TECHNICAL REPORT STANDARD TITLE PAGE 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. FAA-72-32 4. Title and Subtitle 5. Report Date Investigation of Parastic Loop Counterpoise Antennas December 1972 and Their Application to VOR Systems 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. DIPAK L. SENGUPTA JOSEPH E. FERRIS 9. Performing Organization Name and Address 10. Work Unit No. The University of Michigan Radiation Laboratory 330-001-03N Department of Electrical and Computer Engineering 11. Contract or GrantNo. Ann Arbor, Michigan 48105 FA-69WA-2085 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Final Report for Period Federal Aviation Administration; Systems Research and Aug. 1969 - October 1972 Development Service, Washington, D. C. 20591 14. Sponsoring Agency Code 15. Supplementary Notes 16. Abstract The radiation fields produced by conventional VOR and parastic loop counterpoise antennas have been investigated both theoretically and experimentally. Theoretical expressions for the side band mode radiation fields produced by conventional VOR antennas have been obtained by applying the.concepts of geometrical theory of diffraction. Using similar techniques: expressions have been obtained for both carrier and side band mode radiation fields.produced by single parastic loop counterpoise antennas. It has beenifound that for large separation distance between the parastic loops, the mutual coupling":effects may be neglected during the evaluation of double parastic loop counterpoise antennas. | All the above theoretical results-have been compared with the experimental results obtained from model measurements.' Within the.'ranges of approximations made in the theoretical analysis and the experimental errors, the agreement between theory and experiment has been found to b,e -satisfactory. On the basis of the parametric studies of the radiation patterns, optimum double parastic loop counterpoise antennas have been developed so that the side band mode patterns have maximum field gradients at the horizon. Full scale flight testing of a conventional VOR system using the above optimum antenna indicated that the new antenna system reduces the scalloping errors by a ratio of six to one. Large polarization errors have been observed with the conventional VOR system using the double parasitic loop counterpoise antennas. More work should be done to reduce this undesi - ablepoarization error. _____., 17. Key Words 18. Distribution Statement Parastic Loop Counterpoise Antennas Availability is unlimited. Document may VOR Antennas be released to the National Technical Geometrical theory of diffraction Information Service, Springfield, Va. TInproved VOR systems I22151, for sale to the public. Optimum VOR antennas 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price UNCLAS UNCIAS 192 $3 PC.95 MF Form DOT F 1700.7 (8.69)

3051-1-F INVESTIGATION OF PARASITIC LOOP COUNTERPOISE ANTENNAS AND THEIR APPLICATION TO VOR SYSTEMS Final Report (August 11, 1969 - October 22, 1972) December 1972 Contract No. FA69WA-2085 Project No. 330-001-03N SRDS Report No. RD-72 -This report has been prepared by The University of Michigan Radiation Laboratory of the Department of Electrical and Computer Engineering for the Systems Research and Development Service, Federal Aviation Administration, under Contract FA69WA-2085. 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 Dipak L. Sengupta and Joseph E. Ferris The University of Michigan Radiation Laboratory Department of Electrical and Computer Engineering Ann Arbor, Michigan 48105 for Systems Research and Development Service Federal Aviation Administration, Washington, DC 20590

3051-1-F TABLE OF CONTENTS INTRODUCTION 1 1.1 Preliminary Remarks 1 1.2 Discussion on Conventional VOR System Performance 1 1.3 Conventional VOR Performance in NonIdeal Location 3 1.4 The Parasitic Loop Counterpoise Antenna 3 1.5 Previous Work Accomplished 4 1.6 Outline of the Report 4 1.7 Summary of Results Obtained 7 Table I 9 Table HI 10 Scalloping Error Amplitudes 11 Polarization Errors 11 Table II 12 II FREE SPACE RADIATION CHARACTERISTICS OF CONVENTIONAL VOR ANTENNAS 13 2.1 Introduction 13 2.2 Carrier Mode Pattern 13 2.3 Side Band Mode Pattern 18 2.3.2 Description of the Experimental Arrangement 21 2.3.3 Comparison Between Theory and Experiment 22 2.3.4 More Information About the Side Band Pattern 22 2.4 Discussion 28 ]lI INVESTIGATION OF SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA 31 3.1 Introduction 31 3.2 Carrier Mode Pattern 31 3.3 Numerical Investigation of the Parasitic Current for the Carrier Mode Case 34 3.4 Side Band Mode Pattern 38 3.4.1 Theoretical Expressions 38 3.4.2 Comparison Between Theory and Experiment 44 3.5 Discussion 46 iii

TABLE OF CONTENTS (continued) IV INVESTIGATION OF A DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 47 4.1 Introduction 47 4.2 Theoretical Expressions for the Radiation Field 47 4.3 Description of the Experimental Arrangement 49 4.4 Comparison Between Theory and Experiment 51 4.5 Optimum Double Parasitic Loop Counterpoise Antenna 51 4.6 Optimum Antenna Patterns 53 4.7 Full Scale Parameters of the Optimum Antenna 58 4,8 Discussion 58 V FABRICATION OF THE FULL SCALE DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 60 5.1 Introduction 60 5.2 Standard VOR Antenna at NA FE C 60 5.3 Full Scale Parasitic Loop Assembly 60 5.4 Discussion 61 VI NAFEC FACILITIES AND INITIAL GROUND TESTS 67 6.1 Introduction 67 6.2 Standard VOR Experimental Station Terrain 67 6.3 Ground Test Facility 67 6.4 Introduction of Known Scattering Sources 68 VII GROUND TEST RESULTS FOR STANDARD VOR AND DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNAS 71 7.1 Introduction 71 7.2 Field Expressions 71 7.3 Full Scale Ground Test Results 74 7.4 Discussion 75 VIII FLIGHT TESTS OF DOUBLE PARASITIC LOOP COUNTERPOISE AND STANDARD VOR ANTENNAS 81 8.1 Introduction 81 8.2 Test Antennas 81 8.3 Field Strength Results 82 8.4 Scalloping Effects 83 8.5 Distance Range 85 8.6 Discussion 85 iv

TABLE OF CONTENTS (continued) IX EXPERIMENTAL STUDY OF THE POLARIZATION ERROR 94 9.1 Introduction 94 9.2 Polarization Errors in Standard VOR System 94 9.3 Polarization Error Study with the Passive Polarizer 95 9.4 The Active Polarizer 104 9.5 Parasitic Loop Counterpoise Antenna System n with Active Polarizer 106 9.6 Discussion 112 X APPLICATION OF PARASITIC LOOP COUNTERPOISE ANTENNA TO VOR SYSTEM 116 10.1 Introduction 116 10.2 Limitations of Conventional VOR Systems 116 10.3 Application of Parasitic Loop Counterpoise Antennas 117 10.4 Discussion 118 XI CONCLUSIONS AND RECOMMENDATIONS 120 11.1 Conclusions 120 11.2 Recommendations for Further Work 122 ACKNOWLEDGMENT 123 REFERENCES 124 APPENDIX A (The Radiation Field of a Circular Loop Carrying a Non-Uniform Harmonic Current 126 A.1 Introduction 126 A.2 Nature of Excitation 126 A.3 Far Field Expressions 128 A.4 Discussion 131 APPENDIX B (Mutual Coupling Effects in Parasitic Loop Counterpoise Antennas 133 B. 1 Introduction 133 B.2 Parasitic Currents 133 B.3 Far Field Expressions 137 B.4 Numerical Results 140 B.5 Discussion 141 v

TABLE OF CONTENTS (continued) APPENDIX C (Double Parasitic Loop Counterpoise Antenna Patterns) 144 C. 1 Introduction 144 C.2 Preliminary Experiment 144 C.3 Optimization of the Lower Parasitic Loop Parameters 145 C. 4 Optimization of the Upper Parasitic Loop Parameters 150 C.5 Maximum Obtainable Field Gradient 150 C. 6 Discussion 158 APPENDIX D (Numerical Values for Parasitic Currents in Single Parasitic Loop Counterpoise Antennas 161 D. 1 Introduction 161 APPENDIX E (Computer Programs for IBM 360, Model-67) 166 C. 1 Program for evaluating the far field elevation plane side band mode pattern of a conventional VOR antenna (SA(e) versus 0). The subroutines given in this section are also used in all the subsequent programs 166 E. 2 Program for evaluating the far field elevation plane carrier mode patterns of conventional VOR and single parasitic loop counterpoise antennas (SA(0), S(0)). 174 E. 3 Program for evaluating the far field elevation plane carrier mode pattern of a double parasitic loop counterpoise antenna (mutual effects neglected) 176 E. 4 Program for evaluating the far field elevation plane side band mode pattern of a double parasitic loop counterpoise antenna (mutual effects neglected). 179 E. 5 Program for evaluating the mutual coupling coefficients K12, K21 and also the far field elevation plane carrier mode pattern of a double parasitic loop counterpoise antenna taking into account the effects of mutual coupling 182 vi

TABLE OF CONTENTS (continued) E. 6 Program for evaluating the far field elevation plane side band mode pattern of a conventional VOR antenna above ground 185 E. 7 Program for evaluating the far field elevation plane carrier mode pattern of a double parasitic loop counterpoise antenna above ground 188 E. 8 Program for evaluating the far field elevation plane side band mode pattern of a double parasitic loop counterpoise antenna 191 E. 9 Program for evaluating the quasi far zone elevation plane side band mode field of conventional VOR antenna above ground 194 E. 10 Program for evaluating the quasi far zone elevation plane carrier mode field of a double parasitic loop counterpoise antenna above ground 196 E. 11 Program for evaluating the quasi far zone elevation plane side band mode field of a double parasitic loop counterpoise antenna above ground 199 APPENDIX F (Theoretical Elevation Patterns of Conventional VOR and Double Parasitic Loop Counterpoise Antennas 202 vii

LIST OF ILLUSTRATIONS Figure No. Caption Page No. 2-1 Theoretical model for the conventional VOR antenna. 14 2-2 Carrier mode elevation plane far field pattern of a conventional VOR antenna. 17 2-3 Photograph of the Alford loop model. 23 2-4 Photograph of the two Alford loops mounted above the 15' diameter counterpoise. 24 2-5 Side band mode elevation plane far field pattern of a conventional VOR antenna. 25 2-6 Side band mode elevation plane far field pattern of a conventional VOR antenna. 26 2-7 Side band mode elevation plane far field pattern of a conventional VOR antenna. 27 2-8 Measured side band mode elevation plane far field pattern of a conventional VOR antenna. 29 2-9 Measured side band mode azimuthal plane far field pattern of a conventional VOR antenna. 30 3-1 Schematic representation of single parasitic loop counterpoise antenna and the coordinate system used. 32 3-2 Theoretical field gradient (ag) as a function of H for a single parasitic loop counterpoise antenna operating in the carrier mode. 35 3-3 Carrier mode elevation plane far field pattern of a single parasitic loop counterpoise antenna. 36 3-4 Theoretical model for a single parasitic loop counterpoise antenna. 39 3-5 Dominant rays contributing to the parasitic current. 40 3-6 Side band mode elevation plane far field pattern of a single parasitic loop counterpoise antenna. 45 viii

LIST OF ILLUSTRATIONS (continued) 4-1 Theoretical model for the double parasitic loop counterpoise antenna. 48 4-2 Side view of the double parasitic loop counterpoise antenna. 50 4-2a A close-up view of the double parasitic loop counterpoise antenna model. 50 4-3 Carrier mode elevation plane far field pattern of a double parasitic loop counterpoise antenna. 52 4-4 Side band mode elevation plane far field pattern of a double parasitic loop counterpoise antenna. 54 4-5 Theoretical maximization of the horizon field gradient of a double parasitic loop counterpoise antenna operating in the side band mode. 55 4-6 Theoretical carrier and side band mode elevation plane pattern of the optimized double parasitic loop counterpoise antenna. 56 4-7 Measured side band mode elevation plane far field pattern of the optimum double parasitic loop counterpoise antenna. 57 5-1 150' diameter counterpoise conventional VOR antenna mounted on a 75' tower at NAFEC. 62 5-2 The details of the mechanical fabrication of the full scale parasitic elements. 63 5-3 A section of the two full scale parasitic loops mounted on the counterpoise. 64 5-4 The details of the tension adjuster used for the installed parasitic loops. 65 5-5 Two full scale parasitic loops mounted on the 1501 diameter counterpoise. 66 6-1 The terrain surrounding the VOR station at NAFEC. 69 6-2 Standard VOR Experimental Station terrain. 70 ix

LIST OF ILLUSTRATIONS (continued) 7-1 Geometrical representation of a double parasitic loop counterpoise VOR antenna above ground. 72 7-2 Carrier mode field strength variation as a function of 0 at a distance 300' away from a conventional VOR antenna located 75' above ground. 76 7-3 Carrier mode field strength variation as a function of e at a distance 300' away from the (Systems-II) optimum double parasitic loop counterpoise VOR antenna located 75' above ground. 77 7-4 Side band mode field strength variation as a function 0 at a distance 300' away from the optimum double parasitic loop counterpoise VOR antenna (Systems-l) located 75' above ground. 78 7-5 Measured carrier mode field strength variation in a vertical plane located 300' away from a non-optimum double parasitic loop counterpoise VOR antenna. 79 7-6 Measured side band mode field strength variation in a vertical plane located 300' away from a non-optimum double parasitic loop counterpoise VOR antenna (Systems-I). 80 8-1 Radiation field produced by a standard VOR antenna above ground. 87 8-2 Radiation field produced by the double parasitic loop counterpoise system II above ground. 88 8-3 Radiation field produced by a double parasitic loop counterpoise antenna system nI above ground. 89 8-4 Location of the wire grid reflector with respect to the VOR station. 90 8-5 Scalloping results obtained with a conventional VOR system using a conventional antenna. 91 x

LIST OF ILLUSTRATIONS (continued) 8-6 Scalloping results obtained with a conventional VOR system using a double parasitic loop counterpoise antenna (System-I). 92 8-7 Scalloping results obtained with a conventional VOR system using the optimum double parasitic loop counterpoise antenna (System-fl). 93 9-1 Conventional 4 loop VOR (Mannheim, No Polarizer)Results. 96 9-2 Conventional 4 loop VOR (Mannheim, with Polarizer) Results. 97 9-3 Double parasitic loop counterpoise antenna system II results (Mannheim, no Polarizer). 98 9-4 Double parasitic loop counterpoise antenna system I results (Mannheim, with polarizer). 99 9-5 Double parasitic loop counterpoise antenna system I results (Mannheim, with polarizer). 102 9-6 Active Polarizer No. 1. 103 9-7 Active Polarizer No. 2. 105 9-8 Active polarizer installation. 107 9-9 Field Strength for active polarizer No. 2. 109 9-10 Field strength for double parasitic loop counterpoise antenna system II. 110 9-11 Polarization error for double parasitic loop counterpoise antenna system I. 111 9-12 Polarization error versus angle for double parasitic loop counterpoise antenna system I. 113 xi

LIST OF ILLUSTRATIONS (continued) 9-12c, d. Polarization error versus angle for double parasitic loop counterpoise antenna system II. 114 A-1 Coordinate system used. 127 A-2 Orientation of the circular loop. 129 B-1 Double parasitic loop counterpoise antenna. 133 B-2 Rays contributing to K12. 135 B-3 Theoretical carrier mode pattern of a double parasitic loop counterpoise antenna with and without mutual coupling effects. 142 B-4 Theoretical and experimental carrier mode patterns of a double parasitic loop counterpoise antenna. 143 C-la Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. 147 C-lb Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. 148 C-lc Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. 149 C-2 Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. 151 C-3 Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. 152 C-4 Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna. 153 C-5a Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna. 154 C-5b Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna. 155 C-6a Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna. 156 C-6b Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna. 157 xii

LIST OF ILLUSTRATIONS (continued) C-7a Measured elevation plane side band mode pattern of very large gradient double parasitic loop counterpoise antenna. 159 C-7b Measured elevation plane side band mode pattern of very large gradient double parasitic loop counterpoise antenna. 160 xiii

I INTRODUCTION 1.1 Preliminary Remarks This is the Final Report on Contract FA69WA-2085, Project 330-001-03N, "VOR Parasitic Loop Counterpoise Systems-II", and covers the period from 11 August 1969 to 22 October 1972. The main objectives of the research reported here have been: (i) to investigate the radiation characteristics of parasitic loop counterpoise antennas and to evolve an optimum antenna configuration so that it may be incorporated into an existing conventional (or standard) VOR (V HF Omni Range) system, (ii) to evaluate the improvement in the performance of a conventional VOR system brought about by the above new antenna system. A major part of the present investigation has been devoted to the development of satisfactory theories of radiation patterns of parasitic loop counterpoise antennas and also for the radiation patterns of conventional VOR antennas. The performance of a conventional VOR system using an optimum double parasitic loop counterpoise antenna, developed during the present contract, has been evaluated by ground as well as flight tests. In the following sections of this chapter we at first give some of the relevant background information and discuss briefly the previous work done on this problem. A brief outline of the report is then given. Finally, the main results accomplished during the contract period are summarized in the last section. 1.2 Discussion on Conventional VOR System Performance It is appropriate here to give a short discussion on the performance of a conventional VOR system. This will put into proper perspective the need for the use of parasitic loop counterpoise antennas to VOR systems. The operation of conventional VHF Omnirange systems is described in detail by Hurley, et al (1951). In this section we discuss certain aspects of the conventional VOR system performance and its antenna system which are appropriate for our purpose. A detailed description of conventional VOR antenna systems was given by Anderson, et al (1953) and Anderson (1965) and will not be repeated here. The antenna system of a standard VOR system consists of four Alford loops located at the same height above a 521 diameter circular and conducting ground plane or 1

counterpoise. These four loops are mounted at the corners of a square symmetrically around the axis of the system and they lie in a plane parallel to the counterpoise. The antenna is oriented with the ground plane lying in the horizontal plane. The entire antenna assembly is usually mounted such that the counterpoise is at a height 15' above ground. Depending on the local terrain conditions, the entire antenna assembly may be located at different heights. Henceforth this antenna will be referred to as the conventional VOR or 4-Alford loop counterpoise antenna. The standard VOR system operates at a single frequency within the band 108 - 118 MHz. The requirements of the VOR system are such that the antenna operates in two distinct modes. In the first mode, called the carrier mode, all four loops are simultaneously driven in phase with carrier frequency currents. The carrier mode pattern of the antenna is omnidirectional in azimuth. In the second mode, called the side band mode, at any instant of time each diagonal pair of loops is excited such that the horizontal plane pattern of each pair of loops above the counterpoise is a figure-of-eight. Each figure-of-eight pattern is then rotated about the vertical axis at 30 revolutions per second. The relative phase between the pairs of loops is such that the combined effects of these in space is to produce a single figure-of-eight azimuthal pattern rotating at 30 revolutions per second. The free space elevation plane patterns of the antenna in both modes are symmetrical bout the vertical axis and have principal maxima at 30~-35~ above the horizon and have minima in the axial direction (Sengupta et al, 1968; Sengupta, 1971). Thus when the carrier field is combined with the total side band field at each instant of time throughout the goniometer cycle, a rotating limacon field pattern results. The free space patterns of such antennas show considerable response in directions below the plane of the counterpoise. It is known that the field gradient at the horizon (defined to be the rate of decrease of field just below the horizon) is about 3dB/6~ in both modes of operation. As we shall see later, this field gradient value has significant influence on the accuracy obtainable from a conventional VOR system. In the ideal situation the conventional VHF omnirange produces two 30 Hz signals for reception by a flying aircraft: one is constant in phase and independent of the aircraft position, and the other varies in relative phase directly in accordance with the magnetic bearing of the aircraft from the VOR station. The former is referred to as the reference phase signal and the latter as the variable phase signal. The reference phase signal is obtained by frequency modulating at 30 Hz a 9.96KHz subcarrier signal which in turn amplitude modulates the rf carrier signal. The reference phase signal is radiated by the antenna in the carrier mode of operation having an omnidirectional pattern discussed earlier. The variable phase signal is 2

produced by space amplitude modulating the rf carrier signal with 30 Hz sideband radiated energy. This signal is radiated in the form of a figure-of-eight pattern in azimuth, by effectively rotating it at 30 revolutions per second thereby providing the desired variable signal under this condition. In this case the antenna operates in the side band mode. A phase measuring device in the receiver enables the pilot to determine his bearing with respect to the station by comparing the phase difference between these signals. In the ideal situation when there exists no disturbing object between the VOR station and the flying aircraft the bearing indications obtained by the aircraft in the above manner are found to be quite accurate. 1.3 Conventional VOR Performance in Non-Ideal Location In an actual situation whenever there exists a multipath between the VOR ground station and the flying aircraft, the multipath signals combine with the desired signals at the aircraft. The source of these multipath signals may be trees, buildings, etc., or any other scattering object. The strengths of the multipath signals at the aircraft is directly proportional to the free space response of the antenna in directions below the plane of the counterpoise, if it is assumed that the scattering objects are located below the counterpoise plane. The overall effects of the multipath signals combine to produce siting errors and scalloping in the bearing indications of a conventional VOR (Anderson, 1965). To avoid the errors in the bearing indications of the standard VOR systems the ideal requirements on the free space antenna radiation pattern are such that in the upper half plane of the counterpoise the elevation field pattern should resemble the Alford loop connterpoise pattern and in directions below the counterpoise plane should be zero or negligible. In other words the field gradient at the horizon should be infinite or very large. 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 and expensive. From the discussion given above it is evident that any antenna system having overall free space radiation pattern characteristics mentioned above but which produces little field in directions below the horizontal plane is potentially capable of reducing the VOR siting errors. The parasitic loop counterpoise antenna is such an antenna. 1.4 The Parasitic Loop Counterpoise Antenna The parasitic loop counterpoise antenna, as originally defined (Sengupta et al, 1968), consists of a small excited circular loop (or Alford loop) placed above and parallel to a circular and conducting ground plane along with one or more suitably 3

placed large parasitic loops oriented coaxially and parallel to the counterpoise. Parasitic loop counterpoise systems, defined this way, can be used only in the carrier mode operation described in the previous sections. We generalize the definition of the parasitic loop counterpoise antenna to include the case where the excitation consists of more than one Alford loop so that it can operate also in the side band mode. As we shall see later, the chief advantage of the parasitic loop concept is that it makes it possible to increase the field gradient of the VOR antenna without increasing the counterpoise size; an additional advantage of the parasitic system is that it is relatively simple to convert the existing conventional VOR antennas to the new systems by inserting parasitic loops at appropriate heights. 1.5 Previous Work Accomplished Theoretical and experimental investigation of parasitic loop counterpoise antennas operating in the carrier mode have been reported in our Final Report under a previous contract (Sengupta, et al, 1968). Theoretical analysis of the carrier mode patterns of single parasitic loop counterpoise and of conventional VOR antennas have been discussed by Sengupta and Weston (1969). Detailed parametric studies of the radiation patterns of such antennas may be found in Sengupta and Ferris (1970). All these studies have shown that with the help of parasitic loop concepts it is possible to reduce considerably the free space field produced in directions below the counterpoise by conventional VOR antennas operating in the carrier mode. In particular with an optimum double parasitic loop counterpoise antenna operating in the carrier mode, it has been found that in the elevation plane the rate of decrease of the far electric field just below the horizon is 21dB/5.5~ (Sengupta et al, 1968). Possible application of parasitic loop counterpoise antennas operating in the carrier mode has been reported by Sengupta and Weston (1968). On the basis of the research reported in Sengupta et al (1968) there evolved three specific parasitic loop counterpoise antenna configurations having possible application to a VOR system. As mentioned, all the previous work discussed above has been devoted only to the carrier mode type of operation for the antenna. However, from the viewpoint of VOR system operation, it is the side band mode elevation plane pattern of the antenna which is of importance (Hurley et al, 1951). A major part of the present research has thus been devoted to the investigation of the side band mode patterns of conventional VOR and parasitic loop counterpoise antennas. 1.6 Outline of the Report The theories of radiation from conventional VOR and parasitic loop counterpoise antennas operating in the side band mode have been hitherto unknown. For this 4

reason a substantial portion of our investigation has been devoted to the development of satisfactory theories for these antennas. This study led to an optimum configuration for a double parasitic loop counterpoise antenna and subsequently to its application to a conventional VOR system. The outline of the report follows. The free space carrier and side band mode radiation properties of the conventional VOR antennas are discussed in Chapter II. Theoretical expressions are derived for the side band radiation patterns of a conventional VOR antenna. The theory is verified by experimental results obtained from model measurements done at 1.09 GHz. The free space carrier and side band mode radiation properties of single parasitic loop counterpoise antennas are both investigated theoretically in Chapter Mi. The theoretical results derived in this chapter are of fundamental importance in the development of double parasitic loop counterpoise antenna theory. The theory is then confirmed by results obtained from model measurements. The nature and values of the parasitic currents in the case of carrier mode operation of single parasitic loop counterpoise antennas are also discussed theoretically and numerically. These results included therein may be found useful in analyzing the measured parasitic currents, if such an investigation is carried out in the future. Chapter IV discusses theories of both carrier and side band mode patterns produced by double parasitic loop counterpoise antennas. The theories are confirmed by results obtained from model measurements. On the basis of the parametric study of the side band mode patterns, an optimum double parasitic loop counterpoise antenna configuration is obtained. The antenna is optimized in the sense that the horizon field gradient in the elevation plane side band pattern is maximum. Design parameters are obtained for an optimum antenna with a 150' diameter counterpoise operating at the full scale frequency of 109 MHz. Mechanical fabrication and assembly of the full scale optimum double parasitic loop counterpoise antenna are discussed in Chapter V. The conversion of the experimental conventional VOR antenna, located at Mannheim Avenue Experimental VOR Facility at NAFEC (National Aviation Facility Experimental Center) into an optimum double parasitic loop counterpoise antenna is also described in detail. Chapter VI describes briefly the test facilities available at National Aviation Facility Experimental Center where the full scale testing of the double parasitic loop counterpoise antenna has been carried out. 5

Chapter VII describes the results obtained from ground tests conducted to evaluate the performance of the conventional VOR and the double parasitic loop counterpoise antennas. Results obtained from flight tests conducted with conventional VOR systems using standard 4-Alford loop counterpoise and double parasitic loop counterpoise antennas are discussed in Chapter VII. The results discussed in this chapter indicate the following: (i) verify at the full scale frequency and for practical systems the horizontally polarized elevation plane pattern information obtained earlier for such antennas from theoretical and model measurements considerations. (ii) in the presence of a known multipath signal, the use of optimum double parasitic loop counterpoise antenna reduces the scalloping errors associated with a conventional VOR system by a factor of 6 to 1. Large polarization errors were observed during the flight tests of the conventional VOR systems using double parasitic loop counterpoise antennas. Chapter IX discusses the results of our experimental investigation of polarization errors associated with such antennas. Due to the shortage of time this phase of our investigation remains incomplete. The results of our limited investigation indicate that the polarization errors in the parasitic system can be reduced to acceptable values for 0 < 800; however, for 0 > 80~ the maximum value of the total polarization error has been found to be about 12~. The application of parasitic loop counterpoise antennas to a conventional VOR system is discussed critically in Chapter X. Chapter XI gives our general conclusions and recommendations for future work. The radiation field of a circular loop carrying a non-uniform harmonic current is discussed theoretically in Appendix A. The results given here may have implications in the analysis of polarization errors associated with the parasitic loop counterpoise VOR antenna systems. The significance of mutual interaction between parasitic currents in the evaluation of patterns of a double parasitic loop counterpoise antenna is discussed in Appendix B. Appendix C supplies the investigation which gave rise to an optimum double parasitic loop counterpoise antenna using a 52' diameter counterpoise at the full scale frequency of 108 MHz. 6

Appendix D gives the numerical values of the parasitic currents for a single parasitic loop counterpoise antenna operating in the carrier mode. Appendix E gives Fortran IV computer programs used for various numerical computations. Appendix F gives some selected numerical results. 1.7 Summary of Results Obtained As mentioned in Section 1. 1, the main objectives of the present research program have been to develop an optimum double parasitic loop counterpoise antenna configuration and to investigate its application to a conventional VOR system. In this section we summarize the significant results that have been obtained to this end. The principal results accomplished in the present contract period are: (i) Development of satisfactory theories for the carrier and side band mode far field patterns of 4-Alford loop counterpoise standard VOR antennas. (ii) Development of satisfactory theories for the carrier and side band mode far field patterns of parasitic loop counterpoise standard VOR antennas. (iii) Design and development of an optimum double parasitic loop counterpoise antenna compatible with a conventional VOR system. (iv) Verification of the theories developed in (i) - (iii) by model measurements at 1.09 GHz and by ground and flight tests conducted at the full scale frequency of 109 MHz. (v) Flight test results giving the course scalloping errors produced in the VOR bearing indications of a flying aircraft when there exists a known multipath signal source between the standard VOR ground station and the flying aircraft. Results have been obtained for the standard VOR ground station with and without parasitic antenna system. (vi) Polarization error results associated with a standard VOR system with and without parasitic loop-antenna system. Development of an active polarizer for correcting the polarization errors. This phase of our study remains incomplete due to lack of time. 7

For ready reference, we give in tabular form below some selected results of interest. The following list of symbols may be found useful in reading the tables of results. 2A = diameter of the counterpoise. h = height of the Alford loops above the counterpoise. 2d = separation distance between a diagonal pair of Alford loops, w = width of the conducting strips comprising the parasitic loops, H1, H2 = the heights of the first and second parasitic loops above the counterpoise, 2B1, 2B2 = diameters of the first and second parasitic loops, 68 = direction of the principal maximum in the elevation plane max (0 = 0~) far field pattern. 0 = 0~ is the vertical direction, Ej (96~) a -2 0 log- - = the far field gradient at the horizon in ~g! 0 E (90 ) the elevation plane = 0~, E (90~) af -20 log E0 — E = the far field reduction factor in the direction (~f -20log10 E (0) 0 max of the horizon. For all the test results given below, the operating frequency is 109 MHz and the corresponding wavelength X = 9. 02'. 8

TABLE I RESULTS FOR 150' DIAMETER COUNTERPOISE SYSTEM Standard 4-Alford Loop Counterpoise VOR Antenna Design Parameters: 2A = 150', h = 4', d = 1'4" and 4 Standard Alford Loops. Optimum Double Parasitic Loop Counterpoise Antenna Design Parameters: The above 4-Alford loop counterpoise VOR antenna design parameters plus the following; w = 10", H = 5', 2B = 46'10", H2 = 18'8" and 2B2 = 32'10". Elevation Plane (0 = 00) Pattern Characteristics "___ — Standard VOR Antenna ____Carrier Mode Side Band Mode 0max 620 650 a I 5.56dB/6~ 5.54dB/60 af 14.82dB 14.7dB Optimum Double Parasitic Loop Counterpoise Antennas Carrier Mode Side Band Mode o 1 62~ 66~ max a 5.66dB/6~ 23.7 ldB/60 af 10.3dB 23.18dB 9

TABLE II RESULTS FOR 52' DIAMETER COUNTERPOISE SYSTEM Standard 4-Alford Loop Counterpoise VOR Antenna Design Parameters: 2A = 52', h = 4', d = 1'4". Optiumm Double Parasitic Loop Counterpoise Antenna Design Parameters: The above 4-Alford loop counterpoise antenna design parameters plus the following: w = 10", H = 5'2", 2B = 48'8", H = 15'8" and 2B = 34' 10". 2 Elevation Plane (0 = 0) Pattern Characteristics Standard VOR Antenna Carrier Mode Side Band Mode m 58~ 60~ max ag | 3. 11dB/6~ 3. 05dB/60 af 10. 44dB 9.47dB Double Parasitic Loop Counterpoise Antenna Carrier Mode Side Band Mode 0m 58~ 60~ max a 3. 11dB/6~ 21.22dB/60 g af | 7.4dB 16.5dB Only the 150' diameter antenna systems have been tested at the full scale frequency 109 MHz. 10

Scalloping Error Amplitudes Course scalloping errors in the standard VOR bearing indications of a flying aircraft have been measured with the conventional VOR ground station using standard 4-Alford loop and optimum double parasitic loop antenna systems along with a 150' diameter counterpoise located 75' above ground. In each case the aircraft was flying on a 20 mile orbit, around the VOR station, at an altitude of 6575' (which corresponds to a minimum in the vertical plane pattern nearest to the horizon); there existed a multipath signal source in the direction 0 = 52' and at a distance 1000' awpy from the VOR ground station. In each case the scalloping errors were observed to be maximum in the 0 l 140~ direction and are given as follows: maximum scalloping error for the conventional VOR system using standard 4-Alford loop antenna = 12. 5~ maximum scalloping error for the conventional VOR system using the optimum double parasitic loop counterpoise antenna = 2~ In addition to the above scalloping errors have been measued for the case of a conventional VOR system using a non-optimum double parasitic loop counterpoise antenna. The details may be found in Chapter VIII: Polarization Errors Polarization errors associated with a conventional VOR system with and without parasitic loop antennas have been measured in the range 62~ < 0 < 90~. The measurements were carried out with the help of an aircraft flying at an altitude of 3220 feet along selected radials with respect to the VOR ground station. In each case errors have been measured for VOR ground station antennas with and without passive polarizers. 11

TABLE MII MEASURED TOTAL POLARIZATION ERRORS Standard VOR Using 4-Alford Loop Antenna 0 NO Polarizer With Passive Polarizer Total Polarization Error Total Polarization Error 62~ <0<82~ 11. 5 1~.9 82~ < 0 < 900 13~. 5 (maximum) 5~ (maximum) Stan ard VOR Using Optimum Doub e Parasitic Loop Antenna NO Polarizer With Passive Polarizer 620 < < 80~ 8~ 3~ 80~ < 0 < 90~ 14~ 12~ (maximum) We have developed an active polarizer for the purpose of reducing the polarization errors associated with conventional VOR systems. The details may be found in Chapter IX. From the results given here, it appears that the polarization errors associated with the parasitic system are large in directions 0 > 80~. As mentioned before our polarization error study is incomplete. However, we believe that this error can be reduced further by improving the existing passive polarizers. 12

II FREE SPACE RADIATION CHARACTERISTICS OF CONVENTIONAL VOR ANTENNAS 2.1 Introduction In this chapter, both theoretical and experimental free space radiation patterns produced by a conventional VOR antenna are discussed. The conventional VOR antenna system consists of four Alford loops placed about 4'h above a conducting ground plane or counterpoise. As mentioned earlier the antenna operates in two distinct modes characterized by the method of excitation of these four loops. In the carrier mode, the four loops are excited with equal amplitude and phase all the time. The pattern of the antenna in this mode is omnidirectional in the horizontal plane. The elevation plane pattern is symmetrical about the axial direction; it has a maximum in the direction 30~ - 40~ above the horizon and has a minimum (ideally a null) in the axial direction. The carrier mode radiation pattern of a conventional VOR antenna has been discussed in detail previously (Sengupta, et al, 1968; Sengupta and Weston, 1969) and will not be repeated here. The theoretical expression for the carrier mode pattern along with some relevant pattern details for a specific antenna configuration are given here for future reference. In the side band mode, at any instant of time, each diagonal pair of Alford loops are excited with equal amplitude but opposite phase. The pattern of each pair of loops above the counterpoise is a figure-of-eight in the horizontal plane; in the elevation plane the pattern is similar to that of the carrier mode. Although these facts about the side band mode patterns are well documented experimentally, there has been no satisfactory theory until we developed it recently (Sengupta and Ferris 1970a; Sengupta 1971). In the following sections, we discuss the theory of the side band mode radiation pattern produced by a conventional VOR antenna. The theory is then compared with experimentally measured patterns. 2.2 Carrier Mode Pattern For the purpose of theoretical analysis of the radiation pattern, the conventional VOR antenna operating in the carrier mode is approximated by a small circular loop carrying a constant amplitude current and located above a circular ground plane. Thus the VOR loop counterpoise antenna can be replaced by a point source with appropriate far field variation and placed above the counterpoise as shown in Fig. 2-1. The free space far-zone electric field of the point source (in the absence of the counterpoise) is represented by the following: 2 ikr E _ I(" )sinO1 -,(2.1) gEl = no Ito (-2) sm ' (in. r13 13

z z yt y 0 L2.. X P(R, 0, 0) Point source 00 Counterpoise N 2-;" "7/-' / / / / / // /-/ / 7 S 1 2 ---- 2 A FIG. 2-1: Theoretical model for the conventional VOR antenna. 14

where r, 0, are the spherical coordinates of the far field point with origin located at the point source, ro is the intrinsic impedance of free space, k = 2r/x is the free space propagation constant, a is the radius of the circular loop, Io is the amplitude of the loop current given by: TI = e t, (2.2) 0 is the unit vector in the n-direction, w is the angular frequency, assumed time dependence is e-i. Note that the field in eq. (2. 1) is polarized in the p-direction and is omnidirectional in the 0 = 7/2 plane. The symmetry of the system dictates that the far field produced by the antenna shown in Fig. 2-1 will also be polarized in the O-direction and that the far-field pattern will be omnidirectional in the horizontal or 0 = /2 plane. It can be shown (Sengupta and Weston, 1969) that the complete expression for the far zone elevation plane (x-z plane) electric field produced at a point P(R, 0) and valid in the range 0 < 6 < r is given by: i(kR-74) E A tI 2 ( ) A(0), (2. 3) E o1 ---o~2 R where o 2 ( cos 00- sin 6 e_______ s L(e), (2.4) SAt~)= FO(B47inBlrkrosin/ sn L0 ()t ei(i-kA sin/) 3/2 c - sin3/2 8 k [coscos- sine ikA sine cos e _ _____s/2 5o cose+sin9 (2.5) ikr l+sin(-p I rto ikr sin(+ ) F~(e)=e e dt-e 0 e dt -00 ~-00 (2.6) 15

kr 12 o 0-/2 (2 p = 2 (- ) cos ( ) (2.7) 2 2 2 r A +h, (2. 9) 0 tan0 = (2. 10) 2 A and the other parameters are as explained in Fig. 2-1. The term SA(0) in eq. (2.3) may be looked upon as the complex far field pattern of the conventional VOR antenna operating in the carrier mode. Thus ISA(() I is the conventional far field radiation pattern. Detailed discussions of eq. (2. 3) and its comparison with experimentally measured patterns have been given elsewhere (Sengupta et al, 1968). The measured free space far field elevation pattern of the conventional VOR antenna with a 15' diameter counterpoise is shown in Fig. 2-2. The theoretical pattern of the same antenna, obtained by numerically computing the far field expressions given above, is superposed on Fig. 2-2 for comparison. The agreement between theory and experiment may be considered to be excellent over most of the regions in space. The slight kink in the experimental pattern near the region 0 = 950 is attributed to a reflecting object lying near the outside pattern range. Since the model antenna considered in Fig. 2-2 corresponds to the full scale VOR antenna located at NAFEC, the theoretical values of the important parameters characterizing the free space elevation pattern of the antenna in the carrier mode at 1080 MHz are given below: Direction of principal maximum 0max = 65~ Far field gradient at the horizon = -20 log10 E(960) 5. 56 dB/6~. g E(9 00) Field reduction factor f = -20 log10 E(900) = 14. 85 dB. The normalized parameters of the antenna are kh = 2.75, kA = 51. 69 at the frequency f = 1080 MHz. These correspond to a full scale antenna having 150' diameter counterpoise and the Alford loops located 4' above the counterpoise. Parametric study of the carrier mode radiation pattern for the same antenna under various situations may be found elsewhere (Sengupta et al, 1968). 16

