)) 0024 n0 100 IT=ITS,NTL 0025 TH-SIT =TH~(IT) 100261 IF'(THSIT) 75,76975 0027- 75 NRT = (TH2(IT)-THl(IT))/THSlT 4- 1.5 0028 GO TO 77 002c5 76 NRT = 1 0030 77 THL = THI(IT)-THSIT 0031 DO 100 I=1,NRT 0032 TH = (,THL4I*THSIT)*RCON 0033 CALL FCAL(KHKAvTHPHZKRZ,CFZ) 0034 CALL FCAL(KCHKATHPHPKRP,CFP) 0035 TS = DSIN(TH) 0036 TC = DCOS(TH) 0037 CALL LFAC( TSvTC,KA CF1,fF2 CTA) 0038 ISi =DSQRT(TS) 0C3<3 PC = DCOS(PHP) 0040 PCI = DSQRT(PC) 0041 RSLI = DJONE(KCB*PC) 0042 BSL2 = DJONE(KCB*TS) 0043 TI = (PCI*BSL1-TS1*RSL2)/(PC-TS) 0044 P T2 =PC 1 *B SLI/P C + T S 0045 CLP = CFl*Tl CF2*T2 0046 PC = DCOS(PHZ) 0047 Pci = DSQRT(PC*PC*PC) 0048 TS1-= TSI*TSI*TIl 0049 TI =(PCI-TS1)/(PC-TS)0050 T2 = PCI / (PC+TS) 0051 CLZ = CF1*Tl - CF2*T2 '-'V _ _I t__ _ _.t__ _ _ _ _ _ _ _ _ _ _ _ _K I ( l l;K K L T S I _ _I 97

FORTRAN IV G COMPILER MAIN 05-02-68 10:48.22 005r3 CXZ = CEIX(KRZ) 0054 CSA = (TSISQ2)*CFZ*CTA + T1*CXZ*CLZ 0055 Ti = KCB*KCR 0C56 T2 = P1*T1 0057 KR1S TI + (KCH-KH)**2 0058 CXI = CE IX( DSQRT(KRI S) )/KR IS 0059 KR2S = Ti + (KCH+KH)**? 0060 CT3 =CE.IX(DSORT(KR2S) )/KR 2S 0061 CTI = (T2/CPLKB)*(CXI-CT3) 0062 CT? (B3SL2/SQ2)*CFP*CTA 0063 Ti = DSIN(PFHP*.5D0)/DSQPT(PI*KRP*TS) 0064 CT? y/CT2 + TI*CLP*CFIX(KRP) 006-5 CSP = CT1 * CT2 0C66 Ti = PI*KCR 0067 Ti = DSORT(Tl*Tl*Tl) 0068 CTIL CEIX(KCB3+KCB4-POF) - OS0RT(KCB/KCH)*CEIX(KCB4-KCB-PO'Fi) 0Cf65, CTIL CTI4 CXI * TI 0070 CT1= CTI (-2.DO*CPLKB*CPLKB3) 0071 CSP2 = CTI*CT2 0072 ASA = CDAI3S(CSA)**2 0073 OBCSA = 1O.DO*OLCG1O(ASA) 0074 CSUM = CSP+CSP2 0075 ASUM = COARS(CSUM) 0076 AROSUM -= ARGC(C-SUM)/RCON 0C77 IF (ARCSUM -LT. D.) ARCSUJM= ARCSUM 360. 0078 DASUM = 10.00*DLOGLO(ASUM) 0075 CS =CSA+CSP4-CSP2 0080 ACS =CDABS(CS)**2 0081 oBsum = lo.nOf*DLCGIO(ACS) 008? TH = TH/RCON 0083 IF (TERM) GO TO 79 00394 WRITE (6,2001) THCSUMARCSUMASUMCSACSOBSUM 0035 2001 FORMAT (F1?.4,8G15.7) 0C86 GO TO 100 0087 79 WRITE (6,1001) THtCSAvCSUMCSvACSOBSUM 0088 1001 FORMAT ('0TH = '.G15.7' SA.= '2G15.7/' SP+SP2 1 2G15.7/ S' S = '2G15.7/' IS, SO = '15.7' /S/ DB = '15.7) 0089 100 CONTINUE 0090 GO TO 10.0091 500 CALL SYSTEM 009;2 ENI) 98

SUBROUTINE FORTRAN IV C CCMFILER LFAC 0001 SUBiACLTIIN~E LFAC(TJS,TCKAt(PliCF2-,CTA) 0002 IMPLICIT REAL*E (Ai89E-l',KC- ),CO MPLEX*16(C) 0003 C0MPL-EX*16 IJCPFLX 0004 CAT A SCRT2-/ 1 41,42 135&42.6721 1 0005. T2 = KA*TS OCC6 11 = LCCS(T2) OC0i T2 =OSIN(T2) Occ8 CTA = UCPFLX(1II-T2) OOC9 AIC= IJAES(TC) OCiC IF (ATC.LT*1.D-8) GC iC 6C 0011 T = A1C/CS~RT(1.E0-TS) 00142 CF1 =T*UCPPLX('T2,I1)T 0013 1 = A IC/C!50 RT ( 1 * +TS) 00-14 CF2 = T*CCt'JPLX(Tl,12) 00 1 5 iFETLI~N 0016 6C CFI = SQRTi*O-CP~lX(T2,.TI) OC1I 1CF2 = O.CC 0018 RETURN 0015 ~NU 99

StBOUTINE FW~TRANl -VG. S4P!LER FCAL 04-26-68. I1a8:13.3 0001, SUBRCUTINE FCAL(KHlpKAsTh-.,l KIRtC.FZ-Z) 0002 IMPLICIT REAL*8- (A,BC-HtK,0-Z2) CCMPLEX*146(C.)0003 COMPLEX*16 DCMPLX 004CEIX.(XX). = DCM:FLX(CCCO-(X)~IvDSIN(XX)) 0.005 DATA SQ2/1.~4d14,15621121/ PI'/3.1'.592f5358e9l9l/ O0C6. CATA POT/1*57109432kiS49/.0CC PHI = OATAfN2(I(-,KA) Coca KR = OSQRT(KA*KA4KII*KI-) 00CS. P2 =2*D0*CSGR1(KR/PI') OCICP1I P2*CCCS((F~iI-TH-FC1)/l2oOCJ 0011. P2 =P2*&;CCS((PhI+TH*FCTJJi2.D0) 0012 CALL FRNL(At5,FI)0013 CFl' = CC4PLX (A,8) 0014CALL FRN~L(A9B9P2)0 0 1 5 CF2 =DCMPLX(A,8).0016 CA = CEI.X(KR*D5lN(TH-FIII)) 0011 Ce = CEIX(KR*DSlN(TH4I+I)) 0018-l CfZZ = CA-CB 0015 CFZZ = CF22*(..6CC,.5r.CC) 0020 CA = 'CA*CF1.002-1. CE = CB*CFE2 0022 CFZZ = CFIl+CA'-CE 0023 IRETLN 0C24 END 100

