THE UNIVERSITY OF MICHIGAN 7140-1-F AFAL-TR-66-101 STUDY AND INVESTIGATION OF UHF-VHF ANTENNAS Final Engineering Report February 1965 through February 1966 April 1966 J.A.M. Lyon, N.G. Alexopoulos, C-C Chen, A. M. Kazi, G. G. Rassweiler, D. L. Smith and P.R. Wu Approved by,.A.M. Lyon, F'/fessor Electrical Engineering Contract No. AF 33(615)-2102 Project 6278, Task 627801 O.E. Horton, Project Monitor Air Force Avionics Laboratory AVWE Research and Technology Division, AFSC Wright-Patterson Air Force Base, Ohio 45433

THE UNIVERSITY OF MICHIGAN 7140-1-F FOREWORD This report was prepared by the University of Michigan, under the direction of Professors Ralph Hiatt and J. A. M. Lyon on Air Force Contract AF 33(615)-2102 under Task Nr 627801 of Project 6278. The work was administered under the direction of the Research and Technology Division, Air Force Avionics Laboratory, Electronic Warfare Division, Wright-Patterson AFB Ohio. The Task Engineer was Mr. Olin E. Horton; the Project Engineer was Mr. James F. Rippin, Jr. The studies presented herein began 1 February 1965 and were concluded 31 January 1966. This report was submitted 16 February 1966. Th1A1chnical report has been reviewed and is approved. /o EPH A.DOMBROWSKI Lt Colonel, USAF Chief, Electronic Warfare Division iii

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE OF CONTENTS Page LIST OF FIGURES vii ABSTRACT xi INTRODUCTION 1 II LOADED CONICAL, PYRAMIDAL AND HELICAL ANTENNAS 4 2. 1 Loaded Helical Antennas 4 2. 1. 1 Construction of Antennas 5 2.1.2 Measured Far Field Patterns 5 2.1.3 Near Field Measurements 25 2.1.3. a Probing Equipment 25 2.1. 3. b Near Field Amplitude Measurements 25 2.1.3. c Near Field Phase Measurements 33 2.2 Loaded Conical and Pyramidal Antennas 37 2. 2. 1 Far Field Measurements 39 2. 2. 2 Near Field Measurements 42 2. 2. 2. a Amplitude Measurements 42 2. 2. 2. b Phase Measurements 56 2.3 Conclusion 56 III BIFILAR LOG PERIODIC ZIGZAG PYRAMIDAL ANTENNAS 64 3. 1 Far Field Patterns 64 3. 2 The Near Field Amplitude Measurement of Log Periodic Zigzag Antenna 64 IV FERRITE LOADED WAVEGUIDE SLOT ARRAY 73 4. 1 Preliminary Design and Tests 73 4. 2 Array Design Procedure 78 4.3 Computer Programs for Slot Impedance Properties 83 4.4 Magnetic Bias Control of Ferrite Array 85 V FERRITE LOADED SLOT ANTENNAS 87 5. 1 Power Capabilities of Ferrite Loaded Antennas 87 5.1.1 Preparation for UHF-VHF Heat Run 87 5.1. 2 Observed Temperatures in Ferrite Loaded Slot 88 5.1. 3 Significance of Observed UHF-VHF Produced Temperatures 91 5.2 Slot Antennas With Ridges or Irises 91 5. 2.1 Assumptions of the Study 94 5. 2. 2 Solid Ferrite Loaded Antenna 94 5. 2.3 Loaded Slot Antenna With Irises 96 5. 2.4 Ridged Loaded Slot Antennas 103 5. 2. 5 Conclusions and Summary 107

THE UNIVERSITY OF MICHIGAN 7140-1 -F TABLE OF CONTENTS (continued) Page VI CHARACTERISITICS OF FERRITE MATERIALS 113 6. 1 Derivation of Permeability Determination Equations 117 6. 2 Results of Permeability Measurements 122 6.3 Permittivity Determination Method 127 VII EFFICIENCY MEASURE MENTS 130 7.1 Efficiency Data on Ferrite Loaded Helix 130 7.2 Measurement Procedures 131 7. 2.1 Measurements 131 7. 2. 2 Calculations 131 APPENDIX A -ENERGY TRANSFER BETWEEN A HELIX AND A FERRITE ROD 136 APPENDIX B - LOADED HELIX AND CONICAL HELIX ANTENNAS 147 APPENDIX C - EFFICIENCY FORMS 163 ACKNOWLEDGE ME NTS 167 REFERENCES 168 vi

THE UNIVERSITY OF MICHIGAN 7140-1-F LIST OF FIGURES Page 2-1 Bifilar 4" DiameterWith Balsa Wood Core and Cap. 7 2-2 Loading Diagram: Bifilar Helix (No. 213) Layer Loading. 8 2-3 Fiberglass-Epoxy Tube Form for Helices. 9 2-4 Effects of Balsa Wood and Epoxy-Fiberglass on Helix Antenna. 10 2-5 Helix With Thick Layer Ferrite Loading. 11 2-6 Helix With Thin Layer Ferrite Loading. 12 2-7 Helix With Thick Layer Ferrite Loading. 13 2-8 Helix With Dielectric Loading. 14 2-9 EAF-2 Ferrite Loaded Helix (No. 213). 15 2-10 EAF-2 Ferrite Loaded Helix (No. 213). 16 2-11 Bifilar Helix (No. 213) Antenna Patterns. Loaded Versus Unloaded. 17 2-12 Bifilar Helix (No. 213) Antenna Patterns. Loaded Versus Unloaded. 18 2-13 Monofilar 4" Helix With Small Tube For Center Conductor No. 215. 23 2-14 4" Diameter Monofilar Helix (No. 215) IE I2 Linear Power. 24 2-15 4" Diameter Monofilar Helix (No. 215) IEg1 Linear Power. 26 2-16 Block Diagram For Near Field Phase Measurements. 27 2-17 Antenna No. 223 With Magnetic Probe Above the Surface; Shown in Anechoic Chamber. 28 2-18 Probe Carriage System on Top of Anechoic Chamber. 29 2-19 Block Diagram For Near Field Amplitude Measurements. 30 2-20 Antenna No. 217 With Magnetic Probe in Position. 31 2-21 Near FieldAmplitude of AntennaNo. 217. Probe PositionX/6 Above Antenna Surface. 32 2-22 Near FieldAmplitude of AntennaNo. 217 With Ferrite Layer. Probe Position X/5 Above Antenna Surface. 34, --, vii

THE UNIVERSITY OF MICHIGAN 7140-1-F LIST OF FIGURES (continued) Page 2-23 Phase Shift For Bifilar Helix No. 217 at 500 MHz, 0. 9 cm Above the Surface. 35 2-24 Phase Shift For Bifilar Helix No. 217 at 900 MHz, 0. 5 cm Above the Surface. 36 2-25 Tapered Loaded of Pyramidal Helix No. 223. 40 2-26 Tapered Loaded on Pyramidal Helix (221). 41 2-27 Antenna No. 223 With Magnetic Probe in Position. 43 2-28a Near Field Amplitude of Antenna No. 223. Probe Position 1/8" Above Antenna Surface, Unloaded. 44 2-28b Near Field Amplitude of Antenna No. 223, Unloaded; Probe Position 1/2?" Above Antenna Surface. 45 2-28c Near Field Amplitude of Antenna No. 223, Unloaded; Probe Position 1" Above Antenna Surface. 46 2-29a Near Field Amplitude of Antenna No. 223 With Dielectric Layer. Probe Position 2. 8 cm Above Antenna Surface. 48 2-29b Near Field Amplitude of Antenna No. 223 With Dielectric Layer. Probe Position X/11 Above Antenna Surface. 49 2-30 Antenna No. 221 Shown With Magnetic Probe Above Wire. 52 2-31 Near Field Amplitude of Antenna No. 221, Unloaded Probe Position X/12 Above Antenna Surface. 53 2-32 Phase Shift For Antenna No. 221 at 500 MHz, 0. 9 cm Above the Surface For Four Different Faces, Unloaded. 57 2-33 Phase Shift For Antenna No. 221 at 900 MHz, 0. 5 cm Above the Surface For Four Different Faces, Unloaded. 58 2-34 Phase Shift For Antenna No. 221 Along the Wire 1, Unloaded. 59 2-35 Phase Shift For Antenna No. 221 Along Wire 2, Unloaded. 60 2-36 Phase Shift For Antenna No. 221 at 900 MHz, 0. 5 cm Above the Surface Along Wire 2, Unloaded. 61 viii.

THE UNIVERSITY OF MICHIGAN 7140-1-F LIST OF FIGURES (continued) Page 3-1 H-Plane Patterns of Log Zigzag Antenna (No. 225). 65 3-2 H-Plane Patterns Log Zigzag Antennas at 700 MHz. and 800 MHz 66 3-3 Log Zigzag Antenna. 68 3-4 Near Field Amplitudes of Zigzag Antenna No. 225 Unloaded. 69 3-5a Near Field Amplitude of Zigzag Antenna No. 225 Loaded With 3/8" Inside Layer of Ferrite Powder. 70 3-5b Near Field Amplitude of Zigzag Antenna No. 225 Loaded With 3/8" Inside Layer of Ferrite Powder. 71 4-1 Proposed Mechanical Configuration For Waveguide Test. a) Details of the Feeding Loop. 75 4-2 Experimental Details to Determine Insertion Loss of Waveguide. 77 4-3 Types of Slots and Their Parameters. 80 4-4 Simplified Final Configuration of Array With Shunt Slots. 84 5-1 Block Diagram of Power-Temperature Measurement Set-up. 89 5-2 Peak Temperature (Position 4) Vs. Power Level. 90 5-3 Temperature Vs. Position in Cavity. 93 5-4a Impedance Diagram of Slot Antenna Loaded Entirely With Solid Ferrite (Frequency MHz). 95 5-4b Impedance Diagram of Slot Antenna Loaded Entirely With Solid Ferrite. Double Stub Tuner Used. (Frequency MHz) 97 5-5a Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Iris (Frequency MHz). 98 5-5b Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Iris. Double Stub Tuner Used. (Frequency MHz). 100 5-5c Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Iris (Frequency MHz). 101 5-5d Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Iris (Frequency MHz). 102 ix

THE UNIVERSITY OF MICHIGAN 7140-1-F LIST OF FIGURES (continued) Page 5-6a Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 104 5-6b Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 105 5-6c Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 106 5-6d Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 108 5-6e Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 109 5-6f Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 110 5-6g Impedance Diagram of Solid Ferrite Loaded Slot Antenna With Ridges (Frequency MHz). 111 6-1 Ferrite Properties, Advertised Values. 114 6-2 Ferrite Properties as Measured by The University of Michigan. 115 6-3 Experimental Setup pr and e Measurements. 118 6-4 Geometry For Toroid Measurement Technique. 123 6-5 Z - 0 Chart. 129 7-1 Equipment Setup For Efficiency. 132 A-1 Ferrite Rod Fed By a Helix. 137 A-2 Energy Transfer Between Two Coupled Lines. 144 B-1 k - 13 Diagram of Bifilar Helix. 150 B-2 Effectiveness of p or e Versus Layer Thickness. 160

THE UNIVERSITY OF MICHIGAN 7140-1-F ABSTRACT This report indicates some of the advantages of using ferrite loading in a number of types of traveling wave antennas. Studies have been made on ferrite loaded helices and ferrite loaded log conical antennas. For a given frequency of operation it has been found possible to reduce the diameter of each of these types of antennas by a factor of approximately 55 - 70 per cent. Some variation in performance as a function of the amount of loading or thickness of the ferrite layer was observed. Near field probing techniques were used to show that ferrite loading changes the position of the active region on the log conical spiral. Likewise, near field probing shows that a particular region is active at a lower frequency when ferrite loading is applied to a helix. The effects of ferrite loading on the log zigzag type are also indicated. Relatively high efficiencies have been obtained for the ferrite loading of helices and log conical spirals. The power limitation occasioned by the use of ferrite loading for the rectangular slot antenna has been examined. For rectangular slots loaded with powdered EAF-2 ferrite designed to operate at 300 MHz it is estimated that the cw power limit is less than 50 watts.

THE UNIVERSITY OF MICHIGAN 7140-1-F INTRODUCTION The research and development effort described in this report is concerned with a number of topics related to the ferrite loading of UHF-VHF antennas. A substantial part of the time has been spent on the loading of the log conical spiral and the helical antenna. The understanding of the helical antenna in the loaded condition appears basic to the understanding of the loaded log conical spiral antenna. In general, backward-fire traveling wave antennas of these two types were used rather than forward-fire or bidirectional traveling wave antennas. In this way the influence of any backing reflector or cavity was eliminated. The analytical effort was devoted largely to the helical antenna. This antenna with ferrite loading was studied using a sheath helix model. With this model the appropriate boundary conditions were represented and the determinantal equation obtained. This equation was then used in conjunction with a Brillouin diagram in designating the radiation region of the ferrite loaded helix. The n = -1 mode corresponding to circular polarization of a helix was emphasized. Extensions of analysis to the tape helix with ferrite loading have been started. Computer studies are involved in the analyses. In previous work the ferrite loaded rectangular slot antenna was appraised. In this contract the ferrite loaded rectangular slot was incorporated in a simple linear slot array. A preliminary examination has been made but this report does not presume to present any final analysis of the array. Efforts in this direction will continue under a subsequent contract. Further studies were made on ferrite filled slot antennas utilizing ridges and irises. This work involved experiments where the ferrite filled slot took a different shape other than rectangular due to the use of a ridge. Also, some of the

THE UNIVERSITY OF MICHIGAN 7140-1-F ferrite elements were replaced by balsa wood, thereby effectively changing the shape of the aperture. This later arrangement would correspond to a slot antenna with an iris. Some changes in radiation pattern and efficiency were observed with these various arrangements. Some basic studies were made concerning the manner of energy transfer from a helix to a ferrite slab. In this way the end of the ferrite slab was an excited aperture and its radiation characteristics were observed. However, the experiments and the analysis did not progress to the point where one could evaluate the efficiency of energy transfer or its efficiency of radiation as an antenna. In the study of loaded antennas, it has been necessary to make some refinements in the methods used to determine their efficiencies. Although the problem of measuring efficiency is generally circumvented in much antenna work, the neces sity for such a determination is very apparent when loading is considered for the efficiency of radiation tends to deterioriate with loading. Any resultant reduction in the size of an antenna must be considered in comparison with a reduction in the efficiency of radiation. Thus, the efficiency of radiation is one of the most important criteria. Very acceptable levels of efficiency (on the order of 50 per cent) have been obtained in the case of ferrite loaded helices and ferrite loaded log conical spiral antennas. A loaded log zigzag antenna was designed and tested. The advantage of ferrite loading in this type of antenna was marginal due to a breakup of the near field pattern and excitation of the forward wave region. This effect has also been noticed with the loading of log pyramidal antennas. Further investiagtion of the causes and methods for alleviating the near field breakup will be necessary. For the first time substantial attention has been given to the power limitations of ferrite loaded antennas. However, due to limitations of equipment, information is still lacking on their ultimate power handling capability. It was found possible

THE UNIVERSITY OF MICHIGAN 7140-1-F to test a ferrite loaded rectangular slot with 9 watts power input. Steady state temperatures within the ferrite loading of a rectangular slot were obtained for various positions for three levels of power input. The previously determined efficiency for such an antenna would indicate that approximately one-third of the input power goes into heat in the ferrite material. Power tests up to 100 watts input at 300 MHz are planned for the future effort. This report gives additional information on available ferrite materials useful for the loading of antennas. The materials considered in some detail are the EAF-2 ferrite and the type Q-3 ferrite. The latter material has been obtained from the Indiana General Corporation and is useful for loading for frequencies below 200 MHz. In the work covered by this report, the type Q-3 ferrite was used for the preliminary measurements on the slot array antenna.