0=00 -~~~~~~~~~~~~~~~~~~~~ - o 0"~~~~~~~~ ~:;:1~'': ' '- ~ ~ ~ ~ ~ ~~~~~~....' ' ' _: ~.-... ~ _,- ~~ —.... ----*I,v,.'-.?. —, -r \ ~-: —:~.:::.i- ~:!~i i!'.....I..... 1~s~~~ I ~ i i; j I Soo O= 1800 FIG. 2-2; Carrier mode elevation plae far field pattern of a conventional VOR antenna. kh = 2. 75, kA= 51. 69,P f = 1080 MHz. --- Experimental;.... Theoretical ~`: 1 Ii,,,~? iiZ~~~ t... r:-::f.~~~~~~~~.", "/ t ~!1C __. 110~` ~:::: f:r!ii = 108 MIz Eprmna;... Teret: ~ic al: I IL17

2.3 Side Band Mode Pattern In this section we develop and discuss the theoretical expressions for the radiation field produced by a conventional VOR antenna operating in the side band mode. The theory is then compared with measured results at 1080 MHz. From the point of view of the side band mode radiation pattern, the antenna consists of a pair of Alford loops suitable excited and placed at the proper height above a counterpoise. The two Alford loops lie in the same plane which is parallel to the plane of the counterpoise. The Alford loops are separated by a distance, 2d, small compared to a wavelength and are excited with signals having equal amplitude but opposite phase. Thus the free space azimuthal pattern of the antenna would be a figure-of-eight. 2.3. 1 Theoretical Expression for the Elevation Plane Pattern. For the purpose of theoretical analysis the conventional VOR antenna operating in the side band mode is replaced by a point source with appropriate far field variation placed above the counterpoise as shown in Fig. 2-1. The free space far-zone electric field of the point source (in the absence of the counterpoise) can be represented by: ikr.i ka.2 e E =rl (-) f(0,9 )sine (2. 11), o 2 r where all the parameters are as explained in Section 2. 2 and f(0, 0) is the source pattern function which is determined by the method of excitation and orientation of the two loops. Note that the field in eq. (2.11) is polarized in the 0-direction. In the present case, the two Alford loops are excited with equal amplitude but opposite phase so that f(0, )) can be written explicitly as follows: f(, 0) = 2i sin( kd sine cos 0). (2.12) Equation (2.12) means that in the azimuthal plane 0 = 7/2, the pattern is a figureof-eight having a maximum along the x-axis. In the following we discuss the vertical pattern produced by the antenna. The exact analysis of the radiation field produced by the above antenna is an extremely complicated problem, if not impossible. We apply the concepts of geometrical theory of diffraction (Keller, 1962) and the results of Sommerfeld's half-plane diffraction theory (Sommerfeld, 1954) to investigate the problem. In obtaining the far field in the high frequency limit (which implies in the present case that kA >> 1), it is convenient to separate the entire space into three distinct regions. Region I, defined as 0 < 0 < I/2 - 00, is the illuminated region, where the total field at the far field point P(R, 0, 0) can be formally written as, 18

i r d E(P)E(P) E ( ( +E (P ), (2.13) where E(P) is the incident field at P, E (P) is the reflected field at P, E (P) is the diffracted field at P. The diffracted field E (P) consists mainly of the fields diffracted by the near and far edges, respectively, of the counterpoise (N1, N2 in Fig. 2-1). Of the two diffracted fields, the near edge contribution dominates in this region. In Region II, defined as 2 0 < ( 2 + o) r d and known as the transition region, E (P) = 0 and E (P) is essentially due to that diffracted by the near edge. In Regioh III, defined E-0o) < e < 7r and known as the shadow region, the field consists of the near- and far-edge diffracted components only. i r The incident and reflected field components E (P) and E0(P) can be obtained very easily. The problem thus reduces to the deter ination of the correct components for Ed(P) and the combination of them in proper phase. Geometrical theory of diffraction and the results of Sommerfeld's theory of half-plane diffraction are used in developing the correct expressions for E (P). We do not go into the details of the method here, since it has been discussed elsewhere (Sengupta and Weston, 1969) for the case f(0, 0 = 1 in eq. (2. 11). In the following we give the final expression for the far field along with the key expressions necessary in obtaining it. It can be shown that the far field expression valid in the transition region 2 0o- - 2 +0o is given by (Sengupta and Weston, 1969; Sengupta et al, 1968): ka 2 eik(R-A sine) r 2 EwVer oIo( ) fk, o0) e U(ro l)U(ro,2] (2. 14) 0 R IsinUN where P 2 U(r, ) = eikrcos0 () ei7t/2 dt, (2.15) 19

, iPo- 2 'o '2 =0 2 +8 tan= A (2. 16) (krV Y2 I p =2() cos (2.17) 7 2 Equation (2.14) neglects the effect of far edge diffraction which is a reasonable approximation in the transition region. If necessary, the incident field Ei (P) in this region can be separated out from eq.(2.14) by asymptotically evaluating the integral given by (2. 15). Proceeding the same way, it is now possible to separate the near edge diffracted field component from eq. (2. 14) valid in the shadow region. The near edge diffracted field component valid in the illuminated region, o<e<2 - is given by: ka2 cosO sin ~ cos3 1/2 EN noo 2(o2) ( ~ cos0 - si n C krOsine(l-sine i ik(R-A sine + r ) 4 o e e. (2.18) The far edge diffracted field component valid in the illuminated region, is given by the following expression: 3/2 00 ka 2o cos 00 cosO sin N 2 ~o cos0 i/l+sinO E, -r7oIo(2 )f(eo,P)cos0o+sine S * 7T -i ( -kA sine) 4 ikR e e A e e — *-^-. (2. 19) Trkr sin& R ' With the help of the above expressions along with the incident and reflected components of the field, it is possible to develop the complete expression for the field at any point in space. It is clear from the above that different field expressions would be obtained for a field point in different regions of space. For computational purposes it is convenient to derive a single expression for the field which would be valid in all the three regions of space. With the field expressions given in eqs. (2. 14) through (2. 19), it is possible to asymptotically develop a single expression for the far field valid in the region 0 < 0 < r. This can be done 20

by starting with the transition region field given by eq. (2.14) and modifying it asymptotically to account for the different contributions in the various regions of space. The details of asymptotic development of such an expression has been discussed in Sengupta and Weston (1969) and will not be repeated here. The complete expression for the far field thus obtained and valid in the region 0<< 7r can be expressed as i(kR- -) E t o -a ka) 2 e 5sA(), (2. 20) 0 oo 2 R where 00 A() F~ ()f(0e.)sine -ikA sin Isec00 sin 2 ikr ~ t 'Jsik 7rkr sinO J PI t2 t2 ikr sin(O-00) 1 i~r- ikr sin(0 ) i F~ ()=e e dt-e e 2 dt, (2.22) t2 -T1 ' -— f( 0)cos - )sin02 0 L~()=0- e 03/0 ic"-iI 'ne)~cos s -sine eikAsinO f(0o, 0)cos eJi.i.n cos sin0. (2.23) 1 + sine C o It should be remembered that in obtaining the above expressions the basic assumptions of geometrical theory of diffraction have been used. In the present case it mainly implies that eq. (2. 20) is valid for kA > 1. Equations (2.20) through (2.23) give the far field produced by a loop counterpoise antenna that is being used in the existing VOR system. To the best of our knowledge the expressions given above are new and appeared for the first time in one of the Interim Reports under this contract (Sengupta and Ferris, 1970a). In the next section we make a comparison between the results obtained by numerical computation of (2. 21) for the case 0=00 and the corresponding measured results. 2.3.2 Description of the Experimental Arrangement Experimental investigations have been carried out at the frequency 1080 MHz with the help of an outside antenna pattern range. Each of the Alford loops 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 (1965). A photograph of the Alford loop 21

model is shown in Fig. 2-3. Each loop is made of brass strips and fed by a coaxial line with the help of a balance-to-unbalance transformer. Each loop is square-shaped with each side equal to 2. 1", which is about X/5 at the frequency 1080 MHz. The excited element here consists of two such Alford loops fed 180~ out of phase and placed in the same plane which is parallel to the 15' diameter counterpoise. The 15' diameter counterpoise was fabricated on a wooden framework. The central portion of the counterpoise consists of a solid aluminum disc mounted on the frame. This was done to mount the Alford loops conveniently. The rest of the counterpoise consists of household aluminum screen stapled to the wooden framework. Thetwo loops are placed at a height of 4. 8" above the counterpoise. They are displaced on either side of the axis of the counterpoise by 1.6" so that the two Alford loops are 3. 2" apart. Figure 2-4 shows a photograph of the double Alford loop counterpoise model used during the experiment. In all the measurements to be discussed below, the above model has been used as a receiving antenna in conjunction with an antenna pattern range. 2.3.3 Comparison Between Theory and Experiment The measured free space elevation patterns of conventional VOR antennas operating in the side band mode are shown in Figs. 2-5, 2-6 and 2-7 for three selected values of the counterpoise diameter. All the patterns have been measured in the x-z plane (Fig. 2-1) and at the frequency 1080 MHz. The corresponding theoretical patterns obtained by numerical computation of eqs. (2. 20) through (2. 23) are shown in Figs. 2-5 through 2-7 for comparison. The normalized dimensions of the antennas given in Figs. 2-6 and 2-7 correspond at 108 MHz to those of conventional VOR antennas with 52' and 150' diameter counterpoises respectively. The agreement between theory and experiment for the cases kA = 17. 92 (2A = 5.2') and kA = 51.69 (2A = 15') may be considered to be very good. The minor lobes in the pattern in directions 0 > r/2 as well as the kink in the pattern just below the 0 = 7/2 for the case kA = 51. 69 are attributed to the outside pattern range and the feed system of the antenna. The measured results shown in Figs. 2-5 and 2-6 were taken with an antenna pattern range inside a large anechoic chamber. The agreement between theory and experiment for the case kA = 6. 32 (2A = 22" ) is not so good, although it may be considered to be fair over most of the region (see Fig. 2-5). The reason for this is attributed to the fact that due to the small size of the counterpoise, the geometrical diffraction theory approximation made in obtaining the far field expressions becomes poor. 2.3.4 More Information About the Side Band Pattern Because of the fundamental importance of the 15' diameter antenna, its patterns were studied in more detail. Figure 2-8 shows measured far field elevation pattern of the antenna at 1080 MHz. Figure 2-8 is the same as 2-7 except for the fact that the pattern here is shown as a rectangular plot for obtaining 22

:i::,:i:::::::::i:-: ~:::::: ii:i:i::-::-:::::::: 'iii:i i::: is:: -ek~ :~al -ug 9L:::'::::: i: ii': P I 'k6d: "r'iiiiii:iil:i::i:i::~.::::::::::::::: i::::.::::r:i: iiai: iliizii~ili FIC. 23: Photograph of the Alford loop model. 23

,.:.,- -:-::-::':;;::::: ;ii::i: ::::[i:::: f2i4iiS:iiiii i:::i;:i:is:::::i':'::: il''r'ii,::lai:-,:;i,i::::: i" "-"~" gairi ~-~,-i :::i:::::~-::::i: i:i::::,:iiiiielii ii2 sa —" --- aiR:nini ' iOR ~:a;, a~,:::-,,::,:::a.,~;:? iiWBiSi.- i —:: -:1::~::I:::;:::::I:::.,::::::i::::::I,::::,:::ii::'~:.::w :::::1::: 1:::::;:::;:I::::':_1:::::1 ;I-r::::::;::~::: -::-:;: i:1::i:i:,:. n :: -:: -::::r:,-:::::l::::r::::::-:;::,:: -;_::r:::l::::::':::i:::::_ ":::::::-I:-:' -.'-;il:~:: -:::-r_'l-::i:::~:;::::: i,,. :,...:!-;.-:: —:: ::,: —:: '.:,-.,:-.:,::::::i'(:l:,:-,: -::::,::::'::-:::, ::i:::i:: I:::i:i i:-::1::i:i i::::: it::;:::-:: --:,:,: i:i:::.::: :i::::i::;1::,,: I,,::,::.:: i::::I::;::l:;:i::::::::::::;::::;:: I '4c ::,,:::;::_;::::::::i:i:iiii-.:: i':::l -j:j::i::::ii.:::i:i:ii:i:1:::::i: -::::i,r,., i.:.:,::: i; —:-':".:-: ::-:g-;:'':: II::::: ii:: i: ':::: ::.:::i::::::::::::i:::;::::::::i:: 1,,::::ii::1:::::::i::::: FIG. 2-4: Photograph of the two Alford loops mounted above the 5' diameter counterpoise. 24

0=00 a=oo 0 I 0 FIG. 2-5: Side band mode elevation plane far field pattern of a 0" 0 0 8-180~ conventional VOR antenna. kh = 2.75, kd = 0.92, kA = 6.32, f = 1080 MHz. -- Experimental, ooo Theoretical 25

09= 0 9 O\II 6=270~0.- =9C 6=l180~ FIG. 2-6: Side band mode elevation plane far field pattern of a conventional VOR antenna. kh = 2.75, kd = 0.92, kA = 17.92, f = 1080 MHz --- Experimental, o o o o Theoretical. 26

aic s=1t80~ FIG. 2-7: Side band mode elevation plane far field pattern of a conventional VOR antenna. kh = 2.75, kd = 0.92, kA=51.69, f = 1080 MHz. --- Experimental, o o o o o Theoretical. 27

better pattern details. Figure 2-9 shows the azimuthal pattern of the same antenna. The shape of Fig. 2-9 indicates that the feed system used has been satisfactory for the side band mode of operation of the antenna. The theoretical values of the other important parameters of the free space elevation pattern of the antenna operating at 1080 MHz and in the side band mode are given below. Direction of the principal maximum 0max = 65~ Far field gradient at the horizon og =5.54 dB/6~ Field reduction factor aF = 14.7 dB. The above parameters are not appreciably different from those for the case of carrier mode operation as given in Section 2. 2. Numerical values for the free space elevation plane side band mode far field pattern of the above antenna are given in Table F-la. Numerical values for the side band mode elevation plane pattern of a similar antenna with 5.2' diameter counterpoise (i. e. 52' diameter at 108 MHz) are also given in Table F-lb. 2. 4 Discussion Both the theoretical and experimental free space radiation characteristics of conventional VOR antennas operating in the carrier and side band modes have been discussed here. Theoretical expressions for the side band mode given here are new and have been developed during the present contract period. The results given in the present chapter will be used later in evaluating the performance of the parasitic loop counterpoise systems. 28

I I711 w_ [l i" ~' " A 0 co S 1i5i.0 L120:/'91:0!' 0.0.................... 1. 1, t, i j- ' 7!,'1VT I. 7. 7 -- 5 L 'i - ': ' I I, - 4. Itt. ~r-W -:1 Angle 0 FIG. 2-8: Measured side band mode elevation plane far field pattern of a conventional VOR antenna. kh = 2.75, kd = 0.92, kA = 51.69, f = 1080 MHz.

8=00 - I 6 L ~:..~...,...:.~..:............ 0 =180 FIG. 2-9: Measured side band mode azimuthal plane far field pattern. of a conventional VOR antenna. kh = 2..75, kd = 0. 92, kA = 51.69, f = 1080 MHz. ~~~~~~~~', ~.::... r. 11"' \/: t30:'

III INVESTIGATION OF SINGLE PARASITIC LOOP COUNTERPOISE ANTENNA 3.1 Introduction In this chapter we discuss the theory of radiation from a single parasitic loop counterpoise antenna. The theory of such an antenna is of fundamental importance for the investigation of the radiation from double parasitic loop counterpoise antennas to be considered later. As we shall see, the theory developed here can be generalized directly for the latter antenna operating under some constraints of practical interest. The study of the single parasitic loop counterpoise antenna is also quite important on its own merit. In some applications where the required field gradients in the pattern are not very large, this type of antenna may be found to be more advantageous to use. The single parasitic loop counterpoise antenna is obtained by placing coaxially a large parasitic loop at a convenient height above and parallel to the counterpoise of a conventional VOR antenna. Figure 3-1 shows a schematic diagram of such an antenna. The parasitic loop has a radius B and is placed at a height H above the counterpoise; it is assumed to be made of a conducting wire of radius b (or equivalently, of a conducting strip of width w = 4b). Theory and performance of single parasitic loop counterpoise antennas operating in the carrier mode have been discussed in detail elsewhere (Sengupta et al, 1968; Sengupta and Weston 1969; Sengupta and Ferris, 1970) and will not be repeated here. In the following sections we first give some of the important pattern characteristics for such an antenna with a 15' diameter counterpoise and operating in the carrier mode at the frequency 1080 MHz. These pattern characteristics will correspond to those of a full scale parasitic loop counterpoise VOR antenna with a 150' diameter counterpoise operating at the frequency 108 MHz. For the carrier mode operation, the nature of the induced current in the parasitic loop and its dependence on the antenna parameters are then studied numerically. Finally, we develop the theory for the side band mode radiation pattern produced by a single parasitic loop counterpoise antenna. The theory is then compared with results obtained from model measurements. 3.2 Carrier Mode Pattern Theoretical expressions for the carrier mode pattern are given here for future reference. It can be shown (Sengupta and Weston, 1969) that the far zone electric field produced by a single parasitic loop counterpoise antenna shown in Fig. 3-1 is given by the following: 31

z i 0 Field point (R, )0 Parasitic loop H Counterpois T Phase center of the feed 71 0 i __|_0 origin of coordinates,//,////,//// //.//,////////// /, //// -"A - FIG. 3-1: Schematic representation of single parasitic loop counterpoise antenna and the coordinate system used. 32

i(kR-T/4) ka 2 e E 2 0 ) -- R- S(O), 0 < e r. (3.1) where S(0) is identified as the complex far field pattern and can be written formally as S(e) = SA(e) + S12() + S56(0) (3. 2) In eq. (3.2), SA(O) is the free space complex far field pattern of the antenna in the absence of the parasitic loop and is given by eqs. (2.4) - (2. 10). The last two terms in eq. (3. 2) constitute the complex far field pattern produced by the parasitic loop only in the presence of the counterpoise. The conventional radiation pattern of the antenna is given by S(e). Explicit expressions for SP2(e) and s5L6() are given by the following r2 ikrl ikr 2 (e) = - - F(e) (3 3) 1 2 iM2 (2kB ) (kr ) (kr ) )1 2 2 2 ikr 1/2 i(2kB + P (e)i(kB) e r( 1 4 56 2M2 (k 2 rkB 1/2 i(2kH-) - kH e i F(e) (3.4) 2 2 2 2 2+(H +h)2 1 =B +(H-h) 2 B+(H + h) M = 0.577 + n ( )-i 2 2 Ji(kB sine) P (e-ikA sine F(e) F ) e. 0 Icosel sin(. ) ikr + 2 e LP(e), (3.5) PJkrpsine' i(2-kAsine) 1/2 Y2(kB TLP~e)= 2 Cos osJ p)-sin e J (kB sine) Lp(")= e... p.. -- 1-si'n' L cos pP-sin 0 1/2 eikA sine rJ(kB cos 0p) cos /2 P +'sin L ^ cos- + sin 1' (3.6) ikrpsin(0-0p) f5 i7rt FP(e)= e e dt - (continued) -CD00 33

ikr sin(0+p) r '6 (3.7) -e e dt, -Co p.2.p. - p5=2(-) cos (po), (3.8) krp 1/2 0p- P =2(-) cos ( 2(3 9) 2 2 2 rp=A +H, (3.10) tan0p =, (3. 11) and J1 is the usual notation for the Bessel function of the first kind and first order. The far field expressions given by eqs. (3.1) - (3.11) are valid under the following approximation: kA> 1, kB>> 1, kH>> 1, kb<< 1 andkA>kB. (3.12) From a numerical investigation carried out with the help of the above expressions, it appeared that a parasitic loop having a radius B such that kB = 37r (i. e. 2B = 3X) would produce a good field gradient when placed at a proper height H above the counterpoise having the normalized dimension kA = 51.69. The parasitic loop was assumed to be made of 1" wide conducting strip (i. e. b = 0. 25"). The theoretical field gradient as a function of the height H of the parasitic loop above the counterpoise is shown in Fig. 3-2. It can be seen from this figure that a parasitic loop counterpoise antenna having kH = 13 and kB = 3?r produces a maximum field gradient of 9.6 dB/6~. It should be mentioned here, for comparison, that the carrier mode pattern of a conventional VOR antenna with the same counterpoise (kA = 51. 69) has a field gradient of 5. 56 dB/60. The measured far field elevation pattern of the above parasitic loop counterpoise antenna is shown in Fig. 3-3. The corresponding theoretical pattern of the antenna is also superimposed on Fig. 3-3 for comparison 3. 3 Numerical Investigation of the Parasitic Current for the Carrier Mode Case In this section we give the results of a numerical investigation carried out to study the nature of the induced current in the parasitic loop and its dependence on the antenna parameters for the case of carrier mode operation. Detailed discussions of the theoretical expressions for the induced current in the parasitic loop have been given in the Final Report under our previous Contract (Sengupta et al, 1968). Here, we only quote the final expressions without derivation. The normalized induced current in the parasitic loop can be formally written as follows: P0 = 12 + 34 + 156 (3.13) O-I +I (3. 13) Io P0 P0 P0 34

10 i I L _________ _ _________ _________ ______ t l 10 11 12 kH - 13 14 15 FIG. 3-2: Theoretical field gradient (ag) as a function of H for a single parasitic loop counterpoise antenna operating in the carrier mode. kh = 2.75, kA = 51.69, kB = 3 r, f = 1080 MHz, kH is variable. 35

-10. -20 i-30 -40 -150 -120 -90 -60 -30 0 30 60 90 120 150 Angle in degrees -- FIG. 3-3: Carrier mode elevation plane far field pattern of a single parasitic loop counterpoise antenna, kh = 2.75, kA = 51.69, kB = 3r, kH = 13, f = 1080 MHz...... Theoretical, - Experimental 36

where I is the current in the excited loop and Ip is the current in the thparasitic loop. The first term on the right hand side of (3. 13) represents the current induced due to the direct wave from the driven element and due to the wave singly reflected 56 from the counterpoise. The other two terms, Ip4 and 1po in (3. 13) represent the currents due to the waves diffracted by the counterpoise edges. The reason for splitting the current expression into three terms is to study the order of magnitude of the different contributions so that the information obtained can be used for proper approximation in the far field analysis. It can be shown that the three terms on the right hand side of eq. (3.13) are given by (Sengupta et al, 1968): 12 27rB e X e (3.14) IPO ikM 2 r2 - 1 r21 22 2 22 2 H+hr2 rB +(H-h), r2=B +(H+h), M=0. 577+ n )- i, (3. 15) -i37 34 iT A ikr0 e 4 A 1/2 I = e X P ikM r2 B * /2 ikr3 -0-3 0+3 x F )'2 ee sec ( - - ) -sec (Lkr3 2 1 1/2 ikr4i 0-20402+4 f + i ( 4 e see ( )-sec( ) (3.16) 2 22 2 22 r = (A-B) +H; r = (A+B) +H 3J4 2 2 2 r =A +h (3.17) 0 H H h tan %)3 =.tan 4,tan0 3 A-B 4 A+B A 56 2(k " r 1 1/ i(2kB+) 1/2 i(2kH —f 156 = w (kB) e2-( ) e j. (3.18) P - 2 ( kB rkH The various notations used in eqs. (3. 14) - (3. 18) are as explained in the reference cited. A computer program has been developed for obtaining the current induced in the parasitic loop with the help of the above expressions. We give here the results obtained for a specific single parasitic loop counterpoise antenna having the following 37

parameters: kA=17. 92, kb=0. 15, kh=2.75, kB=3r and kH=11. 78. The values obtained for the normalized current are shown in Table II-1. TABLE m-1: Normalized Value of the Parasitic Current Real Imaginary Absolute Value Argument in Radians p2 -0.03893 0.17908 0.18326 1.785 Po 34 Ip3 -0.00070 0.00035 0.00068 2.678 P56 Ip 0.02911 -0.00159 0.02915 -0.055 Po IPo -0.01052 0.17784 0.17815 1.630 io Parasitic currents induced for other values of the antenna parameters are shown in tabular form in Appendix D. From the results shown here and in Appendix D, one fact appears to be consistent, namely that the contribution to the parasitic current due to the second term in (3.13) (i.e. I) is negligible compared to the others for the values of B and H considered here. Hence in the analysis of the far field pattern this term may be omitte< This observation was made in our previous study (Sengupta et al, 1968) intuitively. The results given in this section justify that approximation quantitatively. The results given here will be found useful if an experimental program is developed to measure the current in the parasitic loop of a single parasitic loop counterpoise antenna 3.4 Side Band Mode Pattern In this section we develop the theoretical expressions for the radiation field produced by a single parasitic loop counterpoise antenna operating in the side band mode. The accuracy of the expressions are then compared with the measured values. The theory developed here will be used to calculate the patterns produced by double parasitic loop counterpoise antennas with similar excitation. 3.4. 1 Theoretical Expressions The theoretical model of a single parasitic loop counterpoise antenna is shown in Fig. 3-4. 38

z l z parasitic loop 2B -' — t x point source - H i / counterpoise representing the feed \ A/'///'' ///7 7/ /77 7//////// // 7 I — image of the feed FIG. 3-4: Theoretical model for a single parasitic loop counterpoise antenna. As before, the free space far field produced by the excited elements elements only (represented by the point source in Fig. 3-4) is:, ka)2. f(ikr E= ro I (a) 2 f(e,0)sine er (3.19) o o 2 r where f(, 0)= 2i sin(kd sinO cosp). (3.20) The first step in the analysis involves the determination of the current induced in the parasitic element. Parasitic Current: Let the total field incident at the point P (Fig. 3-5) on the parasitic loop be denoted by Einc(P). Then the parasitic current Ip is given by 2o inc(32 I =. E (P) (3.21) Po irikM 0 where M =0.577+ in c-) -i (3. 22) The basis and nature of approximations involved in (3. 21) has been discussed elsewhere (Sengupta and Weston, 1969) and will not be repeated here. inc The incident field E0 (P) consists of direct, reflected and diffracted fields. 39

A representation of the different field components that would be used in obtaining the parasitic current are shown in Fig. 3-5. Thus Emc(P) can be written formally as follows: inc) 12 56 E P) = E (P) + E (P).(3.23) z typical point on the p parasitic loop 2b 5 1 H 6 2 l l / counterpoise K, A FIG. 3-5: Dominant rays contributing to the parasitic current. Explicit expressions for the component fields E1 (P) and E (P) can be obtained by following a method similar to that discussed b5y Sengupta et al (1968) and by Sengupta and Weston (1969). These expressions are: B e Bikr2 -or2 E oo2 L 0l' 0) 7 -f(e20) r2 (3.24) where rl=B2+(H-h), r2 B+(H + h) (3.25) 1 2 ikr E56 =ka.2 7Lf(l,) Be oo 2 2iM f( r 1 2r,l, i (2kB4) 1rk (2kH. (3.26) 40

Using (3. 21) and (3. 24) - (3. 26) it can be shown that Ip = Ip2 + Ip6 (3.27) Io -0 P0 where ikrl ikr2 I12 =o(I2 ikM2 1') rl f(e2, ei) r2 ] (3.28) P0o02 ikM 21 r1 2 ikr1 56 = ka2 2 (kB)e ~o ~ 0 M2 (kr) I I/ i(2kB+) 1 1/2 i(2kH/212kH kBX (- e (4 -(- e. (3.29) If -kB frkH We now make the following approximation valid for kd < < 1, f(81, ) = 2i sin (kd sine8 cos p) - f(08) cos 0, (3.30) f(e2, ) fe2) cos, (3.31) where B f0e,)= 2ikdsin0l= 2i(kd) r, (3.32) f(02)= 2i kd sine2= 2i (kd) -. (3.33) 1 2 2 r2 After introducing (3. 30) through (3. 33) into (3.28) and (3. 29) we obtain ikrl ikr2 12 ka2 27B e - e 2 cos (3.34) I =I (-) ve -f (e Cos (3.34) P 0 o 2 ikM 1 2 2 2 0 o r! 1r j 2 ikr1 56 Oka 2 i2(kB) e. o 2 M2 (kr2 x/2i2k 11/2 i(2kH-)~ LrkB nkH L. ^B> e -<,k5' e _c~ (3j35) Thus we can write the parasitic current expression Ip in the following form. I =I1 + = Ip cos, (3.36) where explicit expressions for Ip may be obtained after introducing eqs. (3. 34) and (3. 35) into (3. 36). It is important to note there that due to the nature of excitation, the parasitic current is not independent of 0. This completes the 41

derivation of the theoretical expressions for the current induced in the parasitic loop in a single parasitic loop counterpoise antenna with figure-of-eight type of excitation. The Radiation Field: The complete side band mode radiation field produced by a single parasitic loop counterpoise antenna is obtained by vectorially adding the individual fields produced by a pair of Alford loops above the counterpoise and the parasitic loop above the counterpoise. The Alford loop counterpoise side band mode radiation field is given in Section 2.3. The parasitic field expression under this condition is derived below. The free space radiation field produced by a circular loop carrying a current of the form given by eq. (3. 36) is discussed in Appendix A. In general, the far electric fields are given by the following. i kB, eikR Erir Ip ( 2-)J (kB sin0)cos (3. 37) J (kB sine) eikR oi, 1 (3.38) E irIp (- ) sj cos9 sine (3. 38) e "wlrloIPo( ----)2 (kB sinG) cosO sin R where R, O, 0 are the usual spherical coordinates of the far field point with origin in the center of the parasitic loop which lies in the x-y plane, and J1 is the first order Bessel function of the first kind and the prime indicates differentiation with respect to the argument. For obtaining the principal plane field we are interested inthe 0x 0~ plane and thus we have: i, kB e iR E ir )Ip( ) J (kB sinG), E 0 (3.39) o 0o 2 R 1 ( Let us obtain the p - component of the far electric field. With the incident field given by (3. 37) it can be shown that the far field produced by the parasitic loop only above the counterpoise is given by the following expression valid in the region 0 < 0 < r, i(kR- | ) EP r IPo( - -- i F(e) cos 0, (3.40) ow2 R where 1(kB sin0) pc -kAsn [os sin(2-) ikrp F(G)= F()e- sine + 2 e LP(e), (3.41) 4 A%/ikrp sin' 42

p i( -kA sin ) Cos2 pJi(kBcosp)-sin 1OJ(kBsin8)l -ikA sin ( 2 [COsin' Lcoskp-sinO j - sin ' e Coso /2pJ{(kBcosopl X [coS IpJ(kB 1 cosp (3.42) cosOP+sinO ikrp sin(e-0p) irP5 i 2 F P()=e e 2dt-e e 2dt -oo -co (3.43) krP 1/2 p-f- krP 1/2 _++ 2 ( 12 P-)- P 12 2 P^(3.44) k2 p= 2(cs cos( 2 ) (3. 2 2 2 tH rp = A + H, and tanp (3.45) The complete far field is now obtained by combining eqs. (2. 20) and (3. 40). It can be written formally as i(kR- ) ka 2 e E ^'o I (2 eS(e), (3.46) where S(e)= SA(e) + SP2(e)+ S56(). (3.47) Explicit expressions for SA(e) are given by eqs. (2. 20) through (2. 23). The last two terms on the right hand side of (3.47) are given by P S(e)=(kB)2 e ikr1 e ikr2 S1 () M (Oe) - -f(2) -- F(e)cos0 (3.48) 12 M 1 2 2 2 (kr 1) (kr2) ( 2 2 2 ikr SP () i r7 (kB) e 56 2M2 (kr 1 [ i(2kB+) 1/2 i(2kH-'4 A......B e e F() cos. (3.49) 43

For the purpose of numerical computation, the principal plane pattern (0 = 0~ plane) is written in the following final form: 00 A()= FO(0)2ik)sin2e -ikAsin lcos08 sin( i) ikr (3.50) 7r v2 + V/rkrosine' i -kAsinO) /2 Y2 (2^-1^n) 2i(kd)cos -2ikdsin 0 L~ (8)=e 1 - sin8 cosO -sine ikAsinO 2i (kd)cos 5/2 ~1 +sin * cos -+sin0 ' (3.51) 2 -ikr1 ikr2 B e i k 2 s2(e)= )L 2ikd - -2ikd — F(2), (3.52) 12 M L rl (kr)2 2 (kr2 1 2 2 2 ikr B) 1h i(2kB+4) 1 12 i(2kH-i) 56 2M2 (kr! 2 (kr) i kB )kH and the other parameters are as defined before. This completes the derivation of the elevation plane pattern (x-z plane) of the single parasitic loop counterpoise antenna for the side-band mode of operation. In this plane (0=0~) the only component of the field is the Es component. However in other elevation planes, i. e. for 0 X 0 there will exist a 0ycomponent of the field as evidenced by eq. (3. 38) (see also Appendix A). During the present contract we have not investigated the 0-component of the field produced by the antenna. 3.4.2 Comparison Between Theory and Experiment A single parasitic loop counterpoise has been fabricated by placing a parasitic loop of diameter 2B = 31. 75" at a height H = 22. 5" above the double Alford loop counterpoise antenna whose patterns are shown in Figs. 2-8 and 2-9. The measured electric far field pattern produced by this antenna in the 0 = 00 plane is shown in Fig. 3-6. The computed theoretical points are also shown in one half of the pattern in Fig. 3-6 for comparison. It can be seen that the agreement between the theory and experiment is quite satisfactory. It should be noted that except for the excitation the parameters of the antennas whose patterns are shown in Figs. 3-3 and 3-6 are kept the same so that the patterns can be compared. From a comparison of Figs. 3-3 and 3-6 the 44

-10. -20 30 -30 -40 -150 -120 -90 -60 -30 0 30 60 90 120 150 Angle in Degrees - FIG. 3-6: Side band mode elevation plane far field pattern of a single parasitic loop counterpoise antenna, kh = 2.75, kA = 51.69, kd = 0.92, kB = 37r, kH = 13, f = 1080 MHz. -- Experimental,..... Theoretical 45

following two observations are made; (i) non-uniform excitation of the parasitic loop gives rise to minor lobes in the pattern near the axial region 0 = 00. However, it is anticipated that with proper choice of height H of the parasitic loop it would be possible to reduce this lobe considerably by utilizing the concept of image. (ii) The result shown in Fig. 3-6 does show some improvement in the field gradient (7. 5 dB/6) compared to that of the corresponding conventional VOR antenna pattern (5.54 dB/6) but it it s less than that obtained in the case of single parasitic loop counterpoise antennas operating in the carrier mode. However, the field gradient in the side band mode case may be improved up to at least the carrier mode value by adjusting the parameters H and B. 3. 5 Discussion The free space radiation patterns of single parasitic loop counterpoise antennas operating both in the carrier and the side band modes have been discussed and theoretical and experimental results are shown. Theoretical expressions for the side band mode given here are new and have been developed during the present Contract. We have also discussed the nature and value of the parasitic current when the antenna operates in the carrier mode. The current information given here may be found useful in developing some future experimental programs. From the pattern information given in this chapter it appears that from the viewpoint of optimum field gradients, the necessary parameters H and B of the antenna will be different for different modes of operation. Thus in an actual case a compromise must be made. On the basis of the results reported above it is found that for a full scale 150' diameter counterpoise the introduction of a parasitic loop in the conventional VOR antenna increases the field gradient by about 4dB/60. In order to improve the field gradient further, it is necessary to use more than one parasitic loop. Double parasitic loop counterpoise antennas are discussed from this viewpoint in the next chapter. 46

IV INVESTIGATION OF A DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 4. 1 Introduction The results discussed in Chapter III indicate that a single parasitic loop counterpoise antenna produces a field gradient at the horizon larger than that of a conventional VOR Alford loop counterpoise antenna. However, from the viewpoint of improved VOR system performance it is desirable that the antenna should produce much larger field gradients. Field gradient values larger than those of single parasitic loop counterpoise antennas can be obtained from double parasitic loop antennas. The latter type of antenna is obtained by inserting coaxially another parasitic loop at an appropriate height (Fig. 4-1). In the present chapter we at first develop an approximate theory for the radiation patterns of double parasitic loop counterpoise antennas operating in both carrier and side band modes. The theory is then compared with measured results. Finally, the parameters for a specific double parasitic loop counterpoise antenna are obtained such that the field gradient produced by the antenna is maximum. Such an antenna will be referred to as the optimum antenna. 4. 2 Theoretical Expressions for the Radiation Field The theoretical model of a double parasitic loop counterpoise antenna is shown schematically in Fig. 4-1. It consists of a conventional VOR antenna with two large parasitic loops placed parallel to each other and to the plane of the counterpoise as shown in Fig. 4-1 with the origin of coordinate system located at the center of the counterpoise which lies in the x-y plane. The point source in Fig. 4-1 represents the excited elements. During the analysis the free space far field variation of this equivalent point source is assumed to correspond to that of the carrier or side band mode operation of the antenna. If the distance between the two parasitic loops is small compared to a wavelength, then the mutual coupling effects between them may be strong and must be taken into account. Under these circumstances the theoretical analysis of the radiation field becomes complicated. However, from our previous study (Sengupta et al, 1968) it has been found that for the cases of interest the two parasitic loops should be separated by a distance of at least the order of one wavelength or more. The theory of double parasitic loop counterpoise antenna given in this section therefore neglects the effects of mutual interaction between the parasitic loops. The mutual coupling effects and their influence in the far field patterns are discussed in Appendix B. 47

z t I z parasitic loop No. 2 rw- 2B2 ---- ) Y %vL HH2 2B1, -- TJ -- point source representing the feed | i h counterpoise - f ///// the doube p c lp ce /////a FIG. 4-1: Theoretical model for the double parasitic loop counterpoise antenna. In the absence of mutual coupling, the theoretical expressions for the radiation field produced by a double parasitic loop counterpoise system can be obtained by simple modification of the theory given in Chapter m. The far electric field produced at a point P(R, 0, 0) by an antenna consisting of the excited Alford loops, parasitic loop No. 1 and the counterpoise can be written as: i(kR- I) ka 2 e where R where s(O) A(0) + s(e+) + () (4.2) 12 56 and all the other notations are as explained in Chapter HI. Explicit expressions for the different terms in eq. (4. 2) are as shown in the previous chapter and should pertain to those with parasitic loop No. 1. 48