SUBROUTINE 0001 $UBROUTINE FRNL.iCS,XX). 0002 IMPLICIT REAL*8 (A-H,0-Z) 0003 ZZ = XX*1.2533141373155 -0004. Z = ZZ*ZZ 0005 GO TO 3 0006 ENTRY CS(C,S,X) 0007 Z = ODABS(X)____________,0008 ZZ = DSQRT(Z) 0009 3' IF (Z.GT.4.DO) GO TO 4 0010 ' C = ZZ 0011 S = Z*C 0012 Z = Z*Z 0013 C = C*((((((.50998348D-10*Z-.10140729D-7)*Z+.11605284D-5)*Z & -.852246220-4)*Z+.369385860-2)*Z-.079788405)*Z+.79788455) 0014 S = S*(((((-.66777447D-9*Z+.11225331D-6)*Z-.10525853D-4A)*Z & +.604353710-3)*Z-. 1899711OD-11*Z+.26596149) 0015 RETURN C 0016 4 D = DCOS(Z) _ 0017;S = DSIN(Z) 0018 Z = 400DO/Z., - _0019 A = ((1(((.876825830-3*Z-.41692894D-2)*Z+.79709430D-2)*Z & -.67928011D-2)*Z-.30953412DU-3)*Z+.597215080-2)*Z-.160642810-41*Z & -.024933215)*Z-.44440909D-8 0020 B = ((((((-.66339256D-3*Z+. 340140900-2)*Z-.72716901D-2)*Z & +.74282459D-2)*Z-.402714500-3)*Z-.93149105D-2)*Z-.120799840-5)*Z & +.1994715 _ 0021 Z = DSIGN(.500,ZZ) 0022 ZZ = 2.DO/ZZ 0023 C = Z + ZZ*(D*A+S*B) 0024 S = Z + ZZ*(S*A-D*B) 0025 RETURN 0026 END _____ --- —— _ —_ --- —--- 101

SUBROUTINE 0001 FUNCTION DJONE(X) 0002 IMPLICIT REAL*8 (A-Z) 0003 REAL*8 CJ1( 7)/.500,-.56249985,t.210935739-.3954289D-1,.4433190-2i & -.3176ID-3,. ll9D-4/ 0004 REAL*8 CY1(7)/-.6366198900.2212091D0,2.16827099-f.31648279 &.3123951D0,-.400976D-1,.278730-2/ 0005 REAL*8 CFl(7)/.797884569.156D-5,.1659667D-l1.17105D-3,-.2495110 —2, &.113653D-2,-.20033D-3/ 0006 REAL*8 CT1(7)/- 2.35619449,.124996129.565D-4,-.637879D-2,.74348D-3, &.79824D-3,-.29166D-3/ 0007 ENTRY JONE(X) 0008 IF (DABS(X).LE. 3.00) GO TO 600 0009 TOX = 3.00 / X 00,10 Fl = P(TOXCF1,7) 0011 TI X + P(TOXtCT197) 0012 JONE F fl*DCOS(Tl)/DSQRT(DABS(X)) 0013 98 DJONE = JONE 0014 99 RETURN 0015 600 TOX = X*X/9.DO 0016 9 JONE = X*P(TOXCJ197) 0017 GO TO 98.0018 ENTRY YONE(X) 0019 IF (X.LE. 3.00) GO TO 700 0020 TOX = 3.00 / X 0021 Fl =_P(TOX*CFL,7) 0022 Til X + P(TOXvCTl7) 0023 YONE = FI*DSIN(TL)/DSQRT(X) 0024 RETURN 0025 700 TOX = X*X/9.DO 0026 Fl =.6366197723676*X*DLOG (X/2.DO)*P(TOXCJl,7) 0027' VONE = Fl + P(TOXCYl,7)/X 0028 RETURN 0029 L END -_ ____ _ 102

APPENDIX C THEORETICAL ELEVATION PATTERNS OF ALFORD LOOP COUNTERPOISE ANTENNA The far field produced by an Alford loop above a counterpoise is given by the following expression: A ka 2 ei(kR-4) A E V r I o(-) R (0), (C.1) where the various notations are as explained in Section 2. 2. The term SA(0) is identified with the complex far field elevation pattern produced by the Alford loop counterpoise antenna. The complete expression for S(0) is given by Eqs. (2.2) - (2.8). SA(0) has been computed in the range 0 < 0 < wr for different values of the counterpoise radius A and a fixed value of h. The results of the computation are given in Tables C-1 - C-6. The following explanatory notes will be helpful in using the tables. The elevation pattern S (0) is expressed in the complex form as follows: SA(0)= Re SA(e) + i Im SA(0) (C.2) where Re SA(0), Im SA(0) represent the real and imaginary parts respectively of S (0). In all the tables the different columns represent: Column 1 gives the elevation angle 0 Column 2 gives the real part of S (0) Column 3 gives the imaginary part of SA(0) Column 4 gives IsA(0) 2 which is the power pattern Column 5 gives 20 log10 SA(0). The phase of the far field can be easily obtained from Columns 2 and 3. 103