THE UNIVERSITY OF MICHIGAN 7140-1-F II LOADED CONICAL, PYRAMIDAL AND HELICAL ANTENNAS It is very desirable to solve for the effect of loading material on the conical log-spiral antenna. The log-spiral antenna is inherently broadband; thus the decrease of bandwidth noticeable in some loaded antennas may not be a major problem in loaded spirals. The helix and conical antennas are discussed together because, as has been shown in the literature, the bifilar helix antenna at its best radiating frequency behaves very much as the active zone of a conical-helix antenna of equal diameter. The helix has the advantage that it may be solved theoretically for some material loadings since it is a periodic cylindrical structure. 2. 1 Loaded Helical Antennas Solutions for the propagation velocities and attenuations of the currents on the helix are possible for a loading of concentric cylinders with a material of arbitrary!u and e, the permeability and permittivity. A theoretical discussion of the loaded bifilar helical antenna appears in Appendix B, where it is shown that a possible rough approximation to the antenna diameter reduction with full core or thick-layer material loading is given by the formula, -+1 Reduction = e +1 cE+1 where e, p = relative dielectric and magnetic constants, respectively. This calculation assumed an approximate sheath analysis and only a small E( < 10). Calculations using a tape model (Shestopalov, 1961) show the same dependence on E, using the same small e assumption. All the theory to date is for the slow wave region, extrapolated into the radiation region. It should also be noted that this reduction is in diameter. No theoretical estimation of length of the active zone

THE UNIVERSITY OF MICHIGAN 7140-1-F has been made yet, since the entire radiation process has not yet been solved. The diameter reduction is due to the phase velocity and wavelength reduction of the current traveling around the wire, which causes a smaller circumference to be phased properly for radiation when the structure is loaded with a material. 2. 1.1 Construction of Antennas The experimental portion of the helix antenna investigation consisted of making a number of monofilar and bifilar helix antennas wound on fiberglass shells and loaded with powders of various p and e. Table II-1 describes the helix-type antennas used in the past year of work. Figure 2-1 shows a picture of a bifilar helix with a balsa wood core. This balsa wood, which has been found experimentally to have little electrical effect on the antenna, is used as an inside retainer to the loading powder so that a layer of loading powder may be inserted next to the bifilar helix windings as shown in Fig. 2-2. Figure 2-3 shows a sample fiberglass epoxy tube, made in this laboratory, as a form for winding the helix antennas. Figure 2-4 shows the effects of the building materials on antenna patterns; the effect of these materials is small at the frequencies (> 300 MHz) used in most of the experiments. The fiberglass does seem to affect the patterns at 300 MHz, possibly due to a loading effect since fiberglass has an e = 4 and a thickness of.04", comparable to our thinnest shell loading; however, this frequency is much too low for good operation with a loading of this thin shell of fiberglass, according to present theory and experience. 2.1.2 Measured Far Field Patterns Figures 2-5 through 2-12 show the normalized antenna patterns ( E ) for various loadings of bifilar helical antennas. The loading materials used were the EAF-2 ferrite powder (e = 3. 8, p = 2. 2), described in Section VI and a dielectric powder (Eccoflo Hi K 10, c = 10) obtained from Emerson and Cuming, Inc. Thus, powders with two different values of and e were available as a partial

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE II- 1: SPECIFICATIONS OF HELIX TEST ANTENNAS I.D. Number Dimension 213 214 215 217 218 231 Type Bifilar Monofilar Monofilar Bifilar Bifilar Bifilar Diameter 4. 15" 4. 13"? 3. 85" 4. 65" 2. 1" 1. 1" Length 10" 10" 14. 5"? 16"? 15" 8" Conductor 58-U -" cu. tube | 58-U 174-U 174-U 8 Turns 6. 5 7. 0 5 9. 5 20 20 Pitch 6.60 130 70 6.50 6.60 (1.5").7" 3" (1.8") (.75") (.4") * 7-strand, 14 gauge copper antenna wire. Note: All antennas above, except No. 218, are constructed on three-layer fiberglass epoxy tubes,.04" thick and fed by infinite baluns. No. 218 used a paper phenolic tube. Conductor was commercial coaxial stripped of the outer insulation, and is specified without the RG prefix.

THE UNIVERSITY OF MICHIGAN 7140-1-F.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................-........................................................................................................................................................-...............................-....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................:- x............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ -X X.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... -. n-........... -.44:X..............................................................X.....................................................................::::................ X.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... Fi j i................ in!!................................................ limit: X.............................................................................. X..................................... X X.................................................................................. X............. -.X...........x................................................................ X X. X................X.................................................XX.......... X. X. X X............. X............................................................ X................................................................................................................... X................................................................................................................................ X............................................................................-................................................................................................................-......................................................................................... X........................... two,:;........................................................................................................................................................... X:.......................................................................................................................................................... X.X.......................................................... ::X.......................................................................................................................................................................................................................................................................................................................................................................................................................................................... Fiji..............-............................................................................................................................................................................................. X................................................................................................................................................................................................. —;.....................................................................................................................................................................X............X................................................................................................................................................................................................................................................. -..............................-.............................................................................................................................-.........................................................................................................................................................................................................................-............................................................................................................................................................

THE UNIVERSITY OF MICHIGAN 7140-1-F 4" Dia. Fiberglass Tube, 11 3/8" Long. 1/2" Layer Ferrite Powder 3" dia Balsa Wood Core 1/2" Balsa Wood Plugs Side View 1/2" layer Ferrite Powd End View FIG. 2-2: LOADING DIAGRAM: BIFILAR HELIX (No. 213) LAYER LOADING.

]%,.i mg ONOEl iM. Bolivia:!.......................... i:j ilir.r i- igm

THE UNIVERSITY OF MICHIGAN 7140-1-F I ii,1 i I II I / I 900 MHz 710 MHz 600 MHz N 500 MHz 400 MHz Unloaded Helix Balsa Wood Core -_ _ Fiberglass Tube Inside Against Helix. 300 MHz FIG. 2-4: EFFECTS OF BALSA WOOD AND EPOXY-FIBERGLASS ON HELIX ANTENNA 10

THE UNIVERSITY OF MICHIGAN 7140-1-F 0' // 400 MHz 500 MHz 550 MHz 600 MHz ~J 650 MHz o00 MHz "x v) \,'X 750 MHz 900 MHz 800 MHz - -- unloaded --- -— 1/4" layer —. full core FIG. 2-5: HELIX WITH THICK LAYER FERRITE LOADING Linear plots of E:. Ferrite p=2. 2, e=3. 8, Helix Diameter = 4. 5". 11

THE UNIVERSITY OF MICHIGAN 7140-1-F 400 MHz 500 MHz 550 MHz NI \ ' 600 MHz 650 MHz 700 MHz 750 MHz 900 MHz 800 MHz unloaded --— 1/16" layer 1-k1- 13" layer. FIG. 2-6: HELIX WITH THIN LAYER FERRITE LOADING Linear plots of E2 Ferrite I = 2. 2, e = 3.8, Helix Diameter = 4. 5".

THE UNIVERSITY OF MICHIGAN 7140-1-F 400 MHz 500 MHz 550 MHz 600 MHz 620 MHz N'b MHz 750 MHz 800 MHz 900 MHz --- unloaded -—.5" interior layer -.. full core load FIG. 2-7: HELIX WITH THICK LAYER FERRITE LOADING Plot of E, Ferrite i =2. 2, e = 3. 8, Helix Diameter = 4" 13

THE UNIVERSITY OF MICHIGAN 7140-1 -F a I'm 400 MHz 50 500 MHz 600 MHz 650 MHz 700 MHz 750 MHz 900 MHz 800 MHz — ~ ---unloaded - 1/8" layer 1/4" layer FIG. 2-8: HELIX WITH DIELECTRIC LOADING Plots of E2 Dielectric e=10. Helix Diameter = 4. 5". 14

THE UNIVERSITY OF MICHIGAN 7140-1-F 400MHz 600 MHz 500 MHz L./ I f 700 MHz 800 MHz 900 MHz FIG. 2-9: EAF-2 FERRITE LOADED HELIX (NO. 213) AIR LOADED, - - - 1/2" INSIDE LAYER FERRITE. 400 - 900 MHz. 15

THE UNIVERSITY OF MICHIGAN 7140-1 - F I 400 MHz 500 MHz 600 MHz I 1 I: I 700 MHz 800 MHz 900 MHz FIG. 2-10: EAF-2 FERRITE LOADED HELIX (NO. 213) - AIR LOADED, --- FERRITE LOADED 1/2T" LAYER OUTSIDE, 400 - 900 MHz. 16

THE UNIVERSITY OF MICHIGAN 7140- 1- F /'T 1.,0 1.0 ',I ' ' I r I'I? 500 MHz 550 MHz (a) (b) 1.0.0 /1.5. 2.3 vertical 600'MHz 620 Mlz (C) (d) 700 MHz (e).0' ' 71 0 MHz 750 MHz 720 MMz (h) ~~~~~~~(f)~~(e (g) FIG. 2-11: BIFILAR HELIX (No. 213) ANTENNA PATTERNS. UNLOADED VS LOADED E= LINEAR POWER, 0 = POLAR ANGLE, P = POWER RECEIVED, AIR LOADED, ---- FULL CORE FERRITE POWDER LOADED, - - - 5" INTERIOR LAYER FERRITE POWDER LOADED

THE UNIVERSITY OF MICHIGAN 7140-1-F 1.0 (a) (b) (d) ( \' 5 I 4., Ii, 'I~~~~~~~~~ _ IOI.% 550 MHz 450 MHz 68500 Mz Hz (g) (h) ( FIG. 2-12: BIFILAR HELIX (No. 213) ANTENNA PATTERNS. LOADED VS UNLOADED. E = LINEAR POWER. 0 = POLAR ANGLE, P = POWER RECEIVED, - AIR LOADED, ---- FULL CORE FERRITE POWDER LOADING.,. 5" INTERIOR LAYER FERRITE PON.DER LOADING 18

THE UNIVERSITY OF MICHIGAN 7140-1-F check on the theoretical formulations being done. A major parameter of interest is the thickness of loading necessary in order to achieve good antenna reductions, since a full core loading may weigh too much. In assessing the effectiveness of loading (i. e., the "best" loaded frequency versus the "best" unloaded frequency) from far field patterns, many criteria are available, such as maximum radiation efficiency, pattern shape, specific pattern requirements such as beamwidth or front-to-back ratio, etc. In addition, either the lowest frequency for acceptable operation or a center frequency may be chosen as the "best frequency". Unfortunately, not all criteria give the same reduction. Two criteria will be used to compute reduction factors: 1) The center frequency for maximum radiated power on axis; (for a fixed net input power, after allowance for mismatch). 2) The lowest frequency for reasonably axial, backfire antenna patterns. The first criteria evaluates the backward wave radiation characteristics, and will prove more applicable in extrapolating to a conical helix performance, since the "active zone" of the conical helix (discussed in the next section) is a zone of maximum radiation. The second criteria above applies to helical antennas, but is not readily extrapolated to conical helices, since the low frequency operation of a helix corresponds to the operation of the tip, or apex of the conical helix. The apex is not a critical region in conical helix design. Table II-2 shows the center frequencies (criterion No. 1) for loaded helices, taken from data not shown in the figures. Normalizing the thicknesses to wavelengths and the frequency reduction to a fraction, the reduction factors for criterio No. 1 (from Table II-2)and for criterion No. 2 (from Figs. 2-5 to 2-10) are shown in Table II-3, along with the theoretical reduction factors from Appendix B. Two important things are summarized in Table 11-3. First, a reduction factor for a helix antenna diameter can be achieved which approximates, but is

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE II-2: FREQUENCIES OF PEAK RADIATED POWER LOADED BIFILAR HELICES Antenna Loading Thickness, t Loading Frequency for Maximum (Inches) (-) Material Radiated Power, MHz No. 217 0 Air 730 "t 1/16.0033 Ferrite 625 i" 1/8.0064 " 600 t" 1/4.0116 " 550 i" Full Core 450 No. 213 0 Air 820 1/2.0238 Ferrite 560 1/2 (Outside).0216 " 510 Full Core " 530 No. 217 0 Air 730 1/8.0064 Dielectric 610 1/4.012 tt 570 Note: a) Thickness relative to X is taken at the center frequencies listed in column two. b) Layers are inside and within. 04" of the conductor, unless specified otherwise. c) Frequencies for best circular polarization were usually lower; e. g., for 1/8" dielectric, 550 MHz was the best frequency. 20 --

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE 11-3: REDUCTION FACTORS FOR LOADED HELICES Loading Inside Experimental Sheath Material Loading Reduction Theoretical Thickness ( ) Factor Factor Lowest Freq. Center Freq. (Eq. B. 29) Ferrite Full Core. 7.64.58 " ~.022 (Outside).7.62 ~. 58.024.78.68 '. 58.012.7.75 ~. 58.006.75.82.003.8.85 Dielectric Full Core -.45.012.74.78 ~.45.006 1.0.83 21

THE UNIVERSITY OF MICHIGAN 7140-1-F always larger (less reduction) than the full core theory for thick layers of ferrite. Second, thick layers greater than.25-. 5 of the radius behave as full core loading while thinner layers can be used with less than full core diameter reduction. The layer-effect predictions of theory, given in Eq. (B. 45), show that layers of.015X thick, (for the helices used) should give approximately full core loading. Table II-3 partially verifies this. In addition, these are two indications from the data that contradict the simplified theoretical approach used; 1) The effect of the dielectric was not as great as theory predicts, although about equal to the ferrite. This contradicts later near field measurements as well. Notice that, due to a lack of material, thick layers of dielectric have not yet been tried. 2) The outside loading of ferrite appears considerably more effective in size reduction than the inside loading, although in Section VII, efficiency is shown to be reduced with outside loading. Intuitively one might expect trouble with interferences at the outside ferrite-air boundary, causing poorer patterns and smaller radiated power than with inside loading. Further data will be required on the above two contradictions. In addition, the reduction factors shown with either criterion are not as good as those achieved for the pyramidal helices discussed later, nor are they as good as the phase measurements on the helix. In general, the antenna pattern measurements of loaded helices do not allow as good a prediction of loaded conical helix operations as first anticipated. A monofilar antenna (No. 215, Fig. 2-13) was constructed similarly to the bifilar helices. Although most of the theory in this report applies only to backward wave radiation, it is certainly expected that a decrease in current phase velocity will decrease the diameter of a monofilar phased for forward radiation. The patterns in Fig. 2-14 (vertical polarization) show that based on criterion No. 2, the lowest operating frequency of the monofilar helix has been reduced 22

- --------------- - - - - -- - ---- - --------------------------- --.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... I............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... r an.......................................................................................................................................................................................................................... X............................................................................................................................................................................................. f ail,.............................................................