Similarly, the far electric field produced by the parasitic loop No. 2 only above the counterpoise can be written as i(kR-f) 4p ka 2 e P E2 rl o(-) S (0), (4.3) where P P' p' S2 (0) S12 (0)+ S56 (0) (4.4) 2 12 56 Explicit expressions for the different terms in eq. (4.4) may be obtained from Chapter III with the understanding that the different parameters involved pertain to the parasitic loop No. 2. The complete expression for the far field produced by the double parasitic loop counterpoise antenna is obtained by superposition of the above two fields and is given by: i(kR-) ka 2e E I (ka)2 - [S()+S2(] (4. 5) o 2 R1 2 for 0 <0 < r. The approximations involved in (4.5) are the same as discussed previously. Thus, S1(0) + S (0) gives the complex far field pattern of the double parasitic loop counterpoise antenna. The patterns of the antenna for the carrier and side band mode operations are obtained by using the appropriate expressions for S1(0) and SP(0). 4. 3 Description of the Experimental Arrangement For experimental investigations, the parasitic loops were positioned coaxially on the axis of the basic model of the conventional VOR antenna described in Section 2.3.2. Figure 4-2 shows the side view of the 15' diameter counterpoise along with the installed pair of parasitic loops mounted on a 40' tower. A close-up view of the double parasitic loop counterpoise antenna is shown in Fig. 4-2a. Foam cylinders were used to hold the parasitic loops in place in such a way that the diameters and heights of the parasitic loops above the counterpoise could be easily adjusted during the experiment. The parasitic loops were 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 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 and w, b < X. The parasitic elements were fabricated from 1" wide brass strips 9.15 x 10-3X thick at 1080 MHz. 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 element. All the patterns were measured onthe outside range with the antenna under test mounted on the 40' tower (Fig. 4-2) and used as a receiving antenna. 49

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4.4 Comparison Between Theory and Experiment The theoretical electric far field pattern for the elevation plane of a double parasitic loop counterpoise antenna operating in the carrier mode is given in Fig. 4-3. The corresponding measured far field pattern is also shown in Fig. 4-3. A similar set of patterns is given in Fig. 4-4 for such an antenna operating in the side band mode. Notice that the counterpoise size as well as the measurement frequency are different for the results shown in Fig. 4-3. This has been done so that the results may correspond to a full scale 150' diameter counterpoise at the changed full scale frequency of 109 MHz. Considering the fact that the theory ignores the effects of mutual coupling, the general agreement between theory and experiment as found in Figs. 4-2 and 4-3 may be considered to be fair. Thus for the ranges of parameters used here (particularly H2-H1 > X), the theory given here can be used with sufficient accuracy to investigate the double parasitic loop counterpoise antenna radiation patterns. It is anticipated, however, that the theory may be improved further by more rigorous analysis (Appendix B). 4. 5 Optimum Double Parasitic Loop Counterpoise Antenna The results given in section 4.4 reveal the fact that double parasitic loop counterpoise antennas produce field gradient values larger than those obtained from single parasitic loop counterpoise or conventional VOR Alford loop counterpoise antennas. Of course, the field gradient produced by the antenna is a function of the antenna parameters. In this section we vary the parameters H1, B1, H2, B 2 while keeping the other parameters fixed and theoretically study their effects on the field gradient. In this manner an optimum set of these parameters is obtained so that the antenna produces maximum field gradient. It is realized that other criteria may also be used for optimizing the antenna (for example, maximum field gradient and minimum side lobe below the horizon). As mentioned in the previous Chapter the field gradient produced by the antenna is different for different modes of operation. Here we optimize the antenna parameters so that the field gradient is maximum in the side band mode of operation of the antenna, since this is the mode which is of most interest from the viewpoint of VOR operation. The optimization is done for an antenna having the normalized parameter, kA = 52. 16860 for the counterpoise so that it may correspond to the 150' diameter counterpoise at the full scale frequency of 109 MHz. Figure 4-5 summarizes the results of the optimization procedure. Preliminary studies indicate that large field gradient values may be obtained for the following approximate normalized parameters, kH,1= 3. 48190, kH2= 12.76710, kB1= 37r and kB2 = 57r. The optimization procedure is then initiated by keeping kH1 and kH2 fixed at these values and computing the field gradient ag as functions of kB1 and kB2. Curve A in Fig. 4-5 shows crg as a function of kB1 for the fixed value of kB2=3. 07r. 51

Theoretical -5 E * * * ~ Experimental -10 -20 * -25 -30 I I ~~~\ / -35 -40 -45 -50 1 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Angle in degrees - FIG. 4-3: Carrier mode elevation plane far field pattern of a double parasitic loop counterpoise antenna. kh = 2.75, kb = 0.15, kA = 17. 92, kH1 = 3.70, kB1 = 4, kH2 = 11.78, kB2 = 3, f = 1080 MHz. 1~ w0k 2 a 2 I

It can be seen that ag appears to be a periodic function of kB2, i.e. for the range of values shown ao reaches a maximum for kB1= 5. 27r and kBl= 6. 27r. The maximum value of ag m this case is 4.75 dB/6~ which is rather low. The second optimization is now carried out by calculating ag as a function of kB2 for kB1= 5. 2r. The smaller value of kB1 is chosen for the reason that it will give rise to a smaller physical size of the antenna. Curve B in Fig. 4-5 shows the results of this computation. A maximum value of a = 23.7 dB/6~ is obtained for kB2 = 3.6r. Curve C shows ag as a function of kBl for kB2= 3. 67r. It is found from Curve C that the maximum value of a = 23.7 dB/6~ is obtained for kB1 = 5. 2r. Finally, ag has been calculated as functions of kH1 and kH2, for kBl= 5. 2r and kB2= 3. 6r and it has been found that ag does reach the maximum value for the values of kH1 and kH2 cited above. On the basis of the results given here we obtain the following normalized parameters for an optimum double parasitic loop counterpoise antenna: kh= 2. 7755, kd = 0. 9276, kb = 0. 1514, kA = 52. 1686 kHl = 3. 4819, kB1 = 16. 3363, kH2= 12.7671, kB2 = 11.3097 Before closing this section it is appropriate to mention that the physical mechanism by which a large field gradient is obtained in the optimum configuration is the method of cancellation of the Alford loop field in a certain pref erred direction by the parasitic fields. It is therefore obvious that the performance of any such optimum antenna will be highly frequency sensitive. Frequency sensitivity of such antennas has been discussed earlier (Sengupta et al, 1968). 4.6 Optimum Antenna Patterns In this section we discuss the carrier and side band mode elevation plane patterns of a double parasitic loop counterpoise antenna optimized for the side band mode of operation. The elevation plane patterns for the carrier and side band mode of operation have been calculated theoretically for the optimum antenna described in the previous section. The unnormalized results are shown in Fig. 4-6 so that the two patterns can be compared directly. The antenna has ag= 23.71 dB/60 in the side band mode but the carrier mode value of a is 5.67 dB/6~. In a practical situation if one wishes to have larger field gradient vaues in the carrier mode, a compromise must be made. Figure 4-7 shows the experimentally measured elevation plane pattern of the optimum antenna operating in the side band mode. 53

10 0 -10 i 20 40 50 60 0 90 100 0 120 = -10 -15 - -20 -25 -30 -35 - Theoretical ~ ~ ~ ~ Experimental -40 FIG. 4-4: Side band mode elevation plane far field pattern of a double parasitic loop counterpoise antenna. kh = 2.7755, kb = 0.1514, kd = 0.9276, kA = 52, 1686, kH1 = 3.4819, kB1 = 16.1704, kH2 = 12.7671, kB = 11.4144, f = 1090 MHz. 1 1 2 2

25 kB2 =3.6r fr'"=5@2 A t l 2 ~ kB 5.2 20 ag dB/60 15 B 10 kB =3.0r 53 4r kB orkB2 5\ 6r 6.2rA II I 3r 47r kB1 or kB2 5 6 6.27r FIG. 4-5: Theoretial maximization of the horizon field gradient of a double parasitic loop counterpoise antenna operati In the side band mode. kh = 2.7755, kb = 0. 1514, kd = 0.9276, kA = 52.1686, kH1 = 3.4819, kH2 = 12.7671, kB1 and kB2 are variable. f = 1090 MHz.

10 side band mode g = 23.71 dB/6~ -10 g10w' I~~~~I \ fI \ \ /~ ~carrier mode \ \ / aga =5.668 dB/6~ -20 -30 -40 Angle in degrees - -50 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 FIG. 4-6: Theoretical carrier and side band mode elevation plane pattern of the optimized double parasitic loop counterpoise antenna. kh = 2.7755, kb = 0.1514, kd = 0.9276, kA = 52.1686, kH1 = 3.4819, kB1 = 3.67r, kH2 = 12.7671, kB2 = 5.27, f = 1090 MHz. 1 2 2

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4.7 Full Scale Parameters of the Optimum Antenna In this section we give the full scale values of the different parameters of the optimum double parasitic loop counterpoise antenna. Also given are some of the important pattern characteristics of the antenna. This section should serve as a handy reference for the full scale antenna and its expected performance. The antenna is assumed to operate at the frequency f = 109 MHz. The mechanical dimensions of the antenna are: h=4' d=1'4", w=10", A=75', 2B1= 46. 8', Hl=5', 2B2=32. 5', H2=18'4", operating wavelength opt= 9.02'. The expected elevation plane pattern characteristics are as follows: Carrier Mode Direction of principal maximum 0max = 60~, Far field gradient at the horizon ag = 5.66 dB/6~, Field reduction factor aF = 10.3 dB. Side Band Mode Direction of principal maximum 0max = 66~, Far field gradient at the horizon ag = 23.71 dB/6~, Field reduction factor aF = 23.18 dB, Amplitude of the minor lobe below 0 = 900: 13. 63 dB down relative to the field in direction 0=900, Position of the minor lobe below 0=90~ is 1060. For the carrier mode the level of the field immediately below 0 = 90~ is much larger than that in the side band mode (Fig. 4-6). The meaning of all the notations used here are as explained before. The complete numerical values for the theoretical patterns discussed above are given in Appendix F (Tables F-II and F-III). 4.8 Discussion In the present chapter we have developed approximate theory for the elevation plane radiation patterns produced by double parasitic loop counterpoise antennas operating in both carrier and side band modes. Although the theory neglects the effects of mutual interaction between the parasitic loops, the general agreement between theory and experiment has been found to be satisfactory. On the basis of the above theory the design parameters have been obtained for an optimum configuration for such an antenna using a 150' diameter counterpoise and operating in the side band mode at the frequency f = 109 MHz. The characteristics of the optimum antenna patterns have also been discussed from both the theoretical and experimental point of view. 58

During the contract period we have also obtained experimentally the design parameters of an optimum antenna using 52' diameter counterpoise and operating at the frequency 108 MHz. This was done before the theory for such antennas was developed. However, because of the contract priority, the emphasis of both theoretical and experimental investigations have been shifted to the 150' diameter counterpoise case operating at 109 MHz. Since the standard VOR antenna systems use 52' diameter counterpoises, the results of our investigation of such antennas are given in Appendix C. Theroetical optimization of this antenna can be carried out following a similar procedure discussed in this chapter. 59

V FABRICATION OF THE FULL SCALE DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 5.1 Introduction On the basis of model measurements, we obtained in Chapter IV the physical dimensions for a double parasitic loop counterpoise antenna designed for optimum side band mode performance at the full scale frequency 109 MHz. The full scale double parasitic loop counterpoise antenna has been obtained by installing two appropriate parasitic loops on the standard VOR Alford loop counterpoise antenna located at the end of Manheim Road outside of the NAFEC (National Aviation Facility Experimental Center). In the present chapter we describe the mechanical fabrication of the parasitic loop assembly and also the method of incorporating it into the standard VOR antenna located at NAFEC. 5.2 Standard VOR Antenna at NAFEC The experimental standard VOR antenna system at NAFEC uses a counterpoise 150' in diameter and is mounted on a 75' tall tower so that the counterpoise level is 75' above ground level. Figure 5-1 shows a photograph of the tower which supports the counterpoise along with the conical dielectric housing which contains the standard four-Alford loop assembly. The necessary electronics to operate the station as a VOR system is housed in a building on ground. The details of the electronics involved are not discussed here. Interested readers may find the description of the VOR equipment in Hurley, et al (1951). 5.3 Full Scale Parasitic Loop Assembly As described in section 4. 7, the two parasitic loops for the optimum double parasitic loop counterpoise antenna have the following full scale dimension: 2B1 = 46'10", H1- 5', 2B2 =32'6", H2 = 18'4". The loops are to be made of 10" wide conducting strips. The other dimensions of the complete antenna are as given in section 4.7. The parasitic loops were fabricated from expanded aluminum. This material was chosen so as to reduce the surface area exposed to wind forces. The expanded aluminum came in 8' long sections, 10" wide and 0. 085" thick. Aluminum tubings, 3/4" in diameter have 0.049" thick walls, were used to hold the expanded aluminum in place. The structure was then cut to the appropriate length and bent to the proper radius of curvature for the appropriate loop. The expanded aluminum was attached to the tubing with rivets. At the junction points additional pieces of expanded aluminum were attached with screws over the junctions in order to ensure good electrical contact between the junctions (see Fig. 5-2). 60

The loops were held at the appropriate heights with redwood poles. Figure 5-3 is a photograph showing a section of the two parasitic loops installed on the counterpoise. Sixteen redwood poles were used to support each parasitic loop. This number of poles was selected on the basis of the support structure associated with the 150' diameter counterpoise located at NAFEC. To ensure a rigid structure upon which to mount the parasitic loops, each of the wooden poles was mounted over one of the principal spokes of the counterpoise (Fig. 5-2). The set of poles supporting the lower parasitic loop were 6' tall and the set supporting the upper loop were 20' tall. Each of the 6' poles were held in place by three 3/16" Mylar guy ropes; six such guy ropes were used to support each of the 20' poles. The counterpoise ends of the guy ropes were attached to chains such that they would provide some fine adjustment in the tension associated with the ropes (Fig. 5-4). Provisions were made also so that the heights of the parasitic loops could be adjusted slightly if necessary. Mylar was chosen as the rope material because of its stability and also because of the hostile environment in which the entire antenna assembly is located. The redwood poles were treated with wood preservative and moisture resistant solution so that a minimum amount of moisture would be absorbed by the poles. The bases of the redwood poles were placed on metal supports welded to the 16 spokes that run radially out from the center of the counterpoise (Fig. 5-2). These metal bases were located at the appropriate distances from the geometric center of the four Alford loops mounted above the counterpoise. A plumb line was used to ensure proper orientation of the poles with respect to the counterpoise and its geometric center. Figure 5-5 shows a photograph of the two parasitic loops mounted on the 150' diameter counterpoise. The central conical structure is a dielectric housing which contains the standard four Alford loop assembly used in a VOR system. 5.4 Discussion In this chapter we have described the mechanical fabrication and assembly of the full scale double parasitic loop counterpoise VOR antenna. It should be noted that provisions were made so that the heights of the parasitic loops could be adjusted if found necessary during the time of testing. 61

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FIG. 5-5: Two f:ull scale parasitic loops mounte:d i:;,:: FEDERAL AVATION ADMiNISTRATN ATLANTIC CITY, NIEW JERSEY i U - 0 1. A~~tAN~tC CtTY, NIW ^ERSCY 1 0 ~ 2 ^ 0 I

VI NAFEC FACILITIES AND INITIAL GROUND TESTS 6.1 Introduction In this chapter we comment briefly on the test facilities available at National Aviation Facility Experimental Center where the full scale testing of the double parasitic loop counterpoise VOR antenna has been carried out. In the following sections we mention only the relevant information about the arrnagement. 6.2 Standard VOR Experimental Station Terrain The standard VOR antenna at NAFEC has been described in section 5.2. For the purpose of analyzing the data discussed later, it is appropriate to discuss briefly the terrain surrounding the VOR station, parts of which can be seen in Fig. 6-1. The east side of the station (foreground in Fig. 6-1) is relatively clear with no major visible obstructions. On the west side of the station there are a number of trees whose heights range from 65' to 70'. The trees run in a westnorthwest to east southeast direction such that there is a fairly straight line of trees starting just to the west of the station. A geometrical representation of the terrain and the coordinate system used are shown in Fig. 6-2. 6.3 Ground Test Facility Facilities are available to probe the fields along a vertical line above ground and at convenient distances from the VOR antenna. We have made use of a wooden pole 75t tall located 300 feet from the center line of the counterpoise. A vertical track is attached to the front side of this pole and oriented such that a small horizontal detecting dipole antenna can be oriented normal to a radial of the test antenna and can be readily raised and lowered by use of a rope. The height of the detecting antenna above ground can be varied from 0' to 85' in steps of 5'. The output of the detecting dipole feeds a Micro-Tel receiver connected to a Hewlett-Packard model 415 standing wave indicator. The area between the test antenna and the 75' pole where the field probing is done, consists primarily of marsh grass approximately 5 - 6 feet tall and a 8' fence that encloses the VOR facility. It is estimated that the fence is approximately 125' from the vertical line through the center of the counterpoise. 67

6.4 Introduction of Known Scattering Sources Facilities are also available to introduce known scattering sources in the vicinity of the VOR antenna system. These scattering objects act as the known sources of scalloping errors and thereby enable a flying aircraft to be used to evaluate the performance of the VOR antenna system under test. One such scattering object is in the form of a wire grid reflecting structure mounted between a pair of poles, so that the plane of the structure is vertical. The reflecting grid structure is made of eight conducting wires, each approximately 1/16" in diameter and 200' in length. The eight wires are placed parallel to each other and to the ground. The wires are oriented 18" apart and the topmost wire is located 30' above the ground. The entire structure is positioned approximately 1000' from the VOR station and oriented 45~ with respect to the 52~ radial from the north of the VOR station. A second pair of poles is located at a distance of 2000' from the VOR antenna and supports a similar reflecting screen. A theodolite mount and a small shelter are located midway between these poles. The theodolite is used when making accurate bearing measurements (with respect to the theodolite position) of an aircraft circling the station at a constant altitude and at a constant distance from the station. 68

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Boundary of the Woods Flat Marshy Land North / i Woods with / 270~ - VOR ) 90 / tall5te / 4 // 1\ 1800 / // / / FIG. 6-2: Standard VOR Experimental / ~/ A/ Station Terrain. 70

VII GROUND TEST RESULTS FOR STANDARD VOR AND DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNAS 7.1 Introduction In this chapter we discuss the results obtained by probing the fields at 109 MHz produced by the full scale standard VOR and double parasitic loop counterpoise antennas located above ground. The probing of the fields is done at a distance 300' from the antenna and along a vertical pole above ground in a manner described in section 6.3. The reduced data obtained from the ground tests are compared with the corresponding theoretical results. Theoretical results given here have been obtained on the assumption that the test antenna is located above a perfectly conducting plane earth. The full scale ground test results discussed here have been obtained at the National Aviation Facilities Experimental Center. Thus the results given in this chapter will also indicate the validity of the design of optimum double parasitic loop counterpoise antennas whose theory and design have been discussed in earlier chapters. Before discussing the test results we give a brief theoretical discussion of the fields produced by the test antennas located above a conducting earth. 7.2 Field Expressions In view of the fact that during the full scale testing on the ground, the direct and reflected rays reaching the detector at the field point are not parallel to each other, it is clear that the field point in such a case is located in the quasi radiation zone of the antenna under consideration. For this reason we investigate here the case when the field point lies in quasi radiation zone so that the results can be compared directly with the full scale test results. Figure 7-1 shows the theoretical model used for the analysis. The VOR antenna represented by a point source in this figure is assumed to correspond to the particular antenna configuration under consideration. In this zone the usual geometrical optics approximations are used. We consider the arrangement sketched in Fig. 7-1 along with the coordinate system used. Let the field point P be located below the x-y plane at (R, 0) from the origin of the coordinate system. The distance of the point P from the center of the antenna is D. It is evident from the figure that the field at P consists of the contributions from a direct and a reflected ray originating from the antenna. 71

z VOR Antenna Direct Ray / r ~WR -R -A- P (field point) x " Z1 X Reflected ~YR~ Ray C nt Conducting Image of VOR Antenna FGround Plane7ricl p ntio o a e FIG. 7-1: Geometrical representation of a double parasitic loop counterpoise VOR antenna above ground. Let the free space electric field of the VOR antenna at a point (R, 0) in the radiation zone be given by the following expression: ikR E=K S() a (7.1) where S(0) is the free space complex far field pattern of the antenna, a is the unit vector in the 0-direction, k = 2r/X is the free space propagation constant, R, 0 are the coordinates of the field point in spherical system, and K is a constant. Note that the field is polarized in the j0-direction, i. e. horizontally polarized. In the present case, it is quite simple to show that the direct and reflected components of the electric field at the point P are given by eikR ED=K. - S( 0) a (7.2) 72

eikR' A E =-K - S(Or) a (7. r R 'r where R' is the path length of the reflected ray between the source and field points and the other parameters are as shown in Fig. 7-1. The negative sign in front of (7. 3) appears because of the assumption of infinite conductivity for the ground. For a more realistic ground the negative sign in (7. 3) should be replaced by a general reflection coefficient r =Irl ej6 where I Ir lis the amplitude and 6 the phase of the reflection coefficient. From Fig. 7-1 it can be shown that 0 2+ a, Or 21 (7.4) 2 J r 2 and and Z1-Z2 Z1+Z2 tan a = 2 tan = (75) D D It can also be seen from Fig. 7-1 that R2 D2+ (Z- Z2) R'2 = D+ (Z+ Z) (7.6) 1 2 12 Assuming Z1, Z2 < D it can be shown that 2Z 1Z2 R' - R + D (7.7) D Using eqs. (7. 2), (7. 3) and (7.7) it can be shown that the total field ET at P is given by ~r~cp 2r S(2Z ET=ED+E K - (e e R (a)-e D. (7.8) Thus the complex field pattern ST(e) produced by the antenna configuration shown in Fig. 7-1 can be written as 2Z 1Z2 ik D S T()= S(0)-S( r)e (7. 9) where 0 and 0r are given by eqs. (7.4) and (7. 5). If the field point P is taken to be above the x-y plane, then the complex field pattern is again given by (7. 9) but with the following modified definitions of 0 and Or: 73

z +z ~D 7tn Z= 1 + Z2 tan 0= Z - Z ' + tan = (7.10) Z2- Z1 r 2 D In Eq. (7.9) S(0) is the free space elevation plane complex far field pattern of the antenna under test. Analytic expressions for S(0) for double parasitic loop counterpoise and standard VOR antennas operating in both carrier and side band modes are discussed in Chapters II - IV. In the following section we compare the theoretical results obtained from Eq. (7. 9) with the corresponding ground test results. 7.3 Full Scale Ground Test Results In this section we compare some of the relevant full scale test results with the appropriate theoretical results discussed earlier. The description of the full scale testing facility and the method of obtaining results have already been discussed. We only mention here that the full scale test facility consists of a conventional or double parasitic loop counterpoise antenna located 75' above ground. The counterpoise has a diameter of 1501. The antenna system is excited at a frequency of 109 MHz, X = 9.028'. The field produced by the antenna is detected by a horizontal dipole mounted on a vertical pole located at a distance 300' away from the antenna. The detector height can be varied from the ground level to about 85' above ground in steps of 5'. Figure 7-2 shows the theoretical field strength variation in a vertical plane located 300' away from the standard VOR antenna operating in the carrier mode. In the same figure we also show the reduced results obtained from the full scale test. In view of the approximations made in the theoretical analysis, the agreement between numerical and experimental results may be considered to be very good. It should be pointed out that the accuracy of the measurement deteriorates as the detector approaches the ground. Figure 7-3 shows similar results for the optimum double parasitic loop counterpoise antenna operating in the carrier mode. Within the experimental range of accuracy, the agreement between theory and experiment in this case may also be considered to be satisfactory. Figure 7-4 gives the results obtained for the side band mode operation of the double parasitic loop counterpoise antenna. The agreement between the critical regions of the theoretical and experimental curves may be considered to be good in view of the various approximations made in the analysis and the experimental errors involved. 74

The parasitic loop dimensions corresponding to the experimental results in Figs. 7-3 and 7-4 are: 2B1 = 46'10", H = 4'9", 2B2 = 32'6", H2 = 192". The corresponding theoretical values for the same dimensions for the optimum configuration as given in section 4.7 are: 2B1 = 46'10", H1 = 5', 2B2 = 32'6" H2 = 18'4". Comparing these values it may be concluded that the parameters for the optimum antenna obtained on the basis of theretical and model measurements are within the range of full scale measurement accuracy. The slight adjustments of the heights that have been necessary during the full scale testing is not surprising if one considers the effects of terrain and other possible mechnical maladjustments on the performance of the entire system. From now on we shall refer to the antenna considered in Figs. 7-3 and 7-4 as the optimum parasitic loop counterpoise antenna system II. The optimum double parasitic loop counterpoise antenna system whose quasi radiation field characteristics are shown in Figs. 7-3 and 7-4 has a theoretical field gradient value of about 23dB/6~ in the side band mode of operation. In addition to the above optimum configuration we have chosen another double parasitic loop counterpoise antenna to be flight tested. This antenna is designed to have less than optimum value for the horizontal field gradient. The parasitic loops for this system have the following settings: 2B1 = 46'10", H1 = 3'10", 2B2=32'6" H2 = 18'7". The ground test results obtained from this antenna are shown in Figs. 7-5 and 7-6 for carrier and side band mode operations respectively. The theoretical horizontal field gradient of this antenna is about 15dB/6~. This antenna will be referred to as the parasitic loop counterpoise system I. 7.4 Discussion The full scale ground test results discussed in this chapter indicate the validity of the theoretical design and the proper mechanical fabrication of the optimum double parasitic loop counterpoise antenna. Considering the various approximations involved, the agreement between the theoretical and actual measured full scale design values may be considered to be satisfactory and within the range of experimental accuracy. 75

0 Gt\;r\ X XX~~ tho a ex 8-154 -oE I * -2%;FIG. 7-2: Carrier mode field strength variation as a function of 0 at a distance 300' away from -25r a conventional VOR antenna located 75' above ground, kA = 52.1686, f = 109 MHz. theoretical - -- experimental X X X 28 90 92 94 96 98 100 76

5 Angle in degrees 89 92 94 96 98 100 ~I ~x t -5 -10 Theoretical X X X X X Experimental -15 X FIG. 7-3: Carrier mode field strength variation as a function of 0 at a distance 300' away from the (Systems II) optimum double parasitic loop counterpoise VOR antenna located 75' above ground. f = 109 MHz. 77

5 Theoretical X X X X Experimental 0 -5 X X 10 X -15 X -20 I,, 88 90 92 94 96 98 100 Angle in degrees -- FIG. 7-4: Side band mode field strength variation as a function 0 at a distance 300' away from the optimum double parasitic loop counterpoise VOR antenna (systems II) located 75' above ground, f = 109 MHz. 78

8 44 --4 I0 -) -12 - -16 - -20 I 86 88 90 92 94 96 98 Angle in degrees --- FIG. 7-5: Measured carrier mode field strength variation in a vertical plane located 300' away from a non-optimum double parasitic loop counterpoise VOR antenna (Systems I) f = 109 MHz. 79

4 0 -4 e -81 "4 \; -12 -16 -20 -24 I 1 I I I I 88 90 92 94 96 98 100 Angle in degrees — w FIG. 7-6: Measured side band mode field strength variation in a vertical plane located 300' away from a non-optimum double parasitic loop counterpoise VOR antenna (Systems I). f = 109 MHz. 80

mII FLIGHT TESTS OF DOUBLE PARASITIC LOOP COUNTERPOISE AND STANDARD VOR ANTENNAS 8.1 Introduction In this chapter we discuss the results of flight tests carried out on 109 MHz to determine the performance of a standard VOR system when the VOR ground station uses double parasitic loop counterpoise antennas and standard four Alford loop counterpoise antenna. The primary purpose of the flight tests has been to compare the observed scalloping errors in the VOR bearing indications in a flying aircraft produced by a known scattering object for the two cases. The secondary purpose has been to verify at the full scale frequency and for practical systems the horizontally polarized radiation field information obtained earlier for such antennas from theoretical and model measurements considerations. For this purpose the radiated fields produced by the test antenna were measured with the help of an aircraft flying at a constant altitude along chosen radial paths to and from the test antenna. The tests described here were performed at NAFEC. 8.2 Test Antennas The standard VOR antenna consists of the four Alford loops located above a 150' diameter counterpoise elevated 75' above ground. The details of the antenna have been given in section 6.2 - 6-3. The double parasitic loop counterpoise antenna system was obtained by installing two parasitic loops of proper dimensions at appropriate heights above the standard VOR Alford loop counterpoise antenna in the manner described in Chapters IV - VI. As mentioned in section 7.3, two double parasitic loop counterpoise antenna configurations have been chosen for the flight tests. These are referred to as antenna Systems I and II. The key design parameters of the two systems are: System I (non-optimum) 2B1 =46'10" H = 3'10" 2B = 32'6t H = 18'7" System II (optimum) 2B1 = 46'10" H 4'9" 2B = 32'6" H = 19'2" Notice that the two systems differ with each other only in the heights of the parasitic loops above the counterpoise. 81

The free space side band mode horizon field gradient values produced by antenna systems I and II are about 15 and 23dB/6~ respectively. These field gradient values are much larger than the corresponding value 5.54dB/6~ obtainable from the conventional VOR antenna. On the basis of this criterion alone, it was anticipated that for a given scattering object located near the antenna, a standard VOR system using the antenna systems I and 11 would produce reduced amounts of scalloping effects in the VOR indicator of a flying aircraft. The main purpose of the flight tests discussed in the present chapter were to verify quantitatively the above statement. 8.3 Field Strength Results In this section we describe the measured far fields produced by a standard VOR antenna and by the double parasitic loop counterpoise antenna system II. The field strength results presented here were obtained by employing an FAA aircraft flown at an altitude of 3220' along a specified radial toward the experimental VOR station operating on 109 MHz. Each selected inbound radial was flown three times and continuous recordings of test data were made beginning at a point 35 nautical miles from the station and ending after the aircraft had passed over the station. Similar tests were conducted while using each VOR antenna system. To ensure that the aircraft was flown along the same flight path each time, aircraft guidance was provided by an air traffic controller stationed at a precision tracking radar system station (EAIR at NAFEC). All the results have been obtained only for the side band operation of the appropriate antenna. To operate the system in the side band mode, the omnidirectional radiation function (carrier mode) of the VOR was disconnected and after turning off the synchronous motor the goniometer was set at 45~. The aircraft was then flown along the prescribed course (see Fig. 6-2) and the horizontally polarized field was received by the horizontally polarized element of a crossed dipole mounted on the nose of the aircraft. The received data was then fed to a calibrated VOR receiver and strip chart recorder along with range marks. The results shown here are expressed in dB and have been obtained from the raw data after removing their dependence on the range. Figures 8-1 and 8-2 show the reduced results obtained for the standard VOR and for double parasitic loop counterpoise system II antenna respectively when the aircraft was flying along the 90~ radial (Fig. 6-2) of the station. The corresponding theoretical results are shown in Figs. 8-1 and 8-2 for comparison. Theoretical results have been obtained by assuming that the test antenna is located at a height Z1 above a perfectly conducting infinite planar ground and the aircraft is in the far zone of the antenna. When the effects of the distance on the received field of the antenna are removed, the received field as a function of 0 may be expressed as: 82

-ikZ cos 0 ikZ cos 0 St(6) = e S(e) - S' (7r-0) e where S(6) is the free space elevation plane complex far field pattern of the test antenna. Explicit expressions for S(0) for the test antenna have been given in earlier chapters. Notice that the results are shown only for 70~ < < 90. For e < 700 the aircraft was flying at a relatively high rate of change of 0. Consequently the raw data recorded in the aircraft was changing too fast. It has been found that for 0 < 70~ the results were too erratic to be reduced. The agreement between theory and experiment is excellent in Figs. 8-1 and 8-2. In both cases the theory quite accurately predicts the positions of the pattern minima. The experimental results in Fig. 8-1 do not show the first few maxima and minima in the range 70~ < 0 < 80~. This is attributed to the fact that the amount of undulations of the field within this range is too small (as evidenced by the theoretical results) to be recorded. It is anticipated that the theory may be improved further by assuming a more realistic reflection coefficient for the ground. Observe that the minimum nearest to the horizon in Fig. 8-1 is about 10dB down locally whereas the corresponding minimum in Fig. 8-2 is about 3dB down locally. The smaller value of the theoretical minimum in Fig. 8-2 is due to the large value of the free space field gradient associated with the antenna system II. The experimental value of the local minimum in Fig. 8-2 isS 5.3dB which seems to indicate that system II does not have the gradient of theory. In order to investigate the effects of trees on the fields produced by the double parasitic loop counterpoise antenna, the aircraft was flown above the woods along the f = 220~ radial (Fig. 6-2 ). The results are shown in Fig. 8-3. As compared with the f = 90~ radial case shown in Fig. 8-2, Fig. 8-3 indicates that the ground reflection effects are much reduced. This is attributed to the fact that the trees reduced considerably the scattered energy reaching the aircraft. 8.4 Scalloping Effects It is known that a scattering object located in the vicinity of a VOR station produces scalloping effects in the VOR indications of a flying aircraft. The mechanism and approximate analysis of scalloping effects in some ideal situations have been discussed in the FAA Handbook (1968). In the present section we do not go into any theoretical results but only compare the scalloping effects observed with different antennas in the presence of known scattering objects located above ground. In order to collect the scalloping data, the aircraft was flown in a 20 mile orbit around the VOR station and at an altitude of 6575 feet. This altitude corresponds to the minimum direction nearest to the horizon in the elevation plane pattern including the effects of ground of a conventional VOR antenna. It has been found 83

during orbital flights of conventional VOR systems that the scalloping effects become strongest at heights which correspond to these minimum directions. It should be noted here that for an optimum double parasitic loop counterpoise antenna above ground the depths of these pattern minima are considerably smaller than those of the standard VOR antenna (see Figs. 8-1 and 8-2). From this consideration we expected to see reduced scalloping effects with the parasitic antenna systems. To produce the scalloping effects a wire grid reflector was installed 1000' from the test antenna in the manner described in section 6.4. The orientation of the scattering object with respect to the VOR station is shown in Fig. 8-4. A typical set of scalloping data obtained at a height of 6575' with a standard VOR antenna is shown in Fig. 8-5. The abscissa in Fig. 8-5 represents the azimuth of the aircraft with respect to the VOR station and the ordinate gives the amount of course scalloping amplitude due to the scattering object. The two sets of results shown in Fig. 8-5 correspond to the two receivers used in the aircraft. The full scale scalloping in Fig. 8-5 is 12.5~. Thus we observe from this figure that with a conventional VOR system there appears 12.5~ scalloping at the azimuth of about 140~ when flying at 6575' altitude on a 20 mile orbit. Similar sets of data obtained with VOR systems using antenna systems I and II are shown in Figs. 8-6 and 8-7 for the same elevation of the scattering object and for similar orbital flights. As anticipated earlier, it is found that both the double parasitic loop counterpoise antennas produce reduced scalloping effects. The optimum antenna system I produces the least amount of scalloping. The scalloping observed in three cases are given below for comparison. Standard Alford Loop Counterpoise Antenna 12.50 Double Parasitic Loop Counterpoise Antenna System I 2.50 Double Parasitic Loop counterpoise Antenna System II 20 It is clear from the results given above that the optimum double parasitic loop counterpoise antenna produces a 6 to 1 reduction in the scalloping effects observed in standard VOR indications of a flying aircraft. On comparing Figs. 8-6 and 8-7 with Figs. 8-5, it is found that the parasitic antenna systems produce strong bending of the course. This observed slow bending of the course is attributed to the vertically polarized radiation from the parasitic loop counterpoise antennas. 84