U Skm-3O* A Mila 7500.00,. kAL=., - - - i- I 1. " - THFTA R E( SA ) I M( S A SQ I ScI ISAI CO 5.0000()-O.*7318962D-02 11 0.r0O 0.16072480 15.0000:- 0.2908073, 2.00IOC00 0.4013844 25.0000 0.4949663 32.0000- 0.5739326 4n.000, 0.7066404 45.1P00 3. 771'92 C7 9i.0000 0.P41641n' 5.9)0 0.. 3.9147507 61."00O. 0.9851334 65.I'100.. 1.042304 7 I0 000 1.0731422 75.0003 1.0661318 82.0000. 0.9756,674 8.I0 000-I 0.9317655 86.0000- 0.88,022734 9 000 0. 8215809 90. 00003' 0.75654Q7 9?.0000 0.6861445 94.0000. 0.6112559 96.0000 0.53130169 98.I10000 0.4526682 1CC.1000 0.3715168 l 0? I000 0- 0.2909021 10,4.0000 0.2121611. 106.'1000- 0.1365943 108o0000O 0.6543182-1 110.000qY -0.19780140-C3 115o.1000. -0.1338972 120.0000 -0.2162103 125.0)000 -Oo24369C5 13oOlOOQ -0.o2207825 135.oO,1000-0.159045) 140.o0000 -0.74994270-31) 145.0000- 0.12761870-01-; 151.0000, 0.86779870-0!1 155000 0.l133621.7 160.00n00 0.1455062 -165.,0000 01.120067? 171oOO00 0.57122-740-Cl -0.3- 1834890O-ClI -0.1 33996091,0-01 -0.S3 762 3C0-01 -0.20-99433 -4O. 562457 7~.7 32 8 16 -0.91S465C0 -1.* '29769 -1.C87012C -0. P64 1r43.6 7C9 1 73, -00 2C7 720~4 -0. 1146591I ~- C *:2 248P376 5 I 0.6C'166220-0 1 0.l30166?5 0.2 7 5: 939 C. 3293376; 048 3.4 C C0.4459 Th6 0044925?2U 0.442-7:94 03.4269.227 0..t C 2 702_;?8 3, * 7 1 4 1 ' 7 32 - -0 * 137843035 -0.1 2.3- 5 029c -0* o I 83'32930 -- 7. 146490-3 (3o b'q1I4 350-C1I 0.J.10670280-02 -29.71824 0. 26 813277D-01 -'15.e7133 5 0.93360270-01 - 10.o2 9 8328 0. 20 51 857 0.6457550 C.98 02945 _ 1.3 44756 -1.676004 100c?13 289 2.0 183 82 I1.9f84521 1.P33075 10 -- 0236 b 1.3 3 472 4 1 00;A~0482 20 9` 5U730 Y.8 (-883 8 '. 77P84443 C * 6 9 4 5 0 0.6172,45U '7.54647'37.48?0G7 1 0.42 C" 9l4 0.3716&5 CI 0. 324962J 0 42 36 5 2 C). 2 1 4 8 40 4. 2 4496 2." P6 54 43 3. P21696".1 1 53 1331.34 5l 9 5'U-1 4 047%98'' C-I. I937701 2.37 233 1 -01 '..?46~21 3.tfC-J i 3.15415630-21j 13 l2 Oi 2 8UL- 3J.1 79386 2 1.- J1 '723 262)3C- 01 0.22)D3I4 1 7 2 -31 0. 80 4 O'7 1' 32 -6.878530 -4. 156931.-1.899322 -0.86434471 1. 286436 2.2427.500 2.817806 3.o 0 500 3~4~ 2.976556 2. 63 1802 2.047616 1. 2539 14 c.2795335 -0.15-43958 -0.6107828 -1.387725 -2o 9 54 24,g-20 62 Z T~~O 7 -3. 168655 - 3. 72 7198 --— 4.298658 -4o 88 1674 -5.*4,7409 -6. 0758 37 -6. 682699 -7.292179 -7.900305 -91.380-d4569 -10.730A43A -11.9077 - 13.01128 -14.3 1430 -16 0 8b6 8, -18.o12Z033~ — 18.79384 -17 *- 450 —60 --16.. 3297'9 - 16.916 12 --20.94381 104

TABLE C-2: '-kh, =_2.750000, kA =10. 34000 THETA RE(SA) IM(SA) SQ 1SA41 ISAI C2 i 5.00000 0.41894840-01 10'.0000 0. -273064?D-01 15.0000 9.:85498C20-01 21.0000 0.2087572 25.0000 0.3770130 30.0000 0. 55-83464 -35.0000 0.7209331 401.0000 0.8447479 45.0000 0.9262710 50.00000 0.974759?. 55.OCOO 1.003601 60.0000 1,0?20194 65.0000 1.03,1216 71.0000 1.,0? 4 1 1 79.0000 1.9898519 80.0100o 0.918-34,64 8?.i10n1 8.77991'3 84 1 84~ -.10107.8~30713- -~4 R6.100ooo 1.7768561, 83.1000 0.7168?135 9 q.110O0 n1.6512765 9 2. I}0 0.981387?94.0000 0.5078847 9~.100.4319648 99.1000 0.3549521 10n.C0010 0.?7782635 IC2.'1000 0.20336&S 104.0101 0.1317465 106.1009 1.64940460-01 108.1000 )1.40113-590-02 111.0000 -1.49511120-cl.115.0110 -0.1449854 121.1100 -0.17924'99 125.0000 -0.!.54B3C7 130.0900_ -1.8 7664 879-3 1 135.01~ -04692763P.-02 i14 0.0000r. Oo 0.63 1132160-Cl 1 4 5. 1;000 10.911'53360-01 150.11000 i 3.7 1193 691 -0-1 155.0,000 0.15663510D-01 160,.0000_-1.47121240-01 165.0000 -0.852421'31-01 171.1000 -0. 75818 850-01 -0.740 4 5720- 01 0.72379470-J2 --0.1599882 1.26341Lb5U-'21~ -0.2014075 0.47874 900-01 -0.23381'98 0.9 P2 5 12 40D-01 -0.30C2n758 0.2333886,1.4?46Iq 4 -.5OC7C73 -0.6267114 0.9125118 -0.8428692 1.424028 -1.C35155 1.92952d_ -1. 161908e 2,3 00 186.. -1.119 11 2 2.445084 1. 14 22 2.349357 -1.001-050 2.067511 -0.7990158e 1.687228 -0.559P4590 1,?G1683 -0.3-C73693- 0.9378359 -0.20994172 0.81487-33 -C.116-38.70-3- 6 8 9 4 -0.28946140-01 0.6043433 3,51779289-01~.5 1 6517 1 0.12432957 0.43Sb179 0.1872-157 0.3730607 0.2400253 0. 31 55 590 0.2C321C96 0.2661795 0.3130Dq59C 0.223199o9 0.3327136 01991289 0.3411766 0."1577602 0.3-389207.316 -0.32629C1 0 3 1 LI 0,2746044 *).7785811-3 0.1741515 0. 51314950-l 0.5q117740-01 0. 3562 52 80-01I -0 4C 6 91C 2D0- O1 0.25627480-31 -O.1 4 i O.,7 C.1087752u"-J1 -0.6-12'~4 6C-O01 07 7 32945 5 0-012 0.3C693707-02 0.8318349C-0Z2 0.5-46-1-312-Cl 0.78?07310-J2 0.5q226A760-C1 0.375828710-02 I 22%60~C C270 9935C-02 -0.5686-2990C-Cl C. 8~8188oL-02 -21.403 85 -15.79354 -13. 19892 ~T0.O762 -6.3 19204 -3. 004161 -0.3976153' -.- 1.573 5-1-8'4 2. 8545 12 3.617629 3.882938 3,,709490 -— 3.154479_ 1.111560 -0.8890989 -1. 526 190 -2.1871631 -3.569246 -4.282205 -5. 009195 -5.*7A48253 -6.4975 79 — 7.254 4 —5 -8. 0200 25 -8.789112 -9.55C97 19 -10.32762 -11.08692 -12.*89464 - -14.48242 -15.91-2 9 4 -17.5492 7 -19.63470 -21.11655 -20.7 la963 -~-21. 06753 -2 4.-2-50d10 -25.675 1-3 - 20. 85 831-1 -20.466.32 105