THE UNIVERSITY OF MICHIGAN 7140-1-F 1.5 1.5 1.5 - 1.0 1.0 5 5@\s45 P Ik,'7/10 X1,5 Mo (a) (b) f' (C) 250MHz 300 MH 400 MH: 600MHzI 650MH. 700 MH FIG. 2-14: 4"1 DIA. MONOFILAR HELIX (NO. 215) IE I LINEAR POWER. UNLOADED --- FULL CORE FERRIE POWDER LOADED........ 24

THE UNIVERSITY OF MICHIGAN 7140-1-F from the 650 - 700 MHz to the 450 MHz region. This is more reduction than the bifilar helix experienced for criterion No. 2. Data for the use of criterion No. 1 has not yet been taken. Figure 2-15 shows similar plots for a horizontally polarized receiving dipole. These patterns are far worse than Fig. 2-14; they resulted from early data when great interference from ground reflections existed on the antenna range. It is felt that these poor patterns are due to reflection problems that have since been greatly reduced. 2.1.3 Near Field Measurements 2. 1.3. a Probing Equipment. The preliminary measurement method used for the near fieldpattern for helical and log-conical antennas was similar to that of other workers (Dyson, 1965), (Patton, 1962). These measurements were made with surface current measurement facilities of the Radiation Laboratory. The facilities involve an anechoic chamber, a magnetic probe with its carriage system, and receiver-recorder system. The block diagram of the set-up for the near field phase measurement is shown in Fig. 2-16. The details of the anechoic chamber are described fully in the literature (Knott, 1965). The picture of the facility Fig. 2-17 shows the probe assembly hanging from ceiling. The probe carriage above the ceiling is shown in Fig. 2-18. Figure 2-19 shows the near field amplitude set-up. The shielded vertical loop probe was used throughout the measurement. It has a diameter of 0. 131". The highest frequency used in the measurement.was 1600 MHz; thus, the pick-up error due to E-field is assumed very small (Whitesid 1962). 2. 1.3. b Near Field Amplitude Measurements. The bifilar helix (No. 213) was measured as shown in Fig. 2-20. Figure 2-21 shows a result without loading from which it can be predicted that the bifilar helix will probably have a backfire radiation at 700 and 800 MHz (which is confirmed by radiation patterns). At 600 25

THE UNIVERSITY OF MICHIGAN 7140-1-F.5.5.5 P/5 / (g)' ()\.;5 (i P/10 ol I P/5 (a) - (b) (e 250MHz 300MHz 400MHz 1.5. 5 -.5 - N I \! I \ /,/I~~~~~~~~ ~ / \\~~~~~0\! (d) (e) W 450MHz 500MHz 550Mz 1.5 1.5 -1.5 1.0 1.0 / 1 "N 'I ) (g) (h) ~\~x (i) 600MHz 650MHz \ \ 700MHz FIG. 2-15: 4" DIA. MONOFILAR HELIX (NO. 215) 1E912 LINEAR POWER. - UNLOADED, --- FULL CORE FERRITE POWDER LOADED. P = POWER RECEIVED. 26

THE UNIVERSITY OF MICHIGAN 7140-1-F Anechoic Chamber Signal l Generator I I Coaxial L Coupler Probe Attenuator Tuner Phase Shifter Slotted Line Hybrid High Gain Receiver Null Display FIG. 2-16: BLOCK DIAGRAM FOR NEAR FIELD PHASE MEASUREMENTS. 27

THE UNIVERSITY OF MICHIGAN 7140-41 F 7140~......F..........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~....~,iiiiiiiiii 0 Fuji~ ~ ~~(i Asia! ~ ~ ~ ~ ~ c\) 0 28~~~~~~~~~~~~~~~~~~~~~~......................................~~ ~ ~ ~ ~~l~o~................................................!........................................~..

.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................I......................................................................................................................................................................................................................................................................................................................................................................................... -.1...........I I —...........................................................................................................................................................................................................II I I I I..............-.............................................................................................................................................................................................................................................................................................................................. M Illil................................................................................................................................................................................................................................................................................................................................. S.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... I....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... *K-=............ isom.-PA I WI....................... Ralph" is- It"m............ 11-111111111"EX.I.: lffi$jii'ij jii..?, El FIG. 2-18: PROBE CARRUAGE SYST'FM ON TOP: OF ANECHOIC CHAMBER

THE UNIVERSITY OF MICHIGAN 7140-1-F Anechoic Chamber I~ I I I I Probe Tuner Relative High Gain CRO Amplitude Receiver Display (db) x-y Recorder FIG. 2-19: BLOCK DIAGRAM FOR NEAR FIELD AMPLITUDE MEASUREMENTS. 30

.0~~~~~~~~~~~~~~~~ FIG* 2-20: ANTENXNA NO. 217 WITH MAGNETIC PROBE: IN POSITION

mmn800 MHz 700 MHz 1 -- -- — 6 —600 MHz H 900 MHz 2 -c~3~ I 3 L- I X. 4 End of Antenna 5 6 87 9 1 00 30 TFeeding 7 14 21 p (cm) 28 35 4 z Tip FIG.2-21:NEAR FIELD AMPLITUDE OF ANTENNA NO. 217. PROBE POSITION X/6 ABOVE ANTENNA SURFACE.

THE UNIVERSITY OF MICHIGAN 7140-1 -F and 900 MHz the standing wave patterns due to the interference of higher order modes suggest the lower and upper bounds for the backfire radiation. Nevertheless, from Figs. 2-5 - 2-8, it can be seen that the axial patterns remained good below 600 MHz and above 900 MHz (no axial ratio information is available). Notice that the radiation axial power level did peak at 730 MHz, from Table II-2. This indicates, as stated before, that axial radiation power level may be a good far field measure of antenna reduction. The measurements were repeated for the same antenna by loading with a ferrite shell of 3/8" (.02X) thick. Figure 2-22 shows that the frequencies of operation have now changed to between 550 - 700 MHz. Table II-2 shows a 3/8" layer has a center frequency of 520 MHz from antenna pattern criterion No. 1. The radiation, and possibly the lossy nature of ferrite at the higher frequencies, explain the observed decay of the standing wave patterns toward the base of the antenna. The comparison of Figs. 2-21 and 2-22 shows a reduction factor of about 0. 78 in the near field amplitude pattern due to a 3/8"1 ferrite layer. 2. 1.3. c Near Field Phase Measurements. The relative phase shift for the bifilar helix No. 217 was measured above the antenna conductor along the axial direction of the antenna for both the air core and ferrite loaded cases. The results are plotted in Fig. 2-23 for 500 MHz and Fig. 2-24 for 900 MHz. An almost linearly changing phase shift was obtained for both cases. The effect of the ferrite shell was to increase the phase shift constant,1 by a factor of approximately 1. 68 corresponding to a decrease in size of 0. 6. The near field phase measurement contains information that the amplitude plot alone cannot predict. First of all, the rate of increasing or decreasing phase angle determines whether there is a forward wave or backward wave as seen by Figs. 2-23 and 2-24. The bifilar helix No. 217 supports a backward wave at 500 MHz and a forward wave at 900 MHz. The loading effect is readily seen by comparing 33

Probe, Bifilar Helix \.,I \I i |u \-8 00 MHz 700 MHz 1- I. 2 2,i_..k PROB // r C End of a, ~~~~~~~~~~~~~~~~4 ~Antenna 5 6 (in) 7 8 9 10 Feeding 7 14 f (cm) 21 28 35 42 Tip FIG. 2-22: NEAR FIELD AMPITUDE OF ANTENNA NO. 217 WITH FERRITE LAYER. PROBE POSITION X/5 ABOVE ANTENNA SURFACE.

-1000 - 900 rl - 800 - - 700 - - 600 - o- 500 P. - 400 j;- 400 I = - 300 200 - 100- 0 100I I I I I I I I I I I I I I I I I I I 1 3 5 7 9 11 13 15 17 19 Number of Turns FIG. 2-23: PHASE SHIFT FOR BIFILAR HELX NO. 217 AT 500 MHz, 0. 9 cm ABOVE THE SURFACE. ( o o ) FERRITE LOADED, (. *) AIR CORE.

100 200. 300 C d3 400 Z 900 100 -0 o dI ~\C 800. \ O 1100 - 1000 o \ 1200 - Number of Turns 1 17 Number of Turns FIG. 2-24: PHASE SHIFT FOR BIFILAR HELIX NO. 217 AT 900 MHz, 0. 5 cm ABOVE THE SURFACE (o o) FERRITE LOADED (- *) AIR CORE

THE UNIVERSITY OF MICHIGAN 7140-1-F the change of the phase shift constant f1' This provides the information for the effect of the ferrite loading or, for the same frequency, the factor will correspond to the size reduction factor due to the ferrite loading of the antenna. The reduction in size (0. 6) is close to the theoretical reduction factor for full core loading (0. 58) and is greater than the very approximate antenna pattern reduction factors. Thus, a good check of sheath theory is provided from phase measurements. Nevertheless, phase measurements alone are not sufficient to measure the whole active region problem with loading; in particular, it does not give any idea of radiation attenuation. 2. 2 Loaded Conical and Pyramidal Antennas A possible theoretical analysis of the loaded log-conical helix can be made by way of the loaded helix solution. Although no extension of the loaded helix solution has yet been tried, the method is indicated in Appendix A. The experimental effort began with the construction of two pyramidal-helix antennas, described in Table 11-4. These have been shown to operate approximately as conical helix antennas (Tang, 1962). Antenna No. 223 used a styrofoam construction to minimize any fiberglass loading. The antennas had identical properties except for wire width, feed, and apex truncation. Near field data of both in air, as discussed later, show that the fiberglass construction shifted the active region by no more than several per cent. However, some consistent differences such as beamwidth and active zone size have not yet been completely explained. The loading experiments of these antennas have just begun; only one loading type was done for each antenna, and not all measurements have yet been made even on these. Nevertheless, significant conclusions can be drawn particularly from the near field measurements. First, near field measurements are especially important in tapered antennas, since the far field patterns are extremely insensitive to changes in active region position; only by going below cutoff frequencies of the 37

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE 11-4: SPECIFICATIONS OF CONICAL-HELIX ANTENNAS I. D. Number Dimension 221 223 Base, Side 9.47" 9.47" Apex, Side 1.56".47" Height 13.44" 15.38" Apex (cone) Angle 450 450 Pitch Angle 850 850 Turns 8.5 14.75 Outer Conductor RG 58-U No. 20 Enamel Coated Wire Feed Infinite Wideband Balun Hybrid Nominal Frequency Range, 500-900 500-3000 Unloaded MHz MHz Note: Both antennas were pyramidal with a square cross-section. Construction of No. 221 consisted of two-layer fiberglass epoxy layers forming the inside supporting pyramid upon which the coax was wound. Antenna No. 223 was made of 1" thick styrofoam layers forming the outside supporting pyramid, with the antenna conductor cemented inside with epoxy. 38

THE UNIVERSITY OF MICHIGAN 7140-1-F antennas can one make any significant change in the patterns. It is worthwhile noting that criterion No. 1 for evaluating antenna patterns (see helix section) is not available here; the data indicates that the normalized radiated power does not vary much with frequency. The cutoff frequency for "fair" antenna pattern shape or a rapid change in beamwidth will be used as the far field measure of loading effect. 2. 2.1 Far Field Measurements Both antenna Nos. 221 and 223 were first measured in air and then with a tapered loading of the Emerson and Cuming, Inc. material (pu = 1, e = 10). The results and descriptions of the loading are shown in Figs. 2-25 and 2-26. Figure 2-25 shows that with 1/4 radius (constant ratio), partial-height loading, the antenna patterns are acceptable down to 250 MHz. Air patterns below 400 MHz on antenna No. 223 have just recently been taken, but are not shown in Fig. 2-25. Severe disturbances below 350 MHz were noted. Complete collapse of the patterns of Antenna 221 is shown in Fig. 2-26. The poor pattern region in Fig. 2-25 from 500 - 600 MHz has not yet been fully explained. However, the near field measurements discussed later show that in this frequency region; 1) The near field amplitude has several major peaks rather than one. 2) The total active region width does not decrease with loading, causing the forward radiation zone to be excited. 3) The near fields extend into the unloaded region past the dielectric, although at a low amplitude. Any of the above cause pattern disruption. The major unanswered question is whether there is a basic loading limitation indicated by the double-peaked near field. Figure 2-26 shows the patterns for a somewhat unusual loading on antenna No. 221, an attempt to load only the low frequencyar, (large size) portion of the 39