8.5 Distance Range In order to determine the distance range of a VOR system using an optimum double parasitic loop counterpoise antenna, a radial flight was conducted at an altitude of 6575'. As the aircraft was flown radially away from the VOR system, it was observed that the signal did not reach the 5 microvolt level until a range of 65 miles had been reached. The distance from the antenna at which the signal level reached 5 microvolts is taken to be the distance range of the VOR station. Perhaps we should make a comment here about the manner in which the above data were collected. Initially when efforts were made to collect aircraft data it was observed that the sawtooth amplitude (note the sawtooth nature of the scalloping data shown in Fig. 8-5) was not of the proper magnitude. Upon some consideration of this problem it was concluded that the cause for the reduced amplitude sawtooth was the improper space modulation of the VOR signal. A reason for the reduced space modulation is due to the fact that the parasitic rings create such a small signal near the horizon that the signal radiated in the side band mode was considerably less than that radiated in the carrier mode. We should also note here that the carrier mode intelligence is carried by frequency modulation, whereas in the side band mode the intelligence is carried by amplitude modulation in the form of space modulation of the rf characteristics of the VOR signal. In order to achieve the necessary amplitude required for the sawtooth associated with the scalloping data, it was necessary to make some adjustments in the side band carrier powers. To achieve the proper space modulation it was necessary to reduce the carrier power by approximately 50 percent. This was achieved by introducing a length of RG-8 cable in the carrier transmission line from the transmitter to the antenna. This is of importance because we have mentioned above that the distance range was approximately 65 miles. After taking into consideration the fact that the power radiated in the carrier mode was reduced by 3dB, we can say that one could achieve approximately a distance range of 84 miles by operating the station at full power assuming that the station employing the parasitic system radiates the same amount of power in the carrier mode as the conventional VOR without the parasitic rings. The distance range associated with the conventional VOR with a 150' counterpoise is in the neighborhood of 87 miles. Although we have noted above that it was necessary to juggle the power characteristics through the use of an attenuator, in an actual situation in which parasitic rings are to be installed on a station, one would construct a power divider to properly distribute the power between the carrier and the side band modes rather than using a lossy attenuator. 8.6 Discussion The flight test results discussed above clearly indicate that conventional VOR antennas can be converted into double parasitic loop counterpoise VOR an85

tennas with some distinct advantages. The measured field strength results discussed above indicate that the theories developed for the radiation fields produced by double parasitic loop counterpoise and standard VOR antennas have sufficient accuracy for the practical design of such antennas. Detailed discussion of the radiation properties of double parasitic loop counterpoise and standard VOR antennas located above ground may be found elsewhere (Sengupta and Ferris, 1971). With an optimum parasitic system, the scalloping effects have been observed to be reduced by a factor of 6 to 1 over the conventional system. It appears that the parasitic system has a distance range comparable to that of a conventional system. During the flight tests of the double parasitic loop system, large polarization errors were observed in bearing indications. In the next chapter we discuss the experimental study of the polarization errors involved in a standard VOR system using such antennas. In the above we have given only those flight test results which clearly demonstrate the application of parasitic loop counterpoise antennas to a VOR system. Detailed discussions of the flight test results will be given in a separate publication by FAA. 86

THEORETICAL ---- EXPERIMENTAL ANGLE O IN DEGREES - 70 80 90 0 -2- F 8 df-1 du b - \\ / -i' antenna above ground, 90 -8- - \ 8 E; -14 \ II8 -~s - - ntnn abv Iudi=9 87~~~~~~~~~~~~~~

THEORETICAL _ EXPERIMENTAL ANGLE 0 IN DEGREES 9 70 80 90 0 -2 \ z 6 -4__ \ \ H —i H -10 \ \ -14 -16 < \ -20 — -22 — 1 -24 -2461 FIG. 8-2: Radiation field produced by the double parasitic -28+ loop counterpoise system II above ground, B = 90. -30 1 88

ANGLE 0 IN DEGREES 70 8p 9 01 -2 -4 t - -6 -14- -16 9 -18 -20 -22 --24- -26 --28% -30 -FIG. 8-3: Radiation field produced by a double parasitic loop counterpoise antenna systemII above ground, B = 2200. 89

North 00 IsAyi\ Wire Grim IJ / s Reflector V 52~ Sa t VOR Station FIG. 8-4: Location of the wire grid reflector with respect to the VOR station. 90

:L.... -I -. — -- -.I = _ 1 - - t ---_ _ _R....... _ 1-.:__.|_ 4 = 1 i '|J. _ _ f............... - l __ _t --: ""-:, -::::*-l:-:::.:: 1 -- — 4t - f- - -- - - ----: —L-:-::::i::-: -:-:ii f~~~l ^,,f,,,,, l, i _ ji1~~ I91 1 r _ I _ ^ |-&! -I- - ii -i^H'r 1 1 ___|tl -f|- - -t — ~ | -- _ _ ____ __II FIG. 8-5: Scalloping results obtained with a * t L \ * j i ____"" - ^ **' — _.___ ___ _conventional VOR system using a 4 — | 0:Hd-f___ _______ ________g g_____________________van io x ^___________

]H- - -: ---.1'.~.~ ~ V H ~ 0 N!t <QA I -"'l1 q H.0)'1 C4 i= ----....l" V\-= 'S 'N r- $10 -7- [' 7 -I- m [-= 1-" — 't- "" _ n -_.__ _._. —. -t > -- -1 --- - t ~ -1 — < i —j~ - - -- _-_ -1___ --- ---— 1 --- -___ -- ---------- --- -- ------ --- __ [ _____j i ' I __ __l _'-LK I' 1 1 ll - l[ FIG. 8-6: Scalloping results obtained with a conventional 1. |~:-' V VOR system using a double parasitic loop - I t- -—. —_ - - I — _ tcounterpoise antenna (System I). =t ___* _._ l lt- - - 9 ^ sO _ b L^ rB A ^ V ":) O N J s H o::g_3M l,_______________ ^ — vs n Nl CM31NIUd_________________________________^ r_______________

....-.. -- ____ _. — r-1 1I 1- 77 7 —1- __-_ --- = I -H --- -- -- - i... -.. _. ---- t ---- I -- t -.. / -. I....._; r ____ I- 1-1- X r-( b I j1 t ----;....... - t.... = --- --—!.-. --- -- ---- ---- t --- —-- -1.+, _ I:I.... I loop:ou --- — ise I I.. I- I r W g,,1.0.,, n I, - ^* Q O *^^ ^ ^ ^1~~~~~~~~~~__ r~ __ - T __ ___ __ tN______ __ t__ ---- - ^ -- -: - -1?...... I _., _--- 4...... 2_7,._ I I. ---, —I -I- 1 f --- — l}::i C _ _ _ __ ~~~~f~~~ I-1.. _ _ _ I- ~ ~~ --- ~ ---1 ---~ —r _ -- T -_:_- 1~:_.'l. __1_-_l_ ~~~~~~ ~~ Scloigrslt bandwthacnetoa LLJ L L7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'~~~~~~~~~7I~~~~~~~

IX EXPERIMENTAL STUDY OF THE POLARIZATION ERROR 9.1 Introduction The results discussed in chapter VIII indicated that the use of a double parasitic loop counterpoise antenna in a standard VOR system reduced the scalloping errors in the bearing indications of a flying aircraft by a factor of 6 to 1. However, the polarization errors associated with the VOR station using the new antenna system have been found to be + 6~ at certain distances from the station. As recommended by the FAA, the acceptable polarization error in a conventional VOR is + 2~. Basically, the polarization errors are generated by the cross-polarized component (vertically polarized) of the field produced by the antenna (Anderson et al 1953; Anderson 1965). In addition to the polarization errors, the observed slow course bends in the scalloping data discussed in section 8.4 are believed to be due to the cross-polarized radiation from the antenna. In the present chapter we discuss the results obtained from an experimental study of the cross-polarized radiation characteristics of double parasitic loop counterpoise and standard VOR antennas. During the course of this study we have developed an active polarizer configuration to reduce the polarization errors in a standard VOR system. Due to lack of time our polarization study remains incomplete. We report here the results obtained from only this limited investigation. 9.2 Polarization Errors in Standard VOR System The standard 4-Alford loop VOR antenna produces appreciable amounts of undesirable vertically polarized radiation (Anderson, 1965). At the present time the FAA employs a parasitically excited element, called the polarizer, in the antenna system of a standard VOR ground station to bring down the polarization errors associated with the station within the acceptable limits. The design and performance of such a polarizer is discussed in a FAA report (Anderson et al, 1953). Basically, the polarizer produces a vertical component of field which is in phase opposition to the vertical component of the field produced at the far field point by the VOR antenna. The magnitude of the polarizer field is determined primarily by the element lengths of the polarizer and somewhat by its position relative to the 4-Alford loop array; the phase of the polarizer field is controlled mainly by the position of the polarizer with respect to the Alford loop system. It is clear that, for ideal operation, the vertical plane radiation pattern of the polarizer must be identical to the vertical plane crosspolarized radiation pattern of the VOR antenna and that the two fields must be equal 94

and out of phase at the far field point for all elevation angles. As reported by Anderson (1965), the use of a passive polarizer reduces the polarization errors associated with a standard VOR system to acceptable values. 9.3 Polarization Error Study with the Passive Polarizer In this section we discuss the results obtained from an experimental investigation of the horizontal and vertical components of the fields and the associated polarization errors produced by a double parasitic loop counterpoise and standard VOR antennas. The passive polarizer, mentioned in the previous section, has been used to reduce the cross polarized fields in both cases. The investigation discussed here has been carried out at NAFEC at the full scale frequency of 109 MHz. The test plan employed during this part of the investigation is as follows, (i) The parasitic loops and the existing FAA polarizer were removed; the wooden parasitic loop supports were left in place. The antenna system thus consisted of 4-Alford loop array above a 150' diameter counterpoise located 75' above ground. (ii) The polarization error, horizontally and vertically polarized field components were then measured employing an aircraft. The reduced results are shown in Fig. 9-1. (iii) The FAA polarizer was reinstalled and the polarization error of the standard 4-Alford loop system minimized. Data were collected as noted in (ii) and the reduced results are shown in Fig. 9-2. (iv) The parasitic loops were then reinstalled with the polarizer removed so that the antenna behaved as a double parasitic loop counterpoise system II, discussed in chapter VIII. Similar data were collected and the reduced results are shown in Fig. 9-3. (v) The polarizer was then installed in the same location and it was adjusted for minimum polarization error for the antenna system II. The flying aircraft collected similar data and the reduced results are shown in Fig. 9-4. The results shown in Figs. 9-1 to 9-4 were obtained employing an FAA aircraft flown at an altitude of 3220 feet along the 900 radial (Fig. 6-2) of the Mannheim experimental VOR facility with the VOR operating at a frequency of 109 MHz. 95

-15... -/ ~5 _ +: 90 cdQ)^~~~~~~~~ l l Frequency = 109 MHz - Horizontal Component --- Vertical Component -45..... FIG. 9-1: Conventional 4 Loop VOR (Mannheim, No Polarizer) Results. III I I I - - W |1~ 00 -60 L_ Angle (8) 0 620 70~ 96 800 900

0 -15 L i -30 — 45 - Frequency = 109 MHz Horizontal Corn. FIG. 9-2: Conventional 4 Loop VOR (Mannheim, with --— Vertical Com. Polarizer) Results. I 62~ -70 80 90 97

.0 -0X -15 -30 \ l m4 'I <l I l U11 0 0 -45 900 = 90~ Frequency = 109 MHz FIG. 9-3: Double Parasitic Loop Counterpoise Antenna Horizontal Component System II Results (Mannheim, No Polarizer). ---- Vertical Component _ 1 / 1:___________A__ 10 l l --- —--— 8 — 0 --- —0Angle (9) | -60 62 70 98 0 90

-30 \ -30.. \ { /'i A I \ I".' I I I ma I ll \ I I -45 _ _ _ _ \ _1 \_ 1, \ FIG. 9-4: Double Parasitic Loop Counterpoise Antenna | = 900 System IIResults (Mannheim, with Polarized I Frequency = 109 MHz \| -- Horizontal Component --- Vertical Component A 10~ | - 60 _____Angle (O), 62~ 70o 99 80~ 90~

The aircraft flew along the same path three times and data were recorded during each flight starting at 35 nautical miles from the station and continuing until the aircraft passed over the station. No data were plotted for 0 < 0 < 62 because the raw data recorded in the aircraft were difficult to reduce accurately into pattern form due to the relatively high rate of angular change while the aircraft was flying through this region. To provide assurance that the aircraft was flown along the same flight path each time, aircraft guidance was provided by an air traffic controller stationed at a precision tracking radar system (EAIR at NAFEC). The horizontally polarized field strength was measured in the flying aircraft as described in section 8.3. The vertically polarized data for the VOR side band mode was obtained in a similar manner with the following changes. The VOR goniometer was set at 1350 and the signal was sensed by the vertical element of the crossed dipole mounted on the nose of the aircraft. The polarization error data was collected by having the VOR station operating in its normal mode and the data were sensed by the crossed dipole and reduced to polarization error data by means of a polariscope and recorded on a strip chart. The field strength data shown in Figs. 9-1 to 9-4 are relative plots in dB with the range effects removed. However, the differences between the vertically and horizontally polarized components are factual for each case. Thus the difference between these two plots is an indication of the polarization error associated with the system. Notice that both the horizontally and vertically polarized data exhibit interference pattern structures in the region 800 < 0 < 900, i. e, from 100 above the horizon to the horizon. The explanation for this is as discussed in section 8.3. It should be observed that the interference patterns differ for the horizontally and vertically polarized components recorded for each condition tested. This phenomenon results from the fact that the reflection coefficient of ground for horizontally and vertically polarized energy has a 1800 phase difference at shallow angles of incidence (< 10~), (Westman, 1956). Comparing the horizontally polarized data, for the conventional 4-loop system (Figs. 9-1 and 9-2) and the double parasitic loop system II (Figs. 9-3 and 9-4), it can be seen that their gradients (change of field strength versus angle) differ significantly. Further, it can be seen that the vertically and horizontally polarized field strengths associated with the parasitic system (Figs. 9-3 and 9-4) also differ and tend toward equal amplitudes, (in the 80 to 90 degree region), more rapidly than do the same components of the 4-loop system (Figs. 9-1 and 9-2). A comparison of the vertically polarized data of Figs. 9-1 and 9-3 shows that the parasitic loops have a slight effect on the absolute value of the vertically polarized component. 100

It can be seen from Figs. 9-1 and 9-2 that the passive polarizer reduces the vertically polarized component of the field relative to the horizontally polarized component by better than about 23dB for 82~ < e < 90~. Whereas for the parasitic system the corresponding reduction in the vertical component has been found to be about 10dB in the range 82~ < 0 < 90~. To obtain a better understanding of the differences between the vertically and horizontally polarized energy, additional field strength and polarization data was collected by having the aircraft flown along the 2200 radial of the Mannheim facility. Radiation from the antenna was directed toward a densely wooded area (Fig.6-2) where the trees are approximately 60 feet tall and in full foliage. The effect of the trees is either to absorb or randomly scatter much of the energy radiated below the counterpoise for both senses of polarization. Horizontally and vertically polarized field strength and polarization data collected for the 2200 radial are shown in Fig. 9-5. From a review of this data it can be seen that both the field strength and polarization data are less erratic, as might be expected due to the reduction in the reflected component from the earth. Referring now to the polarization data plotted at the bottom of each figure (Figs. 9-1 to 9-5), it can be seen that this data is well behaved from 62~ - 80~; however, in the region of 800 - 90 the polarization error becomes erratic. Upon close examination of the field strength and polarization data, it can be seen that the polarization error increases when the difference between the vertically and horizontally polarized field components decreases and vice versa. Figure 9-2 indicates that the passive polarizer is capable of reducing the polarization errors to tolerable limits for the standard VOR antenna case. Comparing Figs 9-3 and 9-4, it can be seen that the passive polarizer is capable of reducing the polarization error for the parasitic system to tolerable levels in the range 62~ < 0 < 80~, however, for 0 > 80~ the polarization error increases up to about 12~. It appears from the results shown in Fig. 9-4 that the polarizer field is not strong enough to reduce the vertical component of the field produced by the parasitic antenna system such that the polarization error stays within acceptable limits in the range 800 < 0 < 90. It can be noted also that in the parasitic loop counterpoise VOR antenna system there are at least two additional sources of vertically polarized energy, each at a different height above the counterpoise and above ground. Each source of vertical polarization has a field strength pattern with a distinctive number of lobes. It was stated in section 9.2 that the radiation pattern of the polarizer should be identical in shape and magnitude, but opposite in phase, to the vertically polarized signal that it is required to cancel. Inasmuch as more than one vertically polarized signal is being generated by the parasitic loop counterpoise system, and because the field strength patterns of these signals are different in shape, a separate vertically polarized cancelling signal is required for each vertically polarized signal generated. 101

0 -15 P4. 670 \ Vrl - 45 = 220~ FIG. 9-5: Double Parasitic Loop Counterpoise Antenna Frequency = 109 MHz System II Results (Mannheim, with Polarizer) - Horizontal Component.. — Vertical Component 0 _620 _ 700_ F0 on________10 62 70 102w of0

I___ - I- w - Iw I I - < — 10" dia.- - FIG. 9-6: Active Polarizer No. 1. 103

It is conceivable that the polarizer field may be increased further by increasing the number of parasitic elements in the passive polarizer and/or by using two passive polarizers in the system. Another alternative is to use an active polarizer which is described in the next sections. 9.4 The Active Polarizer Two active polarizer designs were considered: the first choice was to convert the parasitic polarizer into an active polarizer as shown in Fig. 9-6, the second choice was to design a polarizer made of dipole elements as shown in Fig. 9-7. The second choice was to be a four-element dipole array, vertically polarized. Initially it was thought that the simplest approach would be to convert the existing parasitic polarizer to an active polarizer. The necessary design drawings were prepared and the conversion made at the NAFEC shop facilities. Preliminary tests were conducted at the NAFEC antenna range and the results of these tests showed that the active polarizer (No. 1) radiated equal amounts of energy polarized horizontally and vertically. This polarizer design was felt to be unacceptable because of the large horizontal component being radiated. Therefore, the second polarizer (No. 2) was designed and a full-scale model fabricated. This model consisted of a four-element vertically polarized dipole array as shown in Fig. 9-7. The antenna was then installed at the Mannheim facility and later adjustments were made to reduce the unwanted vertical component radiated by the VOR system. The large horizontal component being radiated by polarizer No. 1 was believed to be caused by the horizontal current flowing in the hub of the polarizer (see Fig. 9-6). However, for polarizer No. 2 this horizontal current component has been eliminated by providing only vertical paths for the currents to flow (see Fig. 9-7). Polarizer No. 2 consists of four dipoles arranged in dipole pairs (see Fig. 9-7). Excitation for each dipole is the same except as will be noted below. Therefore, the excitation for one dipole will be discussed. To excite a dipole properly two RF sources of equal magnitude and opposite phase are required. Because a coaxial transmission line is used in the VOR system it is necessary to provide a conversion (balun) from the unbalanced (coaxial system) to a balanced transmission line for the dipole. Since the dipoles are spaced close together ( > A/10) each balun was fabricated employing a type BNC coaxial Tee and two lengths of RG-58/U coaxial cable whose lengths differed by 180 electrical degrees at 109 MHz. Four coaxial baluns were fabricated (one for each dipole). In Fig. 9-7 there are four dipole elements labeled 1-4. Each dipole has two elements labeled T (top) and B (bottom). To achieve the desired figure of eight pattern in the horizontal plane, it was necessary to excite a dipole pair 180~ out of phase. To obtain the proper phasing between dipole pairs two co-axial baluns were required and were attached to the dipoles such that the top element of one dipole was 1800 out of phase with the bottom element and vice versa for the second dipole element. The two balun tees were then interconnected by a third (BNC) Tee which functioned as the input for one of the dipole pairs and was fed by one of the VOR side band excitation sources as noted below. The second dipole pair was excited in a similar manner. 104

2 Cable Balun Inside c1 ( 3 4 ^ I Top a _.! Bottom FIG. 9-7: Active Polarizer No. 2. 105

Basically polarizer No. 2 consists of two simple arrays each consisting of two dipoles that radiate two figure-of-eight patterns in the horizontal plane. The two figure-of-eight patterns are orthogonal to each other and are excited such that elements one and three are excited by a cosine wave and elements two and four are excited by a sine wave. These cosine and sine wave excitations are obtained from the VOR system as noted below. In this manner the figure-of-eight pattern is caused to rotate in the horizontal plane at the frequency of the sine and cosine patterns exciting the two dipole arrays. Excitation for the active polarizer is obtained from the VOR side band excitation sources. The excitation from the VOR side-bands is connected to the polarizer such that the vertically polarized figure-of-eight pattern maximum occurs in space quadrature with the horizontally polarized pattern maximum associated with the VOR Alford loop system. The active polarizer excitation is fed through a variable attenuator and phase shifter to facilitate adjusting the amplitude and phase excitation of the polarizer antennas independently from the VOR side band excitation. This provides a means for adjusting the amplitude and phase of the signal being radiated by the polarizer to minimize the unwanted vertical component being radiated by the Alford loop system. The pattern shape of the active polarizer may be adjusted by varying the height of the polarizer above the counterpoise. To completely cancel the unwanted vertical component it would be necessary for the active polarizer antenna to be located at the phase center of the unwanted vertical component being radiated by the system. There has not been a study conducted to determine either the source, or the phase center of the vertical component being radiated by the Alford loops. Therefore, it was not possible to know the precise location at which the polarizer should be located. As a consequence our initial effort was to place the polarizer at a convenient location above the Alford loop system and to adjust the amplitude and phase of the excitation to cancel out the unwanted vertical component at specific elevation angles. 9.5 Parasitic Loop Counterpoise Antenna System II with Active Polarizer In this section flight tests and results using the active polarizer (polarizer No. 2) with the parasitic loop counterpoise antenna (system II) are discussed. The active polarizer was positioned such that each of the four dipoles was mounted directly above and on the center line associated with each of the four Alford loops presently employed in the conventional four-loop VOR. The plane including the dipole centers was located 40?' above the plane associated with the top of the Alford loops as shown in Fig. 9-8. This orientation was chosen partially out of convenience and also to insure that the active polarizer would not be influenced by the 106

I FIG. 9-8: Active Polarizer Installation. 107

vertical component radiated from the Alford loop system. Polarizer No. 2 consists of four dipoles that are arranged in dipole pairs (shown in Fig. 9-7) and its operation is discussed in the previous section. The two inputs associated with each of the dipole pairs are interconnected through a pair of phase shifters and attenuators to the side band outputs from the VOR transmitter. The power level sampled for the active polarizer is approximately 7dB below the power level fed to the Alford loop system in the side band mode. For example, the power available for the side band mode is approximately five watts and the power available to the active polarizer is approximately one watt. After the polarizer was installed at the Mannheim facility as noted above, a radiation pattern was measured by having an aircraft flown at a constant altitude (3220 feet) and from a distance of 35 miles from the station along the 900 radial over the station. The field strength was recorded and later the pattern was plotted and is shown in Fig. 9-9 with the range effect removed. In addition, patterns were also collected for the horizontally and vertically polarized components of the double parasitic loop counterpoise antenna system II. Figure 9-10 shows the horizontally and vertically polarized patterns for the 4-loop VOR with parasitic rings at Mannheim with the active polarizer unexcited. A comparison of the vertically polarized pattern for the double parasitic antenna system II and the active polarizer (Figs. 9-9 and 9-10) show that the two patterns do not agree. However, because of the time element it was decided that additional positioning of the active polarizer should not be attempted but instead efforts should be made to reduce the polarization error in a particular direction (O = 90~) and at a particular elevation angle (0 = 86.9~) to determine the effectiveness of the active polarizer in controlling the polarization error. Since much of the previous work had been performed along the azimuth angle of 900 it was decided that the polarization error should be reduced to a minimum along this radial and at an angle of 3.1~ above the horizon (0 = 86.90). The aircraft was flown along a 3.10 depression angle starting approximately 35 miles from the station to within a mile of the station. During this flight radio communication was maintained between aircraft personnel and the ground personnel. Instructions were radioed from the aircraft to the ground as to the settings of the polarizer attenuators and phasors. The procedure used was first to adjust the attenuators in IdB steps until a minimum polarization error was observed. Then the phasor was adjusted in 10~ steps for a similar indication. This procedure was repeated for two flights after which it was felt that the polarization error had been reduced to a minimum (+2.50). The aircraft was then flown down the depression angle (third flight) with no adjustments being made and the polarization error recorded as a function of distance from the VOR station. A plot of these data is shown in Fig. 9-11. It is inter108

0 -15 -30 13.2, -45 62 70 80 90 (0 in degrees) = 900 Frequency = 109 MHz - Vertical Component FIG. 9-9: Field Strength for Active Polarizer No. 2 (Mannheim). 109

0 -15 I vI: 900 Frequency = 109 MHz l- Horizontal Component --- Vertical Component - 45 62 70 80 90 (0 in degrees) FIG. 9-10: Field Strength for Double Parasitic Loop Counterpoise Antenna System II, (Mannheim Active Polarizer Unexcited). 110

30- A c~~-d3~~~~~~~ 0=86.90.H 0 =90~ l g Frequency = 109 MHz 20 -2 b0 o Attenuator = -4 dB ~ 9 Phasor = 60 0 1 2 3 4 5 6 7 8 9 10 20 30 Distance from VOR (Nautical Miles) FIG. 9-11: Polarization Error for Double Parasitic Loop Counterpoise Antenna System II (Mannheim/Active Polarizer Excited).

esting to observe that the polarization error is relatively small at low elevation angles, however, as the aircraft approaches the station the polarization error builds up to a maximum of +6~, approximately 3 miles from the station. The cause for this buildup is unknown. A suggested cause may be that to fly along the 3.1~ depression angle it was necessary for the pilot to have before him the altitudes_ he should be at as he approached pre-specified mile markers from the Mannheim VOR. These mile markers were the measured horizontal distances of the aircraft from the Mannehim VOR. These data were radioed to the pilot from a precision ground-tracking radar (EAIR) that skin tracked the aircraft. Therefore, it was necessary for the pilot to keep the aircraft in a shallow dive towards the VOR station (by adjusting his altitude at the mile markers) and it is conceivable that as he approached the station he was not able to maintain the proper altitudes necessary to be on the 3.1~ slope. It should be noted here that the 3.1~ null associated with the horizontally polarized energy radiated by the Mannheim facility is approximately 0.5~ wide. As a consequence to ensure that the aircraft remains in the null, it would be necessary for the pilot to adjust his altitude to within + 10 percent. After the settings of the attenuators and phase shifters associated with the active polarizer were established as described in the previous paragraph, several radials were flown while the aircraft was held to a constant altitude of 6575 feet. The purpose of these flights was to determine the manner in which the polarization error varied as a function of the elevation angle. Figures 9-12 a-d show the polarization error as a function of elevation angle for the following radials: f = 90~, 180~, 220~, and 335~. It is interesting to note that along the 90~ radial a minimum in the polarization error does occur at approximately 30 above the horizon. However, outside of this region the polarization error is found to be excessive. 9.6 Discussion On the basis of the results given in this chapter, it is found that a single FAA passive polarizer is not capable of reducing satisfactorily the polarization errors associated with the double parasitic loop counterpoise antenna system II. A passive polarizer with more than four parasitic elements should be investigated for further reduction of polarization errors in parasitic loop antenna systems. It is also recommended that the parasitic loop system II, with passive polarizer adjusted as in Fig. 9-4, be flight tested for scalloping data. Careful considerations should be given to the use of two passive polarizers in the antenna system. As discussed before, a single polarizer whether active or passive is not likely to do a satisfactory job on the parasitic loop counterpoise VOR antenna system. With regard to the active polarizer, it can be said that it is relatively easy to adjust the polarization error in the aircraft when the active polarizer is used in the VOR ground station antenna system. It has been shown that using this technique the polarization error can be reduced to a reasonably small value in a 112

30 T' ~ A) 0=90~ JJc.L~~ t Frequency = 109 MHz c- Attenuator = -4 dB 20 0 Phasor= 60 20 o 10 - N '4 62 70 80 90 Angle (0 in Degrees) 30 -Td^~ t | B) = 180~ ICg~~~f~ aSFrequency = 109 MHz Ea Attenuator = -4 dB 20- 0 Phasor =60 <. \ 10-Jy1 N / 62 70 80 90 Angle (e in Degrees) FIG. 9-12a, b: Polarization Error versus Elevation Angle for Double Parasitic Loop Counterpoise Antenna System II (Mannheim, Active Polarizer Excited). 113

30 O / C) 0 - 2200 I o IFrequency 109 IMHz 20 - Attenuator = 4 dg / / k WINk"~~ lPhasor- 60 70 7~ ~ ~80 Angle (0 in degrees) 30 re)90 30T ~ 2 | D) 0= 3350 |0- Frequency - 109 Hz 20 | Attenuator= - -4 dB -I P r ~ IPh asor 60 o C80 Angle (0 in degrees) 90 FIG. 9-12c, d: Polarization Error versus Elevation Angle for Double Parasitic Polarizer Excited). e 114

minimum amount of time and with a minimum amount of effort. This was done for one specific vertical angle only. However, the results shown in section 9.5 indicate the existence of large polarization errors in certain directions. Time did not permit us to investigate this problem further. It is believed that insufficient time has been spent working with the polarization problems associated with the parasitic loop counterpoise antenna system. It is thus inappropriate to draw any definite conclusions as to the manner or to what degree the polarization errors could be reduced for a standard VOR system using double parasitic loop counterpoise antennas. It is recommended that tests be continued using the active polarizer. As mentioned in section 9.1, the dominant source of the polarization error is the cross-polarized radiation from the standard VOR antennas. We therefore feel that a theoretical investigation of the cross-polarized radiation fields from standard 4-loop VOR and double parasitic loop counterpoise antennas will be of fundamental importance here. The results of such investigation will be immensely helpful in the proper design and adjustments of a polarizer so that the vertical components of the field produced by the test antenna may be reduced to the desired value. 115

x APPLICATION OF PARASITIC LOOP COUNTERPOISE ANTENNA TO VOR SYSTEM 10. 1 Introduction In the previous chapters we have discussed in detail the radiation characteristics of parasitic loop counterpoise antennas. Satisfactory theories have been developed for the radiation fields produced by such antennas operating in carrier and side band modes. These new antennas are compatible with the conventional VOR systems in the sense that a conventional VOR antenna can be converted into the new system by introducing parasitic loops of proper dimensions at the appropriate heights above the counterpoise (Sengupta and Ferris, 1972). We have already seen in Chapter VIII that such a conversion does have some distinct advantages. In the present chapter we discuss in greater detail the application of parasitic loop counterpoise antennas to conventional VOR systems. It will be shown that such antennas are capable of bringing out superior performance from the existing conventional VOR systems. 10. 2 Limitations of Conventional VOR Systems The performance of a conventional VOR system located in ideal terrain has been discussed in section 1.2. In an actual situation the scattered and/or specular reflections from the ground and other nearby objects (in-fact whenever there exists a multipath between the VOR station and the flying aircraft) combine with the desired signals at the aircraft. The overall effect of this is to disturb the direct relationship between the previously mentioned phase difference and the bearing of the aircraft and thereby produce omni-range course scalloping. This causes siting errors and scalloping in the bearing indications of a VOR. Detailed discussions on the scalloping amplitude and frequency under various situations are given by Anderson and Kepry (1952). In general it can be said- that the phenomenon of scalloping and associated effects depend mainly on two factors: (i) the free space vertical plane pattern characteristics in the directions near and below the plane of the counterpoise, and (ii) the nature of the scattering properties of the disturbing objects and of the multipath sources. The second factor is more or less beyond the control of the 116

designer. There are a number of locations where the antenna must be installed at a considerable height above the ground in order to avoid interference from surrounding objects such as heavily wooded or built-up areas (Winnick and Brandewie, 1970). In such cases, the first factor, i. e. the vertical plane antenna pattern characteristics near the horizon become quite important in determining the accuracy of the existing conventional VOR bearing indications. From the viewpoint of scalloping effects, the ideal requirement on the free space vertical plane pattern of a VOR antenna would be such that the response of the antenna goes abruptly to zero in all directions below the horizon, i. e. the field gradient at the horizon would be infinite. As mentioned before, the field gradient obtainable from existing conventional VOR antennas using 52' diameter counterpoises is about 3dB/6~ which may be considered to be rather low. This is the fundamental reason why an elevated conventional VOR stations located in non-ideal terrain tend to produce inaccurate results in the presence of multipath signals. Another undesirable phenomenon that is encountered in a conventional VOR is the appearance of nulls in the vertical plane patterns of such antennas elevated above ground. Assuming a perfectly conducting infinite ground plane, it is easy to show that for the horizontal polarization due to reflection from the ground there will appear some minima and maxima in the vertical plane patterns. -The number of these minima (or maxima) will depend on the height of the antenna above the ground. Depending on the free space elevation pattern of the antenna, some of these minima in the pattern may in some cases actually become nulls. It is quite straightforward to show that the radiation from the antenna in directions below the horizon are mainly responsible for such minima or nulls in the pattern. Usually the minimum in the pattern nearest the horizon is deepest. Siting errors and scalloping effects become most intense in these null directions. It is again obvious that such undesirable effects are produced by the conventional VOR system because of the unfavorable vertical plane characteristics of the antenna near the horizon. 10. 3 Application of Pprasitic Loop Counterpoise Antennas It is evident from the discussions given in the previous section that an antenna having a large field gradient, if incorporated into the present-day conventional VOR system, would produce at least two-fold improvement in the overall system performance: (i) it would reduce the multipath signals caused by scattering objects in the vicinity of the VOR station, and (ii) it would reduce the depths of the minima that appear in the vertical plane patterns of a VOR antenna above a perfectly conducting ground plane and thereby improve the accuracy of the system. 117

As mentioned before, the field gradient of a conventional VOR antenna with a 52' diameter counterpoise is about 3dB/60. A much larger field gradient is necessary if one desires to obtain better performance from the system. Theoretically it is possible to improve this gradient by increasing the diameter of the counterpoise (Sengupta and Ferris 1970). This increase is very slow, e.g. as discussed in Chapter II, the field gradient of a similar antenna with a 150' diameter counterpoise is about 5. 5dB/6~. Such a technique of improving is thus considered to be unwieldy mechanically and expensive. From the discussions of the radiation characteristics of parasitic loop counterpoise antennas given in Chapters mII, IV and VII, we single out the following two properties of an optimum double parasitic loop counterpoise antenna: 1) the antenna is capable of producing a field gradient of about 23dB/6~ at the horizon. This field gradient is much larger than that of a conventional VOR antenna. 2) the side band mode vertical plane pattern of a double parasitic loop counterpoise antenna above a perfectly conducting ground has a 3dB minimum near the horizon whereas for the conventional antenna the depth of the corresponding minimum is about 10dB for the given height of the antennas above ground. Thus it can be said beyond any doubt that an optimum double parasitic loop counterpoise antenna when used in a conventional VOR system will greatly reduce the scalloping and other associated errors that appear in the bearing indications of a flying aircraft. This should be weighted against possible decrease in distance range at low altitudes. An additional advantage of the parasitic loop concept is that it provides a way for easy and inexpensive modifications of the existing VOR antennas to obtain a large gradient performance. 10.4 Discussion In the above we have discussed briefly the performance of existing VOR systems and their limitations under unfavorable siting conditions. It has been clearly demonstrated that an optimum double parasitic loop counterpoise antenna would greatly improve the performance of the existing conventional VOR system located in environments where multipath propagation of some kind exists. On the basis of the results discussed in chapter VIII, it can be concluded that such an antenna located 75' above ground will reduce the scalloping errors of a conventional VOR system by a factor of 6 to 1. Thus, on a given site if it is 118

necessary to mount the VOR antenna on a tower, the use of parasitic loop counterpoise antennas will give superior performance. However, the polarization errors associated with the antenna has been found to be large. As mentioned in chapter IX, efforts should be devoted to reduce the polarization error so that the new antenna system may be brought into use in a practical standard VOR system. 119

XI CONCLUSIONS AND RECOMMENDATIONS 11.1 Conclusions The radiation fields produced by conventional VOR and parasitic loop counterpoise antennas have been investigated both theoretically and experimentally. Theoretical expressions for the side band mode radiation patterns produced by conventional Alford loop counterpoise VOR antennas and by single parasitic loop counterpoise antennas have been obtained by applying the concepts of geometrical theory of diffraction and the results of Sommerfeld's theory of halfplane diffraction. Within the range of approximation the agreement between theory and experiment has been found to be very good. The theory of double parasitic loop counterpoise antennas has been developed by generalizing the above theory for single parasitic loop systems and by taking into account the effects of mutual interaction between the parasitic loops. It has been found that if the separation between the parasitic loops is larger than a wavelength, the mutual interaction effects may be neglected. The agreement between theory and experiment has been found satisfactory within the range of approximation. On the basis of theoretical parametric studies of the double parasitic loop counterpoise antenna patterns, we have developed two optimum antennas using 150' and 52' diameter counterpoises. The antennas have been optimized in the sense that the free space side band mode elevation plane patterns possess maximum field gradient at the horizon. Theoretical optimum field gradients have been found to be about 23dB/6~ in both cases. These findings have been confirmed by results obtained from model measurements. The design and the method of mechanical implementation of a full scale optimum double parasitic loop antenna with 150' diameter counterpoise have been carried out. The conventional VOR antenna at NAFEC has been transformed into the above optimum system by installing two parasitic loops at appropriate places. The performance of this new antenna has been tested by ground and flight measurements at 109 MHz. The results of the full scale measurements have verified the validity of the design procedure used and have confirmed the predictions arrived at from theoretical considerations. Finally, this new VOR antenna system has been flight tested in order to compare its performance with that of a conventional VOR antenna. It has been found that the new antenna system reduces the scalloping errors in the bearing 120

indications of a flying aircraft by a factor of 6 to 1. The distance range of the VOR station with a new antenna has been found to be comparable to that of the same station using a conventional antenna. Although the polarization errors associated with the parasitic loop system have been found to be large in directions of 0 > 80~, we believe that this error can be reduced to acceptable limits by improving the existing passive polarizer and by adding an active polarizer. We have discussed only the essential flight test results which are pertinent to the application of double parasitic loop counterpoise antennas to a standard VOR system. Further discussions of the flight test results will be given in a separate report by FAA. It is concluded that a properly designed double parasitic loop counterpoise antenna will greatly improve the accuracy of conventional VOR systems. Where the terrain surrounding the VOR station is not ideal, the use of such an antenna mounted at a proper height will definitely bring out superior performance from the system. The most significant contributions and findings of the present research are enumerated below. 1) Development of an accurate theory for conventional VOR antenna radiation patterns. 2) Development of satisfactory theory of double parasitic loop counterpoise antenna patterns and the optimization of such antennas with regard to the horizontal field gradient characteristics. 3) Demonstration of the fact that optimum double parasitic loop counterpoise antennas definitely reduce by a significant amount the scalloping errors associated with conventional VOR systems located in a non-ideal environment. In such situtations, therefore, we feel that the use of a double parasitic loop counterpoise antenna rather than the conventional antenna should be seriously considered. We therefore conclude that the purpose of the present investigation as given in Chapter I has been fulfilled. 121