TABLE C-3: kh= 2. 750000, kA = 13. 74000. - THETA RF(SA).o0000 0. 72801 290-01 10.0000 0.1618747 15.0000 0.2023407 20.0000 0.2345164 25.0000 0.3098724+ 30.0000 0.455538_ 35.0000 0.6520306 40.0000 0.847108? 45. 000t.90171 76 50. ~0000 1.066722 55.~0000 1.08363? 6. 30CO0 1.0669? 65.0:)00 1.03549 7nm ~!00~ 0.9943?59 7.^"C:" ^.9367,q64 8). 3,rn0 0.8516547 89.m0 O. 080797q39 8-4-.0000 0.7583916 86. 0000. 702978; qq,0000 3.642?C6C4 9".0)00 0.5762?.5 92. 000. 50662 4 94.0000 0.4 34036 5 q6. ^.qO ' 0..596431 98.0O 0. 2 84c749 IC.0000 0.211 57 1)o?.000 09.141C0346 104.000n O. 75185910- 1 16.0 00' 00. ] 5508" 90- 1 1 08.0000 -0.364 238? D- j 1 11n.1n00 -0.79294?6C-,-C 115.0000 -n.1407091 120.0000 -0.13447?2 125.0000 -0.74799250-01 13.0000 0.42q75340-C)2 135.0000 0.6C75191n- 1l..-1 c -. n, ~..... 6 - ~ 14'.OC 0 n.6547357C-01 145.0000 0.22 53910- I 15C."OOO -0.31614480-01 155.0000 -0.5147214n-1-:: 165n. 00n -0.?1361 970-"l' 1 i-6 -. n -.! 6 1,'l rD - 1 179.n^ 0 0.58749) 440- 1 IM(SA) -0 o1 3 p?c -0,5873657 -0. 1751 153 -0. 297738 -0.3 51 576...4 59.. 5.. -0. 577697 -7 5 5 7C 3 -0,c683712 -1 148A- 46 - 1. 24 1 3 9 -1. 17735 -1.CF8p46C -0.8 &94556 -0 62391 -0.36 06 924 -C.25F~57! -0o 16 C185 -0 717 -752 0. 1 4 715 0. 8 3 4 555 O 14 90 35 0.197'"C39 O, 2 7: 1 3 4 (). '?? - 7. 1 1 ^ s 4 ' 2; 154 6434 0.t 401 t C 7 * 7 l 7 1 3 -C,41 66C52.-0............... 51.4 O-.-..7. C SQ ISAI ISAI Ce -... O-Cl C.54910220-02 -22.60347 -01 0. 29653400-01 -15.27925 0. 716071 1-01 -11.45044 0.1436464 -8.427052 0.2443673 -6.119570 0.419 0778 -3.777033 0.7566547 -1.211023 1.2 89083 1.102810 1.921247 2.835831 2.4572'82 ----.3. 90455C 2.712203 4.333222 2.621204 4.185009 2.256992 3.535301 1.762126 2460370 1.268542 1.033047 C.85 41"48 -0.6782323 C.71 98288 - 1.427708 C.6014078 -2.208309 0-01 0.499328 3 -3.016136 -COl 0.4123513 -3.847326 C-C! C. 3 8965 -4.698023 0.27 7955 9 -5.5624 0.22 72511 -6.434941 0.18538343 -7.319271 C.1509817 -8.210758 '.1228217 -9.107250 3. 9984^500-01 -10.00672 0.811 5 588 -01 — 10. 90680 n.66 C:o480D-01 -11.80413. 3784'4 '3-0J1 -12.69343 C.43cd74oC-01 -13.56671 0D-01- 0.2749732C-01 -15.60710 0-1) 0.18 33 7480U- 1 -17. 3666C C-C1l.? 271c901-;1 -19.11117 0- 01 0.74526150-02 -21.27691 C-C' 0.50 8968 0-2 -22.93285 0-01 0. 494544 70-02 -23 05794 0-Cl 0.341219J-i02. — 24.66967 C-01 0.1738944L-02 -27.59714 0-C1 0.32 164430-J2 -24-.92624 Q.-C1. 22C60370-C2 -26.55876 -02 0.10177340-02 -29.92366 o-C 1 0.54218 530-02 -22.65852 106

TABLE 0-4; kh = 2. 750000 kA=1. 20 THETA. RE(SA) I_ _ M( SA) _ SQ I SAI ISAI Ce 5.0000 0.57729350-01 -0.95845q10-Cl 0.2I? ).) 1,22~ 10.0000 0,9646671D0-01 -0.39930.289031~0-1 -153O5 15.00,00 0.15-67395 -0.1430.116 0.4501959C~-01 -13.465'98.20.0000 0.26607034 -0.?22239759 0.1.2C4671.-9,191314 -29.0000 0,38?.7133 _ -0.1282'4236 0.2911916 -5.358212 31.0 00 0.47901967 5 -567-7-2 0.95064275 -2.954828 5.0000 O.5q66636 -O.6?-58072 0.747b421 -1.263063 40.0000 0.77307952 -0.73399S38 1. 13 6392 0.55528231 45.0000 0.9708266 -C.89S9C07 1.752326 2.436148 901.0000 1.11346? -1.0394396 2.437501 3894 55'. 00 00 1.160419 -1.2 4A363 5?.876329- 4.588385 60O.1~000 1.128228 -1.2?6251?.666176 4,573tC;29 65,.0000 1,C5774," -1.156383?.45b6036 3.902348 7 0.0000 3.1977606 3 -0.G472533 1.853J0.s 2.678761 75.0000 1.8927447 -0.6823.5042 1.26OC793 1.003978~ p 3. I000 0.n792954?- - ICI06 4 4 0.7896292 -1.025_769_ __82.0000 0.746C39'n -0.12943~2131.i643199;2 -1.916545 984. '101)0 0.6 9423i2 I -13? 48 -.95212 -2.843967 P6.!1000 0.6375999 -J1244.4166165 -3.8026315 33."-00o0.576C4?6 1.'5180C 0.3320C~77 -4.787341 O900 'n.5101)79 I 67~6- 1 0?E3 44t -5.79-3107. 9.3.000) C.440636? 0J1-1'?35.?) 8 2?z7 -6.813595 94.0000 01.36P6le4 0.1.'-8957C 0.19642%283.-7.843669 96.0000 5-?C56 3 A.'i 2 3 8 0.1294740" -8.878153 99.0000 0.22303993.2?&7 79 )1 2?U 04U3- -9.912281 1091.0000 0.1528713.2914J84 9*t5U0-U -10.94207 11300 18 6 992120-%01I e 3.2367 31 CAo3175>C- -11.96483-.104.10000 0. 27371 P90-C" l.2227221 0 5O 315 434'D'-.J-1-12,9796i 105.00110 -0.?40871'70-0~1 2.198'3591 D.3992o'5i0-Jl -13.987.39 10f8.0000 -1.65674460-01 — — I165 4 7 6 O..31693:ts-K)1-J - 1~.39001 111.1100 -0.96013,900-Cl 0.1263669 0.25187230-31 -15.98820 11C0001841.l 8C 0-0 1.429 0-8.4085 ~121.3000 -C.731159;4D-01 - 0. 6 J9 C7 630-1C1C 0.90S5 6-7 9C 02 -20.43079 123.01000 0.198635930-C02 -0.78433,470-Cl- 0.615105uU-JU2-22,11051 130.0000O 0.51033200-01 -0.319d7132C-01 0.31627O95C-02 -24.40441 1-35.0000 0.l9e60P7D-CI 0.31064980-Cl 0.25539220-J2 -25.92792.~ 140.0000 -0. 851594170-02 0.4 7 6'.409,CO c10.23429190-J32 -26.3'02'43 145.OC03~ -0.33116110-0-1 0.39725810-C02 0.11124'f580-2 -2.3716, 150.0000 -0.81331.110-C2 -0,31?'a1s90)-C1 0.15968730-02 -27.96730 155.0000 0.213,68760-Cl -C.lGC7911C0-oo O.-82C-6-3610-03 -30,85849 161.30000 0.10192010-31 0.330:)252C-C]. 3.11930430-'02 -29.2334A: 165.0000 -0.,149)03 64D-01! 0.277?5 50- fCI C96 489uI1-03 -30.15522 1,70.0000 -0.665855.20-0? -0.3 5865r060C-Cl X14C332690-u2 -28.52828, 107'