THE UNIVERSITY OF MICHIGAN 7140-1-F antenna conductors Outer layer of styrofoam 1/4 radius loading, e = 10, p = 1 Antenna No. 223 T 200 MHz 250 MHz 290 MHz X/S(/X ///<( Go / / \ I ~' I I / \ / \ I \, 2600 MHz 25700 MHz 90 MHz ---- loaded, plots of (E 40O

THE UNIVERSITY OF MICHIGAN 7140-1-F Antenna No. 221 Loading Material A/=1, e=10 -1/4 a a I I 300 MHz 350 MHz 230 MHz. - I 400 MHz 500 MHz 600 MHz 400 MHz 500 MHz 600 MHz FIG. 2-26: TAPERED LOADING ON PYRAMIDAL HELIX (221) unloaded, - dielectric loaded 41

THE UNIVERSITY OF MICHIGAN 7140-1-F antenna. Because of the infinite balun, the air patterns of No. 221 have some beam tilt and lack of symmetry below 600 MHz whereas the patterns of No. 223 are fairly good to 400 MHz (with some increase in beamwidth). Nevertheless, the loading on No. 221 was very successful, decreasing the frequency for fairly good patterns to 230 - 250 MHz. Near field patterns have not yet been taken. Only a very approximate conclusion on reduction with loading can be made from far field patterns. Using the lowest frequency for an acceptable pattern as a criterion, a reduction factor of approximately 0. 66 - 0. 76 is obtained with the loadings shown, compared to an approximate factor of 0. 74 - 0.83 with the loaded helices. The above factors are very pessimistic, since the air patterns in Fig. 2-26 were clearly disturbed below 600 MHz, but 350 MHz was chosen as the lowest acceptable air pattern. Actually a first - pattern - disturbance criterion would give a reduction from 600 MHz down to 300 - 350 MHz, (reduction factor 0. 5). Similar reduction factors are obtained by taking the frequency at which a large increase in beamwidth (without beam tilt) occurs with and without loading. 2. 2. 2 Near Field Measurements 2. 2. 2. a Amplitude Measurements. The log pyramidal helix antenna (No. 223) was first measured without any loading (Fig. 2-27). Several probe positions were tried to find an optimum distance for showing the active zone clearly. Figure 2-28 a, b, and c shows data for probe positions of 1/8", 1/2", and 1" respectively above the unloaded antenna surface for various frequencies; the well known shift of the center of the active region toward the feed point as the frequency is increased is readily apparent. The greater smoothness of the near field patterns at 1" is evident since the probe is far enough away to integrate and smooth the individual wire contributions. At closer distances, large probe signal variations are seen due to individual wire contributions. For a given effect, probe distance must be measured in wavelengths; thus as frequency is lowered for a constant probe distance, the wire _________________________________ 42

:I M:::i:~~~~~~~~~~~~~~~~~~~......... --------------------------------------------------------------- OX:.. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~::::::::::5::::i~::::.................................................... ~ ~ ~ ~ ~ ~ ~ ~ ~,:~ iiiiii~~~ii~'i~:ir................................................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ i ~~j:~:~....................................................................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~-~.ii~iii~:iiiiiiii ~ ~~~~~~:~~~~~:: ~~:: ~~~~:~~~~................................................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~:i~::~::::::~i~:::~::::::...............................:" '':.:.:.....................~::::: s~j i::::::::::::s:...........................~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~':"~iii~iriiiii~iixii~~i~i...............................~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~' ~~~i~~~ii~li~i:~iI:j~ii........................................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~:::::~ii~i~~ii~~i~::Si~~ij l::......................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~r~,:.r'' ~~:~~cp::~: ~........................................ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -- --— ~ --- —-—: ~~. —::::::............................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~::.ji::::i::::::i:~i::: iliiiiiiiiil~ iiiiiiiii............................................. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~''''''''' ~:''': ~~~''::''.................. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~: ~ii~i~i)i~~~i~)iiiii l~~.................. ~ ~ ~ ~i ~ ~ ~ l~,l~ii~i~llii~iiii~i jiiilliijiii~~~ill............................................................................... ~~~~~::::~i~: j::::~: j~::::::: a::::...........................................................................::j::s:::::::;:x ~:................................................................~i::::~i:::l::::: i:::::::::....................................1 ~~3........................................................................................:::~~'~'~:'~'~'' '................................................................................................................::~: i::::::::i:::::::::: ~~iii..............................................................................: Biiiiiiiiiiiiiiiiliiiiiiiiiiiii........................................................................... ~i~i:.~~~~~l ~ ~ j~i:::::::::........................~::1:1::1: ~ ~ ~~i B~~~~::' ~ ~................................................:::::::i~~~~~~~~~~~~~~il~::::::::s:::.:I:I:I:I:::::I: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~................. FIG. 2-27:ANTENNA N. 223 -V~TH MAGNETC PROBE I POSITION

1600 MHz 900 MHz Probe 500 MHz 300 MHz 1 _ I End of 1~~~~~~ Groove r //I',:'-r-F?,,' 2 3 ~~~~I ll ~ 2~~~~~~~~~~~~~~~~~ I l /I /,P~~ ~~i~ //r,-[/ t,_ "1 hr (,I Conductor ~i9 I 1 IlilIi ~~~~I~~~I < I a( a~~~~~~~~~~~~~,, End of Groove FvI7 I I IITruncated Base *I. I -, i/ z 8 9 I I Truncated o15 (cm) 30 42 Tip FIG. 2-28a: NEAR FIELD AMPLITUDE OF ANTENNA NO. 223. PROBE POSITION 1/8" ABOVE ANTENNA SURFACE, UNLOADED

THE UNiVERSITY OF MICHIGAN 7140-1-F P4 0) 0 4-4 NN NN ii~~~~~~~~~~~~~~~~~~~~~~~~~C 0.9 C4 ~ O~~~~~~~~~~~~~~~~~~~~~~~0 oc~ a,..~~~~~~~~~~~~~~~~~~o,66 0*40L o~~~~~~~~~~~~~~~~~~~~~~~~~~~~s FIG. 2-28b:. NERFEDAPIUEO NTNAN.23 NODD 45 f4 co Co - co

T N V E R S I T 1,HGA 7140- F A 4-3 Cd~ 0000 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 0000 V3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~00 ~~~ o,~~~~~ ~~~, I.~: I~~~~~~~~~~L C43 NP) 19PnIT~~~~~~rTTI-T -T-1~~~~

THE UNIVERSITY OF MICHIGAN 7140-1-F variations become larger (see, for example, 250 MHz versus 500 MHz in Fig. 2-28c). The variations in probe signal due to passing individual wires is a local perturbation effect and should not be confused with standing waves due to traveling waves in opposite directions. The observed probe signal at 300 MHz was so weak near the tip of the antenna that considerable noise was seen in the plot, but an increasing standing wave amplitude is seen toward the base of the antenna. The groove length was not sufficientlylong to allow afull-length plot at this close probe position. Due to the frequency response of the receiver, measurements were not taken above 1600 MHz. Therefore, higher order mode active regions cannot be observed in this plot It was found from these plots that the probe distance of 1/20 -1/5 wavelength above the antenna surface provides good information on the location of the center and the width (3 -db width) of the active region. The same antenna (No. 223) was measured again with dielectric loading. The result is shown in Fig. 2-29 for a fixed probe position and 2-29b for a probe position of X/11 above the antenna surface. The comparison of Fig. 2-29a versus 2-28c clearly points out the shift of the active region for the same antenna due to dielectric loading. The amount of dielectric material available permitted the loading to extend only to within 8 cm from the base of the antenna. The effect of this discontinuity can be seen from Fig. 2-29a and b. The centers and width of the active region for antenna No. 223 are measured and tabulated in Table II-5 for comparison. The shift of the center of the active zone of No. 223, when loaded, corresponds to a reduction factor of 0. 57 at 900 MHz and 0. 53 at 500 MHz. This is a very important result. The reduction factor with 1/4 radius loading is almost * 5, and much more than is indicated from either helix loading experiments or far field patterns of the pyramidal helices, with the exception of the first-pattern-disturbance criterion. This measured reduction factor (0. 55) is felt to be the most accurate and basic measurement made yet. 47

0.....900 MHz H 500 MHz 1 -................300 MHz T - - 250 MHz / ---_____-100 MHz 2 4 -' I End of I/ i~i ~Dielectric Layer -I I I' Truncated I I- I Base 6 \ \ I u 10 I \.I."'\ u C) 8 / ili I 10 \~~.&~4Y#7\x.I U**....*.* 0 ~~~~fm- z Truncated 7 14 f (cm) 21 28 35 42 Tip FIG. 2-29a: NEAR FIELD AMPLITUDE OF ANTENNA NO. 223 WITH DIELECTRIC LAYER. PROBE POSITION 2.8 cm ABOVE ANTENNA SURFACE.

_ ---900 MHz H 1 L- _500 MHz o........300 MHz t --— 250 MHz 2 i Z I - 3 r 1 I I Q0. End of -4 I Dielectric 1a,~ Layer, I I 6 - Truncated Base 8 \ 9 10 d0 0 TTip 7 14 21 A (cm) 28 W 35 FIG. 2-29b: NEAR FIELD AMPLITUDE OF ANTENNA NO 223 WITH DIELECTRIC LAYER. PROBE POSITION X/Ii ABOVE ANTENNA SURFACE.

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE II-5: CENTER AND WIDTH OF ACTIVE REGION FOR ANTENNA NO. 223 Frequency Air Core Dielectric Shell Loading f Center 3 db Width f x Width Center 3 db Width f x Width (MHz) (cm) (cm) (GHz-cm) (cm) (cm) (GHz-cm) 1600 4. 3 2.13 3.40 - - - 900 9.5 3.88 3.49 5.18 4.1 3.69 500 19.0 7.00 3.50 9.8 6.52 3.26 300 - - - 30.1 11.6 3.48 250 36.4 - 50

THE UNIVERSITY OF MICHIGAN 7140-1-F The breakup of the near field into several peaks, on the other hand, is a very serious problem. In the zigzag Section (III), this same phenomenon is discussed. It appears that some of the energy transmitted along the antenna wires is getting past this first mode radiation zone, and radiating in other regions, including the first mode forward-fire region. It is also possible that the second peak in the near field plots is not "active" (i. e., radiates poorly). Although near field patterns of No. 221 loaded are not yet available, the setup and measurements of the unloaded antenna are shown in Figs. 2-30 and 2-31. It may be seen from a comparison of Figs. 2-31 and 2-28c that the epoxy-fiberglass, material used to construct antenna No. 221 has no significant effect on the antennas active region position (assuming the polystyrene foam plus epoxy glue construction of antenna No. 223 has no effect). The centers and widths of the active regions are tabulated in Table 11I-6. It is found from Tables II-6 and II-7 that when the product of the frequency and the 3 db width of the active region is taken, it remains fairly constant for either antenna. In other words the active region width in free space wavelengths is approximately constant at 0. 1 for antenna No. 223. This is indeed a very important and interesting result. The loading of a dielectric does not appear to change the normalized active zone width. This perhaps explains the band narrowing effect of a conical antenna after loading. If we define band narrowing factor to be: Upper bounds-lower bounds\ center frequency air Upper bounds-lower bounds center frequency jloaded then the factor for antenna No. 223 is 1.47. Notice that the active zone width used above is a total width, including both peaks.

..... 900 MHz 0 _ - -- 800 MHz Probe 700 MHz -- _ 600 MHz -'_ x ""'_ 500 MHz H are i t 11 0A0/ 0...-... —. 400 MHz 1/| I, |- 1 Conductor....300 MHz t i I d 1 X P2 -01 \ -r 4) I I ~I Tip 6 oe Truncated Base r —.I /I~~~~~~~~~~ \ Truncated 7 14 (cm) 21 28 3 Tip FIG. 2-31: NEAR FIELD AMPLITUDE OF ANTENNA NO. 221, UNLOADED PROBE POSITION X/12 ABOVE ANTENNA SURFACE.

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE II-6: CENTER AND WIDTH OF ACTIVE REGION FOR ANTENNA NO. 221 Frequency Center 3 db Width fx Width (MHz) (cm) (cm) (GHz-cm) 900 4.1 4.82 4.34 800 5.18 5.6 4.48 700 7.10 6.2 4.35 600 9. 10 7.8 4.68 500 12.6 9.6 4.80 400 19.6 11.3 4.52 300 29.4 - 54

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE II-7 VSWR OF LOADED LOG PYRAMIDAL HELICES NO. 221 Frequency VSWR (MHz) AIR LOADED 250 - 3.3 300 3.4 350 3.7 400 2.5 1.6 500 1"9 2.1 600 1.7 1.6 700 1.9 1.5 800 2.3 1.3 900 1.7 1.3 55

THE UNIVERSITY OF MICHIGAN 7140-1-F 2. 2. 2. b Phase Measurements. The unloaded log pyramidal antenna (No. 221) was next measured on all four antenna faces above the wires along the antenna without any loading. Figure 2-32 shows the results at 500 MHz. The phase angle decreases toward the truncated base and stays fairly constant over the active region. When the frequency was increased to 900 MHz, the phase angle decreases first and levels off over the active region and then increases rapidly toward the truncated base as shown in Fig. 2-33. Thus, the regions of backward, active and higher order mode standing waves are distinguishable. The phase shifts along each wire are plotted in Figs. 2-34 and 2-35. The dotted line indicates a net shift of 27r degrees. The actual phase shift should be continuous and increasing toward the truncated base; the phase velocity calculated from 13 along the wire is found to be very close to the velocity of light as shown in Figs. 2-36 for wire 2. Phase measurements again show good potential for indicating effects of loading on antenna active regions. Table II-7 is a record of VSWR of the antenna No. 221 with and without loading. The loading does not affect VSWR greatly, and with impedance corrections, the effect would be less. 2.3 Conclusion Table II-8 shows a very abbreviated list of the best results obtained with various loadings and measurement methods. All of the loadings shown are inside. Out side loadings (with the exception of the one promising factor,. 62 for a 1/2" outside shell on a helix) have yet to be investigated. A reduction factor of 0. 5 appears within reach. The breakup of the near field with loading seems to be the most serious loading problem yet uncovered. It must be thoroughly investigated. The fact that the active zone region in free space wavelengths (or the frequency-width product) was observed to be a constant may place a basic limitation on the minimum antenna size 56

THE UNIVERSITY OF MICHIGAN 7140-1-F 0 E 0 cn co + I I + + O i r.., I) ) Q) ) + '4 Rt Pa (r *+<~ ++4 z -r0 0 0 0 0 0 0 0D 0 0 0 00 0 Cm co LO- (0 I Relative Phase (degrees) FIG. 2-32: PHASE SHIFT FOR ANTENNA NO. 221 AT 500 MHz, 0.9 cm ABOVE THE SURFACE FOR FOUR DIFFERENT FACES, UNLOADED. 57

THE UNIVERSITY OF MICHIGAN 7140-1-F CaD - c' 0, d. ~1 -00 00 c{ Ec c~ c * + 4 oa LO '-4 0o 0 0 0 0 0 0 o 0 0 0 0 Relative Phase (degrees) FIG. 2-33: PHASE SHIFT FOR ANTENNA NO. 221 at 900 MHz, 0. 5 cm ABOVE THE SURFACE FOR FOUR DIFFERENT FACES, UNLOADED. 58

-1200 -1000 - M I / -600 \ -400 -.) I b -200 - I, CN o CD (0 a0 + 200M 0b |I (cm) linear scale33c 800FIG. 2-34: PHASE SHIFT FOR ANTENNA NO. 221 ALONG THE WIRE 1, 0.5UNLOADED. 1000 1 f FIG. 2-34: PHASE SHIFT FOR ANTENNA NO. 221 ALONG THE WIRE 1, UNLOADED.