11.2 Recommendations for Further Work Although we have discussed in detail the radiation characteristics of parasitic loop counterpoise antennas and the application of specific antenna configuration to a conventional VOR system, we feel that further work should be done to exploit the parasitic loop concept to the fullest extent. In particular we recommend the following. 1) Investigate the double (or multiple) parasitic loop counterpoise antennas when the parasitic loops are located in the same plane. In certain cases this configuration may be preferable mechanically. 2) It is conceivable that desirable performance may be obtained from a VOR antenna with smaller counterpoise by judiciously placing one or more parasitic loops above it. Reduced size counterpoise will provide definite advantages in many cases. 3) Investigate the radiation characteristics of an array of parasitic loops with VOR Alford loops (or loop) as the only excited element and having no counterpoise. 4) The polarization error associated with a conventional VOR system using double parasitic loop counterpoise antennas should be studied further. 5) The general application of large gradient antennas to VOR systems under various situations should be investigated in further detail. Since our polarization error studies are incomplete, we strongly recommend that the item (4) above be investigated further before making a final evaluation and judgement on the application of double parasitic loop counterpoise antennas to a conventional VOR system. 122

ACKNOWLEDGME NT We are pleased to acknowledge the benefit of several helpful discussions with Mr. Sterling R. Anderson and we acknowledge also the valuable counsel and suggestions by Professor Ralph E. Hiatt. Our thanks are due to Mr. E. Bublitz for his help in carrying out the model measurements and in the construction and assembly of the full scale antenna. We also wish to acknowledge the work of Dr. A. T. Lin who prepared the computer programming for this report. Finally, we are grateful to the Federal Aviation Administration for making available their experimental facilities at NAFEC and for providing assistance during the full scale measurements. The cooperation and help obtained from Mr. S. Taggart and Mr. E. Lind at NAFEC are gratefully acknowledged. 123

REFERENCES Anderson, S.R., H. F. Keary and W. L. Wright (June 1953), The Four-Loop VOR Antenna, T.D.Report No.210, Civil Aeronautics Administration Technical Development and Evaluation Center, Indianapolis, Ind. Anderson, S.R. (1965), "VHF Omnirange Accuracy Improvements," IEEE Trans., AME-12, No. 1, pp. 26-35. Anderson, S.R. and H. F.Keary (1952), "VHF Omnirange Wave Reflections from Wires, " Civil Aeronautics Administration Technical Development Report No. 121, Technical Development and Evaluation Center, Indianapolis, Ind. Federal Aviation Administration, Department of Transportation (1968), Handbook: VOR/VORTAC Siting Criteria, No. 6700.11, Systems Research and Development Service, Washington, D.C. Hurley, H. C., S. R. Anderson and H.F. Keary (1951), "The Civil Aeronautics Administration VHF Omnirange, " Proc.IRE, 39, No. 12, pp. 1506 -1520. Keller, J.B. (1962), "Geometrical Theory of Diffraction," J.Opt. SocAmer., 52, No. 2, pp. 116-130. Sengupta, D. L. and J. E. Ferris (1970), "On the Radiation Patterns of Parasitic Loop Counterpoise Antennas," IEEE Trans., AP-18, No. 1, pp. 34-41. Sengupta, D. L. and J.E. Ferris (1970a), "VOR Parasitic Loop Counterpoise Systems-I, " The University of Michigan Radiation Laboratory Report 3051-3-T, Interim Report. Sengupta, D.L. and J.E. Ferris (1971), "VOR Parasitic Loop Counterpoise-I." Interim Report No. 6, Contract FA69-WA-2085, Project 330-001-03N, The University of Michigan Radiation Laboratory Report 3051-6-T. Sengupta, D. L. and J.E. Ferris (1972), "A Double Parasitic Loop Counterpoise Antenna and its Application to Aircraft Navigation Systems", IEEE Trans. AP-20, No. 1, pp. 97-99. 124

Sengupta, D.L. (1971), "Theory of VOR Antenna Radiation Patterns, " IEE London, Vol. 7, No. 15, pp. 418-420. Sengupta, D. L., J.E. Ferris and V. H. Weston (1968), "Theoretical and Experimental Investigation of Parasitic Loop Counterpoise Antennas," The University of Michigan Radiation Laboratory Report 8905-1-F, FAA Report SRDS RD-68-50. Sengupta, D. L. and V. H. Weston (1968), "A New VOR Antenna System, " Proc. IEEE 56, No. 7, pp. 1284-1286. Sengupta, D. L. and V. H. Weston (1969), "Investigation of the Parasitic Loop Counterpoise Antenna," IEEE Trans., AP-17, No. 2, pp. 180-191. Sommerfeld, A. (1954), Optics, Academic Press, New York, pp. 247-265. Westman, V. (1956), Reference Data for Radio Engineers, Fourth Edition, pp. 696-698. Winick, A.B. and D. M. Brandwie (1970), "VOR/DME System Improvements," Proc. IEEE, 58, No. 3, pp. 430-437. 125

APPENDIX A THE RADIATION FIELD OF A CIRCULAR LOOP CARRYING A NON-UNIFORM HARMONIC CURRENT A. 1 Introduction The radiation field produced by a circular loop carrying a non-uniform current is discussed theoretically in this appendix. The problem under investigation has direct bearing on the determination of the radiation field of a parasitic loop counterpoise antenna with a figure-of-eight type of excitation in the azimuthal plane. This type of excitation is used in the double parasitic loop counterpoise antenna operating in the side band mode. The non-uniform excitation causes the induced currents in the parasitic loops to be non-uniform. The performance of parasitic loop counterpoise antennas with non-uniform excitation cannot be explained by the theory developed for similar antennas with omnidirectional excitation. A. 2 Nature of Excitation In a practical VOR antenna system, the figure-of-eight pattern in azimuth is obtained by placing two Alford loops side by side and exciting them with equal but out of phase signals. Let us consider two small circular loops (i. e. radius of the loop < < X ) carrying the currents of the form I eWt and I ei(t (A. 1) o o be oriented along the x-axis as shown in Fig. A-1. The two loops lie in the x-y plane. The two loops are separated by a distance 2d and the phase difference ' between their currents is kept arbitrary for the present. It can be shown that the far field produced by the system at the point P(Ro, 0, 0) is polarized in the p-direction and is given by: i(kRl- ) E r I (ka )2 e 2 sinO coslkd sin0 cos0 + (A.2) o o 2 R — where ro is the intrinsic impedance of free space, k = 27T/X is the propagation constant in free space. 126

z P (Ro 0, 0) Alford loop Alford loop I X~ x FIG. A-i: Coordinate System Used. If V = -T, then eq. (A. 2) reduces to ikR ka 2 e 0 E= i2rnO(I(2 eR sin0 sin kd sine cos. (A. 3) p 0 02Z s\ ~ - Equation (A. 3) indicates that in the azimuthal plane (=constant) the far field pattern is a figure-of-eight having maxima along Ox0 and ir. Usually kd << 1 and under this assumption we can simplify (A. 3) as follows: ikR ka 2 e 2 E= i27 ()2 — e (kd) sin 0 cos. (A. 4) Any parasitic loop placed with its axis along the axis will carry an Any parasitic loop placed with its axis along the z-axis will carry an induced current proportional to the field given by (A. 4) or (A. 3) as the case may be. To simplify our analysis we assume that the parasitic current in the present case is of the form: 127

I = cos a, (A. 5) 0 where I is a constant and 0 is measured around the loop, the origin being at the x-axis. Equation (A. 5) physically means that I(0) vanishes at 0 = + Tr/2, where it reverses direction, so that the currents in the range lr< < 7r < are always counterclockwise when the currents in the range are clockwise. This may be looked upon as a dipole mode such that the charge density on the loop is q(0) oC sin0. This means that the loop is oppositely charged at 0=7r/2 and 0 = -ir/2 and the current oscillates in synchronism on the two halves much as in two parallel dipoles that are driven in phase. Notice that this is true regardless of the fact whether the parasitic loop is large or small. A. 3 Far Field Expressions In this section we obtain the far field produced by a circular loop carrying a current of the form given by eq. (A. 5). The loop is oriented in the x-y plane as shown in Fig. A-2. To obtain the far field it is convenient to determine the vector potential i produced by the current at the far field point P(Ro, 0, 0) and then obtain the field from the potential. With time dependence eiwt and using standard notation the following expressions define the relationships between the fields and the vector potential. =. A E -iwrox(roxA)=i AO + AJ, (A. 6) B =ik (rlxA) =ik[ A^- A 0, (A. 7) A4 A where r,,, are the unit vectors in Ro, 0 and 0 directions respectively. The components A0 and Ap of the vector potential in terms of the rectangular components are: A= Ax cos0 +Ay sin cos, (A. 8) A =-A sinp+A cos0. (A.9) ft x y In the present configuration, as shown in Fig. A-2, Ax and Ay are given by the following: 128

z P(Ro, 0) ^ / 8 g^ K ~00) = Io cos 0' FIG. A-2: Orientation of the circular loop. ikR 2ir x 4 -ik B sine cos(-) (A. 1 ikR 2r o -ik B sine cos( A- - i(, )e-ik B sine c - cos(-) do0 (A. 11) y 47r R o o0 where po is the permeability of free space. After introducing (A. 5) into (A. 10) and (A. 11), the following two equations are obtained: ikR 2-r psBI o 0o0 129

ikR 2ir B BI o o o e -ik B sinecos(0-0') OA=-g r- I(1 e (1 +cos 20') d0'. (A. 13) y 8 0 j 0o To evaluate the integrals in (A. 12) and (A. 13), we make use of the following result: 27r i(n + 1)0e ikBsinecos(0-0') d 2i i(n )j (kBsin e e do 27r -1 e J (kB sine), nJQ -ia e.i, (A. 14) where Jn+ 1 is the standard notation for the Bessel function of the first kind. Using (A. 14), we obtain the following from (A. 12) and (A. 13). ikR p BI o A = o e J2(kBsin0) sin 2 (A. 15) x 4 R 2 ' 0 ikR o- BI o Y 4 0 e - J- (kBsine) -J2(kBsine)cos 20J (A. 16) 0 After introducing (A. 15) and (A. 16) into (A. 8) and (A. 9) and with some algebraic manipulation, we obtain ikR p BI o J (kBsine) A-o oe cos sin (A. 17) 0 2 R (kBsin) (A17) uBI o ~A= o o e J'(kB sine) cos 0, (A. 18) % 2 R 1 where the prime in (A. 18) indicates differentiation with respect to the argument. Using eq. (A. 6) along with (A. 17) and (A. 18), we obtain the two components of the electric field in the far zone as given by the following: ikRo J (kB sine) E0 ioI( -) R (kBsin) cose sin, (A. 19) 19 00 2 R, (kB sine) ikR kB e 0 E=i i I (-2 ) - J' (kB sine) cos0. (A. 20) E i 00Io 2 R 1 With uniform current, a circular loop does not produce any 0-component of the electric field. Thus, the existence of E0 in the present case is attributed to 130

the non-uniform current carried by the loop. Equations (A. 19) and (A. 20) have been used in Section 3. 4 to derive the far field produced by a non-uniformly excited single parasitic loop counterpoise antenna. A. 4 Discussion On the basis of eqs. (A. 19) and (A. 20), we make the following comments with regard to the radiation field produced by a circular loop carrying a nonuniform current I=Iocos. (i) Near 00 0~ the Bessel functions in (A. 19) and (A. 20) may be replaced by their small argument values, i.e. J'(x) - 1/2 and J1(x) / x l/2. Thus the total far field may be written as ikR E=E +E 00 2ir7 I ( cos sin0+ cos0) 2 I )R 2(e ooze 0 ikR o =~ I kB e 1 A 00ir i ( R e (A.21) Equation (A. 21) means that near the axial region of space (6m0~) the far electric field is not equal to zero and it is polarized along the y-direction. (ii) In the 0=0~ plane, i. e. in the vertical plane containing the directions of maxima of the figure-of-eight excitation, the field is polarized in the idirection and is given by: kB e 0 E _O, E= iro I (-) - J' (kB sin). (A. 22) u 0 0oo 2 0 1 (iii) In the p = 7r/2 plane, i.e. in the vertical plane containing the directions of minima of the figure-of-eight excitation, the horizontal (i. e. 0-component) component of the electric field is identically equal to zero and the electric field is given by kB R o J (kB sine) E -,0 Ee iI( 2) R (kB sin) cos,. (A. 23) 019 o 2 R (kB sinO). 0 (iv) In the 0 = r/4 plane ikR o J (kB sine) kB e 1 cos0 E io I (-) (A. 24) 9 oo 2 R0 (kBsin0)? 131

ikR io J'(kB sine) E irl I ( kB ) 1 (A.25) (v) In the horizontal plane (e = r/2), ikR kBE 0 E Q 0, E=iro I ( ) e J (kB)cos. (A. 26) = 0 2 R 1 The important findings of the present investigation are that the non-uniformity of the current in the circular loop produces the following two effects: (i) the field is non-zero in the axial direction, and (ii) there exists a cross-polarized component of the field. It is thus anticipated that a parasitic loop counterpoise antenna operating in the side band mode may give rise to appreciable amounts of crosspolarized components in certain directions of space. The results given here will be found useful in the analysis of the cross-polarization characteristics of parasitic loop counterpoise antenna systems. 132

APPENDIX B MUTUAL COUPLING EFFECTS IN PARASITIC LOOP COUNTERPOISE ANTENNAS B. 1 Introduction This appendix deals with the theoretical investigation of mutual coupling effects in a double parasitic loop counterpoise antenna. In Chapter IV an approximate theory was developed for the double parasitic loop counterpoise antenna by neglecting the effects of mutual coupling. There, the far field radiation pattern produced by the antenna was obtained by simply superposing individual free space fields. This theory explains with a fair amount of accuracy the far field for the cases when the spacing between the parasitic elements is large compared to wavelength. In a situation where the loops are not widely spaced, the interaction between the parasitic currents may become quite important. It is the purpose of this appendix to develop theoretical expressions for the parasitic currents and also for the far field produced by a double parasitic loop counterpoise antenna by taking into account the effects of mutual coupling. B. 2 Parasitic Currents Consider a double parasitic loop counterpoise antenna as shown in Fig. B-2. It is assumed that the antenna is operating in the carrier mode. I Parasitic loops -. -o! cr iv rB2 0 0 iO I _0 I ~, O 2b f.1 44- 4 ---Alford loop L// /)/ // ///// //////.- Counterpoise FIG. B-l: Double parasitic loop counterpoise antenna. 133

The Alford loop situated at a height h above the counterpoise is the only excited element. Let IT and IT be the total currents in the two parasitic loops maintained by the excited element. Symmetry of the system and the nature of the excitation dictate that the distribution of the current along each parasitic element will be constant. Let us assume that in the absence of mutual coupling between the parasitic loops, the induced parasitic currents will be represented by I? and I respectively. The method of determining IO and I for the above configuration 1 2 has been discussed elsewhere (Sengupta et al, 1968). By taking the mutual interaction into account we can write T O T I1 I + 21 I2 (B. 1) T O T I2 =I +K12 (B.2) 2 2 12 where K12 and K21 may be defined as the coefficients of coupling for the mutually induced currents. Notice that these are not the conventional coefficients of mutual coupling and hence K12 K21. From (B. 1) and (B. 2) the following are obtained for the parasitic currents. O+K O T +K IT IT i 21 2 (B. 3)! 1-K21K12 O 02 IO+K I T 2 12 1 I - K1 (B. 4) 2 1-K K 12 2 In general K12,K21 are complex constants for a particular configuration of the antenna and |K12, K211 < 1. Thus the problem reduces to the determination of these two coefficients. We discuss this in the next section. B. 2. 1 Determination of the Coupling Coefficients K12, K21 We outline here the basic mathematical steps involved in obtaining K12,. For this purpose we represent the configuration as shown in Fig. B-2. In this representation the first parasitic loop is replaced by a point source of suitable strength placed at a height H1 above the counterpoise. The current in the first parasitic loop being IT, the field produced by the current at the point P located on the second parasitic loop is given by prikr1 ikr' E () i ( ) L1(kBlsinO12) er -J(kBs inO02) I. L- 1~~~~1342 J(B.5) 134

Ti9 r^ p <I Hl<I) |9l2/ H (2 P FIG. B-2: Rays contributing to K12. where rl is the intrinsic impedance of free space, k= 27r/X is the propagation constant in free space, 2 2 2,2 2 2 r12 = B2 +(H2H); (r) B 2 (H2+H)2 (B. 6) B2, B2 sine; sin = - (B.7) 12 r12 12 r'2 12 J1 is the Bessel function of the first kind and first order. In eq. (B. 5) only the direct and reflected fields due to the parasitic current IT are used to obtain the incident field at P produced by this current; the contribution to the field at P due to diffraction effects at the edges of the counterpoise are neglected for the present. If necessary, they will be taken into account later. The current induced on the second parasitic loop due to the field Enc(P) is obtained by using the following relation. T' A 27 inc 2 i7okM Ih i ~kwM ^E (P), (B. 8) where M = 0. 577 + In (- )- - (B. 9) 2 2 135

After introducing (B. 5) into (B. 8) we obtain the following expression for K12. ikr ikr' 27 kB 12 k12 _K12 27r ((kBlsinOl2) k - -J1(kB sinel. (B. 10) K2-iM 2 L 1 12 kr 1 1 12 kr' 2Bln O) 1212 kr12 Following a similar procedure it can be shown that the other coupling coefficient K21 is given by: ikr ikr! 2M kB 2 e 21 e 21 <-. — ( ) kB sine ) - -^ (kB sine' e(B. 11) K21= iM ("2 (kB2sin021 kr21 kr'1 I. 2 1 21.J where 2 2 2 2 2 2 r 1=B +(HH1) (r) B +(H+H1) (B. 12) 21 1 2 1 '(21 1 2 1 B1 BI sin2= +-; sin21= - (B. 13) 21 r21 21 r21 This completes the derivation of expressions for the coupling coefffcients. In the next section we derive the explicit expressions for the parasitic currents due to the fields produced by the Alford loop carrying a current of magnitude Io B. 2.2 Expressions for the Parasitic Currents It can be shown (Sengupta et al, 1968) that in the absence of mutual coupling the current induced in the first parasitic loop is given by I1 = ka )2 +Q (B. 14) where a is the radius of the excited loop and, (kB) kr ikr pi iM 2 2 — 21 (B. 15) 1L.(kr) (kr)J 1 2 136 136

2 ikr T IT 7r (kB) 1 1/2 i(2kBl+) 1/2 i(2kH_____ e 2 j BL 1 4 1 e 16) Q1- M2 (krl)2, M 2 (kr) kB1 e rkH1(B. 16) 2 2 2 2 2 2 rl= B + (H -h); r2 B1 + (H+h). (B. 17) Similarly, the current induced in the second parasitic loop due to the field produced by the Alford loop only is given by I2 = Io( ) )2 + Q2 (B. 18) where2 2hreB2) - ikr' ikr' 2: iM l ~ -(k 2 (B. 19) (kr ) (kr J 1 2 (kB) ikr' 1 1/2 i(2kB2 +) 12 i(2kH2- ) Q2 M2 (kr)2 2 e 12 ~TF~ e 1irkH2 e 2 4], (B. 20) (r) =B2+ (H2-h); (r2 =B2 + (H+ h)2 (B. 21) 1 2 2 2 2 After using (B. 3), (B. 4), (B. 10), (B. 11),(3. 14) and (B. 18), the parasitic currents 1T and IT are obtained as follows: 1 2 I =Ika2 ) -(P1+ )+K 21(P2Q (B. 22) 1 0 2 1-K12 K21 TI ( ka 2 1 r +)+ K(P l (B. 23) 2 ( 23)1 12 21 reduce tons (B. 2214) and (B. 2318) res expressed so that they may be computed numeri-y. cally. It should be noted that in the absence of mutual coupling, (B. 22) and (B. 23) reduce to (B. 14) and (B. 18) respectively. B. 3 Far Field Expressions In this section the far field produced by the double parasitic loop counterpoise antenna will be given. The method of obtaining the expressions is similar to that discussed in the case of a single parasitic loop counterpoise antenna (Sengupta and Weston, 1969) and hence will not be repeated here. All the expressions are arranged such that they may be programmed for numerical computation. The _ 137

far field is expressed formally as: i(kR-3 ) ka22e E ar I ( ) S(0), (B. 24) whereA s(e)= s ^() + si(e) +s6(e). (B. 25) In the above equations S(0) is identified with the complex far field pattern of the antenna; the three terms on the right hand side of (B. 25) are the complex far field patterns produced by the Alford loop, the first and second parasitic loops above the counterpoise. Explicit expressions for the three terms in (B. 25) are given below for future reference. SA(e) =~F~(0)sin -ikAsin0 Icosel sinikr [ 2 ^rkr sin0'( 5A () tFosin eJikAsinO e L2(e), (B.26) ~2; 7~~~/ i(-kAsine) c3/2 3/2 3/2 i(-kA cos -sin n/ ikAsine cos L~ (0)=,e.... r. lcos- -sine Je o e o-sin0 1Oosi sin, ' (B. 27) pi t2 P2 t2 ikr sin(0-p ) 1 i t ikr sin(0+ ) ) 2 o 2 F~ ()=e e dt -e e 2dt, (B.28) -00 -Q kro 1/2 0- - p=2(kr) 1/ cos ( (B. 29) kro /2 _o-e+_ P= 2( - ) cos (- ) (B. 30) r2 A 2 h; tan = (B. 31) O ao p k=B;I S( 2(1-K K ) r +Q )+K21(2 2 F1(e) (B. 32) 12 21 where Pi, Q1 are as given by eqs. (B. 15) and (B. 16) and 138

~P1 Jl(kBlsin0).. 0 cos0 sin( ) ikrp 1 1 P -ikAsine 2 i1, F(6)} r - F 1(e)e + e L1 (), (B. 33) 1 2~ {^ 1 bTrkr sine 1 i(f -kAsine) Y2 -1 OTpL pine 1/2 ikAsine 2Jl(kBlcos0p)C )cos (0 )j( ce ~ _ 1 cos op+sine L 1 ()=-./As' 1 ikrpsin(e-Op,) ' "rl ikrspl-sin(- ) F1()=e f e 2dt -e f I e 2 dt, (B. 34) -OD -00 p= 2(- 1)Y cos( 2pl ) ' (B.37) re dt -e +2 (B. 38) 1 Pta= 2= (B.39) 2 2 kB P 2 S2 (e)= P 2+Q2)12(P+Q)F2 ) (), (B. 40) 2 =A1-K12K2+) 2 2 12 1 1 2 where P2, Q2 are given by (B. 19) and (B. 20), F2(e) is given by (B. 33) - (B. 39) with the parameters Hi, B1 replaced by H2, B2 and K12, K2l are as given by (B. 10) and (B. 11) 139

B. 4 Numerical Results Expressions for the complex far field pattern produced by a double parasititic loop counterpoise antenna in the presence of mutual effects as discussed above, are: S(e)= SA() + S (0) + S(0) (B. 25) where p kB 1 (1) 2(+Q1+K 21(P2Q2)] () ' (B. 32) kB S2(e) = 2 P2+Q2+K12(Pl+Ql) F2(), (B.40) where all the other notations are as explained in the previous sections. In the absence of mutual effects, eqs. (B. 32) and (B. 40) reduce to (K2=K =0 ) 21 12 S (0)= (P + Q1) F1() kB1 (B. 41) S(0) = (P2 +Q2) F(0) kB2/2 (B.42) It is instructive to study the orders of magnitudes of the various quantities K12, K21, P1, Q1, P2 and Q2 which are constants for a specific configuration of the antenna. Let us consider the case of a double parasitic loop counterpoise antenna operating in the carrier mode. The antenna has the following parameters: kh = 2.75, kb = 0.287, kA = 17.69, kH1= 4.02, kB= 7.759, kH2= 12.06 and kB2= 7.759. Note that for this antenna H2-H1 ^ 1. 3X and 2B1=2B2= 2. 5X. The parameter kb is deliberately chosen to be large (usually we have considered kb=O. 15) for the reason that large values of kb give rise to large values of parasitic currents which in turn should increase the mutual effects. The parameter H2-H1 is chosen to be larger than a wavelength because this is the case of interest to us and we intend to study the quantitative effects of mutual interaction for such values of the separation distance between the parasitic loops. For the above parameters of the antenna, the following numerical values have been obtained for the quantities mentioned above: 140

K1 = 0. 146036-i 0.001367 K2 = 0. 012024-i 0. 047119 P = -0. 254652+i 0. 505098 P = 0. 140834-+ 0. 125070 Q1 = -0. 105669-i 0.085823 Q2 = 0.0132312+i 0.010157 It can be seen from the above values, that the mutual interaction terms in eq. (B. 40) are not appreciably large in the present case. This can also be seen from Fig. B-3 which shows the computed theoretical far field patterns of the same antenna with and without mutual coupling effects. From Fig. B-3 it is found that over most of the regions, the two patterns are almost identical. Near the region 90~ < 0 < 110~ where the pattern has a minimum, the two currents are found to be sharply different. It is desirable to consider the mutual effects in such regions. The comparison between the theoretical and experimental patterns of the same antenna is shown in Fig. B-4. It is found that over most of the region of the main beam of the antenna, the agreement between theory and experiment is excellent and also that mutual effects may be neglected in this region. Careful inspection of Fig. B-4 indicates that the pattern obtained by taking into account the mutual effects is in slightly better agreement with the experimental results. It is anticipated that if H2 - H1 < X, the mutual effects need be considered to obtain accurate patterns theoretically. On the basis of the results given here we conclude that for (H2-H1) > X, the mutual effects may be neglected for pattern computations. B. 5 Discussion Expressions for the parasitic currents and the far field produced by a double parasitic loop counterpoise antenna have been derived above by taking into account the dominant effects of mutual interaction between the parasitic elements. From a comparison between theoretical and experimental results it has been found that the mutual effects may be neglected for cases when the separation between the parasitic elements is longer than a wavelength. 141

10 50 -10 i~~~m I'~~~~~~~~~ \ ~with coupling X o~no coupling -15 <-30 no coupling FIG B-3: Theoretical carrier mode patterns of a double parasitic loop counterpoise antenna with and without mutual coupling effects, -45 - kh = 2.75, kA = 17.92, kb = 0.287, kH1=4.02 kB=kB2 = 7.7584, kH2 = 12.06, f = 1080 MHz. -50 I I I I I I 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 15! Angle in degrees

0 * ~ ~ * Experimental -5 X- y^^9 >^^^ ---— H e TTheoretical without coupling _/v \ vX^ ^Y x x X X X X Theoretical with coupling -10 -15 -20 I. 2 -25 -30,0 X. ~ t I a\ xX X i -35 -40 X -45 FIG. B-4: Theoretical and experimental carrier mode patterns of a double parasitic loop counterpoise -50 - antenna. X -55 -60 L A I 0 10 20 30 40 50 60 70 80 90 100 110 120 130 p40 150 160 170 180 Angle in degrees 0 -

APPENDIX C DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA PATTERNS C. 1 Introduction In this section we summarize the results of a systematic experimental investigation of a double parasitic loop counterpoise antenna elevation patterns. The antenna operates in the side band mode and at the frequency f = 1080 MHz. The counterpoise size used is 5. 2' so that the results will be applicable to a VOR antenna using 52' diameter counterpoise at the full scale frequency f = 108 MHz. The excitation used has been a pair of Alford loops spaced 3. 2" apart and located at a height 4. 8" above the counterpoise. The two loops are excited out of phase so that the combined field produced by them has a figure-of-eight variation in the azimuthal plane. All the parasitic loops used have been fabricated from 1" wide conducting strips. All the measurements have been carried out in an indoor pattern range. The basic purpose of the present investigation has been to develop an optimum configuration so that the antenna produces a maximum field gradient at the horizon for the side band mode of operation. C. 2 Preliminary Experiment An initial radiation pattern investigation has been carried out for a double parasitic loop system with H2= 22 /8f, 2B2 = 36" and H1, B1 variable. The purpose of this experiment has been to determine the effects of the parameters H2, B2 on the pattern and in particular to search for those values of H1 and B1 which may produce large field gradients at the horizon. The parameters H2, B2 where initially chosen on the basis of our previous investigation of single parasitic loop counterpoise antennas (Sengupta and Ferris, 1969). The far field elevation patterns of the antenna have been measured at 1080 MHz with 2B1 varying in steps of 4" from 36" to 60" for each value of H1. H1 was varied from 4" to 7" in convenient steps. The main conclusion from this set of pattern results is that for low axial lobe and reasonably large field gradient H126" and 2B1 should lie between 48" - 60". The important pattern characteristics obtained from this experiment are shown in Table C-I. The different notations used in the table are given below: 144

Emax Amplitude of the far field in the direction of the principal maximum. E (7/2) Amplitude of the far field in the direction of the horizon (i.e. 0 = 7/2). E (96~) Amplitude of the far field in the direction 0=96~. Es Amplitude of the first secondary lobe maximum below the horizon. ag Field gradient/6~ at the horizon. E (00) Amplitude of the far field in the direction 0=0~. B1s=E (/2) Level of the secondary lobe maximum field relative to the field at the horizon. All the above results are expressed in dB. TABLE C-I: PATTERN CHARACTERISTICS OF NON-UNIFORMLY EXCITED DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA H2- 22 3/8", 2B2 36", H=6", 2B1 variable. 2B 36" 40" 44" 48" 52" 56" 60" E - 3.0 - 5.5 - 3.0 - 3.0 - 5.0 - 5.0 - 6.0 - max E(7/2) -28.5 -22.0 -19.0 -25.0 -22.0 -22.0 -32.0 E(96~) -35.0 -25.5 -28.0 -35.0 -29.0 -33.0 <-40.0 Es -27.0 -- -32.0 -28.0 -- -35.0 -33.0 E(00) -22.0 -17.0 -16.0 -19.0 -19.0 -25.0 -23.0 ga 6.5 3.5 9.0 10.0 7.0 11.0 > 8.0 Eg-E ( 12) 1.5 -- -13.0 - 3.0 -- -13.0 - 1.0 The values that are left out in the above table were found to be not applicable to the measured patterns. Three complete patterns are shown in Figs. C-l(a) - C-l(c) for three selected cases. C. 2 Optimization of the Lower Parasitic Loop Parameters The next set of data have been taken for the purpose of obtaining the best values of the lower parasitic loop parameters H1, B1 for some fixed values H2, B2 of the upper parasitic loop parameters. During this experiment the upper loop parameters are fixed at H2 = 22 3/8", 2B2= 36". The diameter of the lower parasitic loops were varied from 54" - 60" in steps of 2". For each value of 2B1, H was varied from 5" - 7" in some convenient steps. The various pattern characteristics as obtained from the measured elevation patterns are shown in Tables C-II, C-III and C-IV. 145

TABLE C-II PATTERN CHARACTERISTICS OF NON-UNIFORMLY EXCITED DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 2B2=36", H2= 22 3/8", 2B1= 54", H1 variable. H1 5 1/2" 5 34" 6" Emax - 7.0 - 7.0 - 7.0 E(Q/2) -22.0 -23.0 -23.0 E(96~) -28.0 -30.0 -32.0 Es --- -— __ E(0O) -27.0 -28.0 -22.0 1a 66.0 7.0 9.0 TABLE C-II ------ 2B1 = 56". H1 5" 1/2" 5 3/4" 6" 6 14" 7" Emax - 5.0 - 5.0 - 5.0 - 5.0 - 5.0 - 5.0 E(r/2) -20.0 -21.0 -22.5 -23.0 -24.0 -26.0 E(960) -26.5 -30.0 -32.0 -32.0 -33.0 -35.0 Es -37.0 -- -- -36.0 -33.5 -31.0 E(00) -22.0 -30.0 -30.0 -24.0 -20.0 -15.0 cag1' 6, 5 9.0 9.5 9.0 9.0 10.0 Es-E(7r/2) -17.0 --- --- -13.0 - 9.5 - 5.0 TABLE C-IV ----- 2B1 = 58" H 5 1/2" 5 3/4" 6" Em - 6.0 - 6.0 - 6.0 max E (r/ 2) -24.0 -25.0 -26.0 E(960) -35.0 -35.0 -35.0 E -36.0 -36.0 -35.0 E(00) -28.5 -29.0 -26.5 ag 11.0 10.0 9.0 E-E (7/2) -12.0 -11.0 - 9.0 146

el t t\rt 3 i;L+; \\,* i;~I *il C; tr I Xr;i t J 'i t t iii f 'i o \i t t?~ 4 (tit fW I:1 rL,, fi: ir ~r /I \ tl i:rr r z \t ~ trt-'trlt rtr;li ~~~~i~ ~~~lii ~~ I t \~ rrr :LC t'tl-ru ur I ~.u I.r , t / Txl:y N ~ XL/y,% cc,, -- rj )i v\i t~, \~ ~~, \,, 25 f:,T~:T~r r ':e 2S-Z ,~~ 30iCC~J-I `c-~(\/5( iTf/~~IViY;c'(;: - 4 -~. i i i1 I!,,,,,,,,,,,,,,c,,, t I ///f/;c/;(Lr; 1 ,-ScS~l-tT,T~ts -— IS —c` i.. ---1-4- 1 c.,.., -t L7-t C-CLC. --- r, c, ----- _ 25f-~LTZ -C -r_._., ----c'-~TT7-r ----c —+-e,-r --- -L-. - ~ ~ - -.. --- -ect-+-c-c --- - t- r —c —t-c, ----— 1 --- ----'1-C I,.. In,-e;I -~i r\ t~ --- —i.cc '~-e I, --- —- 4 --- - I ----2-, I — ~ C ~ t... C-* ~ \ r —..;c4 —, e- "C,, -- I —~ I r -c-" ~-.. t- -- cc I/ *. * -r, C, ii ~,, ___ 4_ --- " *;r- t~ -- * 30 \i x --- - ~ ~ ~~ -.r. iC1 r n r\ 25 -f ~ x, r b II C /' X~,.~,~ \\ r r r, r. r, c';X r~;r; / ' ~t r~.... ~' j. r r I~r i z:*J~)iZ ~~~ ~-C., r I, -4 \ r: / 15 -- ~~c~*,,cc~ ~T.' z *. 2, ^ `*i r" ` r I I"` L4h i'l, i Li: i IO c?\ I " h 111 LW \ \ rz`j.,, -?;L1 r I \ CSL1 5 I, rr-i'fJ-iL! TTT;77TI-\1: ( _f?FIG. Cla Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna, 2AL,5. 2', h=4, 8' r f=1080 MHz, 2B2 L 38", H2= 22 3/8", H1= 6" and 2B1' 36", 147

FIG. C-lb' Measured elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. yf 2A=5. 2', h=4. 8", f =1080 MHz, 2B2=36"1,H2 =223/" 11 H1=6~and 4 8

~1: 10. 15- - 2 r 30r li: 1 i.- 20T'l r FI.C-c Maurdelvtinpln sd bn md pter f oul parsitc lopcouterois atena. /, 2A=.2. =4.11 f100 M z.2B =36.., 2

From the previous tables it is found that for values of the parameter H1 between 5 1/2" and 5 3/4" the lobe maximum in the direction 0 = 00 is minimum. Notice that theoretically, for minimum axial lobe H1j X/2 = 5.465" at f=1080 MHz. From the results given in this section it appears that the best pattern for possible VOR application is obtained when 2B2=36", H2 22 3/8", 2B1=56" and H1=5 /4". The measured elevation pattern for this case is shown in Fig. C-2. C. 3 Optimization of the upper Parasitic Loop Parameters In this set of experiments the lower parasitic loop parameters were fixed at 2B1=56"' and H1= 5 3/4". The height of the upper loop was fixed at the value H2= 22 3/8 " while the diameter 2B2 was varied from 34" - 40". The results are shown in Table C-V. Note that the field gradient values shown in Table C-V have been obtained from the measured polar plots and hence are approximate. More accurate values for a in some specific cases will be discussed in the next g paragraph. A typical measured pattern having desirable characteristics is shown in Fig. C-3. TABLE C-V: PATTERN CHARACTERISTICS OF NON-UNIFORMLY EXCITED DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA 2B1=56", H1 5 3/4", H2= 22 3/8", 2B2 variable. 2B2 34" 35" 36" 37" 38" 39" 40" E - 5.0 - 5.0 - 6.0 - 6.0 - 6.0 - 5.0 - 5.0 max E(7Q/2) -19.5 -20.5 -21.0 -22.5 -24.0 -25.5 -24.5 E(960) -26.5 -28.0 -29. 5 -32.0 -35.5 -36.0 -34.0 Es -- -- -- -36.0 -34.0 -32.0 -31.0 E (0O) -27.0 -28.0 -28.0 -29.0 -35.0 -35.0 -35.0 ag 7.0 7.5 8.5 9.5 115 11.5 9.5 E -E (/2) --- -- -- -13.5 -10.0 -10.0 - 6.5 To obtain more accurate esimates for the field gradients, rectangular plots for the patterns have been obtained in ordinary and expanded scales for some selected cases. The patterns obtained in a few interesting cases are shown in Figs. C-4, C-5(a) - C-5(b), C-6(a) and C-6(b). As can be seen from these figures a field gradient value better than 12 dB can be obtained without appreciably increasing the field in the axial direction. C. 4 Maximum Obtainable Field Gradient Two main criteria governed the basis of the investigations discussed in the preceding sections. These are: (i) the field gradient at the horizon be high, and 150