TABLE C-5: 1kb. 2. 750000, kA = 34.47000 TH ETA' RE(SA) I MA"S A) SQ ISAI I SAi 0B '5.0000 0.34639600-01 -0.32358590-01 0.22469800-02 -26.48401l 10.0000 0.1136654 -091164559 O.o2648182D'Ol -15*77052 15.0000 0.1605864 -0.1585087 0.509130b-0l1' -12.931711 20.0000 0.2668658 -0.2666501 0.1423410 -8.466700 25.0000 0.3489614 -0.3534914 0.2467302 -6.077717 30.000'0 0.5002848 -0.4892249 0,4896259 -301013561 35.0000 0.6190433 -0.6367660 0.7886855 -1.030962 40.00000783395 7 -0.163301 1.199440 0.7897848' 45.0000_0.9448698 -0.9473152 1.790185 2.528979 50.0000 1038925 -1.066157 2.2160-55. 3*4558C5 55.0000 1.160583 -1.128156 2.619688 4.182496 60.0000 1.239838 -1.210420 39002314 '4.774561 65.0000 1.170540 -1.228707 2.819883 4.593749 70.0000 1.001446 -1.C85881 2.182030 3.388607 75.0000 0.8267790 -0 8079897 1,336411 1.259400 80.0000 0.6767148 -0.4855049 0.6936580 -1.588546 82.0000 0.6197454 -0.3622031 0.5152755 -2,879605 E4.0000 095618642 -0.2475894 0.3769919 -4.236680 86.0000 0.5017048 -0.1441876 0.2724977 -5.646371 88.0000 ( 0.438484? -0.53937560-01 0.1951776 -7.0956S9 90.04000 0.3720962 C, 21665740-01 0.1389250 -8.57-2197 92.0(00 -O*3039478 0.8149880,10-01 0848004D-01 -10.06652 94.0000 0.2327333 0.1247838 0.69735820-01 -11.56544 96.0000 0.16311 7 0.1511592 0.49455820-01 -13.05783 98.0000 0.96746280-01 0.1607960 0.35 215210-01 -14.5327 0 00 03U66320-0-O'-1 5 4- 578-C- 0.2523625D-01 -15.97975 10?.0oO00 -0.13989730-Cl 0.1343081 0.18234380-01 -17.39109 10 4 *. 0000- -0.5 2 01- t80-C 1 o, 1 CA 2 0 9 C, 2 2 9 1 504 C- 0 1 -18.76425 106. 000'0 -0.74901440-01 0.64438900-01 0. 97625970-02 -.20,1043'5 108.0000 -0*81420760-C1 0.24114r5 20-01 0.72108500-02 -21.42014 110.0000 -0.72174590-01 -0.12260450-01 0.53594910-02 -22.70876 115.00 00- 056620590-C2 -0.52505390-CI1 0,2788875-0-02 -25.5457'1 120.0000~ 0.38494370-01 -0o9C758730-C2 0.15641880-02 -28.05711 0000 02158o29-02o.3o027 510-01 0.92123710-03 -30.35629 130.0000 -0.23499150-01 -0o373240C0-02 0.5661408D-03 -3?.47076 135.0000 0.13904100-01 -0.16349530-01 0.46063130-03 -33. 36647 140.0000 0*17610580-C2 '0.0163040CO-Cl 0.26892170-03 -35.70374 145.000 -0.10736470-01.-0.69862210-02 0.1640792D0-03 -37.84941 150.0000 0.13132060-01 -0.20722410-02 0.1767453C-03 -37.52652 1 55 00-03123839-01 0.785 315 5 0- 02 20. 21501300-03 -36.67 5 3 35 160.0000.10987390-01 -0.10811730-01 0.23761620-03 -36.24124' 165.0000 -0.10153'730-01 0.12231460-Cl 0.25270680-03 -35.97383 171.0000 0.10540160-Cl -0.1-33 30680-01 0.28880190-03 -35.39400 108