-120 -1000 I + / H -800 / / I trl -600 I ~ zco - 400 - ~~~~~b~~~~ / - 200 / 200 400 5 + + + 500 MHz, 0. 9 cm Above o o o 900 MHz, 0. 5 cm Above - 800 1000 3 1 10 14 06 108 2b 22 24 26 28 30 32 Truncated Tip Number of Turns Truncated Base I- (cm) linear scale 33 cm FIG. 2-35: PHASE SHIFT FOR ANTENNA NO. 221 ALONG WIRE 2, UNLOADED.

-500 0 500 H %14~~~~~~~~~~~~~~~~~~~~~~~ 2000 C, 2500 4 000 a)C 4 500 Wo a) 4000 - Tb~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C H500 /c N2, c ALONG WIRE 2, UNLOADED.

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE II-8: Measurement Type Sheath Antenna Patterns Near Field Near Field Theory, Full (criterion 2) Amplitude Phase Core Core Helix-Ferrite.62.78. 7. 58 Helix-Dielectric ( 1/18 Radius Max. ) Pyramidal Helix (Dielectric).5 -.7.55 -.45 1/4 Radius Max. ) 62

THE UNIVERSITY OF MICHIGAN 7140-1-F for a given pattern. Nevertheless, this width is only 0. 1X; thus, considerable reduction may yet be possible. The near field measurement method has proved very useful in measuring the effects of loading of antennas. Antenna patterns have proved a somewhat less sensitive measure of loading effects, although normalized radiation amplitude appears to be a useful measurement. 63

THE UNIVERSITY OF MICHIGAN 7140-1-F III BIFILAR LOG PERIODIC ZIGZAG PYRAMIDAL ANTENNAS 3. 1 Far Field Patterns Figure 3-1 shows the H-plane patterns of a solid-ferrite loaded log zigzag antenna No. 225, the characteristics of which are shown in Table III-1. The log zigzag is fed at the small end with two coaxial cables from a wideband hybrid junction. As the wave travels along the zigzag conductor, the period increases progressively with distance along the antenna axis. As the frequency increases, the active region moves up along the antenna axis. Figure 3-1 shows that EAF-2 ferrite loading patterns at 500 MHz and 600 MHz are bi-directional. At frequencies higher than 800 MHz, the radiation patterns with and without ferrite become nearly the same, since the ferrite loading did not extend to the apex and did not cover the active zones at these frequencies. Figure 3-2 shows patterns of the loading effect of the solid EAF-2 ferrite material at 700 and 800 MHz on two different log zigzag antennas, Nos. 219 and 225, described in Table III-1. 3. 2 The Near Field Amplitude Measurement of Log Periodic Zigzag Antenna The near field amplitude was measured on antenna No. 225, loaded with powdered EAF-2 ferrite as shown in Fig. 3-3. The near field pattern, Fig. 3-4, shows a backfire radiation from higher than 900 MHz down to about 450 MHz. At 400 MHz the near field amplitude begins to deteriorate. Thus, the overall frequency band of this unloaded antenna is about 450 MHz and the centerfrequency is approximately 680 MHz. The antenna was then loaded with the ferrite powder layer with the thickness of 3/8" as shown in Fig. 3-3. The near field amplitude was measured and is shown in Fig. 3-5a and Fig. 3. 5b. The near field amplitude does not have a single peak as didthe unloaded case; however, it is still possible to observe the effect of the 64

THE UNIVERSITY OF MICHIGAN 7140-1-F 300 MHz 400 MHz / /\ \ — 5-EA2r00 MHz 600 L i I -l\ Air Loaded FIG. 3-1: H-PLANE PATTERNS OF LOG ZIGZAG ANTENNA (No. 225) 65

THE UNIVERSITY OF MICHIGAN 7140-1-F I\ i 700 MHz. 800 MHz. (a) Log Zig Zag Antenna (No. 225) a = 120 = 100 T = 0. 85 10 cells on each side 700 MHz. 800 MHz. (b) Log Zig Zag Antenna (N. 219) c = 100 T' = 0.7 6 cells on each side Air Loaded - - - -E A F 2 Ferrite Loaded FIG. 3-2: H-PLANE PATTERNS LOG ZIGZAG ANTENNAS AT 700 MHz. AND 800 MHz.

THE UNIVERSITY OF MICHIGAN 7140-1 -F TABLE III- 1: BIFILAR LOG-ZIGZAG PYRAMIDAL ANTENNA SPECIFICATIONS Antenna Numbers 219 225 Apex Angle, 2a 20~ 240 Growth Factor,.7.85 Pitch Angle, ~ 100 Base Width 32. x 32. cm 32.5 x 32.5 cm Apex Truncated Width 16 cm 6.4 cm Height 44.2 cm 10 No. of Cells Per Arm 6 10 Length on Plane of Conductors 45 cm 62 cm 1) from truncated tip 45 cm 62 cm 2) from virtual tip 92.5 cm 77. 5 Loading Material EAF-2 EAF-2 Solid Ferrite Along Solid Ferrite (antenna Entire Length Pattern); powdered ferrite EAF-2 (near field meas.) Loading Configuration 1/2" Inside Layer 3/8" Inside Layer from From Base to Tip Base to Tip (Fig. 3-3), powdered ferrite EAF-2 67

THE UNIVERSITY OF MICHIGAN 7140-1-F cw - `12~ -- ~~~~i2O -y =10o / I -1 n / o =. 0.85 Feed point R-1RI n / CI~ Rn-1 Rn n n I _ _ * I 60 cm I ~ ~~~~ \) 3/8" thick powder ~ ' \I I ~~~~jferrite la er I ___ _ -32.5 cm —2 -- FIG. 3-3: LOG ZIGZAG ANTENNA 68

X,-X 900 MHz 0 ----'"O 600 MHz. "-'O-c 800 MHz -C~ 500 MHz. 0C0O 700 MHz e- 400 MHz. ] 0 \Or~~ ~,rq~ ~ ~ ~ ~ \ 1 I~~~ \! Z r 4 2 4001, ~ ~ ~ ~ ~, 3~~ ~,~~~~C 10' ~~~~~~~~~~~~~ 'd ~~~~~\I 0 15 ~e(cm) -~ 30 45truncated truncated base fed ipFIG. 3-4: NEAR FIELD AMPLITUDES OF ZIGZAG ANTENNA NO. 225 UNLOADED 4 moor~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5 C 7 C 8 9 10 2 01 15 l~~~~~1(cm) - 3 trunc ate truncated base fee tPFIG. 3-4: NEAR FIELD AMPLITUDES OF ZIGZAG ANTENNA NO. 225 UNLOADED

Q'-O 450 MHz. 0 ~ IO.D 400 MHz. i1 I X —X 350 MHz. /\ tri —T 300 MHz. / 1~' / /\ z fA- 2/ // 3~~~~~~~ E~~~~~ I 4~~~~~~ 2, / 5 ~~01,X~T ~ / r (1 6 x' / 70 0 8~~~~~~~~~~~~~~~~~~~~~~~~ / 0 I mo 0 15 30 4 p. (cm) -3 FIG. 3-5a: NEAR FIELD AMPLITUDE OF ZIGZAG ANTENNA NO. 225 LOADED WITH 3/8't INSIDE LAYER OF FERRITE POWDER

X —X 800 MHz. O-C) 700 MHz. 0 0- - 600 MHz. L~-~ 500 MHz. 1 I x -z I I td I I ct~~ Cd~~~~~~~~~~~~~~~~~~~~~~~~~~~~PC 4 5 b 6 0~~~~~~~~~~~~~~~~~~~ \\X/~~~ 730 I0 8 ' 9 / ( 10 \ ~,\ ~~~~~~~ 15 30 (30G i(cm) -~ FIG. 3-5b: NEAR FIELD AMPLITUDE OF ZIGZAG ANTENNA NO. 225 LOADED WITH 3/8" INSIDE LAYER OF FERRITE POWDER

THE UNIVERSITY OF MICHIGAN 7140-1-F ferrite loading for different frequencies. First of all, we observe that two or more active regions usually appear. The first (left or closest to the tip) one is shifted by a reduction factor of approximately. 57 toward the left, or apex, of the zigzag. For example, the first peak of 300 MHz for the loaded case (Fig. 3-5a) is practically at the same position as the 500-600 MHz peak in air (Fig. 3-4). Also the first peaks for 350, 400, and 450 MHz (Fig. 3-5a), (the small ones on the left hand side) are roughly at the same position as 700, 800, and 900 MHz in air (Fig. 3-4). In addition, patterns taken on the pyramidal helices show forward fire as well as backfire radiation. Thus, in conclusion, the loading appears to produce the undesirable effect of allowing much of the energy to pass the desirable first mode backfire region without being radiated. This energy then passes into regions of forward fire for the first order modes and to other radiation regions, thus destroying the antenna pattern. These results are undoubtedly dependent upon the pitch and cone angle of the antenna to be loaded. They will be thoroughly studied. 72

THE UNIVERSITY OF MICHIGAN 7140-1-F IV FERRITE LOADED WAVEGUIDE SLOT ARRAY The ferrite loading of a waveguide array cannot reduce the length of the array; however, the cross-section of the waveguide is reduced considerably (Jones, 1965). The loading of an individual slot with ferrite can reduce the resonant length of the slot, thus reducing the proximity of the slot to its neighbors. Hence the mutual coupling effects can be reduced (Kay, 1956). Furthermore, electronic scanning of the array pattern is possible through magnetic bias control on the ferrite without additional ferrite devices (Cheo, 1965). Some preliminaries have been commenced in the utilization of ferrite filled slots in a short linear array. The array has been designed to have a pattern with side lobes down 26db (i.e. the side lobe field level should be 0. 5 per cent of the main lobe field) and a beam width of 25 at half power points. The efficiency is to be determined with these requirements fullfilled. The pattern will be scannable by variation of the magnetic bias. The ferrite material used for loading is the Q-3 ferrite supplied by Indiana General in the form of 7.16 cm x 1. 246 cm x 0. 3 cm (2. 82" x 0. 49" x 0. 12") sticks. The center frequency has been chosen to be 200 MHz, which is within the range for Q-3 ferrite as published by Indiana General. 4. 1 Preliminary Design and Tests The Q-3 ferrite material was tested for r and E and loss tangent values for frequencies from 100 to 300 MHz. The account of these tests along with the complete procedure is given in Section VI of this report. The results of the p and e tests are summarized as follows: 73

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE IV-1: f prr | r r 100 MHz 12.5 7.96 200 MHz 14.3 7.81 300 MHz 16.0 7.7 The measured values of p and e at 200 MHz were used in the preliminary design of the waveguide assuming cutoff frequency at 126 MHz and a TEl0 mode. The waveguide width "a" is, (Fig. 4-1) 3 x 1010 a = - 11.23 cm. 2 x 126 x 106/ E r r The dimension "'b" was assumed to be 0. 3 cm which is the height of one ferrite stick. The dimension a = 11. 23 cm. can exactly accommodate nine ferrite sticks widthwise and this is the reason to choose the cutoff frequency at 126 MHz with a cutoff ratio of fc 1 f 1.59 With these values then: 377/ p er r r - rr (4.1) TE10 1 ( 2.) = 45.75 2 74

+ + + -F (~~~~ r ~~~~~~~~~I 3-1 (a) (upper plate " Thic 1384 h Aluminum Plate ' Insulated Feed Loop Gon ln Grounded to the loopnd Pane 3-o(a) (upper plate of waveguide) p Coaxial feed ferrite ferrite I FRTEST from the side piece piece 0.3Fcm h I,~ 11.23cm 138 4h Grounded to thelO flo1 -bottom plate FIG. 4-1: PROPOSED MECHANICAL CONFIGURASTION FOR WAVEGUIDE TEST. a) DETAILS OF THE FEEDING LOOP

THE UNIVERSITY OF MICHIGAN 7140-1-F X X = -(4.2) /rer a (2a X = 150 cm at 200 MHz o0 Then - 150 =18.25cm. g 112-44.5 The waveguide was tested for insertion loss. The waveguide was excited with a current loop. This method of exciting the waveguide was chosen on account of its convenient form considering the odd assemblage of ferrite sticks. A rectangular strip was used instead of a round wire for the loop. With this loop arrangement a voltage standing wave ratio of 1. 95 was obtained at 200 MHz with the other end of the guide short circuited. The length of the guide used for this test was 1.08 meters. For the insertion loss test, a hybrid junction was connected at the input end and the other end was short circuited. The input power and the reflected powers were measured then: P. exp(-2ao) = Pout (4.3) The attenuation constant, a, in nepers/cm was calculated from the reading of P. in and P (the reflected power). out P.in was measured at port B with a matched load connected at port D; the output in power was measured at port D with the matched load on port B (see Fig. 4-2). 76

Hybrid Junction D ] Pout in Shorted End Feed 2 (D c 115cm 0.3cm 4O1 FIG. 4-2: EXPERIMENTAL DETAILS TO DETERMINE INSERTION LOSS OF WAVEGUIDE. ~ C) C) z