-) - I tf' t: T Ii -.10+1 1~ ~Iifi~' ict f ct — t~'f i::- t~ r t:; V. FIG C-: easredelvaton lae sdeban moe attrn f dobl parsitc oopcontepoie ntena 2A =5 21 =,d t f insi 'N ury n-m zft ff --- CC) /ot

~~~~ f;\cttt:!: i ~~! r'rt-~~( t;1' i.:.1, r~;i, jrc 1iiiill't ~~ ~tf i (1.. r ~ D-ro;: /.? c-~;~i: :t-~1~~- I ~~\~'''1' r~l'''-1~~~~ / ~ ~'\~.'.:~'.\~ 1!:~:::`:: ~~~~!5''~~ i~~.: ~~I~i,~,r.~,~ iji.~,~ CW r '' ~,, A ~ 7~j; ~i; ~Y ~c-hl'J;,~ '~; /C, 1. -- — ~~ r ~ -t.':' tr~:~,:1 I; 25 = J)Llr. —1- % ~ r -,., ~ r= i: f-t7 33; t \\f ////lis(/l3,~s-"r'S=-3t \r~\~'t ;-;-'~sst~4~_-'-S;*ccC- L-c ----c272 r ( ~ ~ ~-,f '2 ~- c"-t — i f [ f-Z:rrrf __f -- ''' — =.- r " "i- i"! ":~t I:~(~; f `~C-4 — i:1:: /, 1"~: ~:: L,li ~I~r r t t f t 't,:-.1-i f~ I:, ~ ~Y -x t — i 1 r-,: i.._,.,-, i I r-t r = 25 t --- r.-f.i — i-~ ----, '~.~ Ztc`' i., ----- -."- ~ =~;; 1 .i"I "~h: I t ~~~~:- ?, ~I r' ~ —r~~Tlf ~: ---: cc- 1'-' I 4 JL~~~ ;i. I )) 1 ---- i --- f-` r:. Ic-2-t —f'''-I;..~,c~ r v~; -L 5 -~A, _t_;-*41 ~~; ~X 7c.7 — t-~t~-:r'' ' -e t*ct' 'C ' FIG. C-3: Measured elevation plane side band mode pattern of a doube parasitic loop counterpoise antenna, 2A=5. 2', h=4. 8", f=10801VIHz, 2B2-4011, H2 22 3/8", H1= 5 3/4" and 2B1 56" 152

Ij^ V I:-! -: /::.I i. V u l 0 '. -. t...:........* I.l- - - a..... L.,.. -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1 f~~~~~~~~~~~~~~~~~ I io- 1 10- I FIG. C-4: Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna, 2A = 5.21 h = 4.8? 2Bi = 56 l HI= 5 4 2B2 40" 2H =~~~~~~~~~~~~~~~~ 22 ~~~~3/8??, f =1080 ~MHz. H 2 = 22 ft 0 f = 1080 M z

i II ' I I '*!'' ^ i '"' j. r * [ i;' ';~.! FIG. C-5a: Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna - complete pattern, 2A = 5.2', h = 4.8", 2B1 = 56", H1 = 5 3/4", 2B2 = 39", H2 = 22 3/8" f= 1080 MHz.

........................aft.....I.I, e I: 'l iI, i '.... aa be 2I a.~. I. a antenna - details near and below the horizon, 2 = 5. '2 h 4 - 8", CJ1 ~ ~ ~ ~~21=6 1=54,22=9 H22 3 /,o =100~ or~~~~~~~~~~~~~~~~~ t i I ~ ~ ~ I ~: ~~: ~

I..~~ ~ - I I ~~~~a)~~~~~~~~~~~~ i;,o I.o 1, $ s 1o J5 ~ ~ ~ I ' ~ FIG. C-6a: Measured elevation plane side band mode pattern of double parasitic loop counterpoise antenna, complete pattern, 2A = 5.2', h = 4.8, 2B1 = 56, H1 = 5 3/4, 2B2 = 38, H2 = 22 318? f = 1080 MHz. H2 22 3/" f I ~ ~~~ f~: 1080~ M ~~f z. l~

i. l,..! i!.i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i-~~~~~~~~~~~~~~~ i 1. ''.ii I I ou.O~~~~~~~~~~~~ I a. L i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:~~~~ 't i~~~~r: a~~~~~~ FIG. C-6B: M i antenna - details. near and below the horizon, 2A = 5.2', h = 4.8"', 2B1 56" H 5 3/4It 2B2 38", H2: 22 3/8", f 11080 MHz. 2~2 /8 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~i

(ii) the axial lobe amplitude be as small as possible. In this section we give the results obtained from an experiment where the second restriction on the pattern has been removed. The aim of this part of the investigation has been to determine the largest value of the field gradient that can be obtained from a double parasitic loop counterpoise antenna. The results are shown in Figs. C-7(a) and C-7(b). In this particular case the field gradient at the horizon is found to be better than 22dB/6~ which may be considered to be a dramatic improvement. C. 5 Discussion On the basis of the results given above it can be concluded that the parasitic loop concept has been found to be highly effective in improving the field gradient characteristics of a non-uniformly excited parasitic loop counterpoise antenna. From our investigation of the radiation characteristics of a double parasitic loop counterpoise antenna having figure-of-eight type of excitation we make the following two important observations. (i) It is possible to obtain a field gradient at the horizon better than 12 dB/60 while maintaining the field in the axial direction to be less than 25 dB down from the field in the principal maximum direction. (ii) It is possible to obtain a field gradient at the horizon better than 22 dB/60 while maintaining the axial field to be less than 16 dB down from the field in the principal maximum direction. In all the above cases the secondary lobe maximum below the horizon has been found to be about 9 - 12 dB down from the field at the horizon. 158

": I.... 's ': II ~. ilo:5 FIG. C-7a: Measured elevation plane side band mode pattern of very large gradient double parasitic loop counterpoise antenna - complete pattern, 2A = 5.2' h = 4.8", 2B1 56", H1 6", 2B2 39", H2 22 /8" f = 1080 MHz

0~.,y,^0 ~0 t. y 1 ~> *^ ~-! '.'<* *M01~ loop counterpoise antenna - details near and below the horizon, 2A = 5.2', h = 4. 8", 2 = 5 2B2 = 39", H = 22 3/8" f = 1080 MHz. a " i i 2

APPENDIX D NUMERICAL VALUES FOR PARASITIC CURRENTS IN SINGLE PARASITIC LOOP COUNTERPOISE ANTENNAS D. 1 Introduction In this appendix the numerical values for the amplitude and phase of the different components of the parasitic currents are given for single parasitic loop counterpoise antennas operating in the carrier mode. The notations used are explained in Chapter III. The basic parameters associated with the feed and the parasitic loop in all the antennas have the normalized dimensions kh=2. 75, kb=0. 15 at the frequency 1080 MHz. TABLE D-I: PARASITIC CURRENT VALUES FOR kA = 17. 92 kB 47r kH=3.7 Real Imaginary Absolute Argument (radians) 12 I12 0.235203 0.060884 0.242955 0.253 34 Ip4 0.000214 0.000635 0.000670 1.246 56 Ip6 -0.003516 0.079530 0.019844 1.749 IPo/I 0.231900 0.081049 0.245656 0.336 kB = 30 kH 5 11.9 12 Ip2 -0.053762 0.171890 0.180102 1.874 I34 -0.000723 0.000275 0.000774 2.778 I56 +0.028226 0.004028 0.028512 0.142 o IPo/I1 -0.026258 0.176194 0.178140 1.819 161

TABLE D-II: PARASITIC CURRENT VALUES FOR kA = 51. 69, kB=37r AS FUNCTIONS OF kH. kH X 3.75 Real Imaginary Absolute Argument (radians) 12 Ip -0.320886 -0.174901 0.365456 -2.643 38 Ip0 -0.000005 0.000008 0.000009 2. 150 156 0.005060 -0.020825 0.021431 -1.332 Po Ip0/Io -0.315831 -0.195718 0. 371557 -2.587 kH = 4. 00 12 Ip2 -0.312799 -0.203302 0.373062 -2.565 P0 Ip4 -0.000006 0,000008 0.000010 2.171 o I56 0.016357 -0.000828 0.016378 -0.051 P0 Ipo/Io -0.296447 -0.204122 0.359926 -2.539 kH= 6. 28 Ip2 -0.028638 -0.362861 0.363990 -1.650 Po I34 -0.000012 0.000011 0.000016 2.425 156 -0.022557 -0.034135 0.040915 -2.155 PO o Ip /I0 -0.051207 -0.396986 0.400275 -1.699 kH - 9. 424 12 Ip 0.253751 0.036038 0.256298 0.161 I34 -0.000025 0.000005 0.000026 2. 950 Po IP /I 0.273649 0.016660 0.274155 0.061 o o kH = 12. 5664 I12 -0.118024 0.113270 0.163584 2.377 Po I34 -0.000032 -0.000018 0.000036 -2.616 o Ip6 0.006505 0.077561 0.018727 1.216 IPo/I -0.111550 0.130813 0.171917 2.277 o o (continued on next page) 162

kH = 13.00 Ip -0.139680 0.064187 0.153722 2. 711 o 134 -0.000031 -0.000023 0.000038 -2. 502 I56 -0.002196 0.008552 0.008829 1. 822 Po IP /I -0.141906 0.072716 0.159452 2.668 kH = 13.5 12 Ip2 -0. 143060 0.005611 0. 143170 3. 102 Po Ip4 — 0.000028 -0.000028 0.000040 -2.367 o I56 0.003864 0.001230 0.004055 0.308 Ip0/I -0.139224 0.006813 0.139391 3.093 163

TABLE D-III: PARASITIC CURRENT VALUES FOR kA = 51. 69, kH = 3. 75 AS FUNCTIONS OF kB. kB = 9. 424778 Real Imaginary Absolute Argument (radians) I12 -0.320886 -0.174901 0.365456 -2.643 Po I34 -0.000005 0.000008 0.000009 2.150 Po I5 0.005060 -0.020825 0.021431 -1.332 IPo/I -0.315831 -0.195718 0.371557 -2.587 kB = 10. 99557 12 Ip 0. 107100 -0.27'7345 0. 297631 -1.199 Po I34 0.000008 -0.000004 0.000009 -0.419 Po I6 ~0.040861 0.046749 0.062089 0.853 IP0/Io ~0.148868 -0.230599 0.274477 -0. 998 kB = 4r 12 Ip2 0.236309 0.064329 0.244908 0.266 Ip4 ~0.000004 -0.000008 0.000009 -1.057 0 156 -0. 006193 0. 017157 0.018240 1. 917 PO Ip/Io 0. 230121 0.081478 0.244119 0. 340 kB = 14. 13717 12 IP2 -0.036089 0.200639 0.203859 1.749 I34 -0.000008 0.000003 0.000008 2.812 Po I56 -0.031215 -0.034283 0.046364 -2.309 Po IP /I -0.067311 0. 166359 0. 179461 1. 955 kB = 15. 7096 12 Ip -0. 170716 -0.017859 0.171647 -3. 037 o I34 -0.000004 0.000008 0.000009 2.039 P I56 0.006265 -0.014580 0.015869 -1.165 Ipo/Io -0.164455 -0.032431 0.167622 -2.947 164

TABLE D-IV: PARASITIC CURRENT VALUES FOR kA = 51. 69, kHl = 13. 00 AS FUNCTIONS OF kB kB = 8. 168161 Real Imaginary Absolute Argument (radians) Il2 -0.048299 0.128762 0.137522 1.930 P0 134 -0 000020 -0. 000028 0. 000034 -2. 178 156 -0.020082 -0.001074 0.020110 -3.088 Po Ip/I0 -0.068003 0.127659 0.144829 2.063 kB = 8.796459 Ip -0.098755 0.107530 0. 146000 2.314 0 I34 -0.000030 -0.000031 0.000040 -2.341 Po I56 -0.001798 -0.007079 0.007303 -1.820 0 Ip/Io -0. 100583 0.100420 0. 142130 2.357 kB = 10.05310 I2 -0. 160590 0.003433 0. 160627 3. 120 PO I34 -0.000021 -0.000006 0.000022 -2.856 Po I56 -0.020466 0.017674 0.020522 3.055 Po Ip/I0 -0.181057 0.005194 0.181131 3.113 kB = 10. 68142 Ip -0.153549 -0.064811 0.166667 -2.742 O I34 -0.000005 0.000012 0.000013 1.931 Po 156 -0.012413 -0.020845 0.024261 -2.108 Po Ipo/I -0. 165967 -0.085644 0. 186762 -2. 665 kB = 11. 30973 12 Ip -0.115851 -0. 126891 0. 171822 -2.311 Po I34 0.000012 0.000026 0.000029 1.130 Po 156 0.010212 -0.015715 0.018741 -0.995 Po IPo/I -0.105626 -0.142580 0. 177443 -2.208 165

APPENDIX E COMPUTER PROGRAMS FOR IBM-360, MODEL-67 E. 1 Program for evaluating the far field elevation plane side band mode pattern of a conventional VOR antenna (SA(6) versus 0). The subroutines given in this section are also used in all the subsequent programs. The following flow diagram applies to the Main program for the VOR side band mode. Flow Diagram for the Main Program Read Kh, Ka, Kb, KB, KH PrintKh, Ka, Kb, KB, KH TH =2~ -- Calculation of Jo, Kro, Fo, by FCAL Calculation of CF1, CF2, CTA by LFAC TH = TH+2~, Calculation of f(0, ) by AAA Calculation of cos 0 Lo Calculation of CSA, ACS, DB 166

LIST OF SOME OF THE SYMBOLS USED SQ2 = square root of two PI= = RCON = 180 KH kh KB =kb KA = ka KCB = kB KCH = kH TH =0 PHZ = o KRZ = kr 0 CFZ = F o TS = sin (0) TC = cos (0) (2 /cos 01 i v- KA sin 08 ),s CF1 ='T ei (12 - ka sin 0) CF1 e 2 K n S -n)CF2 =O CXZ -ik ika sin Icos 01 CXZ e o CF2 e 1+sine0*' CSA = SA ACS =SAJ CLZ =cos 0 L DB =201og10S IAI AAA FCAL Subroutines CTA = e LFAC 167

Main t,COC i.I:'IC I l iJAL *d (., E,[-E,F,G-Z),CC ME LEX* 1 (C) O' C2 bkAL.* CALhA,2CC C; L<:1C3 r1ilV(140),C.V V(140),CSUlV (14C) 0 C C 4 C i L X * 16 C PLXCr L E Ei, C ' ^ T CC05 C LX (XA) = DCtPLX (DCC. (AX),LSIN (XX) ) CCC6 LCGiCAL TiEli/. A iS~./ CCC7 Er TA S 42/1.4142 156237-1/, PI/3. 14159265358979/ CCCd LAA CT /1.57C79 3267949/, EGAM/.57721: 6E4901533/ JC ( C 9 L AA L CON/.C17 4 C292c 1 92/ P F/.7 53981 33 97448/ CC 10) LAA INi1L/3/,I S/1/ 011 F E AL*8 Tii 1 ( 10) /S.DC, 2. CC, 115.DJ,7 C. D0/,i 2 (1C) /83.DO, 110. C 6 17C. L0,7*C.D/, S (10)/5 LO,2. C, c 5. 7 C C C.DO uC 12 NALIS. Li / IN/K, KA,E, <C i,iKCH OC 1 111 EAL (1,IN,ENID=10C) (i () 1 4 I.' rl E. S C, c9) CC 15 SCS tCfC;.I ' 1') C0010 A^T (6t, CCO) Kh,KA,KE,(.iC3,KCHI ', 17 lCCO FCihAl(7' I- = ',G15.7,' KA = ',G15.7,' KE = ',15.7/ 1 ' kiCE = ' 15.7,' FCf = ',G15.7//) LJu 18 E ECfL?=L;LS;: i(LA- LX( (C'i.+LCG ( KB *.5DC)) '( j1'9 Ci EI=L;Ci(IX (I:GAi+ELiCT (C E*. 5 DO),- r-I) 'C:C ''J I I X= 1 (i; z t ^ - DCE i LX 0, LO, 1.c4L0) ^;C 1CC i= 17C, t Cz" ^ Ii;-_l I ' CCN,, z 4. L- rCAL (K nr A, 1Hii2 c 2,CF Z) C.'. 5 CAi1 1 CAL (iCii, ~A,, riS, I, KI,CE P) ~.~- -i~. - LI~z N (HIi) CC 7 I L C ( Iil):.Cio CALL L rAC (1S, CKAC 1,Cz,CTA) CC,1 5. 1 = DOSi;r (TS) OC 0 i:C=L CS ( i) CC' 1C tU 1-=LZ C.7 (EC) 0-2 L '=LJ V G (KC 2 C). rC _ j 2i2=L L C:'. E KC El;S) C ')34 1' 1= (rC *E L 1-i 1 4SL ) / (PC- S) {'- ^3 C = -C E:. L 1/ (EC+' I6 S) 168

C 6CLI C 1*'I i-CF2'* 2 C C C = CC S f~i Z,) CC40. C=/.AA (PC) C C 4 1 r.: = P P A ('f ) >i42 LJ: I ^U=l;Ctril.X (C. LC,ALIC) C 43 JE rr L, =LC t. E LX (0. L, OA'Is) 0044 'l 1= (C i.N *aL' C 1-C CNE 1 1) / (PC-I I) CC 5 4 C'12 C A N 4 L1/ ([C+ S) C0 6.6 C L -li'* 1 C'1 1 -C * L ' i JC 47 I - L.;LN (riiZ,.:LC)/CAY'l, (PJlK'L ^z* s) ( C - CCii1 (K i2) 0)'49, L -L 1 A *C; 1*l / + C X ^ *Ci LZ'I 1 C C CC CL CL 25 i (L SA).:OC C 1 L-ZtC.UO4LLCt 10 (ACS) ' C c 3 I. Zl '" 1t,'JO) 'rii,C SA ACS,I E CC055iCO .N^I.YL: C.;: '..' 111 i C:;i 7 L CC'7 169

"{.~2 i[:~..C:I E AL;b ({A-2) Oll'J3 LAT A KJ/C.c/ i;{. CC4,i A/..- Z. LD O~[EIN (~*'L:;} j) C ( C j i i h - L 'LC~AL ifjiCEiY JiL:;- <iPi': T'i'5 CCUJ 15: YIES r"s:':.:.' T *,,/ ". 1 ( ' '. '."!;.. -.... i "... ( TT. *," \, _- _ " ~') _: -t.r,; - -.... -..!.. '-[,-;..: T ' T '" _' ' - '. '. '.,-~^ ' '-,i! * 6 t V ( [ g s, * s. -....-..!... |.... './.........-......-..... - "I ~ ~ ~ ~-,' ': - -'" ' '-1' ' 1 '. ':: '~;_ r____: - _ _ ' _ _ _ _ _ _ _ _ _:,. ~. ~,~ z; r s1 ' | ~ ~ ~ ~ ~ ~.1.' ' 170

r r,'A,! T, I. '. r:r' "-,^, v -r^ Tj,. r" ~.. '.M... (.: '_ -.:,_,(TK '," " CF 7. ) __ __),*-.', -'V 'f1 I 'I \ T - y I ''r ' 'Z I V v 't CT!'T yI/y ___ _____ ____ AT /I.''I'Q1.3^? 73'/,: '"",.", )"'r~.I. f T "-,7! 0:'-, A,.,-: —,,-: ";.'),C " fP: 7 6- 1( 7 ),,, -i-,, n-,/. ~ ~ " ^ ^r~c,a (P"' / 1 r 7 7 o, ',?,r3r 7 r". )/4 <' /:~7 7 ' t j-: ~r T~? ' 7 O if,7c 77,'.," ~,:'?___ -= pA'-.r), (yT',,( _i,)_________ ^*^'*_ r.. = *iC~l ^(*A ) __ ___,, —, — _________/ T I ( -) f) a.I r ' Y (T " (' T '-T ( T D j ) ) *,. 1 -? r '- _ f, - r *";: -....: T. I F "'" T ( '"',. ' r c" 'r-+:.. (r' - (,P )C)1

SUBROUTINE _.?.o2 3 I:_SUROiUaINE FRNL(C,SXX) 0002 I ' MPLICIT REAL*8 (A-H,O-Z) 00___03 UZ: XXt1.2533141373155 0004 | Z = ZZ*ZZ CC05G SGO TO 3 COOo I ENTRY CS(C,S,X) 0007 i = DAS BS(X 0008 ZZ = DSQRT(Z) OCO9 3 IF (Z GT.4.DO) GO TO 4 C010 * C = ZZ 001! S = Z*C 0012 Z = ZsZ 0013.. C = C_ (t_( (((.5099.34:_D-lO*Z-.10140729D-7)*Z+.11605284D-5)*Z I -.852246220-4)*Z+.369385860-2)*Z-.079788405)*Z+.79788455) 0014 S = S*( ((((-.66777447D-9*Z+.11225331D-6 )Z-.10525853D-4)*Z & +. 604353710-3 ) *Z-. 18'997?11 00-1) *Z.+. 26596149) 0015. RETU.IN! c 0ol06_ L_4 o OS_ _______ O 0017 S = DSiN(Z) ociE Z = 4. noz. _ ______________________ 0019 A = ((((((.876825830-3*Z-.41692894D-2),Z+.79709430D-2)Z _ _____ -.67928011 -?)*Z.3095341 2-3) *Z+ 59721 508D-2) *Z. 160642810-4)*Z & -.0249332215)*Z-.44440909D-8 0020 _ = ((((((-.6633956D-3*Z+.340140900-2 )*Z-.72716901D-2)*Z & +. 742 2459D-2 *Z-. 40271450D-3 ) *Z-. 931491050-2 * Z-.1 20799840-5 )*Z & +.1994711 5 _ 0021 Z = DSIGN(.500, ZZ) 0C22 ZZ = 2.00/ZZ 0023, C = Z + ZZ*(D*A+S*") 0024 ' S = Z + ZZ*(S*A-0*B) 0025 RETURN QEND 172

SUBROUTINE.Q o._ 1 F U NCTIN DJON _ )JONE_ 0002 IMPLICIT REAL*8 (A-Z) 0003 RFAL*8 CJ 1(7)/. 50 -.56249985.21093573t-.3954289D-1.443319D-2 & -.31761D0-,.1109D-4/ 0004 REAL*8 CY1(7)/-.6366198D0,.2212091D00t2.1682709t-l'.3164827 &.3123951D00,-.400976D-1,.27873-2/ 0035 REAL*8 CFl(7)/.79788456,.1560-5.16596670-1.17105D-3,-249511D-2 &.1136530-2,-.200330-3/ 0006 REAL*8 CT I(7)/-2.35619449;.12499612.565D-4,-,6378790-2.743480-3, &.79824D-3,-.29166-3/ 0007 ENTRY JONE(X) 0038 IF (DABS(X).LE. 3.00) GO TO 600 0009 TOX = 3.00 / X 0010 Fl = PITOX,CF1,7) 0011 T1 = X + P(TtOX7CT 7J 0012 -JONE = F1*DCOS(T1)/DSQRT(DABS(X)) 0013 98 DJONE = JONE 0014 99 RETURN 0015 600 TOX = X*X/9.D0 0016 9 JONE = X*P(TOX,CJl,7} 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(TOXCFl17) 0022 Tl = X + P(TOX,CT1,7) 0023_ YONE = FlODSIN(Tl)/DSQRT(X) 0024 RETURN 0025 700 TOX = X*X/9.DO 0026 Fl =.6366197723676*X*DLOG(X/2.D0)*P(TOXCJ1,7) 0027 YONE = Fl + P(TOXtCY117)/X 002'8 RETURN 0029_ END 173

E. 2 Program for evaluating the far field elevation plane carrier mode patterns of conventional VORjnd single parasitic loop counterpoise antennas SA(), S()J. Main '1)( T1'Pl CTT "P I r RTE At. R (!,r- P-F, K I n-7Z ) Cr.IffAPL F X*lS (C ___ ^in,,2 ', r: AL*. P C nAP, S 3__ ___ _t Cf 'l..P1 F1, L 1 6 )DC P L___ X '."4 cF[X(XX) Df^ PLIX (DCns (X Y ), rsTN(xx )) L'' C, I C. A 1. T FP /.FA SF. / t.r,, rf rSnATA SA O?/ 1.4142135627731/, / T.. 41 59 653 5 7 9/ -t"-' "7;__ ATA 2-T r/1* 57n7063 2 6749/, FfGA, /. 77 1 566490 1 5331 ATiR -PC.1T" RCfF /.774:2?519?/, PqF /. 7Q53Q8S 63397448/ 0-f. __ _ ______ _ DCATA NT L/3/, ITS/1/ _ _ n ln!: t-AL- " A - T!- 1! ) / 5, On, 82. D, 1 5,, 7 *.O/ T H2 ( 10) /.,, 1 1 D, Eg. 1 7. r', 7tn,-oD/, THS( 10) /5.0),?.n r,5. lD ),7, n Dn / fnn,'! 1 kI F'RITF 6, f90 ) '"!2 2. Q f-1 F f R',AT ( 1 )__ nr' I i -'R'A-" -, TCS T / I '/KH, KA, KP, KCB,Kr.H I} } 1 4 t? r ' A 1 (, T N r F 11 n -= 9 0 r) ' 14. __ _ A_ _r (1, N,_FD=qron) '"'"IrA;~ - ' Kr r =K C:'.. 1 41. 9 9? 7.9_f6 ' 'TTF (6, 1nI )KH, K8K KA KC FKC R3 (* 17!in -), F rPfR AT( K' H = ' tG1.5.7 KB R - ',15.7, A ' A, 5.7/ &'f K C t ',G 1.5.7, KCRB 1 $. 7 I X) -nr-l-6-............. -TIF (. r T T.TE M) R TF (6,?'6 ^ ). 'IM( FP)+S,?) t 7X, fE(S), 1' Xt ' T )',crt 17X, S Il S ', 1 X,' SI OB' /lX) ~'i(" _'.2'_CPr I KP =!,Pl X ( P Y CT t FC A +? r, CG (+.5 C ) ) rl,? ) ] '! 1 T - T S,NT iL ~^ _^,: T4TS 1T - THS(I) _3 _____ ___ __ _ _ _( - ___IT)..:..... r T!.T. rT.) 75,76,7s,''z 7,c7 r','rT = (t' ( IT -TH IT )) /THSIT + 1.5 ____ __ _ _ _ _ 0n-')5 ' f""r) T 7'7?: 76 r76 t! ' T = I 4: ',?7 77 TtL - Tt1 ( IT )-THSITT '9:20 T- = (THIE1 + T'T-1TJT)*fRC.PN O3 0 C. 1_. CAL( KH, KA,T,PtHZKP, CFZ) - ____________:'n:'",! CTALl Ff'L(KCHtKATH, PHFPKRPCFP) ' 'I Tr T(T7 ).ne ne - __ T S I( T- ). ).. On^3 TF —.ir l fT TH) _ '_4_.( ALl_. _ I_:F AC(TS,TC, KA,CF1,CF?,CTA)_ ______________ 0rtq T1 = S PT T T ) e, 4;~PC =!)C.']. f P T P ) 0_6 _.._,,_. _ __PHP) _ _ _____ -____________________ T( 1 = s:;'pT(PC ) 3'"*ni, RO_____l 1 --,JlnlE( K,8J CC *PC Cn) + 9 '-' f.L,? -= -)F-'NE (fKC r T S) 9a4 ' _ Ti = (P(:! SL.-TS1*BSL?) /( P-TS) 174

n'.t1 T2? = -- PCl-4 SLI/ (PC+TS) nrO 2 Cl P = CF.'-T1 - CF2*T2 ' 43 c7.^ -= CTr1 ( PH7 ) r',4_.__.4 __PC] = '' RPT ( PC*PC*PC) (nn4T =T T1 = TS14TS1 nr_ _f r 1 = ( TCl-TS1 )/(PC-TS)_ __ ^n47 T? = nrl. / (PCr+TS.) 'r', 48'_ Ct 7 = CF 1 T1 - CF2*T2:'i,TI) T T = l 47 ^. 5D, / DS/ T ( I * P 7c T S ) n. t:c;,_ _CXZ7 = -f:X(YKP7),riEl CrA = (TCS/SOf2?)*CFZ*CTA + TI4CXZ 7: CLZ frT -rn - z rJSK _r~~ 57~ 3~T _ = rT I. 1CP C w"r54 KP. 1S T + - (KCH-KH) *2 Ci-) L^.___(._ _ CY1 = C IX(DQ O rPT(KRl S) /KPI1S n(-56%(r, Fr, 2 = r l + (KCH+KH)* t2 ')n'$r>:_ (]1T3 -= r-TX(DSS PT( KP2S) )/KP2S n: ^'cq (T1. = ( T/C. T PLK t *(CX -CT-A);, __ _ _ _ r.T2 ( tl.?/ SC2 )?TCFP CT A '/ "8 ' 1,r1 [= S TM P H P e.5 D ) /DS O S 0 PT ( tKPP )TS):~f.,1. CT2 = r 2 + T 1 CLPr*C TX(KPP) r' (i'? C:P = CT1 T CT? r':6/ f+ T I f r)n PT T1 *T T1 T )..T -- C r.T1 =: X K CP+kCBi-P+frF - r)Ds T ( KSQPT( /(KCf/KCH)*C X (KCH+KCH-POF) lr ', CTt1 -= C!r' l Cr 1 * T Z __~__ __ f cTl = CrTI / ( -?D [l)*CP I.KCFPLt/ )____IT *, ':, f,q? S =.:r T. C, T 1 ''"< 71 C, ClJ" -= C!. F ( TS. ),' ' 7? '...........=Al r'A rC S ( CS, ) I V " 2 a' 7i A[__. __:'CS_ TF'~ c ^_ _ =__U ARGC (CSU )/PCr. N,..7. n&C'7 = _..ngl..? G i n_ ASUM) r'?-1 FCrPAT(,TH = _, IS. = CS, P \*CAP.C S P+CP, = '7P2,-" ', V %S = C, CL f S ( C S R 2 q() 7t 7 O D L e(7tr3 1 7 AC5 r'7 "3 = - T CI/ PCON '"7 q _F (TFr". ) nP TO 7n '"'.. '.1 1:"i. JT F (. S,T ( - 7 '. 1 T) TH, C SS A, r SUM, CS, lS r s, n.Stt' t"K 3 1 _____ 2:'7 1 F' PlAr. 5M T IF 1 3, 1.P P1 l5, 6 ) _ n''~P,>,?.^~~,rni, n n.__. _____...... __.7~_ '^.P.ITF ( ht 1A.n ) T S A, CSIMC t s1 V C S, ACSt t S I ',,1" l4 r- n p1AT( ' TH = ' c,15;7, SA = ' C.15.7/' 7 SP+SP. = P ', G15.7/ '" S = t,',.I /' S/ S:, '.1../ /S/ SO DP=, 5 15.7) = r',;? -! 7n t C N -: T I NJi: t,n c 7 R r i f);'\ |_ {_.s S T p M cC'/ 7ALL SYc T;::'~ 175

E. 3 Program for evaluating the far field elevation plane carrier mode pattern of a double parasitic loop counterpoise antenna. (Mutual effects neglected.) Main.9 -'^ (1H r, \" L- (),* -'., I.. I -, A,,{, - t -,, -Z), C IV t LC ( C&l C) '..., L' 'l;. T,"4(K{,KA,iCc,K,'}.,THV,CSAV,CS UNV1,KK) *' ' i/ 'v ' lJ ( I t. 1 N,; -: 'i ( ) ', ( ^ C^ L TA (KH,KA KC K,C T, HV,CS AV CSU MV 2 ' -i." - ( ~ ' )... ". -' t,'T I'T TCSI AC S C2SUM= ") k X " i~~~~~~':- '.'-' T S C S, C1 5S - - LL ' ~ - " I _ C 5 I,,:=V ^ T V( I ) *..~ " -v= V;: V(t I ). CSi.. iVl ( I +JCSu', V2 I ) * '. ",\.; =.,,. S S(C S):;-. -; ' ' s '.'=:'! '. '. ): ' ' ) -; ('i,. (, C S ):* ~'"C.-, - " " ' j. AL'C LS ) YSS - 5, n - - 9 - _, 1 SY ^ Sn T.,TAL '2,2^ Y ^ CUI. LE..TS,'17?? dYTES 176

Tab '1 ~SUJ^JRCtUTINE TAP( KH,KA,KCB,KCH, TH-V, CSAV, CSU'W, KB ) 2'.Iv t iPL C TT REAL*8(A,R3 D-n K,0-Z), COJPLE X* 16 (C) 3 PEAL*8 C}ARS 4 nCOIvFNSION THV(90) CSAV(90), CSUMV({O)) ' (f^COC1PLLEX 16 DCMPLX Ct IX(XX) = DCMPLX(DCCS(XX),f)S IN(XX )) 7 LDGICAL TERM/.FALSF./ "S,SD ATA SQ2/1.4142135623731/, PI /3. 14159265358979/ c nADATA P OT/. 57n 7963267940/, EGA?/.5772 1 5S66493 1533/ 'DATA PCt N/.C1745329251c92/, POF /.785391 63397448/ 1~ 1 XDATA NTL/3/ ITS/1/ 12:^EALt* THI1( lC)/5.D0~P2.D00,l5.D%7':0.D0/~TH2( 10)/8C.DOC110.DO & 170.D C, ( ) 7 /, THS ( 10 ) / 5. ),2. O,5.') 7*0. C./ 13;RITE (6,1 O, ) KH,K,KAK CH, KCi< L F1CO FD V'AT( ' KH = ',G15.7, K3 = ',G15.7,' KA = ' G15.7/ &' KCH = ',G15.7,' KCi[ = ',G15.7/1X) 1L5 C'PLKB = nCM PLX(POT,FGAY+DLOG(K B:.5fn0)) '17 Dr, lDe100 1=2,170,2 ~~~~183 T H=I*RC [ N 19 CALL FCAL (Kti,KA,TH,PH7,KRZCFZ)?('r C~CALL FCAL ( KCH KA, TH, PHP, KRP, CF ) 21 TS = DSIN(TH) 22 TC = DCCS(TH) 3 rCALL LFACt (TS TC,KA,CF1,CF2 CT4) 2G 4 - =TS1 = DSQT (TS) 25 "C = oCCS(PHP) 26? l~PC = nS -)QPT(PC) 7 7 SL1 = CJ F (K C * C ) 2F 3SL2 = DJCNE KC,*TS)?o TI = (PC^I *rS L1-TS1*,SL2)/(PC-TS) r <T2 P= PC1*PSL1/(PC+TS) 31 CtI P = CF 1*T I - CF2! r2 3? PC = r)CF)(PHZ) 33 PCI = DSORT (CPC*PC^C) -34 TSI = TS 1:TS1*TSI 35 TI = (PC1-TS1)/(PC-TS) 36 T2 = PC1 / (PC+TS) 37 CL7 = CFI*T1 - CF2*T2 j38 TI = DS IN \( PHZ *.5DO )/DSOQRT(PI *KR7*TS) 39 CX7 = CEIX(KR7) 40 CSA = (TS/SO2)*CFZ*CTA + TI*CXZ*CL7 41 T = KC.K' CR 42 T2 = PI *T1 43 K R1S = T1 + (KCH-KH)**2 44 CX1 = CL IX(f)SORT(KR1S))/KR1S 45 KP?S = T 1 + (KC.H+K ) **? 46 CT3 = CTFX(!)SQPT(KPF2S))/KR2S 47 CT1 = (T 2/CPL )*( CX1-CT ) 4's l;CT2 = (:'.L2/SC? ) 'CF oCTA 4c9 T 1 = 'ntSI o tP. 5OC ) /[' q(OPT( I R TS 5~'' (CT2 = CT2 + Tl*CLP"CF1X(KFP) *51 CSP = CT1 ': CT? 52;Tl = PI*CT 53 rl _= t)S'.-T (T *l 1*1 '! ) 177