TABLE C-6:. -kh = 2. 750000, kA = 51. 69000 THETA RE( SA ) 5.0000 3l.f1000 15.0000 20.10000 25.0000 3 * 433-47070-01 0.111l15 61 0.* 1687? =7 0. 250-93315 0 6. 36832 15 1YO7Y0 0O 4 8 2-98691 35.0000 0.6294426 40.0000 0.-785785A 45.0000 0.9244501 53.0000 1.06q255 55.-0000 1.1959923.0 0 0 1.19000 65.0000 1.20659,7 710.0000 1.060788 79.0000 0.8?761C8 0.0 000 3.6286561. 8?-.i0o0 0.561913-7 e'~.oo00 0.43566?2? P900 0.*371317? 93.0300 0.30459%I 92?.0300)." 0,23983;C9 96. 0000 0.9 97 75~0 99.0000 3I.3891449D-31 1 0 0. C)0000 -0. 1142 67T0- ClI 1I?. 0000 -0.46 75114D-01 104.0000 -0.6359?340-C-l 1016.0000_-0.60924550-01 1O-4.0000 -0.4156530C 11ln 0.00f0 - 0 12893 2 C.0C I 1 15, 000,K 0.*3C,3q4 960-1 1.? 5.1000 -3. 253)841.4r-C2 13 -0.000 0 0.68311 9 D-C 135.0000 -0. 651 564-2 145.00030 -0.43371 1 0-C21O 1510.0000 -i468?00 1A0 ()-0.49449220-3"2 1 65.00-0 2 01 4 43'1 C2 173. 0000 C 8 071079,f-; I M( SA) SQ ISAI I SAI 08 -0.r5-4501890-Cl 0.48494240-02 -23.14310 -0C.9738241C-01 0.21 839000-01 -16.60767 -0.1679923 0.56689770-31 -12.'46495 -0.26212-42 036767 - 8.804910 -0.35S2E47___0.26474t62 -5*7717C2 9.63 0.i4666275 -3.310297 -0.6375197 0.8026294 -0.95484932 -0.77.27548 1.2-1406C9 -.43 -0.9.4C5928 1.73932 2.403802 -1.05038C 2.246604 3.515265 -1.175124 2.717)75 4.341016, -1.176753 2.840623 4.5341315 -1.115374 2.369313 765T -0.e765387 1-.453250 1.623432 -0.5.341C4S 0.68C47,65 -1o671 8619 -0.398381E4 0.4744547 -3.238,053 -027273I1 7 -4*909 99 -.1631 93?4 2 3.?215-721 3 -6.6614721 -'3 -1 * 608 8 0-01 C. 1 42 1Th -8.471980 %. 188K5001 2'7?1876D-01 -10.31896. 0.6992j6490-01 0. 052'503U1 1.83 0.307.39457d00-31 -14.03866 212215.9583 i4 2 0-31 -15.'87784 0.124,6-178 0. 17Ck;39zfC-Jl -17.6 843 0 I I 7C.l3o19. ~00-3 1 -19.44549 0.7 4 125960-C-,l.7,6 8032 7 0-2 -21.*14620 C. 152 '..96 C-1 I. 52 879-37C-~j2 -2276-71 4 --0. 24 c 3l14C - C C.71l8j48C-32 -24.2S685 -34 78630-C2C.?65 -2~C-2 -25.7567C 1'.47 540C4iC-1 C. 190,8G620~-J2 -27.19407 -0.5513260 -3 DJ 92413770I' 3-30.34254 D.1e,477590-la1 3.47C-0284-03 -33.27876 13 6~?0C1 C24 9 5 e,00-0 35.45222 0D. 2 4 46 C -C1 I~ "..191737JC-03 -37.17294 5.671c-2 2151351C-C03 -8.6 92 32 PA 87 () 2- C?9 C.9 ~ 1-4-40.17351 0. C9 60C 39238L-J4 -42.216,98.4 C'9 3 7 10-2 3.342-b687D-04 -44.67642 0.2C 2 7 C- C?20.5 29;2 1 7 2 D J4 -42.76366. - 2.62L+ 7 340C -C2 3.63462190-3'4 -4 1.9748 5 C.77% 0 0.116811-34 -49.152161.7 4286E C00-C32 0.q74'7408D-24 -40.1-1111, 109

APPENDIX D RADIATION CHARACTERISTICS OF A SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA NEAR THE HORIZON We give here the theoretical values for the complex far field produced by a single parasitic loop counterpoise antenna in the vicinity and below the horizon. The antenna has the following constant parameters; kh=2.75, kA=17.92 and kb=0. 15. The normalized height kH and the normalized radius kB of the parasitic loop are varied over some selected values. Note that S(0) = SA(0)+SP (0)+SP (0) 1 2 5 6 in Tables D-1 through D-3. The Tables D-.4 through D-6 give the complex far field SP(0), produced by the parasitic current only above the counterpoise. The normalized height kH and the normalized radius kB of the parasitic loop are varied over some selected values. Note that sP(0) = SP (0)+Sp (0) 12 56 for Tables D-4 through D-6 The results given in these tables may be found useful for the design of a double parasitic loop counterpoise antenna whose far field radiation pattern is required to have a sharp minimum in a direction just below the horizon. Controlling the amplitude of this minimum, the field gradient at the horizon can also be controlled if desired. The complete pattern produced by the antenna can be obtained from the theoretical expressions given before. 110

TABLE D-1: 8(0) vs 0, kH = 3.7 kB = 3.8r kB =4.0 r kB = 4.2 r Re(S<() ImS(O) ReS(O) ImS(9) ReS(O) Im8(e) 90 92 94 96 98 100 102 104 106 108 110 0.25629 0.20481 0.15453 0.10679 0.16305 0. 02479 -0. 00676 -0. 03077 -0.04694 -0.05561 -0.05774 0.15064 0.16701 0.175496 0. 17598 0.16881 0.15485 0.13543 0.11230 0.08743 0. 06283 0. 04024 0. 30112 0.26132 0.21683 0.17009 0. 12359 0.07965 0.04025 0.00682 -0. 01987 t,0.08971 -0.05318 TABLE D-2: 8(0) vs 0, kH = 3.8 90 92 94 96 98 100 102 104 106 108 110 0.24392 0.19444 0. 14631 0.10080 0.05935 0. 02335 -0. 00606 -0.02815 -0.04276 -0.05037 -0.05202 0.14453 0.15971 0.16727 0.16715 0. 15975 0.14598 0.12719 0.10514 0.08177 0.05899 0.03840 0.29360 0.25540 0.21248 0.16730 0.12235 0.07994 0. 04196 0. 00978 -0. 01595 -0. 03522 -0. 04859 0.02619 0.07261 0.10835 0.13289 0.14640 0.14971 0.14425 0.13187 0.11463 0.09456 0.07345 0. 01797 0.06442 0.10025 0.12497 0.13881 0.14266 0.13780 0.12669 0.11079 0. 09227 0. 07279 -0.00077 0.04603 0.08232 0.10771 0.12254 0.12784 0.12515 0.11639 0.10355 0.08845 0.07247 0.42019 0. 35525 0.28746 0.21967 0.15459 0. 09462 0.04172 -0.00271 -0. 03788 -0. 06364 -0.08039 0.41644 0. 35178 0.28438 0.21715 0.15282 0. 09375 0. 04185 -0.00157 -0. 03584 -0. 06093 -0. 07736 0.40959 0.34548 0.27894 0.21295 0.15023 0. 09310 0. 04329 0. 00192 -0. 03061 -0. 05452 -0.07052 0.04460 0.10574 0.15067 0.17984 0.19428 0. 19557 0. 18573 0.16708 0. 14211 0.11323 0.08263 0.04044 0.10163 0.14644 0.17542 0.18968 0.19090 0.18120 0.16297 0.13870 0.11077 0.08128 0.03080 0. 09215 0.13679 0.16646 0.17951 0.18082 0.17166 0.15455 0.13199 0.10625 0.07922 TABLE D-3: 8(0) vs 0, kH = 4.0 90 92 94 96 98 100 102 104 106 108 110 0.21969 0.17455 0.13102 0.09029 0.05367 0. 02237 -0.00267 -0.02098 -0.03265 -0. 03841 -0.03950 0.12918 0. 14228 0.14833 0.14739 0.13997 0.12706 0.11006 0.09070 0.07083 0. 05212 0.03589 0.27975 0.24483 0.20516 0.16321 0.12146 0.08215 0. 04703 0. 01725 -0. 00672 -0. 02511 -0.03864 111