THE UNIVERSITY OF MICHIGAN 7140-1-F The observations are tabulated below: TABLE IV-2: f P. (mw) P ut(mw) VSWR Reflection Insertion Loss (MHz) Coefficient Per Foot 160 3.6 2x0.4 3.65 0.57 0.92 db/ft. 180 3.6 2x0. 22 2.10 0.354 1. 28 db/ft. 200 3 2x 0. 11 1.95 0.322 1.6 db/ft. 220 0. 45 2x 0. 004 2.15 0. 358 very high The insertion loss is high. The above readings show that a better center frequency would be either 160 or 180 MHz instead of 200 MHz. 4. 2 Array Design Procedure The array is designed to have 5 slots separated by distance of 2 at 200 MHz. The slots are to be in the broad wall of the waveguide. The array will be a nonXo. resonant array of resonant slots. As a non-resonant array, - is not an odd multiple of Xg/2 at 200 MHz. The slot length is to be chosen such that the reactance of the slot is zero, making the slot resonant. The non-resonant array is chosen because it has a better bandwidth than the resonant array (Jasik, 1961). The slots are to be taken at resonance for the maximum radiated power consideration. The following types of slots are available for a choice: 1) Series displaced 2) Shunt displaced 3) Series rotated 4) Displaced and rotated 78

THE UNIVERSITY OF MICHIGAN 7140-1-F The slots are drawn in the broadface of waveguide in the Fig. 4-3. The first three types above involve a single branch equivalent circuit (Oliner, 1957), either series or shunt; the fourth type involves two branch equivalent series circuits as well as a shunt branch. The calculations of the first three types are quite complicated but since there are standard computer programs available for solutions, the work is simplified. However, these standard computer programs have to be modified to take account of the high permeability of the ferrite material and the ferrite filling in the slots. Section 4. 3 outlines the computer programs for the slot design. The criterion to be achieved is a side lobe level of 26 db from the five slots in the broadface of the waveguide. Assuming a Dolph-Tchebycheff distribution, the procedure is as follows (Kraus, 1950): 20 log10R = 26 (4.4) or R = 20 For five slots the poylnomial chosen is T (x) = 8x - 8x 2+ 1 then 4 2 20 = 8x -ix +1 (4.5) o o x = 1. 455 by a trial and error method Now k=2 E E Akcos(2k) (4.6) k=0 79

Shunt Displaced Type z Series - Rotated Type x - Rotated and Displaced Type Series Displaced HIG. 4-3: TYPES OF SLOTS AND THEIR PARAMETERS. X X ~~~~~~d

THE UNIVERSITY OF MICHIGAN 7140-1 -F = A +A cos2(q)+A (cos4 2)using w = coso 1 2 2 2 2 E5 =A +A (2w -1)+A (8w -8w +1) (4.7) 5 0 1 2 where x x 0 then +24 2 0O 8 8A 2 4 2A -8A ( + x2+(A -A A (4.28) 0 002 8A 4 x 0 giving 4 A =x =4.48 (4.9) 2 o 2A - 8A = -8 2 x 81

THE UNIVERSITY OF MICHIGAN 7140-1-F or 2A1 =8x -8x =19 (4.10) o o giving A =9.5 then A +A1+A2=1 (4.11) giving A = 9.5+1-4.48 o = 6.02 2A = 12.04 o Then relative amplitude distribution would be: 1: 2.12:2.69: 2.12:1 A2 A1:2AO A: A2 Now power radiated is given by: | P = | E 2S10t G Or | H 2 S Rot (4.12) Pslot=IE t 2G IHI slot 2 R (4.12)slot Hence power distribution would be: 1:4.48: 7. 2: 4.48:1 (4.13) 82

THE UNIVERSITY OF MICHIGAN 7140-1 -F Ps1:Ps2: Ps3 Ps Ps (4.14) The center slot should radiate 7. 2 times as much power as the end slots. Higher values of G will be required to compensate for loss attenuation. Hence a larger value of 0 or x (the two slot parameters defined in Fig. 4-3) will be required The different slots will have appropriate values of 0 or x for each location. The difference in the value of 0 involves a complication in the calculation of fields, since slightly different polarizations are radiated at various slots. This is a serious drawback of the rotated type of slots. If the polarization of fields is the same for all slots (i.e. discarding rotated type slots), the reduced fields can be very easily calculated from the Smith chart and the design work is simplified greatly. Once the reduced fields are obtained from the Smith chart, then appropriate values of "xyl can be chosen to achieve the required power distribution above, thus, achieving the specified power pattern. The series displaced and shunt displaced type slots are to be explored completely on the computer and then the most suitable resonant slot length will be chosen. One of the two types will be utilized in the final design. A tentative configuration with shunt displaced type slots is given in Fig. 4-4. The effect of mutual coupling between slots has been neglected since the slot resonant length with ferrite filling inside the slots is of the order of 7 cm while the spacing between slots is 75 cm. Experimental verification is underway. 4. 3 Computer Programs for Slot Impedance Properties Computer programs for the first three types of slots mentioned in Section 4. 2 need the following inputs: 1) a and b the waveguide dimensions in cm. 2) a' - slot length, Fig. 4-3; a series of values is specified by the - starting value, increment, final value. 83

/ Xo g Feed End /. 2 C Lood End - 1 CO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C 00~~~~~~~~~~~~~~~~~~ gzz~~~~~~~~ FIG. 4-4: SIMPLIFIED FINAL CONFIGURATION OF ARRAY WITH SHUNT SLOTS Ferrite/ /,/ /~~~~~~~~~~/ S5 ~/S / ~~ s5 s4 ~/sa /s2, FIG. 4-4: SIMPLIFIE D FINAL CONFIGURATION OF ARRAY WITH SHUNT SLOTS

THE UNIVERSITY OF MICHIGAN 7140-1-F 3) b' - slot width in cm. 4) t - slot depth in cm. 5) f - operating (design) frequency. 6) u err product at operating frequency. 7) 0 - slot angle; a series of values is specified by the starting value, increment, final value for rotated series slot. (See Fig. 4-3) or x - starting value, increment, final value for displace series or shunt type slot. (See Fig. 4-3) The output will be: a) R and X values versus slot length with 0 as a parameter for series rotated type, or with x as a parameter for series displaced type b) G and B values versus slot length with x as a parameter for a shunt displaced type. The curves of R and X versus slot length or G and B versus slot length for 0 or x as a parameter will indicate the value of resonant slot length. This will be the value of the slot length for which the X or B is zero and R or G is a maximum. The general behaviour of R and G, symbolizing the radiated power in series and shunt slots respectively, is that R and G increased for increasing values of 0 and x at a particular slot length. 4.4 Magnetic Bias Control of Ferrite Array The array shown in Fig. 4-4 has been designed to demonstrate the usefulness of ferrites in such an antenna. The use of ferrite material offers a possible metho for controlling beam shape or position by the application of a magnetic field. For the purpose of demonstrating magnetic control, a still simpler array is contemplated. For this purpose an array having only three slots may be used. The space between adjacent slots will be such that a magnetic field can readily be produced by pole faces placed in these regions. The application of a magnetic field in this 85

THE UNIVERSITY OF MICHIGAN 7140-1-F direction offers the possibility of control by causing a phase shift in the transmission mode between each two slots. For the 3-slot array, there are two such intervals for the application of magnetic field. At each of these two locations, the extent of the magnetic pole piece in the direction of propagation would be important. It is through the active width of the magnetic field pole piece that the permeability of the ferrite can be changed (reduced). 86

THE UNIVERSITY OF MICHIGAN 7140-1-F V FERRITE LOADED SLOT ANTENNAS In this section, two principle ideas are explored. The first part of this section is devoted to a consideration of the production of heat in a ferrite due to the UHFVHF power supplied to the slot antenna. The second part of this section, indicates a series of studies which show the effect of replacement of certain sections of the slot aperture with balsa wood spacers. Balsa wood acts very nearly as a void since its permittivity is exceedingly low. In some instances, one or more ferrite blocks were covered on the aperture end with metal foil, and thereby, iris effects were produced. The replacement of ferrite blocks with metal blocks produced ridge waveguide effects. 5. 1 Power Capabilities of Ferrite Loaded Antennas In Section VI of this report, information is given on the physical characteristics of some ferrite materials. Of special interest is the temperature dependence of solid ferrite, EAF-2, which has previously been reported (Lyon et al, 1964). Since a sensitivity to temperature change has been observed, it is important to determine the power limitation imposed by this characteristic. For this reason the effect of heating in the UHF-VHF range on a simple ferrite loaded antenna was studied. 5.1.1 Preparation For UHF-VHF Heat Run A ferrite loaded cavity slot antenna with an aperture 12" x 3" backed by a cavity 9" deep was decided upon as the most typical and mcs t informative construction for studying the power limitation associated with temperature. The cavity was filled with powdered EAF-2 ferrite. The slot was designed for a frequency of 320 MHz. The operating frequency for the heat run was chosen at 338 MHz because of the availability of an adequate power oscillator. The highest available input power 87

THE UNIVERSITY OF MICHIGAN 7140-1 -F was approximately 9 watts for these tests. In feeding the antenna, a VSWR value of 1.06 was observed. The ferrite loaded slot used is very similar to one previously furnished to WPAFB. Copper-constantan thermocouple temperature probes were inserted 2. 5" into the aperture face of the slot. Each thermocouple was 0. 04"' in diameter. The two wires of each thermocouple were fused at the junction. A Leeds and Northrup Potentiometer was used for the temperature measurements. The thermocouples were aligned in the direction of propagation along the waveguide, thus having a position at right angles to the electric field. It was observed that the perturbation of the electric field due to the thermocouple insertion was small. The thermocouple elements were inserted so that the thermocouple junctions were spaced 1 - 1/2" apart along the centerline which is parallel to the broad direction of the waveguide (see Fig. 5-1). Such locations should then include a point having very nearly the highest temperature. These locations are essentially interior points of the mass of ferrite material used in this loaded antenna. Temperatures so obtained should be relatively high. Thermocouple No. 4, which is exactly half way across the waveguide and half way in the up and down direction, should give a temperature reading very close to the maximum existing in the mass of ferrite. 5.1. 2 Observed Temperatures in Ferrite Loaded Slot In Fig. 5-2 are shown the experimental observations of temperature versus input power level for the thermocouple temperature readings of thermocouple No. 4 in the middle of the ferrite mass. Measurements were made after sufficient time was allowed for the temperature to stabilize. The input power levels were net values delivered to the antenna. The temperatures correspond to steady state values for cw operation at these power levels. Tests are being extended to higher power levels (up to 100 watts). A 100 watt source is being obtained for this purpose. 88

Aperture of Slot 4 H 1 33 2 Atno co 3 7Z 7 0 4. Power meter 5. Antenna 0 6. Board with thermocouple switches z, 7. Bridge for temperature measurement FIG. 5-1: BLOCK DIAGRAM OF POWER-TEMPERATURE MEASUREMENT SET-UP FIG. 5-1'

THE UNIVERSITY OF MICHIGAN 7140-1-F o k 100 d 90 P 1 80 3 6 9 Power level (watts) FIG. 5-2: PEAK TEMPERATURE (POSITION 4) VS. POWER LEVEL 90

THE UNIVERSITY OF MICHIGAN 7140-1-F Table V-1 presents all of the temperature versus thermocouple position data for various power levels. Figure 5-3 is the most complete display of all such data. 5.1.3 Significance of Observed UHF-VHF Produced Temperatures The level of temperatures obtained at various interior points of the ferrite mass indicates that for the power levels covered, there is no serious overheating problem for antenna operation. However, as the temperature rises, the values of e", the loss component of permittivity, and p" the loss component of permeability increase. Thus, a simple extrapolation to an 100 watt power input level is not possible. Further work on temperature versus power level is necessary. Both ferrite filled slot antennas and dielectric filled slot antennas are sensitive to the temperature. However, ferrite permits a better impedance match at the aperture. This permits a higher radiation efficiency with ferrite at moderate electric and magnetic Q factors. Because of the aperture impedance mismatch associated with dielectric loading, a higher electric Q factor is necessary for good radiation efficiency. This narrows the bandwidth. The higher Q of a dielectric cavity makes the dielectrically loaded antenna more sensitive to temperature changes and mechanical deformation. This means there may be a substantial advantage for ferrite filled slot antennas over dielectric filled slot antennas for installations where the ambient temperature changes or where mechanical vibration exixts. 5. 2 Slot Antennas With Ridges or Irises In continuing the research on ferrite loaded slot antennas that was initiated by this laboratory on earlier contracts, it was decided to modify the slot antenna, if possible, to allow a wider bandwidth or lower frequency of operation for the same given outside dimensions of the slot antenna. Well-known properties of the ridged waveguide, as well as preliminary experiments performed last year, indicated a possible potential for broadbanding or lowering the frequency of operation of the

THE UNIVERSITY OF MICHIGAN 7140-1-F (a) 9 watt power level Number of Thermocouple ~ F at Equilibrium 1 88.3 2 89.5 3 95.5 4 101.0 5 92.5 6 94.6 7 90.0 8 88.7 (b) 6 watt Number of Thermocouple OF at Equilibrium 1 86.2 2 87.5 3 91.8 4 94 5 90 6 91.8 7 87.3 8 86.2 (c) 3 watt Number of Thermocouple OF at Equilibrium 1 78.8 2 79.4 3 81.8 4 84 5 81 6 81.8 7 78 8 78.7 TABLE V-l: DATA OF THE POWER LEVEL-TEMPERATURE MEASUREMENTS IN FERRITE EAF-2 92

THE UNIVERSITY OF MICHIGAN 7140-1-F b) a).1_ a) a) a ~~~~+ + 9 watt power level o o 6 watt power level - * 3 watt power level 110 100 90 1 + ~g n=+ 80 _ 80 F ambient 9 watts 770F ambient 6, 3 watts. 70 1 2 3 4 5 6 7 Thermocouple number (Distance along length of equity, 1. 5"/division) FIG. 5-3: TEMPERATURE VS. POSITION IN CAVITY 93