'.::-,;= ' ', "-I",:C. K (C, i'f ) - i)S:'RT(K<Cri/KCh) t L K IX( KCLi+Kl -P r ) ~ '', i!'. - C T;1 '- C Xi:' T1 ' -l> (. - C -i / ( -,.. '" C.'LK[l,:CPLK } = i, T - CT, *'h~. A. n C. +, I ( CA )S: P? "C- 2.n,\CS*l;K.~. = A GC (CSU )/RCUiN '" c [}:. v'v dhiL." =. ';, L i, I o A SUM) 'r; C. = CSt +C S CSP+ S'P2 -'':, ' 'S = C )A,' S( (CS) )**2..C. -o-},!'SU;'-; = l1'-. D)' DLOl1 O( ACS):",, 7 r 4= T!-T/R C -;, ] ' (6 'T r -V ( I tnr:; X r) =TH 'C.-,, 6CSAV( I!n;L X) =C SA 'C 7': CSi.! V ( I [ -iX ) =CSUM - c 7 [ ', ~ X= I i\' I Xh + i ',"2 I -t ( TrFP ') n TO 79 > C73 _ ~*f ) 17? t iCr 'C" 74 - 7c;-,' ITT- (6, 1C1 ) TH,CSA C,CSUiCS,ACSTD SU rC75Cl^"'l FJ.'4 ^AT( 'TH = ' G15.7, SA = ',2315.7/' SP S?2 = ' 2G15.7/ ' 157 S S = ',5.7/ // S = G15.7,' /S/ O = 'G15.7):1't '-. C 3' TI:'UE: 77 TU RN C- 73 rE\D TTL M'F:-RV " U^:EENTS 3 1038 BYTES 178

E. 4 Program for evaluating the far field elevation plane side band mode pattern of a double parasitic loop counterpoise antenna (mutual effects neglected). Main ) I' TL CI T Fr AL ( A,r,)-H, SK, -Z), CO PL X 16 (C)."^ <i.-i IS" / I /N//KH,KA,Kt,KC.,KCi{,.'5 111.K.A' ( 1N, I, LND= 1 (.O CCsrc" l.PITf (,<;.s'- ) *.'C,7?c ') FL ''AT ( '1 C.C CS t'I 1 r (_6, 13^ ) ist, KA,K A,KCt3,KCtIf '2CC9 I"'- F','," \T7 ' K, = ',;1 5.7,' KA = ',G1.7, ' K8 = ',G15.7/ 1 ' KC$ = 't,15.7,' KCH = '.GS'.7//).rC 1;i C. L T;: ( KH, KA,KC, KCH, T HV, CS AV, CSIJMV 1,Kb ' ',. 11. Ar)( 1, I:N,E\r):=l C) I i2. -: TiE (6, 1.JO C ) K t,KA,KP,KCB,KCH (!13 (CALL TA\ (K4H,KA,KCi KC H, THV CSAVCSUJMV2,tKB):C1 4._ 2' I = 1, 85:C15 T H=TiV ( I ). ', i C S=C SAV ( I ) +CSUMV1 ( I) +CSUMV2 ( I) C 17 AC S=CDAAS(CS) 0C 1S D 3 S ) r' = =? '.. UCi T L CG(; 10) ( ACS ) 20CCt.19- I. TF (,5') TH,CS ACS, DOSUM OP"'% 5d rFni AT (F 2. 3, 1P4D15.6) * 201 2^ CTIUiJE OC22 2 2 G2 TO I1 1 C0C23 1C, CALL SYSTEM OC24 END TOTAL PE-'' Y EulUIRE E ENTS 0 017C6 3YTES 179

I' ' ', " ~; \', ' T A,"~.(Kir;A.',, KCi-'(, <'"'r T HV, C%,7V, CSUJ V,K7. ), I t.^. I. L (, *,'.,T, "C - Z ) I V i'-Z) LCIV*lr ( 1(; ).... ~ ~-. - X;:: '4 A ",*' " ','( ' f, f ',,PA,-!"S-'l';,, v ( ), -S:;.' v (!> f j \ -' r i. r l^J( C ) t,:',, (- *, (X\ \-. ' ' P I X ( L.( S ( X X ) ) S, I ( XX) ), ^ ';.iC,' l ' T ' "' /.,'- L./ r(,*C:.q )' r A Sc:2/ I.14 1 3. 0-731/, [ /3. 141 59Z. 53 t5d97/ j': ),,,T *.4A P'T/.57. 762C,632)-''4('/, FGA,'1/.5 172 1 56649i0 133/ C!' ) T,',,, PC:, r!i /. n 1 74 ')32;2 51 92 /, t /. 7 5 3 9 16 j39 744 8 / i' 1D i '1AT A Lt /3/, ITS/1/?:' ^ ALl: tH1 ( 1 )/. C Ti)',q12.L115 ).;,77*0.0 /,THd( 10) /I 8. DO I10 i 17,.1', 7: C. ) O/, THS ( 1 i) /5.D ),2.~ D3 5.DO,7*0.)0/ 3Cl: CP L K = C'/PL X ( POT, E OG. P: +tiL C,G( K(i *. 5 )O ) ) '01C l''t ^'.;C LK "=PC" PLX ( EGAM+)IL C ( KB.5 DO ), -POT ) 6Jl ~";.':-\ X= 1 m,)0!6' CFr: LW hA=FO;'-. PLX ( C.D, 1. I 84E') CC!7:i' - 1 7 C,2:' ^ i g Tt= l =' t t cr,,:! CL 'CL (K KA Th, PF Z K Z, CFZ);;, -'> O CALL FCAL (KCH,KA,TH, PhP,KRP,CFP) r? rS = CSI(TH);2 TC = )C T(TH): C 2 3,~L 1 LFAC( S,TC, KA rCF 1,CF2,CTA) Cz-4 TS' = 7S )'TT (TS):c'-,^C = C ' s ( ni ' ) o? PCi ST ( PC) C" - S Ll ="' ) S J' CKCB' (PC) "2 '.i SL?- J'J ',F ( KC C,:; T S) C?""'. fi= ( { P 1;:- ' S L I-T S 1 ' SL 2 ) / ( PC-TS) JC'-0 T 2 =P) C 1-SLI /( PC+TS) C, 3i CLP=CF rIT -CF 2 T2 _)r3_2PC = - (..c(PHZ)?C 33 C! =,5 )fP T (P C DC PC) 0734Tci -= TSLTS1:TS1 (; ^^yG 35 > 'APC=AA ' rA(PC).3AT.=-,^A/ (T ).. 37 CP'r Fr ^. =DCP LX(. D3 A PC),, C 3 C, rr INT = L X ( C. D X 0, AT S) "C C CTi = ( C r ':." P;:- PC -C F EWT TS1 ) /( PC-TS ) CC4 r T=Cr F';: C i/(PC+ TS) 3.41 CL Z=CFi CT1 -C -2 'CT2 L'42 Tl =.S T r PH7,'Z. 5 S )/DSCRT PI*KRZ *TS) C4 3 C. X = CFX r(K 7) "I /.+ 4C CS- ': Tr 7. F T C F7 E T C T*TS/SQ2+CXZ*CLZT 1 '045T! =T ( C KC, OC*6 TJ2=P I;:-T1 04 7 I- i c =T i t ( KCt-K Hi);'2 "", 4::~ C X!i=CEIFl/X(qnSC R T(K < Pl S) ) / K R S 3.04, 9; <!:'?S=Ti1+ ( KC KH ) '2* 0", "C73 C=CU1X (i:qS RT (KR2S))/KR2S &'~ 1i KC-. _tu l=KCt~/,OSQ T(KR1S) '( 52;:' 2 =;3:/ ) S '.f T ( iKC 2 S ),3053C T i = C L '.C tq 1 -i 1C CT 3 RC 2 C54 CTl=CIM 1 CFr:F.:AiT2/CPLKi 180

TAB 3C0 5 CT?=CFP *C A * SL2/S02 nOOTLST 1 =i)S Ii\( PHP*.5DO )/DSCRT ( P I*KRP*TS) 05 7 C T~- CT 2 T ILCLP*CFI X(KRP) "C 5S CSP12=CT I*CT2 C QT1 =P I' = KCi3 C6:) Tl=DSC0 T(T1*T1*T1) CClO!C T 1 C l=C IX (KC K+KCB +P[F )-DSQRT(KCB/KCH)*CFIX(KCH+KCH-P(F ) C'062 C I1=CT 1CXl*T1 ^C6 3 CT 1=-CT1 KC3R 1/2.DO/CPLK8/CPLKM Ci64 CSP50=CT 1*CT2 0C65 C S<J,":=C SP12+CSP56;(:56 TH=TH/P C N CC6 7 THV( INDEX ) =TH CC, 6,~ C SAV( I NDEX)=CSA CT69 C SU,^V ( INDEX) =CSUM CC7, I INEX= I NDEX+I 3C71 10C CONTINUE,C7 2 RETURN 0073 END TnTAL MEMENRY REQUIREMENTS 001104 BYTES FDPTPAN IV C COMPILER AAA 04-13-71 2J:59.24 PAGE F'CO1 FUNCTION AAA(TS) C',2Z IMPLICIT RFAL*8 (A-Z) OC03- DATA KD/0.9276/ C004 AAA=2.CC*DS IN KD*TS ) OC05 R TURN CC6 END TOTAL MEMORY RECUIRLMENTS 00015E BYTES 181

E. 5 Program for evaluating the mutual coupling coefficients K 1, K and also the far field elevation plane carrier mode pattern of a double parasitic loop counterpoise antenna taking into account the effects of mutual coupling. Main: i"J'L__ __1 __ - PF_____ ___ PLITT 9.FLq( A` r-H., K, - Z ),t C__. 1_ ( C )__;L, r-;,L P ',A r) 3 S,'__________ C r FMPL[y- ' l DCM PLX_ —., 1 C. A. _ E.. A_ E_ _._ n'r-'{nz CriX(YXY) = ncMPLX (.C{CS(XX),DSTN(XX) ).'~,:'; - _ r__GI!C..Al. 'E:.M, FAL SEo /............. i,"': n,3". q\rTA Sn?^f/1. 414?135a?2.7317/, P I/ 3..41 59253P 7 Q/:) ' 7 '_.A2 TA Pr ' r'/ 57 ')7 9632 67'-94 t E G A M, /. 5 7 72 1566 49 ')1533 /,,',, ',3 PAT R Crl '/.1745323r?19?2 /, Do F /. 789539P 316 3q7448/ f'n ^ _ _ _ __,___ )\TA NT L 3/, I TSI/ I/_ Ofl '1_ q:AP T!-11{i 1.: /5.r t?.. n, 1 5. n:, 7 n,,), /,TH2( 1 ) /7n9. 00,11]. DO. & ] 7?.P —', 7:n,q.[ )/, THS ( l. ),)/5.n,2.D.)r, 5.0, 3 7*~-. 00/ Yl.- 1 f'-JAM.1Fl.VIST /ThN/ KHtKB, KAKCP1,KCHI,KCB2,KCH? q5r^^12 t_ _F1 f AD Il, I _1_ ' "^"' ~ I " 1 -'. T T E ('-, Cq ) n'" l 0 —, (0 T Ff= " (AT { K ' 1 ' ), KK A 0rl: 1fJ: ^fT(inn r'f" 1 KH = t,G15.7' KB = ',K15.7, KA = t'G15.7/ F KCHI= '^'1.5.7,' KCD1.= ',G15.71 K C H2 I &. 7 ' KC. HI.= ', C..... 7....X, '; KCrH? ',C15.7 ' KCR2= ',sG15.7/1X) ______;___.' ' 7 T (. -- -- - ----- T c M) WRI TE (6 2 n ).1 _-....' -f r.1 n^^AT (', ' SX 'T TA ' 4X, t SA ),t X, 'I' (SA) ', RX, tPF(SP+SP2), 5Xt C. T*'R' P*S-'),7X,,PE(S),,lOX, 'II(S) ',10X, 'SCQ SI S OX,' ISl DB /IX 7:',!0_____ iCrLkB 3= 'CMPLX(P PT,F GA. -. DLCDG( KP,. A )P) C 'I.K " K r'n'rL X (EGCA +DiL n'((KB^ " Fr) ),-PrOT) _ -3 (.:. e,, 2 nr;:0C Cn?<;; + K-t< t PI t P,?l - vr" =i ( KC'1 -I!KtH) *(KCH1-KqH) - j n 7 '':) K. 1.K C R t KC.B 1 -+ K(R. I n "23.........__.P: = (KCI?-KH) _________ __2__________________ "*'!** t_ 7 5____ i,' [)" = ( K{ 1 r?-K HI?^C H! )( K KCHZ-KC n K- 1. } _______ 'q.:?,'-,!.1, = ( ICr Pl-KCR2 ) '( KC Pl-KCB2 )+KD1 ) / n:_ KI 1.g:')-= C( rn1 +KCB2)A ( KCF R1+KC?2 ) +K0) nD".2;,___ _,K i: rP=Dc. (')qT K R 1 P)!"j) F I i= ).Of T ( i(t.F)l 2 ) r', 3V P K!)=, PS, Q F: T f ". r )' /D/ I/ K!) n:... __ ___ _.)__. _. n P ' =n(C' T ( /7. n / P I /K l ) ____,34,, CT!L=r -TY KP+-PF). T CF X 1fF ) ______________________________________ (tf. 7 C) Z S= PT:K 0 '(T i -Vp K *TP DPCT ',7 r 3 7 K ' 1 '': 2 =1 K n'FT ( KC 1 / K CB2 ),: (') 3 ' q -1 ":. 1.=,x $, T ( K lC q 2 / KC r 3 ) ('),~z0...C n T 5= C-_.T X ( KR ) /K. P 182

^^l,...r,..- ~,+.,C,,-;" r K,? i' " '. *. '.< "~;"' v '!". 1 / K"' r' '" z t: '1 ~ '^ ' C T 4' I: r' T ->, n ^ 4. 1_____________(; k -*> i p r-. r r- **^ K C r^ ^ / *<'" P ^:/ ~ ),,.C T....r '.. 44 ':-: ",,- ('4 ' + ',. ), ~:"' '~,'~ 4, v '- ') -!< (' ": ~:'~!' fr ] +: r ". ""{'~4'Z~~~~~~~~~~~~~~~4 v.. I.~~~~~~~~L qn47:/' - T {,-. 9 "! r0~~ 4 3~?~ iC; zr i7 ' ~.- =,,' ( K /~ - ) r.^'::'q'i r -t ---. rr- I v. /.:..l)/ v~, " n s! r T 7-r'! y ( I i D /f'r" ~.. ~"._. ~~~~~~~~~~~,.v, V715 71, ~ ~ ~ _ T T T T TT,"' 5 ~ r';'?,;' ' - * — <,] -t- K r:''. '?; {< K; P n,p K ', '-? *~: - C T 'r,-'.'- T ":~ T /5 p. - 4 t. - T,,- T... T., '7,' 54 6," l' 1? - ~' ' / "1 '~ + F K 1! ') n ''^ ^ r' r:, f i' r;.i i,:- f - 7 V Q 7 7 ^T TT C 7 OF ^ ^ ")0 1 ' * r T ~ T T, r l7 CT T ^ ^....:........................-.-.-...........:: -.-... _......_........L^....-.-....-..........-........ —~ _ - --................. I'f.. " -"'.??+ v? i r, P A7". ^n^?f l ~ Tc r,;;-)r' T^ r7 _ ---^^:*,<~~~ ~~ ~~~~~~~ p,' ITT ^n/S^ '7*7 ~~~~~~~T t - ^^(T )-T I T rC r..^ "' -":'~ ' K )'...... —* — r F -. n(r~' t,.~!t (.,. I )(., r K: <A7 <777l ^ ^ ^ 006i -7 Tr ^-.; c I~-r( T I) V) 7? o~~~~~r i pr ns? (, P '-^ 7 ) '"*^7:: '1)"::.[ ':1 f:,: J-1 q A, I " p 1 ),],-; Q.? ':_" _T 1.' ' fT TC I. 'T l__,' '* 7 ^T~ = ( c i - "^n /(P^-fs.~t 7 - r F: l~l-, T i.. /7 '^CI",t/ < ^c.?Y7 T[ S! i'*7,., 7.~ r )"~( i ^T I -'!: T; = ^~1~~~~~~~~~~~~~~~~~ tKU ir vi IT.^- 9 -l tiK!CR C^ 1,C'01CF1 I qr',P? __ _ ~~r.,AL(4_ ''r^ (, H4 - K A, r t:t n C 2 C CF 1 ) ''*!N~r~~, 7.. ~ t. I, r... T '^ * > ^ /..*<. r ' T i f /, "> / ~_' '~ o i r o 7 _ ^ "*:^ r),- " ] r r {\, '* v C I '~ ("A r~ -~' 1 "''' ' - ' ''."~:? 0 "..': 1. l= F/,( r, 1'~ T I+ r~ 7,: v Z ^,CF>]^ rn^4r? ) ' 1 rT *',',, Tp q -;'~" I~~T F''^r ^? )K 'rQ6':~ T r r-::"": ' (T 1 ) C T Q(!7-" C rl. cA ~c- Sl 'rST2 k' Cr _c (' __,'_ 'r C.r7 ':7 Ti.. ":' ~ ".> ' (T C ^^*^^ i" "t~~~~~~~ ~~~ ~~. c.,;"',. ',r 7>'^^ 7)'".;'; T f 1 Tr r"r T el -.'! - i'.VTr;T - '183 r"?,7n! ": "~~.' Z''.;' ' l~q."~:r PI",k~"7~'TS

t~~~~~~~~~~~~~~~~~~~~~~~~~~8T~~~~~~~~~~~~~~~~~~~~~~~~. V....' ). 4.~, '., '., 1.. 'i..~,d,.. b~^~~~8f1. _/.,, 1 1-.j i ll t _ _ _ _ __ ',*.... ';..-.;*,^..; - L,.-. ~ <* s j -j i.~ ' -, ~~~~~~(ij~~~~~~~~~~~~~~,f,,, ', /: J ' _____________ _____________ ____________________j~.,1 (, 1 1/6 *;. L: I..., ( 1' ' i /L (( (: ( ' ' 'I ' '..... i.I.. 1 ( '~) - > ' L A \ <' -V.; I. { '.. ' '/ L........................* * ^ ^,.... -,; -^.. -- ^-...' /c:,L O U '..":u / '.': <. Lb i::, v.,..,. (. i 1.. #. A 9 uJ/Ut iu' L ~, Ki =~~~~~~ (iii( Sj i I {,.,, / ).j'::, '.)(,I! I,i;... (,,,,, ),x~,:.;'.,: /<j i "',(' L L';' ii. ' l ',..i _.,... I ',) u i::9,- -:-i" -'.., /,: V 5.-, 7 -.<.;(4)9~~~~~ ~ ~ ~ ~ L:*';ld A^ ' ) /<^ _* I '~ -:;.'..* )(~~~~ ~ J.u I' 1' A. I: - i.-......______________. (, i t:; ~; i, '.;. ''.. " '... ).. i... S ~ I c i, '- /, ( ( <:.. i A;.> )X...,;J"T! q ~ ~ ~ _ - _ -C^ {^'A J.~* L~ ~j yl+ o 'j A...:l.; / --..^! I.*;',; C! J- L i: 1.** ( * - + ('>1;~~l-.. )^.J. -.~[. r ~ ~ ~ ~ ~ ~ ~ ( 1 )'. i'^ -"'':." " '" " ^ / c —^ ^ it^ cc^ v i *-. / j */\'' i~~ *^,ic [^ ry^ ^ 'T ' '^^ i~~~~~~~~~~~~~ i -At/ l),^!. V- *i i —;. - ^.i J:. i A <. '

E. 6 Program for evaluating the far field elevation plane side band mode pattern of a conventional VOR antenna above ground. Main 0001 I MPL 10IT REAL*8 ( A L, U-HK, O-Z ), COMPLEX*16 (C) UOJ2 REAL*s CDAtS OiJ U3 O)IML NSIUN THV(90), CSAV(90), CSUMV(90) 004 CCMPLLX* o DCMPLX,CFNLWP,CFNEWT GOu5 CLIX(XX) = UCMPLX(UCOS(XX),DSIN(XXJ) uuub LCG1CAL TERM/.FALSE./ 0Ou7 DATA SQ2/1.4142 135623 731/, PI/3. 1415926535697/ U00J DATA Pu[/1. 570796327949/, LGAM/.577215664901533/ J0009 ATA RCON/.01745329251992/ POF/.785398163397448/ O10 DATA NIL//, ITS/I/ 0011 RtAL*t rHl 10)/5.UO,82.O0, 115.0u7*0.UO/,TH2( 10)/Q0.L)U,11O.DO, & 17u.DU, 7*0.U/, THS(10)/5.D0,2.D0,5.0D,7*O.00/ 0012 NAMEL I T /IN/KH,K.A,KBKCBKCH 0013 RAT=1.09/1.08 0014 111 KtAD( 1 INEND=1OO) O0 1 K h=KH*KAT 00 i O I AKASAKAT 001 7 ibCKb* AT 0016 KCB=KCb*3.1415927 UO19 ARITE (6,999) 0020 999 FCRMAT (' 1) 0021 WRiTE(b,1000)KHKA,KBKCB,KCH Oi32 lt000 FCRMAT(' KH = ',i5.7,' KA = ',G15.7j' KB = ',G15.7/ 1 ' KC =,I15.7,' KCH =,G15.7//) Oi3 CP LKt=DCMPLX (PUT, EGAM+DLOG KB*. 5DO ) 0024 CPLKM=OCMPLX(EGAM+DLOG(KB.5DO),-POT) 0025 INDL-X=1 0026 CFNcWA=DCMPLX (0.00 1.8400) u027 DC 100 J=1,90 0028 IF( (J/z)*2NE.J) TH- (J+1 )RCON 00j9 IF((J/2))*2.EQ.J) TH=PI-J*RCON OO0u CALL FCAL(KH,KA,THPHZ,KRZCFZ 00U1 CALL FCAL(KCH,KATHIPHPKRPCFP) 0032 IS = DSIN(TH) OJ33 TC = DCO((TH) 0034 CALL LFAC(TS,TC KA, CF1,CF2CTA) U035 TS1 = DSQRT(TS) 185

i0 37 P L I-JS,, ( PC ) C'0 L SLIi -= J Jit ( It d; PC ) OUU ~; SLt =, - JL'.L ( KCb* t S ) i 4u T.= ( PC i L 1- TS 1I * L 2 ) ( PC - TS ) UOU4 Tz= i PkoL I./ PCLI S) UJO4 C LP=C-;L r i-C 2v rZ 4L^>P^ I. = L)uS(PHZ) *Ju,4 PC1 -= uSw, T(PCL~PC) u04: rb^T-l = TS 1TS l1TSI Oj4G AAPC=AAA(PC) 4 7 A TS=AAA { S) ZiJ41o~ C F;CFU, =-LJCi<.P L X (.OO, APC) 0~i4~ c PLN\ T= -JuC MPLX (0. 0, ATS ) u5,Oi U'=i i:LAb*P PC -C -FNc 1 IS1 )/ (PC-TS) uui i C T2= C'1 P PC 1/ ( PC+ T S) 52 CLZ= CF i CT -Cr;"C TZ u03.T L i =S N ( S PHZ.JO) /D SRT PI*KRZLTS) O p CXZ uA L= WiX(KKLZ) D (; f 5 I, \^ T 'TS/ Q2+ CX LCL L T 1 tu k A } J AV ( I'\ Ls ) -=L - SA dd /1 t1V( 1 IJLX) =TrH 'JJV- i.\L^A= INULcX+ 1 Uod AI TL ( L) > 1) uJo l1 iiAT ' ', 'LA Tr, CSA,ACSt= ' ) uJ3o2 JC J 1 =1 90,Z OJo3 ThA=TV( I ) OCJo ZI=. 1=o. 9/. 5A/. KAT^OCU (T HA) j o5 Th= I tiV( I) /RCC;N OCoo C^A=Ct iX(- I ) *CSAV( i)-CtIX( ZI )CSAV I+1) Juo7 ACS= ACUAoS (CSA).Wo o6 OIIF( AS.LT. 1.-4) ACS 1. D-4 0o9 C3 =20.uO"DLuOGLO (ACS) J070 J r<ir t t (6, 50 ) TH,CzA, ACS, 0 0071i 5i0 FCMAT (t- 2.3,1P0i)15.6) Ju7. u2 COi\NTiNUE J 73 OG TO ill 0 74 '4,,;o TjTAL v:iui Y L lti\'ENTE oOl iCr,: YTIES 186

$RUN -LUA #+SUo+KLIB 1 =SUURCE* cXECUTlUN 6ttGINS F-JRTRAiN IV CUOMPILRK AAA 04-07-71 10:11.14 PAGE UJOl F LNCTIUN AAA(TS) 0002 IMPLICIT REAL*8 (A-Z) j03. JATA KO/0.9276/ 0004 AAA=2. DDS IN( KD*TS) OOt5 RETURN JUOo EoN TOTAL MEMORY REQUIREMENTS 0001iE BYTES tX ECJT ON TER MINAT ED 187

E. 7 Program for evaluating the far field elevation plane carrier mode pattern of a double parasitic loop counterpoise antenna above ground. F!1 TRAN IV G C]MAPILERA MAIN }0001 IiFL I( LIIT kEAL*8(A,B,D-HK,O-Z),COMPLEX*16(C) 0C 2 P AL * CL)ABS 0'C03U iViENSIt'N THV(90), C S A CSAV(9 CSUMV1 (9), CSUMV2(90), iu0 4 NAMEL IST /IN/H,KA,K KC.,KC H (')005 C PIX( 7.) =DC PLX ( DC S (Z, CSIN ( Z ) LOO 6 n RCUi l '=i. 01745329251992.C83 l l EAD(1,INJENDIO=10) t 11+' 09K '-H) KH= K H,- AT ('00 10 KA=KA'R AT 0: ' 116 K '= tK:, AT ( C12 C ALL TA?(KH,KA,KCB,KCH,THV,CSAV,CSUMV1, KB) ~'013 READ( 1 I I.END =100) 00O/ 14 PKH= K! h KA T ( 01 5 KA=KA*-qA1 -)0 616 6K= K Jb AT ( 017 C 7kL L T A [( KI-,KA KCB,KCH, THV, C SA V,C SUMV2, K ) 0( 18 ',.R IT t,.30) '-(, 19 30 FfRMAT( ' ' 1 t IH,CS,AC S DBStJM=-' ),i,;20z O1. 20 1 =1,90,2 0; '21T A=T ' HV I ) )0 22 7'2/ I =. - 7. b R9 7. * T*).:CS ( THA) ( 23 TH=T V( I )/RClN Ot.'24 t S=CPIX (-ZI ) (CSAV (I) +CSU11 V ( I)+CStLIU V2( ) )-CPIX(ZI)*(CSAV(I+1)+ 1CSUWMV I.( I+i)+CSUMV2( I+1 ) 0025 AS= CDAj,: ( S ) *S 2 C002. IF(ACS. 1. 1.I)-4) ACS=1.D-4 027 S UM'!-= 1 -'. ) 0 *U L G 1 0 ( AC S) ' (2 8J i I T. (b, 50 ) T H, CS, AC S, L)SU N ( 029 O JRPrA T ( F -I1. 3 1P4D15.t) 0' ' 2 0. LU Ct' I IN II 00:31 u 1 TO 111 '( 32 100' ALL SYSIEM 0( 33 E ND TOTAL ME', ORY RECtUI E:c E M1ENTb 0) 019C6 BYTES 188

',F-TRAN IV G COMPILER TAB OCO1 SUbR(UTINE TAB(KHKA,KCB,KCH,THVCSAV,CSUMV,KB) 0002 IMP[L II T REAL*8(A, B,-H,K,0-Z ),COMPLEX*16(C) 0(, 'r3 R E A L: CDABS C;0004 DI.'Ef-sNlN THV(90), CSAV(9C), CSUMV(90) 0)0C0. 5 C(JMPL X*16 OCMPLX ( 06 CEIX( X/) = DCMPLX(DCOS(XX),DSIN(XX) ) "C0 7 L(OGICAL TERM/.FALSE./ 0CC3 ) DATA SuZ/1.41.42135623731/, PI/3.14159265358979/ 009) DATA Pi 1/1. 5707963267949/, EGAM/.577215664901533/ 010l DATA IPCON/.01745329251992/, POF/.785398163397448/ (- 1DATA ITL/3/,ITS/1/ ^012 REAL,' rHi( 10)/5.DO,82.DO, 115.f)0,7*O.DO/,TH2(10)/80.DO,110.DO, 1790.,7*0.0D /, THS(1O)/5.DO,2.DO,5.DO,7*0.DO/ 00 13 'l-IT T: (,1000) KHKB,KA,KCHKCB.'14 K G1iCUO FORMAT(' K ti- = 'G15.7,' KB ',.G15.7,' KA = ',G15.7/ t KCH = ',G15.7,' KCB = ',G15.7/iX) '0015 CPLKb = DCMPLX(POT,EGAM+DLOG(KB*.5DO) ) 0)0f' 1 w6 I tn! DEX= 1 ' 017 )DO 1 ' I =1,90 00C 1R 1 ICF( ( I/2 ) *2.NE.I) TH=( I+1)*RCON 0019 IF((1/2)*2.EQ.I) TH=PI-I*RCON 0('29 CALL F( AL(KH,KA,TH,PHZ,KRZ,CFZ) 0021 CALL FAL (KCHKA TH,PHP, KRP,CFP ) ' 002 TS = DSIN(TH) (0023 IC = I)CtU]S(TH) 0(24 C/ALL LF AC(TS TCKA,CF1,CF2,CTA):0 25 'S1 = i)S)RT(TS) 0026 PC = DCCOS(PHP) C2 7 PC 1 = )SORT (PC) r 028 b SL1 - )J ONE (KCB* PC) 0G029 BSL2 = DJONE(KCB*TS) 0(030 T1 = (PCi*l[SLl-TS1*S3SL2)/(PC-TS) 0031 T2 = PC 1'BSL1/(PC+TS) 0;r 32 CLP = CF I*T1 - CF2*T2 0 C33 PC = l;CGS(PHZ) (' 34 PC1 = D)SQRT(PC*PC*PC) 00 35 TS1 = 7S1*TSI*TS1 U036 T1 = (PC1-TS1)/(PC-TS) (037 T2 = PCi / (PC+TS).)038 CLZ = CF-*T1 - CF2*T2 (00; 39 T 1 = SINi(PHZ*.5DO) /DSQRT(PI*KRZ*TS) 00,40 CXZ = CL IX(KRZ ) 0C/+41 CSA = (TS/SQ2)*CFZ-*CTA + T1*CXZ*CLZ 0042 TI = KCG*KCB (,C43 T2 = PI*T1 0044 KR1 S = T1 + (KCH-KH)**2 0.(U 45 C1 -- CL IX( DSQRT( KR 1 S) )/KR1S C'i046 KP2S.- T + ( KCH+KH)**2. 0047 COT3 -= (IX(DSQP.T(KR2S) ) /KR2S,0048t CT1 = (T2/CPLKB)*(CX1-CT3) 0 4049 CT2 = (bSL2/SC2 ) *CFP*CTA Ct0050 T1 = DSIN(HP*.5D0O)/DSQRT(PI*KRP*TS) r 051 CT2 = CT2 + T1*CLP*CEIX(KRP) 005"'2 CSP -= CTl1; CT2 ('05'3 T1 = PI*KCB 189

- s.:, 4; ' ' -,; '.._. --,u "..,... -j~.. —7 -.. 7<o- t!;~ - -.: t. i,... " ~~,, -,.. I -':., Co...~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -'4^ ^~~~~~~~~~~i* ( - ^-... ~ -— ~... —, ~., '. _,!, —, '_; II4 (-: _ * r —=^~~~" C ' - _; ~. V. r-. ~(. 2'-. X L. '~.,.._ '!-r... —, _ L~r: +... _- -~, C'-~.. *"' - C.: \?' _-T-

E. 8 Program for evaluating the far field elevation plane side band mode pattern of a double parasitic loop counterpoise antenna. Main 1 1,.,PLICI 1P r-AL s 8 ( A,, D-H, K,( J-Z),CCOMPLEX*16 (C) '( 'U! AL;t1 ClDA6S - t )I!t IL ' NS l"V I HV(90), CSAV(90') CSUMV1(90), CSJMV2(90) ^,,C 04 NA!'t L I,ST /I N/KH, KA, KB, KCb,KCH ':C05 LPi iX ( LZ )=DCMPLX( DC[)S( ZZ),D SIN(ZZ ) CL0Xih 6RCL >O, = (. C L 17't5329251992 CC 7 RAT=1.t. /1.08 OC0O, 111 tEAU(1, INEND=lOO O0009A WRITE (6,999) ot3010~ g999 FORMIAT ( 1' ) 30 11 Kt1= KH* kAT 0012 KA=KA*RAT 00 1 3 K8= K t*AT CC14 I. 1TE (6b,0ulO)KHKA, KItKCbKCH 3U 15 1i00'0 FDRNAT(' KH = ',G15.7,' KA = ',G15.7,' KB I ',G15.7/ 1 ' KC6 = ',G15.7,' KCH = ',G15.7//) OOlo' CALL TAb(KH,KA.KCB,KCH,THV CSAVCSUMV1,KB) 0017 REtA( 1, Ir,END=iCO) CC15 KH=KH*RAT C C1 KA=KA*RAT CO20 Kb=KB*RAT 0021 WR IT E (6,1000) KH, KA, KB, KCi, KCH O0022 CALL TAB(KH,KA,KCB,KCH THVCSAVCSUMV2 KB 0C23 WP1 IT I(6., 30) 0024 30 FORMAT ( ', Z 2,THTHR,CS, ACS, DtSUM' ) 3025 OD 20 I= 190,2 CC26 TtHA=THV(I) GC27 Z I=6.8 '*7.5*RAT*DCOS(THA) CC2 TH=THV( I )/RCUN C 0C2 9 CS= CPIX ( -ZI ) * ( CSAV (I ) +CSUMV1 ( I ) +CSUMV2 ( I) )-C P IX( Z I )*( CSAV( 1)+ ICSUMV ( I+1)+CSUMVZ (I+1)) CC30 ACS=CDA3S (CS) L031 IF(ACS. LT..D-4) ACS=1.D-4 0C32 DBSUM=20.DO*DLOG1 O(ACS) C 33 WRIT (O, 50 )TH,CS ACS,OBSUM OC34 50 F RMAT (F12.3,1 P4D15.6) C3 5 20 CJNT INUE 0036 GO TO 111 0037 10g CALL SYSTEM OC33 END TOTAL MEMORY RE)UIREMENTS OO1AA2 BYTES 191

:' '-,;~-'-,* \, ' ' i ' I 1 V L —i c - ].. P A L.~. k <.'k -,. /. I 'i:I 1 Ai.A, A 'i\,.,t KC; -i, Ti HV CS' AV,CSJ'V ',r.),........ I... -:t"(,I,,T,,ItL -H1, K,,J-z C,,^I LL X['1 6(C)..V 7, -.,.(- 1. v.....(. ),/ '*, (',' L '. "S X X LSX....,(. 4;,1 1F (-( /L. r). fQS ) TS=1-('yO) ~.~,,:^ *,' ( ix.) -.i;.".L X (,'i % (XX ),L)~ 1r. (XX ) ) ^C*L 7 i. 7 i (,, >/ T.iPL,4,. / S.";."" I.'.!"'T /..':L 7'-t.,.);o~7UJ4/, E:.,AI l.b77215~t~49;tv V3/ ':,''',,.1 },:.. -:/.1..It'',?',b2 l'J /, PU /.785.:39 1 6 397448/ LI I! '"T..:. T_./ 2/'/ 11 JO*l2-* /',",; T il( t;'.,) /.j-J., '. 1 0.,7 *:u.O./,TrH2 ( i0~/80. UO. 110.0 ] i7....., 7;':,. j,/, Tt~( 1] )/5.UJ.,2.;),JD.') Oy,7 O. JS/.' 1S;-'. '; PLX ( P T,c AN'+ LO&( KG.SD(.) ) 'O 1 $ L ^ =J@\*;LX ( L Mi*L KL. ),-P T)..C 5I 7:L. (X= IFQ,._ I7D- l')^rC (PC) <C1 7 ' r (,t I/i);;.!Ne I ) 1 = (T +DS C2, I I,S ^-1 tf- (F I/ )-; '2. rF.,) T'=PI-I'.qC!JN uL:2.) C,,L1 FC.A'NL( '1,K A, TLt PHZ, KR Z, C FZ) C 2 1 CALL.,( A i C i,KAT ii P -PK l PCt P ), C"?2 T = LiSI, (T-q) * r z I -C~l) (PC-T IS), ' C? jrt C ', j -,, ( T H ':u ); ', C 'A _L L"FAC( rSC1,- T L K e A C F2,CT A / ) " 2 ' S7 L = I_,J' T(TS_ ).,i C:5~'r'C T.2 SL2- U =,.:j: ( F rJ * r C-T ) 'C ",T; ( - ",- ' L t-TS1.; 'SL2 ) /( PC-TS) 'CK31vT='"'!, '':",L i/ (PC+TS) ~ &c47 r r,C327 CL =C (..: T ). r 2 i-C T2 Oc- PL. = -".,':S(: 'Z ) -.,iPC i =,)S']3T ( P 'T (PK PC) ~ O~': 35^)A C=..Ai D ( i PC ) 0 CT 7 I", S ).,;C"~ ) " '',-"T=;C;"n LX (i'.L)',ATS ),C C - T = 7 ", "r,-C, _i-t r ' 't)P'^ciC- C Ft^ -T*'TSi1 / (PC-TS ) O(.4l^1~~~ UT2=c_,: -'; P r I k1/ ( 1 r PC+ +TS) C042 CLZ =CI "C A -C F2 - CT 2 ~)t./*3T,; _, ()HrZ,::D.OS)/DSUKT(PI-.KHZ*'iS) r,(-,!; /, x'7 - C""T IT ( K Zr,, ).L 4:) 4,.'...',=.r i-".;:T >,::-'CFf'; T c T * S/S 02-+CXZ*CLZ *T 1 O..4 7 = - i; rT O()4L^ r.;r: 1 i 3=Tl+(!-<t - K,, i',) I: 1 _ 4 4(j z X1 =C[- TX(':,;-T( KR1S) ) /K. i1S uC. K!-,2" =] L+. C Ki+KPh) *.2 CC (5Ci3= C; X(.J, i <T(Kx2S) ) /KP)2 S "'2? v.i. ' K C'/1. S^; (KR1S) (:.C57,.,C.!2 _.P 2:,, /'-)S (Ji'T ( K- 2 S ) O:s'/s C.T i=CX;:'.C- o': l-CT 3*KC r'R2 192

FnRTRAN IV ( COMPILER TAB 02-16-71 08:31.58 PAGE 00d 9~>55 C TIC cr I CCFNLWAtT2/CPLKM OC56 C1 2=CF;'TCT A 1SL 2/SQ2 OC57 TI=DSI N PHP*. 5D0 /DSQR T PI KRP*TS) 0 53 CT2=C T2+T *CLP*CE I' X KRP t ":,^ CSP12=CT l*CT2 '..'T:,Tl=:PI KC3.-:-l tT 1=DS,SRT (T *T 1*T1) i' 2 b CT':=CE IX (KCB+KCB+POF )-DSORT (KCB/KCH)*CEIX(KCH+KCH-P3F ) 00633 CT1=CiT l:CX I*T 2Cb4 CT1=-CTl*KCbRl/2.DO/UCPLKB/CPLKM )05 C SP5oC T 1 'C. T2 C3 66 CSUM CSPI 1 2+CSP 56 C'067 Tf1V I )ctX ) =TH 0063 CSAV( IN DEX) C SA CCt9 CSUV ( INDEX)=CSUM OC70 INOEX=INDEX+l 071 100 CON T I NUE CC72 RETURN 0 073 END TOTAL MEMORY REQUIREMENTS 001162 BYTES F3RTRAN IV O C.i-1PILLtR AAA 02-16-71 08:32.03 PAGE Oi.30 l rulJNCT TIJN AAA (TS) OCC02 I tPLICIT REAL*8 (A-Z) OCC3 DATA iO0/0.92/ iCC4 AAA=. LDO*DUS IN (KD*TS ) 3iCO5 RETURN CCO0 6 EN) TOTAL tr'tMOURY REQUIREMENTS 00015E BYTES 193