TABLE D-4: iO) vs 0, kH = 11.6 kB 2.88r kB =3Ir e(~) Re SP(O) ImSP(o) Re SP() Im P(e), _ _! i... L....... i iii i i ill 90 92 94 96 98 100 102 104 106 108 110 -0.08413 -0.15008 -0. 19537 -0.21284 -0.19956 -0.15746 -0.09322 -0. 01745 0. 05702 0. 11740 0.15339 0.19023 0.14954 0. 08620 0. 00992 -0.06743 -0. 13365 -0.17807 -0.19350 -0.17769 -0. 13400 -0. 07100 -0.17060 -0.20894 -0.22496 -0.21554 -0.18012 -0.12138 -0. 04569 0. 03707 0.11452 0. 17375 0.20388 TABLE D-5: SP(O) vs 6, kH = 11.8 90 92 94 96 98 100 102 104 106 108 110 -0.10690 -0.16481 -0119864 -0.20281 -0.17643 -0.12366 -0.05319 0. 02219 0. 09163 0.14070 0.16181 0.16762 0. 11797 0. 04925 -0.02760 -0.10014 -0.15648 -0.18721 -0.15681 -0.10200 -0. 03351 0. 03527 -0.17484 -0.20405 -0.20911 -0.18817 -0. 14230 -0.07599 0. 00270 0. 08263 0. 15102 0. 19568 0. 20772 0.10947 0. 05432 -0. 01294 -0.08417 -0.15013 -0. 20126 -0.22890 -0. 22695 -0.19352 -0.13220 -0. 05219 0. 07650 0. 01708 -0. 05085 -0.11844 -0.17625 -0. 21511 -0. 22752 -0. 20927 -0. 61602 -0. 08901 -0. 00478 0. 04558 -0. 01668 -0. 08349 -0.14558 -0. 19359 -0.21908 -0.21606 -0.18251 -0.12169 -0. 04241 0. 04195 kB = 3.2 r Re SP() ImSP(e) -0.08789 -0.05092 -0. 08962 -0. 06495 -0.08766 -0.98270 -0. 07919 -0.10458 -0. 06055 -0.12848 -0.02914 -0.14941 0.01471 -0.16032 0.06650 -0.15411 0.11767 -0.12609 0.15715 -0.07634 0.17422 -0. 01089 - -0. 06946 -0. 06907 -0. 06427 -0.05227 -0.02989 0.00446 0. 04904 0. 09795 0.14168 0. 16925 0. 17128 -0. 04954 -0. 04710 -0. 03974 -0. 02479 0. 00033 0. 03613 0. 07949 0. 12330 0. 15755 0.17181 0.15860 -0. 06429 -0.07820 -0.09497 -0. 11449 -0.13399 -0. 14804 -0.14974 -0. 13293 -0. 09477 -0. 03767 0. 02999 -0. 07242 -0. 08587 -0.10123 -0.11783 -0.13240 -0.13920 -0.13181 -0.10533 -0.05893 0. 00264 0. 06904 TABLE D-6: SP(O) vs 0, kH = 12. 00 90 92 94 96 98 100 102 104 106 108 110 -0. 12523 -0.17388 -0.19564 -0.18675 -0. 14849 -0. 08719 -0. 01332 0. 06016 0.12011 0.15583 0.16131 0.14323 0. 08606 0.01392 -0.06122 -0. 12677 -0.17154 -0. 18778 -0. 17273 -0.12940 -0. 06625 0. 04290 -0. 17361 -0. 19322 -0.18744 -0. 15589 -0.10131 -0.02993 0. 04869 0. 12256 0.17899 0. 20711 0. 20055 112