THE UNIVERSITY OF MICHIGAN 7140-1-F slot antenna. The following study was entirely experimental and consisted of inserting various ridges and metal irises into the ferrite-filled slot antenna and noting the changes and impedance as shown in the Smith Chart of the imepdance to the antenna. To reduce the complexity of the data presentation, all Smith Chart grids have been suppressed except for a VSWR scale. 5. 2. 1 Assumptions of the Study Several assumptions were made in processing the impedance data for a 'bandwidth'. 1) Tuners were usually not used experimentally. 2) A VSWR circle = 3 was placed about each desired grouping of impedance points to obtain bandwidth (equivalent to the use of a wideband phase shifter and a wideband impedance transformer). 3) No further distortion of the impedance plots by compensation tuning was allowed. Actually, with compensation tuning, somewhat larger bandwidths might well be obtained. 5. 2. 2 Solid Ferrite Loaded Antenna Figure 5-4a shows an impedance diagram of the input impedance for the slot antenna entirely filled with solid ferrite blocks. All ferrite is solid EAF-2 material, the properties of which are summarized in Section VI of this report. The slot antenna with solid ferrite loading was thoroughly analyzed by Adams (1964). The operating frequency of the antenna is 352 MHz and the bandwidth is 18-20 MHz for a VSWR below 3, as may be seen by drawing a circle (VSWR = 3) about the origin of the Smith Chart. Nevertheless, this antenna, with its impedance matched properly, could operate from approximately 333 MHz to 383 MHz (50 MHz bandwidth), as may be seen by shifting the loop located in the upper right-hand portion of the Smith Chart clock-wise to the real impedance axis (e.g. by a wideband phase 94

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 all ferrite blocks 310 0~25 0 \ 150 4 0 210\ 330 330 355 VS'R 352 24i 3020 95 I~~~~~~~~~~~~~~~~~~0

THE UNIVERSITY OF MICHIGAN 7140-1-F shifter) and then drawing a VSWR = 3 circle about this loop, keeping in mind that the diameter of this circle changes with position on the Smith Chart. The 50 MHz bandwidth is therefore roughly the optimum bandwidth that could be achieved by this antenna with a wideband impedance matching without other optimizing circuits. In order to show the effect of a simple, but very narrowband transformer in the form of a double stub tuner, this solid ferrite loaded slot antenna was tuned with a double stub tuner in an attempt to move the upper right-hand loop to the central region. Figure 5-4b shows the resulting input impedance, and indicates a drastic change has taken place in the shape of the curve due to the additional phase shift of the double stub tuner. The phase reference for the original solid ferrite loaded slot antenna was at the input to the 'N' connector mounted directly on the antenna. The phase reference for the antenna shown in Fig. 5-4b with the double stub tuner attached, was at the input to the double stub tuner, a considerable distance from the actual antenna. This caused an additional phase shift shown by a more rapid rotation of the input impedance with change in frequency. This second curve (Fig. 5-4b has much less optimized bandwidth (approximately 23 MHz) for only slightly lower center frequency. One can conclude that transformation of the input impedance wit this particular setting of the double stub tuner, and probably with most other settings, would not be satisfactory for transforming the input impedance in the manner desired for increasing bandwidth or lowering frequency of operation. 5. 2. 3 Loaded Slot Antenna With Irises Earlier studies by this laboratory indicated that partial blocking of the loaded antenna aperture significantly changed the input impedance of the antenna such that the bandwidth (as measured by magnitude of VSWR) was improved. Figure 5-5a shows the effect of two irises which are actually aluminum tapes covering the front ends of several of the ferrite blocks used in loading the slot antenna. The actual input impedance (referenced to 50 ohms) is poor by any standard. Nevertheless, 96

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 slot loaded entirely 12>0 - o 250 60 with ferrite blocks 0450 150 30 / 44 O \75 80 / 37097 VSWR I,385 0 4 0 10 0 1.5 410 290 o 425 364 210 335 330 32 /310 o 320 2 -no 97

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 covered with aluminu] /X,,_ A d s b y tape 120- 60 350 180 VSWR /~.3 150 2 30 255 270 Zb3 405 370 VsW 400 98 ~97 10 2.0 1.5 395 2430 0440 98

THE UNIVERSITY OF MICHIGAN 7140-1-F the loop on the left is interesting since it occurs at such low frequencies. A circle for VSWR corresponding to three indicates a possible transformed bandwidth of 16 MHz centered approximately at 259 MHz. Another attempt at transforming the impedance diagram with a double stub tuner is shown in Fig 5-5b, where the lower frequency of operation loop has clearly been moved closer to the center of the Smith Chart. Although the loop is larger in radius, the bandwidth of 20 MHz around 261 MHz is approximately preserved. The reason that the lower frequency of operation loop has not been placed at the center of the chart is an experimental difficulty in controlling the placement of this loop with the double stub tuner (which is essentially a narrow band device). In summary, the possibility of operating at a frequency of approximately 100 MHz lower than the original frequency of the ferrite filled antenna by simply using an iris, is interesting and potentially useful, but it is accomplished at the expense of bandwidth. Another iris experiment (Fig. 5-5c) involved covering the lower row of ferrite blocks. This produced practically no impedance changes in the lower frequency of operation; a bandwidth of 42 MHz around 356 MHz is shown and this iris was therefore discarded. In the final iris experiment (Fig. 5-5d), the iris covered the lower three blocks of the center column. The low frequency loop in the upper left diagram has a VSWR = 3 bandwidth of 13 MHz centered around 273 MHz, which is again potentially useful in decreasing the operating frequency, although it drastically reduces the bandwidth. Experiments attempted using side irises were unsuccessful. In conclusion, irises appear to act as very narrow band tuners since reflections from the iris (sensitive to frequency) are being used; nevertheless, lower frequencies of operation can be achieved with greater bandwidth than would be obtained with an external tuner. 99

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 covered with aluminum tape 120 60 150 / / \ \\ 30 265 / 30 \ 257 300 180 ( / VSWR 262 2010 3 2.0 1.5 260 120 2 310 \ O0 325 385 O5 210 38 330 340 100

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 covered with aluminum tape 120 0 60 / 290 330 150 ~270 37/- 30 0o~~~~~250~101 ~ 60 0 210 330 I o250

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 covered with aluminum tape 120 60 35O 9265 150 6 730 285 i370! 250 20 o 3 400o 39520 390 430 210 330 440 2470 300 FIG. 5-5d: IMPEDANCE DIAGRAM OF SOLID FERRITE LOADED SLOT ANTENNA WITH IRIS (Frequency MHz). 102

THE UNIVERSITY OF MICHIGAN 7140-1-F 5.2.4 Ridged Loaded Slot Antennas Because of the increased bandwidth and lower operating frequency of the ridged waveguide, a series of slot loaded antenna experiments was initiated with various ridges created by steel or aluminum blocks replacing the ferrite blocks usually used in loading the slot antennas. It is important to note that the ridges were used without regard for possible improvement in matching the input probe impedance, even though the input probe was specifically designed only for the fully filled ferrite slot antenna. Figure 5-6a (inset) shows two metal ridges extending down to the lower side of the antenna where upper and lower are distinguished in this antenna by the fact that an electric monopole probe feed is used to excite the slot antenna and is inserted into the center of the antenna from the top. Figure 5-6a also shows the effect of the ridges on the input impedance and indicates again a substantial lowering in the lowest operating frequency obtainable from the slot waveguide. A bandwidth of 35 MHz around 291 MHz is achieved. This is felt to be a significant improvement in antenna performance. The second set of ridges used (Fig. 5-6b) consists of two sets of two steel blocks or ridges substituted for the center ferrite blocks. Figure 5-6b shows the effect on the input impedance of these center ridges and indicates an operatingbandwidth of 50 MHz around 330 MHz. The resulting 50 MHz is essentially unchanged from the fully loaded ferrite slot antenna and the center frequency of 330 MHz is not too different from the original 350 MHz. This loading, therefore, is not considered to be particularly useful. Another double ridge slot antenna (Fig. 5-6c) shows significant improvement in the lower operating frequency with a possible transformed bandwidth of 44 MHz around 317 MHz. This is a shift downwards of 41 MHz in operating bandwidth, a small but possibly useful shift. 103

THE UNIVERSITY OF MICHIGAN 7140-1- F 90 aluminum blocks 120 60 290 180 VSWR o 680 CJo360 390 150 / / i300 \ 30300 370 285 I 0 295 I 290 WITH RIDGES (Frequency MHz). 180 VSWR104 40 10 2.0 1.5 410 210 / ~ 330 0430 104

THE UNIVERSITY OF MICHIGAN 7140-1-F steel blocks 90 120 60 250 "260 270 150 \ 30 2800 290 440 330 5 1 180 VSWR 40.a \ S W R 27 340 /I. 4 20 10 3 2.0 1.5 325 324 o 420 20 310, 210' 330 6O o 400 300 WITH RIDGES (Frequency MHz). 105

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 steel blocks 12180 60 o~400 270 30 i50 / 30 300 m / ~250 20 305 L80 VSWR 315 4 20 10 2 0.0 1.5 314 o 400 210/ 330 o 440 o 420 24 300 106

THE UNIVERSITY OF MICHIGAN 7140-1-F Figure 5-6d shows an asymmetrical ridged arrangement used in the loaded slot antenna and the resulting impedance diagram. Again, an important lowering of the center frequency is noted. The resulting bandwidth of 27 MHz around 292 MHz may be useful. The higher frequency loop on the Smith Chart (around 360 MHz) is not considered valuable. Other less successful experiments were attempted using ridged slot waveguide. Figures 5-6e, 5-6f and 5-6g show such loadings. Although the curves all appear single-looped and reasonably simple, they do not appear to have value either in lowering the center of operating frequency or increasing the bandwidth even when impedance transformations to the center of the Smith Chart are considered. Ridges extending down from the top and ridges covering all (or almost all) of the height of the slot were unsuccessful. Finally, various schemes of replacing ferrite blocks with balsa wood were attempted, the balsa wood acting essentially as free space or air. Such schemes invariably ended in raising, rather than lowering, the center of the operating frequency. 5. 2. 5 Conclusions and Summary Table V-2 summarizes the results of the ridged slot antenna studies. Figures 5-5a, 5-5b, 5-6a, 5-6c and 5-6d showed configurations which were useful in lowering the operating frequency while maintaining a reasonable bandwidth. In all of these, it is noted that a single or double arm iris or ridge in the waveguide is used, extending to the bottom of the waveguide and partially to the top. Most irises or ridges are three blocks high (out of the four) and arranged in a central column. A decrease in center frequency of 60 MHz is not difficult to obtain. Ridges appear to have a wider bandwidth than irises. 107

THE UNIVERSITY OF MICHIGAN 7140-1-F steel blocks 90 120 60 0;320 151330 280o420 2/ \/ 33 00 285 295 150 / dzs 9288 30 291 /292 1290 350 361 360- - 55 180 VSWR _ 4 0 1' o 2'o o 1.5 ' o 210 400 330 0420 208

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 steel blocks 120 - 60 290 310 0270 150 320 30 360 380 0250 55 180 __ VSWR h350 4 0 10 2.0 1.5~ 335 400 345 420 210' 330 109

THE UNIVERSITY OF MICHIGAN 7140-1-F 90 steel blocks 290 120 1 60 31/330 35o 0 ~43070 50300 320 1140!~~~~~~~~~~7 I I.56:IPDNEDCGCM O SLDFRJT ODDSO NEN ~~~WIT IG (rqec z) /~~~~~~~~~~1

THE UNIVERS F _POF MICHIGAN ~ o 440 steel block 120 3 110 60 0o270 320 o 36 /250 380 250 I30 341 180 / 240\ 300

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE V-2: SUMMARY OF RIDGE SLOT ANTENNAS Figure Center Frequency Bandwidth Remarks No. (MHz) (MHz) 5-4a 352 18 No tuner 5-4a 358 50 Optimum tuning 5-4b 344 23 Optimum tuning 5-5a 259 16+ Optimum tuning 5-5b 261 20+ Optimum tuning 5-5c 356 42 Optimum tuning 5-5d 273 13 Optimum tuning 5-6a 291 35+ Optimum tuning 5-6b 330 50 Optimum tuning 5-6c 317 44+ Optimum tuning 5-6d 292 27+ Optimum tuning 5-6e Not potentially useful Optimum tuning 5-6f Not potentially useful Optimum tuning 5-6g Not potentially useful Optimum tuning +Indicates potentially useful results. Although the impedance diagrams for various configurations of ridges and irises appear useful, the efficiency of the antenna as a radiator must yet be investigated. It is assumed that the antenna patterns will be the usual dipole patterns since the antennas are much smaller than 1X. In order to achieve the necessary impedance transformation to make the ridges or irises useful in transforming the impedance of the antenna, a better cavity should be designed for each ridge or iris configuration so that a real impedance is faced by the probe rather than the imaginary or partially imaginary impedances now seen. As mentioned, the probe was designed for a fully loaded cavity rather than the partially loaded cavities tested. In addition it may be necessary to specifically design the ridges or irises such that excessive energy concentrations are avoided, since energy concentrations lead to great losses in ferrite structures; 112 -

THE UNIVERSITY OF MICHIGAN 7140-1-F VI CHARACTERISTICS OF FERRITE MATERIALS Attention has been given to extending the use of ferrite loading to lower frequencies (down to 30 MHz). With this in mind, additional ferrite material was purchased (e. g. Q-3, from Indiana General). Some of the experiments in preliminary design are based upon forms of this material which have been readily available. This material appears to have reasonably good electrical and magnetic characteristics. Some of the designed experiments have been limited because of the availability of ferrite material in proper form. The Q-3 material has been obtained in three forms: 1) Stick (2. 85" x 0. 5" x 0. 12"); 2) Cylindrical Rod (1. 937" x 0. 25"), and 3) Circular Toroids (0. 5" OD x 0. 28" ID x 0. 25" thick). Ultimately, it is expected that powdered type Q-3 ferrite will be obtained by using some of the solid forms mentioned above and pulverizing them through the use of a ball mill. Ferrite type Q-3 appears to have excellent characteristics below a frequency of 200 MHz. Available information on this ferrite, as obtained from advertising circulars, is somewhat controversial. The characteristics of manufacturer's publications are shown in Fig. 6-1 and will be discussed later. Measurements by this laboratory on the characteristics of the material as represented in Fig. 6-2 show some but not complete agreement with the published data. For measurement methods on Q-3 material see Sections 6. 1 and 6. 2. In addition to Q-3, a considerable study has been made of other available ferrites. Table VI-1 gives names and manufacturer for several selected high-Q ferrites. The first ferrite, EAF-2, is the one presently used in this laboratory for ferrite-loaded antenna studies. Its properties have been thoroughly measured by this laboratory. All of the work involving experimental tests of antennas loaded with powdered ferrite have used this material. 113