E. 9 Program for evaluating the quasi far zone elevation plane side band mode field of conventional VOR antenna above ground. Main, t ', ' t i t t ' - ( L i 1. '~;-. ' '. AS *', \.,',' A,., (.. '/,!,. I " ^' ' t'; t. t'I /!.,71: S' (. ='.-' t i//, r1? f^,' /.W.77, 1Thb * ) I /,, i n T c. /.,i. 3, 5 *2 J/, |f /T. 7^ 5 12 j 3 (t744r / ';' ' '* \T' * \ IT / 7 I S/!/ ' s I -', Il I, F( 10') /.- r,,;^',I1S|. 7^0 i. n?/ TrZ ( I, ) / ^0 40 40.:",";' i' \.- i;"', r / I >L"/ "KH,N.AT, ', KCl tKCi.' " 7-^ r- -- T ( ' 1 * ) * <., >. T' = '.: 7: / 1.I7 r = ';'' I1 ri, -T r;> i/ I -A,. KCh = ~'~:F /. 7.5 -:' 7 L 3 5 I7.'?..... i " I _," t 1I( 1 ) ~'- ^~: " ~ >i 1='; LX ( PrT,F;v V+.IFLC,;(,=:0,) ) ) ' ' -L F r&(K: <A,TH,PHZK ZC,O ) i^ LLL. 3 LKC,KATHPHT PCFP) ' *,: = -," - ' 7 );(? yj ".... '-7 C-.ALL LFAC(TSTC KA,CF1(,C 2,CTA) '''3 '" ( TS 1/.-');-'.)'I F (.;SZ23^......PTT T,, -. L T '' ' A.,-'3';?: ';S ( ^. ( L L()i L C T 1=S:1 ' T _ CE, _5 ( r/4I <., -- -:, '..,-,+_ rnl=,;-t(9W) - -'- -~ -~ r- ~, -,- ~

OC41 BSLl =DJCNF( KC B*PC ) 0042 B St. 2D=JONF ( KCR3T S) e,41 TI- (oCIB S(SL 1-TS1*BSL 2 )/(PC-TS) C C44,. T2=PC * 3 SL / ( PC+TS ) C045' CLP CF 1* T 1-CF 2 T2 0046 PC = DC(S(PHZ) 0047 PC1 = DSQRT(PC*PC*PC) 0C48 T S1 = TSl*TS1*TSI 0049 APC=AAA(PC) 0n 59 ATS=AAA(TS 005 1 CFNEWP=OCMPLX. DO, APC) C002 CFNEWT =DCftPLX(O.DO, ATS) 0053 CT1= (CFNEWP*PCl-CFNEWT*TS) /PC-TS) 3054 CT2=CFJF'EWP*'PC 1/ PC+TS) Fr's rCL=CFt1 CT1-CF2*CT2 ~c?5t 1 r 671 - DSJN(PH?7.5 D)/DSQRT( PI*KPZ*TS) fn 57 CyZ = CE-X(KRZ) '3r,$3 CS A= C. F7t C' AC FNEWT,*TS/SQ 2+CXZ *CLZ* T ~OC('^ t^ T tlCSAV(INDcX)=CSA CC 60 THV( r.NEX)=TH 061 I N C X = I NEX+ 1 C 062 100 C3ONTI NUE. 0C63 'lRITE(6 5l) C 'C4 51 FCO.RATt ','Z2 TH, THR,CSA, ACS,DB ' ) 0065 DD 2r I1=1,32, 2 0C.6 7 TH=THV( I )/RCON ~C67 T-,R =ThV ( I +1 ) / RCCN CC00'63 Z2=8.0-( ( I+1)/2 )0.5 O, 9 CSACSAV ( I )-CEIX(Z2Z*6.89*RAT/2. ) SAV(+ 1) C 73 ACS=C')ABS(CSA) 0071 IF(ACS.LT.1.-4) AC S 1.D-4 C072 CD=2C. DOLOGO ( ACS) C073 VRI TE( 6, 50) Z2,TH,THR,CSAACS, DB 3074 50 FFO'l.AT(Fll. 31P6015.6) C007 2C CCNT I NUE 0076 GO TO 111 0077 END TOTAL V'?FMORY REQUIREMENTS 00D16A BYTES AAA er''0,1tUNC TION AAA(TS) C, ^I 2 1 MtIVPLICITr EAL*$ (A-Z) 2C003 [)ATA KD/C.9276/ 0004, AAA=2.DO*DS TN(KD*TS) CCOr5 RETURN C 005 UNn TOTAL ME?:ORY REQUIREM!ENTS 00015E BYTES EXECUTIJ ON TE R MI NA TED 198

E. 10 Program for evaluating the quasi far zone elevation plane carrier mode field of a double parasitic loop counterpoise antenna above ground. Main 0001 IMPLICIT REAL*8(A,B,D-HK,O-Z),COMPLEX*16(C) 'C02 REAL*8 CDAOS L03 O DI MFNSION THV(90), CSAV(90), CSUMV1(90), CSUMV2(90) 't.'-0,4 NAMFLIST /IN/KHKAKBtKCB,KCH 0005 CPIX(ZZ)=DCMPLX(DCOS ( ZZ), OSIN(ZZ ) 0006 RCON=0.01745329251992 0007 RAT=.09/ 1.08 0008 111 READ(l,IN,ENO=100) 0009 KH=KH*RAT 0010 KA=KA*RAT 0011 KB=KB*RAT 0012 CALL TAB'(KHKATKC8,KCHTHV,CSAVCSUMV1 KB) 0013 READ(1,INEND=100) 0014 KH=KH*RAT 0015 KA=KA*RAT 0016 KR=KB*RAT 0017 CALL TAB(KH,KA,KCB,KCHTHVCSAVCSUMV2,KB) 3018 WRITE(6,30) OC19 30 FORMAT(' ','Z2,TH,THRCSACS,DBSUM=') 0020 DO 20 I=1,32,2 0021 TH=THV(I) 0022 THR=THV(I+1) 0023 Z2=8.0-( (I+1)/2)*0.5 0024 CS=CSAV(I) +CSUMV ( I )+CSUMV2( I )-CPIX(Z2*6.89*RAT/2. )*(CSAV( I1) 1CSUMV1( I + 1)+CSUMV2( I +1) ) 0025 ACS=CDABS (CS)**2 0026 IF(ACS.LT.1.D-4) ACS-1.D-4 0027 DBSUM= 10.DO*DLOGl1(ACS) 0028 WRITE (6, 50) Z2,THtTHRtCS ACS,DBSUM 0029 50 FORMAT(F11. 3 lP6D15.6) 0030 20 CONTINUE 0031 GO TO 111 0032 100 CALL SYSTEM 0033 END TOTAL MEMORY REQUIREMENTS 0019BE BYTES 196

-,c.':N IV G COMPILER TAB 02-19-71 10:46.58 PAGE 000 t'001 SUBROUTINF TAB(KHKAKCB,KCHTHV,CSAV,CSUMVKB) 0002 IMPLICIT REAL*8(A,B,D-H,K,0-Z ),COMPLEX*16(C) 0003 REALB* CDA3S 0004 DIMENSION THV(90), CSAV(90), CSUMV(90) 0005 COMPLEX*16 DCMPLX 0006 CEIX(XX) = DCMPLX(OCOS(XX),SIN(XX)) 0007 L3GICAL TLRM/.FALSE./ 0008 DATA SQ2/1.4142135623731/, PI/3.14159265358979/ 0009 DATA POT/1.5707963267949/, EGAM/.5772156649)1533/ 0010 DATA RCON/.01745329251992/, POF/.785398163397448/ 0011 DATA NTL/3/,ITS/1/ OC12 REAL*8 TH1( 10)/5.DO,82.00,115.DO,7*0.DO/,TH2(10)/80.DO,110.0DO & 173.DO,7*0.00/, THS(10)/5.DO,2.DO,5.DO,7*0.DO/ 0013 WRITF (6,1000) KH,KB,KAKCH,KCB 0014 1000 FORMAT(' KH = ',G15.7,' KB = ',G15.7,' KA = ',G15.7/ &' KCH = ',G15.7,' KCB = ',G15.7/lX) 0015 CPLKB = DCMPLX(POT,EGAM+DLOG(KB*.5DO)) 3016 INDEX=1 0017 DO 100 I=1,32 0018 I1=(1+1)/2 0019 DEC=.5*11 0020 Z2=8.0-DEC 0021 IF((I/2)*2.NE.I) TH=DATAN2((7.5-Z2),30. D0) + POT C022 IF((I/2)*2.EQ.I) TH=DATAN2((7.5+Z2),30.ODO)+POT 0023 CALL FCAL(KH,KA,TH,PHZKRZ,CFZ) 0024 CALL FCAL(KCHKA,TH, PHP,KRP,CFP) 0025 TS = DSIN(TH) 0026 TC = DCOS(TH) 0027 CALL LFAC(TS,TCKA,CF1,CF2,CTA) 0028 TS1 = DSQRT(TS) 0029 PC = DCOS(PHP) GC30 PC1 = DSQRT(PC) 0031 BSL1 = DJONE(KCB*PC) 0032 BSL2 = DJONE(KCB*TS) 0033 Tl = (PC1*BSL1-TS1*BSL2)/(PC-TS) 0034 T2 = PC *BSL1/(PC+TS) OC35 CLP = CF1*T1 - CF2*T2 0036 PC = DCOS(PHZ) 0037 PC1 = DSQRT(PC*PC*PC) 0038 TS1 = TSI*TS1*TS1 0039 T1 = (PC1-TS1)/(PC-TS) 0040 T2 = PC1 / (PC+TS) 0041 CLZ = CF1*T1 - CF2*T2 0042 T1 = DSIN(PHZ*.500)/DSQRT(PI*KRZ*TS) 00C43 CXZ = CFIX(KRZ) 0044 CSA = (TS/SQ2)*CFZ*CTA + T1*CXZ*CLZ 0045 T1 = KCB*KCB 0046 T2 = PI*T1 0047 KR1S = Ti + (KCH-KH)**2 0048 CX1 = CEIX(DSQRT(KR1S))/KR1S 0049 KR2S = Tl + (KCH+KH)**2 0050 CT3 = CEIX(DSQRT(KR2S))/KR2S 0051 CT1 = (T2/CPLKB)*(CX1-CT3) 0052 CT2 = (BSL2/SQ2)*CFP*CTA 0053 T1 = DSIN(PHP*.5DO)/DSQRT(PI*KRP*TS) 197

f,'RTRAN IV G CC'IPILLi TAb 02-19-71 10:46. 58 P KC ):'.t, CT2 - CT2 + Tl*CLPx'CEIX(KRP);'55 CSP = CT 1 * CT2 'OCK.6 T1 = PI *KCG 0057 T1 = DSQRT(Tl*TlTl) 2C5SC1 CT1 CF IX(KCR+KCB+POF) - DSQRT(KC/KCH)*CEI X(KCH+KCH-POF) 0, C5 3 CTi = CT1 T CX1 * T1 oc CTL = CT / (-2. DOCPLKB*CPLKb) &,;(C'1 CSP2 = CT1*CT2 0062 ASA = CO)AS(CSA)**? 00C3 DOCSA 10.DO)DLOG1C(ASA) C06, C4 CSU>J = CSP+CS P2 v00r5r ASIJU! = CDA S( CSUMl)**2 30C 6 ARCSUt U = AR GC(CSUM)/RCON ^" 67 DASUM = 10. )DODLOG1 ( ASUM) _C, ",,.,C S = CSA +C S P+ C SP2 6~ 0tAC S = CDABS(CS)**2 00e70f Di3SUM = 10.DO* DLOG1O (ACS) OC 7! TH= TH/RCON CC72 T HV( IND)tX)=TH C(07 3 CSAV(IN)E X) =CSA C ) 74 C SU: V( Nt DEX )=CSlUM 0C75 INDEX=I D3FX+1 0C76 IF (TERM) GO TO 79 0077 GO TO 100 C"7S 79 RI TF (6,1001) TH,CSA,CSUM,CS,ACS, DBSUM CC79 1001 FORMAT('OTH = ',G15.7,' SA = ' 2G15.7/' SP+SP2 = ',2G15.7/ &' S = ',2G15.7/' /S/ SQ = ',G15.7,' /S/ DB = ',G15.7) 0080 100 CONTINUE 0C 81 RETURN 0082 END TCTAL r.MEMORY REQUIREMENTS 001114 BYTES 198

E. 11 Program for evaluating the quasi far zone elevation plane side band mode field of a double parasitic loop counterpoise antenna above ground. Main;'( '1 l'l'L (:1 T PF AL*8( A,B,D-HI,K,-Z1),CnMPLE X* 16(C) 'C '2!t{ AI~'L~'~ C:JA3S ~,C ';)! I.41t:E 'J\ SI N THIV(90) CSAV(90), CSUMV1 (90), CSUMV2 (90) -C4 L A I FL IST / IN/KH,KA,KB,KCIB,KCH (i k. ~"f,'I X ( * ) =I CMPLX ( OCOS ( ZZ ) S IN (ZZ) ) l)' >) RAT =: 1. /1. 0 OC (7 11 Rt-AL( I, IN, LN[)=00l) CO(0.8 WRI Tr (6>999) k30009 9C99 F[}IMH, A T ( ' 1' ) 0010, K tK= KH*R AT c001 1 KA=KAA R A T (i1 2 K?=K,*R AT 001 3 WR I TE (6, 1000 )KH, KA, KBHKCB,KCH 0C14 10C0 Ft'RMAT(' KH = ',G15.7' KA = ',G15.7,' KB = 'tG15.7/ 1 ' KCO = '0G15.7,' KCH = ',G15.7//) (0015 CALL TA (KHKA,KCB,KCHTHV,CSAVCSUMV1,KB) 0 1 6 READ( 1, IN,END=100) C( 1 7 KH=KH*PAT OC' 1 KA=KA-RAT,0019 KriKB*RAT 0020 WR ITE (6, lC:)0 ) KH, KA K, KCBKCH 00 1 CALL TA(KH,KA,KCB, KCH, THV,CS AV, CSUMV2, KB) 0C?2 U?,P IPTE( 630 ) '0023 30 Fi(R.PAT ( ', 'Z2,TH,THR CS, ACS, DBSUM= ) 0024 DO 20 1=1,32,2 0025 TH=THV( I) 02 5 THR=THV(1+1) (0027 Z2=8.0-( (I+1)/2)*0.5 OC28 CS=CS AV ( I ) +CSUMV 1 ( I ) +CSUMV2( I )-CPI X( Z2*6. 89*RAT/2. ) ( CSAV( I +1:l 1CSUMVI ( I+1 ) +C SlJMV2 ( I+1 ) ) OC 29 ACS=CDA3S(CS) CCO3 IF(ACS.LT.1.D-4) ACS= 1.D-4,103,, 1 O SlUM =2 0. DO-D LOG 1 0( AC S) C0 32 WR ITE ( 6, 50) Z2 TH,THR, CS ACS, DBSUM 0C33 5C FORPMAT(F11.3,1P6D15.6) 0C 34 20 CN(TINUE 0C35 GO TO 111 0C036 100 CALL SYSTEM 0 37 EN TOTAL MFMORY RECtJIREMFNTS 001A76 BYTES 199

F(iF T.N TV C, CL'IPIl ER TAB 02-09-71 1l6:12.34 PAGE 000.0t-"r'i SIt-rtJCL01 INF TAH(KH,KAKCB,KCH,THV, CSAV,CSUMV,K8),o")'r3 I rPLICIT REAL*8(A., BD-HK,0n-Z),COMPLEX*16(C) 0, '73 PEAL*8 C ARSS 00 4 DI)YrMSION THV(90), CSAV(90), CSUMV(90) "CS CC',"rPL FX lt6 1)CMPLX,CFNEWP,CFNEWT 'iCt ( - C C[ rX(XX) = OCMPLX(DCOS(XX),OS SIN(XX)) 00C ( 7 LULIC. AL TERM/.FALS. / OCOt,, DATA S02/1.41'42135623731/, PI/3.14159265358979/ OC0i9 DATA PnT/1.5707963267949/, EGAM/.577215664901533/ 0010 DATA RCGN/.01745329251992/, POF/.785398163397448/ 001 1 DATA NTL/3/ ITS/1/ 001? RFAL 8 THI (10 ) /5.DO,82.00D,115.DO,7*.00D/,TH12( 10)/80.DO, 11 0.DO & 170.D0, 7*O.DO/, THS(10)/5.DO,2.D0,5.00,7*0. 0/ 3013 CPLKB=DCMPLX(POTEGAM+DLOG(KB*.5DO)) C 1 4 CPL'KMDCMPLX ( EGAM+DOLOG(KB*.50D),-POT ) OC 15 INDEX=1 0C16 CFNFWA=DCMPLX(O. 00, 1.84DO) C017 Dn 100 I=1,32l ri C, 1 = (I +1)/2 CC,1 9 DDEC =0.5* I1 0020 Z2=8.0-DEC ':021 IF(( /2 )*2.NE.I) TH=DATAN2 ( 7.5-Z2 ),30.ODO) +POT?? 2 IF( (I/2 )*2.EO.I) TH=DATAN2( (7.5+Z2), 30.0 DO) +POT ) 023 CALL FC AL (KH KA TH, PHZ,KRZ,CFZ) 00;24 CALL FCAL (KCH,KATH,PHP,KRPCFP) 0025 TS = DSIN(TH) 30?o TC = DCOS(TH) 0027 CALL LFAC(TS TC. KACF1,CF2,CTA) C728 TS1 = DSORT(TS) 0029 PC=DCOS(PHP) 0030 PC1 =DSSRT (PC) I00 31 BSL 1= DJ1ONE ( KCb*PC ) 003 2 BSL2= UJNE (KCB*TS) 0033 T1=( PC I*8SL1-TS *8SL2 )/(PC-TS) 36034 T=PC1 L *SLl/(PC+TS) 0035 CLP=CFI*Tl-CF2*T2 0036 PC = DCOS(PHZ) 0037 PC1 = TSORT(PC*PC*PC) 003R TS1 = TSI*TSI*TS1 0039 APC=AAA(PC) 0C40 ATS=AAA(TS) 0041 CFN E WP=DC PLX (O. DO, APC) 00 4? CFN E T= DCM PL X ( O.DO,ATS) 0043 C T1=(CFNEWP*PC1-CFNEWT*TS1)/(PC-TS) 0044 CT2=CFNEWP* 1/PC PC+TS) 0045 CLZ-CF 1 CT 1-CF2*CT2 0046 T = DSIN(PiZ*.500)/ DSCRT(PI*KRZ*TS) 3C047 CXZ = CEIX(KRZ)' 0048 CSA=CFZ*CTA*CFNEWT*TS/S02+CXZ*CLZ*T 1 0049 T1 =KCfB KCB 0050 T 2=P T *T 1 C 51 KRI S=T 1+ (KCH-KH) **2 052 CXl( =CE X(DSORT(KR1S))/KR1S 0053 KR2S=T 1+( KCH+KH)**2 OC54 CT3=CEIX(DS RT(KR2S) )/KR2S 200

;TRA\N iV;.,"7-LFi-., 02t< O-09-71 16:12.34 PAGE 0 r ~.', i — <',t/ ) t,:1l ( K'1S ) * *K~t t _.. 2'-K "/" ). )Oi i (Kt? S}.I 1, -I T I,, L T 2 / C P L 2 (Ci k*"C T^i.SL?/S02 *'IT. -./:^I ( *)S.(' T ( P I*KRP*TS);j *: )!CT. =1:C [:.T+ T1 *TCLP'CE IX (KPP)?'S' L?-CT 1 1CT2 I' L)S3RKT( TI'Ti*Ti ),. t. T 1 = C.T'- IX (':..+h C~+*POF)-IISQR T/.C3/KCH CE I X ( KCHttKC t-POF ) n70\ T H=T T H/P ^r,5 -- v '-II 2. D C/C PL K /C P L Kv. *71 TrT-V( I ')LX )=TH 17^ C. SU:-V( I;\N E X ) =C SUP 74 T' X=I N ""EX+l c75 C 10 C r T I rTI.JE 7nRF: fT LrTURN:77 END r TAL ^ F i Y EG EJIMENTS 1 1 E BYTES AAA 'C' I FL^ T II 1N AAA( S ) "<2',? 1,I^ l IL. IT tFAL *84 (A-Z) i, sT ) 3l.i *ATA KF)/O,)2/ P^C' 4 QAAA2.= l)O ) S IN KD[ TS ) OC )iT, 0 L R f\, C." ~ b., I: t.; I ) TGTA l M'W,<Y ^FvOJI f NTS COI15L BYTES 201

APPENDIX F THEORETICAL ELEVATION PATTERNS OF CONVENTIONAL VOR AND DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNAS The complex far electric field pattern functions are expressed as: S() = ReS(0)+ i ImS(0) where ReS(0), Im S(0) represent the real and imaginary parts respectively of S(0). In all the tables the different columns represent the following: Column 1 gives the angle 0 measured from the vertical axis, Column 2 gives the real part of S(O), Column 3 gives the imaginary part of S(0), Column 4 gives S()j2 which is the power pattern, Column 5 gives 20 log10 1 S(0) i. e, gives the pattern in dB. The phase of the far field can be easily obtained from Columns 2 and 3. 202

TABLE F-la: FREE SPACE ELEVATION PLANE SIDE BAND MODE FAR FIELD PATTERN OF A CONVENTIONAL VOR ANTENNA. kh=2.75, kA-51.69, kd=0.92, kb=0. 15, f=1080 MHz. 0 Re S(0) Im S(0)| s(0) 22og10 l S(e)I,.,;t, -,'.-, ' '_.'i:-C *2.34;5122L-Cz. 0354 tSL)-C2 -3.C 3 544 01,....;...'':-CJ 1.2574 1.-02 1. O744D-C2 -.S4115L 01....- *..;.-L-tC2 -4., 36 151L-03 2.534100D-02 -3.192352D 01;,.,, 1., -,__ 'jl:- 2 1. U0966c5L-02 2.5c434L,3D-02 -3. 1f:91'J 01 iJ. uo0 2. oC'7 1L-C2 4.556bC 1L-C '. 134571j-C2 -2.5'/8992D 01 12. 6C D.;C3CC1;;-C2 4.,547t07 -02 '7. Z94172D-C2 -2.2 L 4C4 01 14.000 7'. _o / jO.i:-C _ 5. 3161 5L-02 c.373b84D-02 -2.C561630 01 lo.J u..3 2,). t CZ:cL-C-. c.464147L-0i 1. 299474U-C 1 -1.7 2465D 01 1.6.t,. C L-C 1 6, 4- 1. 1 -C 1 1.00074D-C1 -1.4~9419D 01 C. O.c -C 1. Ct34Cr-1bJdL-01 2.25 b538D-C1 -1.2c234C5D 01. 2Cu ctL-C 1. 49 615- 5-01 2. 5 4210-01 -1.120006v 01 r 4.0C2)vC.3 C0264L -C1 2.5 518 t -0 3 1 3, 4 99446D-C1 -.10o113D 00 _c. j 3.CC; C572L-C 1.Cf50c L-01 4.354115D-C1 -7.222001D 00.5.X3jOC 3.7 3C010l.-C1 3.4031.1L-01 `. 426 1D-01 -5.f^6191D 00 '0. COi. 10 l- 4. d3 1c i-C4l t. C2417 4D-0 1 -4.4C2049b 00 '2.C LC 4 -. 1 5. 1b3122-01 '. 1 - 16 57D-C1 -2.Et 421D 00 0.O 0 5.9j /.7dL-C 5. 9'111 L-C1 ~.4C. 327D-01 -1.L452257D 00 'C.,C '.,Cc C5C-C 1 6b.6.o990L'-0 1 9.6z 1372D-C1. - 'LC84D-C 1 36.000 7.6 706CL-C I. 1/ cL-C1 i.Cl1522D 00 6.8C7070.L-01 C.,~0 o.5731oC -Ci 8.7794f3E-01 1.227104D CO 1.l'.763CL CO V2.u V 9.7_ 7, 27L-C1. E Ei427L-C 1 1.-67642D CO 2.845549D 00 -s.O v0 1.&,LL43 1 C; 1.C7o5o3L 00 1. 537t09D CO 3.;1_19D 0 4o. O 1C i. lcc54L CC 1.1u1515 C 1.6 0716D 0 4.4C59071i GO '.00CC 1.2uLct7CL CO 1.267452LI 00 1. 91471D 00 5.C6 419 00 5. 0 O.:,'27L CC 1. 6717'L CC 1.40723D CO 5. 59272D 00 -2.OCC 1.4qcC9t31L (C 1.4904C1C O 2. C91236D 00 36.40tC67L CC 5-.oC-O i.5.13CCL CC 1.55d Lq( OC 2.13156D CO 6.CG240O 00 Sc._.CC '.c.L 6uL. CC 1.(6C14CL CO 2. 4337D 00.213143D 00 5o.,CC.ci5oL CC 1.447 CC 1.E47S- C,.47953D C0 7.413786L 00 ctC.0C I.ccc977U CC 1.o99541C 00 2;.396056D CO 7.5cC3b6D GC.CJ0 1.7 C4i7CL CC 1. 55dC2C GC 2.471 CD CO 7.77 3355D 00 6.4.0CC i.725450L CC 1.7bt9331 O0C 2.4b520L CO 7.S16822D 00 c6. CO0 i.51183L CC 1.77dv8L. CC 2.496239D 00 7.945723D CO c.C 1.74iJ33ic CC 1.7177GI GEO 2. 45070bi 00 7.7 t581D CO 70. OCL L.7C5 bL CC 1.6142C'L OC 2.3-44EF8j CO 7.4C17C2D 00.OCO 1.6CC5I73L Cc 1.465275L OC 2. 13546D CO e.7t3-246D OC 74. CC 1.4531 L CC 1.34c574D CC 1. 91150D CO 5.938349D 00 7C.OCC 1.zc4utCL CC 1.t t.1 57C )C 1. 754Uc3D 00 4.t49J65D 00 X7.lCO 1.C-5z 1L: CC 1.C96226i; COC 1.216C6D 00 3.646046D 00 cC. CC o.36579L~-C1 9.7lib 61L-01 1. Z951800 C0 2.2 46L605D 0C 203

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TABLE F-II: FREE SPACE ELEVATION PLANE CARRIER MODE FAR FIELD PATTERN OF AN OPTIMUM DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA kh = 2.7755, kb = 0.1514, kA = 52.1686, kd = 0.9276, kH= 3.4819, kB = 16,3363, kH2 = 12.7671, kB = 11.3097, f = 1090 MHz. Re S(o) Im s(o) (S(0)12 20 log10l (o) 2. "'~ i.').,:,"" n- C i * 15?9 1 )-? ' 3. 11 7264J-02 -1. 5J62653 r i4. ' 3:._.':7 1), t-' 1 1.33' o64 [- 2 1.009316D- I1 -9.7: 4Jd9 ) CO. ^. I S' - 2 - I -. 1 3539D-C2 1.714772i)-01 - 7.657 93 D,. ",., 1i:',-..'I -i -?.9~ /.1 c'(,)-02 1 *7864 )-01 -7)40 7.4 07,J 00 _~.?'0 C ",_ 3 ~:?-6.? _ 1F~1[ -. "-C 1. 5 5 0 i ') - 1 -. 137760 ) 9 C 2. ', _ 3: "_ t ^^ -.)''l -. 17:7^74 '~-, 1 ]. 27tvC. 4)- 01 -8.9I762,D O0!4.'? '.-', it,-'C i - l.647J28'0,-)1 1.042.9%2')-:1 -9.31'CJ9lg iC 1o. "..?-;:.?J-, i - 1.~ 41 3i)-3 1 8.3 12 250D-,02 -1. 05491.~ C1 1;.-:? 1. 3 -4'2 ' -C] -.27185i3)- 'i 8.410335i)- 2 -.G1 717D C1 2':.' 1.171 i n-C 1 -9.6lC?6D-r 8. 187C, 50-02 -i.086d7LD Cl,2- i." t~ 7I^7 i47- 2 -2.,i 20 C7-' n 7.93656-3 )-J2 - 1.03b67. Cl '-t.'~ ' - i;..4437, l - 3 l."C0'88- i i 1.09125)D-0i - 5.96u549D iC 2. *"; -;.16 2 69; - 3 - 39 8445)- 1 1. 6252 7D-1 - 7. 8'9oC2 0C 2.. 0, -2.'z 491- 1 -3.462 1C -' 2.424,49D-01 -6. 153i52D C 3 ~ '.- -.:_-,+l -.e4.')~4.. -C. I — 4.4752 7CD- G1 2.875174D-$i - 5.4133061 00 3 2.' _ -1.75')&5 —. ] -5. -'3. 5 32L-C1 2.86726 D-01 -5. 4 2 2 (IC 34.','* - ', 73.:- ' ", -.8,8C211 7D-01 3.40.)57, I)0-0!1 -4.6 44'3-8 C. C 3 3..'? 3. 74- 3D-' 1 -,. 571 5 2 - C' 566 )7 0-0 -2.54451 0 'Ci ^., " C c-..c 2 7 - i - 1 7.1 5 322 - 1.43 C891. i -2 5 4 4 72 3D- 1 L. " ' ~. 7' 7, -Cl - 7.6 9364) D-.4 1.41 32 ) C0 1.5 2 2 C-O 42. l..:l I 3 143. C-,79506L 1 I1 1.3S:9?5D 5)C 2. 6477o05,,C 4.'" 3 1.1'43'4330 CO -.5976 7o )-01 2.046539D 0C 3.11'J4L22 C0 4.":$ l.',',2q -'9.755qCD-'0 2.0118240 00 3.03:9;D C0C i4?.'" i.,-_,/ _-l; -9.4c 919i94-01 i.853758i2) 00 2.692229D CC 5-'J.C 3 c.t: D-,.-i 9-.924 431)-01 1.738410D 30 2.4I15Z30 CU 52. 7.7 21 '7D-. -_1. 4,74CD CC 1.7280)'37D ) 2. 375530J CC _54.?>* 7. i o -. -C 1-1.1129461 4O 1.824955D JO) 2.612524 000 56,.," 7.71 944:)- i -1.174713D C"0 1.9759100:30 2.9 )7671D 00 a58.E:,; 7.78 )o4[-" 1 -1.224)55i) C. 2.1036q4 JO3 3. 2298256 t C 6 C.' 7.2 946C 5 1 3 -, i -1.24?9 t 2.140334D 00 3.3't3ioDL CC 207

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TABLE F-mI: FREE SPACE ELEVATION PLANE SIDE BAND MODE FAR FIELD PATTERN OF AN OPTIMUM DOUBLE PARASITIC LOOP COUNTERPOISE ANTENNA kh = 2.7755, kb = 0.1514, kA = 52.1686, kd = 0.9276, kH = 3.4819, kB = 16.3363, kH2 = 12.7671, kB = 11.3097, f = 1090 MHz. 0 Re S(0) Im S(0) \S(0)12 20 logl0 S(0>) 2.000 -3. 7 1 1,'-1 -n 4.4735SOD-02 3.7392510-01 -P.5546631D 00..000 -6. '^,96,0-01 5.9927260-02 6.3353030)-0I' -3.964653i) 00 6.000 -7. S`-o,:)-1 6.3379450-02 7.4230010-01 -2.- 1409i) no 3;.000 -?7.J-.>:?.>)-01 gF.5055610-0'2 7.0736010)-01 -3.00713-) '00 10.00 - S.3 '?0-)-0) 9. 7920230-02 5.4 10157 -01 -5.3353 02 00.~ O -. 5*9S~. -01 9.0630490-02, 3.091?130)-01 -1. 19742) 01 14.000 -7.60- ^,0D- 0..51 20300-02 1.213060D-01 - I.*f6?, 01 16.0,0 n 1 r?7o ' -1 1. 155412D-01 1.539153D-01 -1.6254340) 01 s.0O0O ^.-5z/?^lI -ni 1.2319290-01 2.8274770-01l -J1.097.000 -01.000 3.97( 70. r I 1.4365D-01' 4.151635 D01 -7.6355120 00 22.000 D.6 tq1896'q),01 1.232012-01 5.752377D-01 -4.$,030530 0 234.000 7.- 33 0 1.-33273D560-0 1 7. 9350270 -01 2. 0 0 26.000 1.0./460 ) 00' I.3 13 5D-01 l.O5369,9D-'00 4.'54333D-01 20 1.00 1. 15 00 99701 1.292692 00.9 0 0.:000 394 4.43492,) 0)0 70.243197-001 I1. 45234qcD 00 3.2414l139 00 39.000.,4a572746) 00 3,.2716130-01 1.501792D130 305327 2 O0 34.000 1.35 7 567 ) 00 4.4945260-01 1.429963 ) 0 3. 1022'?9' OQ 36.000 1. 3?31 600 93333-01 1.26350.2 2.0'3333-) 00 -33.000 3.37qA4390->01 7.47' 63240-01 1. 122914D O0 1-006932D 00 4Z,0.000 6.05'36!5'0I 9'-0256241)>01 1.069360 00 7.24O760-Ol 42.000 5. 03 i 71 1,)-Ol 1'0230210 OC 1. 14006700 D 1O1 1D 44.04 0.5. i,;231 -01 1. 10'3770D' OC I.233633D' 00 1..23721D0/0,' 46.000 7.34?1;)-01 1. 169603) 0 3.5, 2.304233>0 4q53.00)0 I 09?59100 1.9 1032D 00 ' 1. 01104: 00 4.1,2042D 0 -50'.000 1.-3794950) 00;1.3170153-00 1.9072320 00 5.60.07? 2)0 0 52'. 0O0 1 7'76591) 00 1 -.3802830 001 2.21 1332D'00 6.8939777 0) 54.000 2.')n9747ir n)O 1.43/46303) 00 '2.4692600 00 7.R13370 00 56.n000?.9, s0z ) 00 1'.4972360) '00 2.66.667D 00.525R9) 0,) 5.00 0.-3571RD 00 1.5.7434.00,?.8345910 00 9049809000 60.000 2-:4o94,0F 00 1.6469.50) 00 2.9932590,00 9.52 70 00 210

0 Re S(O) Im S(O) S(O)2 20 logloS(0)I 62.000 0.6551O5) 00 1.6842071) 00 3. 144240D900 9.9503130 nn. 64.000 2.036l0?$_ 00 1.668176D 00 3.262361 00 -.027064D.01 66.000 2.qoI59i ) 00 1.606974D -00 -3.31417RD 00 1.- 040752.-0 6..000?o.Q.s941,) 00 1.527080)0 00 3.2'71382.90 900 1.02958, - 01 70.000 2.719?23.3 nO 1.4550450 00.3..1217'58D 00 9.-.q879s84-) 00 72.009,.50.779- 00 1.402477)00 2.86894 44 0 9.1 5 49- 1'Q. On 7Z.r, r.. 1 32 63 00 1.362023D 00.2.535 1 7 ) 00..031332:) 0Q"'Q 76.000,..707-' 00 1.3135370i 00 2.1543610.030 '6663711.) O 78.000 1.2I? 9lI:) O) 1. 2349330. 00 1.760699D 00, 4.9137030 00 0'. 000.o551 37)D-01' 1. 112030D 00 1.384949t) OO 2.8286750 00 82.000 4.6I 7'00U-01 9.439363D-01 1.048647D' 00 4.. 1259639-01 /4.000 1.73R16.?-01 7./434930D-01 7..635404D-01 -2.343359D 00 q6.'00 -1.26654;c0)-02.5. 327631' -0 1 5.3291 37p-0 l-5.46663D 00 3. OO - I.075963i)-01 3.372245D-01 3.5397360-01 -9.0205D20 00 90.000 -1.?65730-01 1.. 79200D-01 2.20352 '-01-O 1- 3-7136 —1-l 92.000 - 1.n1r351 -01 7.112399D-02 1'.2421640-01 -.1.811642D 01 94. 00 -5.5463390)-02 1.568607D-02 5.7638820-02 -2.478570D 01 96.000 -1.4041i34;)-02 3.043054D-.03 1..43677.90-00. -3.,652200.01 98.000 6.9.253s9D-03 l. 5549450-02 1.702.1940-02 -3.537932D.-O I 00.0on 3.752232)-03 3.292354D-02 3.313667D-02 -2.^59332) 01 02.000 - 1.595015i)-02 3. r71 120i)-0.2 4.1 R6R42b-02 -2.'756?70,'01 04.000 -3.7/4, L)570)-02 2.5765060-02 4. 545348>D-02 -2. 6R4S66D 01. nnr'-/-. Ar, q~- n9 -. 4/2, 009 0- 03 4.5. 2430-02 -2. 6767070 01 -1 10.000 -,. A,-::/-i V7))-03 -.4. 1q8303.-02P 4.2261 730D-0 -. 741OSY,01 11 '. 00. lf7l070~0)-02 -3. 1451630-02. 3',9027h21)-02 -2.,172600 01 1 14.N0') 3.515 '/,0-02 -3.R6q.4710-03 3. 53R0770)-02 -2.9024660.0,l t1 1 6.?O'~. 3',0' cO-02 2.26RO0320-02 3. 233353)-02 -2.9506920.01 11q.000DA -q.,~1?~~.60lh)-03:2.952749D-02 2.974769D-02 -3.053093D 01 120. 00 -,,*'~ 3~/)<')-02 1. 2553931)-02 2.649352D-02 '-3. 15334L0 '1 122...00 -2. r0055990233746-02 -1.233746 04 2 2.354,6880 02 -3.256133D 0,1 124.000 1. 132770D-03 -2.191972D-,02 2.194897D-02 -3.317172D 01 126.000 1-75~q7)70-02 -8.2952720-03 1.-9374530-02 -3.425538D1) l } 92. OOO t ~ 0',',1 -69?-02 1 76 1760-02 1.6991550-0 -3. 539534!) 01 130.000 - 5. 7?004D-03 I. 506668D-02..1. 620709D-02. -3.530590D 01 132.000 -.352360-02 -1.6 3156D-04' 1.3524640-02 -3.737748001 134.0-00 -9.3773700-03 - 1.23469D-02 1.26,1000D-02 -3.79051 0) 0O 1 136.000 9.'9zi559D-03 -6.045106D-03 1.1 424880-02 -3. 842970) 01 13.,00r0 5.6 l 41 790-03 7.420672D-03: 9.3536110-03 - 4 0504 1 D 01,14 O.f0 -5-. 333:00-03 7. 7427240-03 9.6945310-03 -4.026946D 01 142.000 -6.03R9930-03 -3.6470 54D-03 7.0548170-03 -4.3030280D 01 144. 000 3.5 5250-03 - 7.43855D-03 8.249330-03-4. 6 71 6. 0 01 146.000 3.3O601 50-03 1.689.840-03 5.6448860-03 -4.496690D 01 148.000 -2.707968.-03 6. 800710D-03 7..353793D-03 -4.2669770 0 150.000 -4.6504590-03 -. 15020PD-03, 4.790580D-03 -4. 639222D0 01 152. 000 3-.03199D-03 -6. 426670D-03 7.-1024 I'D-03 -4:. 297209D 1 154.000 ' 3.9235150-03.1.56630D1-03 A4.2246030-03 -4.74842D 01 156.000 -3.7737520-03 6.2582400-03 7.307994D-03 -4.'279404001 15R.000 -2.934382D-03 2.6396950-03 3..946972D-03 -4.8074720 01 1 60. o 4.62 776D-03:5.990313D0-03 7. 56.60210-03 -4.242265D3 01 162.000 1.4158 I1D-03 4.1980770-Q3 4.4312781-03 4.7069420i 01 164.000 -5.' 1315740-03 5.274048D.-03.7.3585760D'^03 -4.266412D-.01 166.000 7.109189D-04 6.126476D-03 6.167585D-03 -4.41977DD: 0 168.000 4.38332540-03 3.718943D -03.6.0984320-03 -4.4295640.' 01 170.00,0.-3. 322334D-63 8;.2 1237D-03,.:9Q42650-03 -4. '100304d 01 ZSt

UNIVERSITY OF MICHIGAN 3 9015 03525 1944