---- ---— I The University of Michigan Radiation Laboratory, Ann Arbor, Michigan THEORETICAL AND EXPERIMENTAL INVESTIGATION OF PARASITIC LOOP COUNTERPOISE ANTENNAS, by D. L. Sengupta, J. E. Ferris and V. H. Weston, September 1968, Final Report (June 1967-June 1968), 112 pp., incl. illus., 9 refs. (Contract FA67WA-1753, Project 330-004-05N, Report No. RD-68-50) Unclassified Report The radiation field produced by a single parasitic loop counterpoise antenna has been investigated both theoretically and experimentally. Geometrical theory of diffraction is applied to obtain theoretical expressions for the far field produced by such an antenna. Within the range of approximation the agreement between theory and experiment has been found to be very good. In the absence of mutual coupling between the parasitic elements, the present theory can be applied to double- and multiple-parasitic loop counterpoise antennas. The parasitic loops in general reduce the counterpoise edge diffraction effects on the far field patterns. The behavior of the parasitic loop counterpoise anteuna pattern near the principal maximum is not appreciably different than the Alford loop counterpoise pattern near its maximum. Parasitic loops inorease the response of the antenna in regions of space near the zenith 0=00. Detailed results of numerical and experimental investigations of various aspects of the parasitic loop counterpoise antenna have been given. These results bring out the effects of the different parameters of this new antenna system on the radiation patterns. The parasitic loop concept has been found to be capable of shaping the pattern produced by an Alford loop counterpoise antenna pattern in regions of space below the plane of the counterpoise. On the basis of our investigation we conclude that when suitably designed, the parasitic loop counterpoise antenna is potentially capable of minimizing the siting errors associated with existing VOR systems. We have proposed three new antenna systems which may find possible application in a VOR system. ( --------- -~ --- —. --- — - The University of Michigan Radiation Laboratory, Ann Arbor, Michigan THEORETICAL AND EXPERIMENTAL INVESTIGATION OF PARASITIC LOOP COUNTERPOISE ANTENNAS, by D. L. Sengupta, J. E. Ferris and V. H. Weston, September 1968, Final Report (June 1967-June 1968), 112 pp., incl. illus., 9 refs. (Contract FA67WA-1753, Project 330-004-05N, Report No. RD-68-50) Unclassified Report The radiation field produced by a single parasitic loop counterpoise antenna has been investigated both theoretically and experimentally. Geometrical theory of diffraction is applied to obtain theoretical expressions for the far field produced by such an antenna. Within the range of approximation the agreement between theory and experiment has been found to be very good. In the absence of mutual coupling between the parasitic elements, the present theory can be applied to double- and multiple-parasitic loop counterpoise antennas. The parasitic loops in general reduce the counterpoise edge diffraction effeots on the far field patterns. The behavior of the parasitic loop counterpoise antena pattern near the principal maximum is not appreciably different than the Alford loop counterpoise pattern near its maximum. Parasitic loops increase the response of the antenna in regions of space near the zenith 000~. Detailed results of numerical and experimental investigations of various aspeots of the parasitic loop counterpoise antenna have been given. These results bring out the effects of the different parameters of this new antenna system on the radiation patterns. The parasitic loop concept has been found to be capable of shaping the pattern produced by an Alford loop counterpoise antenna pattern in regions of space below the plane of the counterpoise. On the basis of our investigation we conclude that when suitably designed, the parasitic loop counterpoise antenna is potentially capable of minimizing the siting errors associated with existing VOR systems. We have proposed three new antenna systems which may find possible application in a VOR system. mmm --- - - -- --- - -m- - - - - -- - -. - ---- - - ^- ^A^ ---- ^ -- ----- - -- -- _* — ^ UNCLASSIFIED The University of Michigan Radiation Laboratory, Ann Arbor, Michigan THEORETICAL AND EXPERIMENTAL INVESTIGATION OF PARASITIC. 8enguptaD. L. | LOOP COUNTERPOISE ANTENNAS, by D. L. Sengupta, J. E. Ferris and WFserri JV... H. Weston, September 1968, Final Report (June 1967-June 1968), e Contract FA6 3 112 pp., incl. illus., 9 refa. I. Project 330-004-05N (Contract FA67WA-1753, Project 330-004-05N, Report No. RD-68-50) IV. Report No. RD-68-50 Unclassified Report Descriptors The radiation field produced by a single parasitic loop counterpoise ansitic Lop Counterpoise Antentenna has been investigated both theoretically and experimentally. GeoVO st e se Antennas metrical theory of diffraction is applied to obtain theoretical expressions Veomerica Theory f Difrai for the far field produced by such an antenna. Within the range of approxieoetri Theor Diffraction mation the agreement between theory and experiment has been found to be Pattere n Shping very good. In the absence of mutual coupling between the parasitic elements, Reduction of Edge Diffraction Effects the present theory can be applied to double- and multiple-parasitic loop counterpoise antennas. The parasitic loops in general reduce the counterpoise edge diffraction effeots on the far field patterns. The behavior of the parasitic loop counterpoise antenna pattern near the principal maximum is not appreciably different than the Alford loop counterpoise pattern near its maximum. Parasitic loops inorease the response of the antenna in regions of space near the zenith 8=0~. Detailed results of numerical and experimental investigations of various aspects of the parasitic loop counterpoise antenna have been given. These results bring out the effects of the different parameters of this new antenna system on the radiation patterns. The parasitic loop concept has been found to be capable of shaping the pattern produced by an Alford loop counterpoise antenna pattern in regions of space below the plane of the counterpoise. On the basis of our investigation we conclude that when suitably designed, the On the basis of our investigation we conclude that when suitably designed, the parasitic loop counterpoise antenna is potentially capable of minimizing the siting errors associated with existing VOR systems. We have proposed three new antenna systems which may find possible application in a VOR system. UNCLASSIFIED The University of Michigan Radiation Laboratory, Ann Arbor, Michigan Sengupta, D. L, THEORETICAL AND EXPERIMENTAL INVESTIGATION OF PARASITIC Ferris J. E. LOOP COUNTERPOISE ANTENNAS, by D. L Sengupta, J. E. Ferris and H V. H. Weston, September 1968, Final Report (June 1967-June 1968), Weston, V. H. 112 pp., incl. illus., 9 refs. HI. Project 330-004-05N 11 PrConect 330-004-05N (Contract FA67WA-1753, Project 330-004-05N, Report No. RD-68-50) IV. Report No. RD-68-50 Unclassified Report i Unclassified Report Descriptors The radiation field produced by a single parasitic loop counterpoise ansitic Loop Countepoi A tenas I tenna has been investigated both theoretically and experimentally. GeoVOR Antennas metrical theory of diffraction is applied to obtain theoretical expressions Geometrical Theory of Diffraction for the far field produced by such an antenna. Within the range of approxiPattern Shaping mation the agreement between theory and experiment has been found to be Reduction of Edge Diffraction Effects very good. In the absence of mutual coupling between the parasitic elements, the present theory can be applied to double- and multiple-parasitic loop oounterpoise antennas. ' The parasitic loops in general reduce the counterpoise edge diffraction effects on the far field patterns. The behavior of the parasitic loop counterpoise antenna pattern near the principal maximum is not appreciably different than the Alford loop counterpoise pattern near its maximum Parasitic loops increase the response of the antenna in regions of space near the zenith 90~. Dtailed results of numerical and experimental investigations of various aspects of the parasitic loop counterpoise antenna have been given. These resuits bring out the effects of the different parameters of this new antenna system on the radiation patterns. The parasitic loop concept has been found to be capable of shaping the pattern produced by an Alford loop counterpoise antenna pattern in regions of space below the plane of the counterpoise. On the basis of our investigation we conclude that when suitably designed, the parasitic loop counterpoise antenna is potentially capable of minimizing the siting errors associated with existing VOR systems. We have proposed three new antenna systems which may find possible application in a VOR system. m, — — m- -—.,-_mm__ UNCLASSIFIED | I. Sengupta, D.L. I Ferris, J. E. Weston, V. H. I. Contract FA67WA-1753 m. Project 330-004-05N IV. Report No. RD-68-50 I Descriptors Parasitic Loop Counterpoise Antennas VOR Antennas Geometrical Theory of Diffraction Pattern Shaping Reduction of Edge Diffraction Effects UNCLASSIFIED I I. Sengupta,D. L., Ferris, J. E. Weston, V. H. IL Contract FA67WA-1753 m. Project 330-004-05N IV. Report No. RD-68-50 Descriptors | Parasitic Loop Counterpoise Antennas VOR Antennas 1 Geometrical Theory of Diffraction Pattern Shaping Reduction of Edge Diffraction Effects I