THE UNIVERSITY OF MICHIGAN 7140-1-F 300 200 100 IRCA 15569-29E 70 50 30 R AcCA 15569-29B 20 Q Ferrotron 10 107 ~ \RCA 15569-63E 3 l Q-3 1 50 100 200 300 500 700 1000 Frequency (MHz) 30 Q-3 20 -RCA 15569-63E aU', Iz3 10 7 Ferrotron 5.... -- RCA 15569-29B ~~~~3 d ~ - -~IRCA 15569-29E 50 100 200 300 500 700 1000 Frequency (MHz) FIG. 6-1: FERRITE PROPERTIES, ADVERTISED VALUES 114

THE UNIVERSITY OF MICHIGAN 7140-1-F 300 200 EAF-2 Solid 20 Ferrotron \4- EAF-2 Powder 10 7 5A 3 Q-3 50 100 200 300 500 700 1000 Frequency (MHz) 30 20 - Q-3 20 Q3 EAF-2 - different samples 2 EAF-2 Powder 50 100 200 300 500 700 1000 Frequency (MHz) FIG. 6-2: FERRITE PROPERTIES AS MEASURED BY THE UNIVERSITY OF MICHIGAN

THE UNIVERSITY OF MICHIGAN 7140-1 -F Its formula is Ni Zn Co Fe A 0 (6.1) Ni.9696.0404 C.03F 1.84.04 4 ' TABLE VI-1: SELECTED HIGH-Q FERRITES Ferrite Manufacturer Remarks EAF-2 Motorola Production not repeatable. No longer available. Tested at U. of M. Q-3 Indiana General Several sizes on order. To be tested. Tested at U. of M. Ferrotron Polymer Corporation Not a ferrite. Iron impregnated plastic. Excellent at high temperatures. Q and ' measured at U. of M. IZ3 Ferroxcube Measured resonance in c' at 100 MHz. RCA 15569 Series RCA Tested for USAEC by RCA. RCA does not produce. Formula said to be reproductible. USAEC has indicated these materials are all magnetically oriented. Eccosorb CR Emerson and Cuming, Inc. Recently tested at U. of M. The EAF-2 material (designated in previous reports as type A) has been satisfactory for experiments on earlier contracts. It is the same material which was used in the detailed studies of the rectangular cavity-backed slot. The temperature dependence of this material has been reported (Lyon et al, 1964). Attempts to purchase more of this material have failed, due to the difficulty experienced in reproducing the high quality of the first batch. 116

THE UNIVERSITY OF MICHIGAN 7140-1-F The second ferrite, Q-3, has already been discussed. The third ferrite, Ferrotron, has been recently tested by this laboratory (see Section 6. 1). The tests did not substantiate its advertised high-Q properties at 300 MHz and above. The fourth and fifth ferrites have not been tested by this laboratory except for brief dielectric tests on IZ3. The RCA materials (1963) are experimental and were developed for the US Army Signal Corps. Currently, RCA is not manufacturing this ferrite, although sufficient information is available for others to manufacture it. Figures 6-1 and 6-2 show the Qm (magnetic Q) and pu' properties for the various ferrites investigated. From Fig. 6-2 it can be seen from the Qm curves that the present EAF-2 ferrite from Motorola is better than any other available ferrite except for the RCA experimental ferrite shown in Fig. 6-1. Note that the RCA ferrites with very high Q at high frequencies also have very low,u properties. This is a common characteristic of ferrites - a very low loss factor usually is accompanied by a low permeability. Nevertheless, it does appear that several of the RCA ferrites are worth investigating for future application in antenna loading where the anisotropy associated with a favored orientation for magnetization can be advantageous or at least acceptable. 6. 1 Derivation of Permeability Determination Equations A resume of the method of obtaining both the real and imaginary components of relative permeability is given. See Fig. 6-3. First, a lossless calculation will be derived for thin samples. Later, a thick sample measurement for more accurate loss measurements will be given. Let Z tan. (Considering a lossless transmission line. ) (6 2) 117

Model Quenching z 803-A I Phase adj VHF Bridge < Volume Control,Magnitude L J Generator Adj co Power E, Supply Phones Detector Unknown Impedonce is - Connected Here C) FIG. 6-3: EXPERIMENTAL SETUP FOR u AND E MEASUREMENTS. Z r r

THE UNIVERSITY OF MICHIGAN 7140-1-F where Zf - characteristic impedance of ferrite medium =Z — r (6.3) I 0 r Z - characteristic impedance of the medium in the coaxial line. 13f - propagation constant in ferrite ~27r 1rr e.(6. 4) Ar, cr - Relative permeability and permittivity. The small thickness d validates the approximation tan 3fd. Ifd is within 60 with,uTre' = 10. This is reasonable for type Q-3 ferrite for AL and e at 200 MHz. or 0 (6.5) 7 j o. 2 rr r o jZ. z 27r r o X d.... 0119

THE UNIVERSITY OF MICHIGAN 7140-1-F Then: jZ x S. C. O s.-c. 0 (6.6) r Z.2rd o Since Z is almost purely imaginary, =- (6.7) r Z 27rd o In order to measure losses, a much thicker sample was used. The following derivation does not use the tan6m 6 approximation, and thus is valid for much thicker samples. Let Z =Zftanyfd (6.8) S.C. ff z =f-L S.C. Zf C Z -tnh' (, and E are relative values) (6.9) Hence, 2( 2 2 (6.10) Z tanh yfd Let P/ = m' - j/i" (6.11) and Z =Z' + jZ" (6.12) s.c. r r 120 -

THE UNIVERSITY OF MICHIGAN 7140-1-F Then assuming E real, 2 2 (Z - Z" 2+ 2jZ' Z") e I _? = r r r r (6.13) Z tanh yf d Solving: (Z 2 _ ' 2), 2r r (6.14) Z tanh yd o f -2Z' Z" E t,,= r r (6.15) 2 2 Z tanh yfd o f Then: -2Z' Z",u6=~" r r tan6 - = t' ( 2,Z 2 r r 2Z' Z" r r (6.16) 2 2 Z" - Z' r r Now: Z = Z' + jZZ" s.c. r r Z' = jZ j cosO (6.17) r I s.c. Z"1 = Z]| sinO (6.18) 121

THE UNIVERSITY OF MICHIGAN 7140-1-F Let 0 = 90 - 0 Then Z' =1Z i sin0 (6.19) r s.c. ZT= z COS (6. 20) r s.c. Then 2 Iz 2cos0sin0 tan6 = s (6. 21) IZ 2(cos 0 - sin20) sin20 cos20 = tan20 (6. 21) Let: Qm = Q magnetic Then: Q -=-= cot20 (6. 22) Im tan6 6. 2 Results of Permeability Measurements Using the apparatus shown in Fig. 6-4, the procedure to obtain Z was as follows: 122

THE UNIVERSITY OF MICHIGAN 7140-1-F e< Sr i Toroid of Material Shorted End er _Sd=e - id d Pr Pf 0.525" d =0.3cm as 0 573 I FIG. 6-4: GEOMETRY FOR TOROID MEASUREMENT TECHNIQUE. 123

THE UNIVERSITY OF MICHIGAN 7140-1 -F 1. The bridge is shorted and a null is obtained. The magnitude and phase readings corresponding to this null are the reference values for the short-circuit impedance without the ferrite specimen in the holder. This point is plotted on Z- 0 chart (S on Fig. 6-5). This point should have been at the short circuit point of the chart (Ohms, 900). However, since the bridge measures impedance not at the plane p, (See Fig. 6-3) but at pr, the reference plane, this reading has to be translated by 0 onthe Z - 0 chart to make it coincide with the true short circuit point of the chart. 2. The ferrite specimen is inserted in the holder of the coaxial cavity and a null is obtained as indicated by the detector. The readings on the VHF bridge corresponding to this null are plotted on Z - 0 chart and this point is translated by (0 r- ed) in wavelengths to give Z at the plane pf. 3. Z at the plane pf represents the magnitude and phase of the impedance of the coaxial cavity with the specimen. The phase difference between reading in (1) and this reading indicates loss in the ferrite specimen corresponding to the loss tangent for the material. Actually the loss tangent equals the tangent of twice this difference angle (see derivation of formulas). A tabulation of the results based on data and simple calculations is given below in Table VI-2 for Q-3 ferrite and rable VI-3 for Emerson and Cuming, Inc., Eccosorb "CR". The "CR" (casting resin) material was a very recent measurement. Although it was designed to be a lossy microwave ferrite material, Table VI-3 shows that below 300 MHz, the p is reasonably high and losses very low. Since the material has a high e and can be easily cast, it will be further investigated as a useful loading ferrite. The data obtained as outlined cannot give a small loss tangent very accurately, since it is difficult to obtain with precision the phase difference in step (3) from Z - 0 chart. However, high losses can be measured accurately. The measured/ur curve of Q-3 is somewhat lower than the published value; the measured loss curve 124

THE UNIVERSITY OF MICHIGAN 7140-1-F TABLE VI-2: PERMEABILITY OF TYPE Q-3 FERRITE f /( M Loss Tangent Q-Magnetic (MHz) 100 12.4 0.01746 57.290 125 12.3 0. 02444 40. 917 150 13.2 0.03492 28. 636 175 13.2 0.05241 19.081 200 14.3 0.08749 11.43 225 16.0 0.1763 5.67 250 16.82 0. 3244 3.07 300 16.4 very high very low The values of p found above agree closely with published values. Data taken by the same method on "Eccosorb C-R" material results in the information shown in Table VI-3. 125

THE UNIVERSITY OF MICHIGAN 7140-1 -F TABLE VI-3: PERMEABILITY OF ECCOSORB C-R f Z short Z eccosorb Z eccosorb |t Q (MHz) 0 Z translatedand r Magnetic 100 91.00 8.6 90.5 10 89.5 1.25 3.98 57 150 60 12.8 59.5 15.4 89.25 2.5 5.3 38 180 51 15.5 50.5 18.5 89.1 2.55 4.52 32 200 45.5 17.2 45 20.8 89 3.0 4.72 28.6 230 39.5 20.5 39 24.5 88.75 3.25 4.5 22.9 250 36.5 21.9 36.0 26.3 88.7 3.5 3.72 22 300 30.7 27.5 30.2 33.25 88.6 4.25 4.51 20.4 400 22.75 39.3 22.1 49.5 85 5.7 4.55 5.6 126

THE UNIVERSITY OF MICHIGAN 7140-1-F is much higher than advertised. The utmost care was taken in obtaining data. The final readings are the result of an average of three trials. 6. 3 Permittivity Determination Method Using Figs. 6-3 and 6-4 the method is similar to that described in Section 6. 1 except the specimen is placed at a location in the coaxial cavity corresponding to a maximum of electric field. Thus -jZf = (for a lossless line). oc tanlfd -jz oor/ 00 r r r r -jz x 00= ~ (6.23) 2we d r Therefore, -jz x OzX O = 00 (6.24) r 27rZ d oc And Z X (6.25) oc The problem here is to create a perfect open circuit. This is done as follows: 1) A short is created and the impedance is measured. Use dotted lines on Fig. 6-5 127

THE UNIVERSITY OF MICHIGAN 7140-1 -F 2) Open circuit impedance corresponding to (1) is found from the Z - 0 chart. 3) The open circuit impedance obtained from (2) is adjusted on the bridge dial and a null is obtained corresponding to that by means of a short circuited adjustable line X/4 length beyond the specimen. 4) The length of the short circuited stub is clamped. This is the exact X/4 length which will create a perfect open circuit. 5) The ferrite piece is put then inside the holder and with the same length of stub as in (4) a null is obtained but the reading on the dial is not the Z in the above formula. 6) Z-open in (2) is not actually open. It has to be co. So translate the value in (2) to oo points on Z - 0 chart and note the angle of translation. 7) Translate impedance in (5) by the angle in (6) in the proper direction. (See the Z - 0 chart Fig. 6-5 with construction done on it. ) 8) The new point represents Z used in the above formula. The results of data so obtained are in Table VI-4. TABLE VI-4: PERMITTIVITY OF TYPE Q-3 FERRITE f measured/open actualopen E short open with ferrit with ferr te r (MHz) 0 (Z) 0 (Z) 0 (Z) r 0 0 100 900 130 -90~ 19 -90~ 16.3 -90 1000 7.96 200 900 16 -900 155 -90~ 116 -90 510 7.81 300 90~ 14 -90~ 180 -90~ 115 -90 345 7. 7 The ferrite is relativity lossless as far as the dielectric loss is concerned. Though a loss is detected at frequencies higher than 225 MHz, it is not accurately measurable without the help of very accurate instruments. 128 --

THE UNIVERSITY OF MICHIGAN 7140-1-F 60 \, rSO.I Note: Calculations of Ct and E for Q-3 ferrite are made at 200 MHz from Z -0 Chart Sp - Short circuit impedance for /r measurements Se - S. C. impedance for Er measurements S - S. C. impedance with ferrite for r measurements 0 - open circuit hence - 0f - Open circuit impedance with ferrite for Er measurements etc. FIG. 6-5: Z -8 CHART 129

THE UNIVERSITY OF MICHIGAN 7140-1 -F VII EFFICIENCY MEASUREMENTS In this procedure, an arbitrary antenna is fed with constant power and the power received by the test antenna is compared to that of a standard dipole by means of a calibrated attenuator. The difference in attenuator settings is the relative gain of the standard antenna. Corrections are made for the VSWR of each antenna and for other non-antenna losses. 7.1 Efficiency Data on Ferrite Loaded Helix Loading of a helix antenna with a low loss ferrite does not significantly alter the efficiency as a radiator at resonance. Table VII-1 gives the values of efficiencyfor various loadings of EAF-2 powdered ferrite. The resonance frequency of antenna No. 217 corresponds to 750 MHz with air and 550 MHz with a 3/8" loading of EAF-2 ferrite. TABLE VII-1: EFFICIENCY OF A HELIX ANTENNA (No. 217) WITH SEVERAL FERRITE LOADINGS Frequency (MHz) Loading Efficiency(per cent) 750 Air 60 550 3/8" Inside Layer EAF-2 61. 2 550 1" Inside Layer EAF-2 41 550 Air 31.8 550 3/4" Outside Layer EAF-2 54. 5 The efficiency of the outside loading of ferrite was measured at a frequency that was near resonance. Note that the reduction of efficiency is not statistically significant. 130

THE UNIVERSITY OF MICHIGAN 7140-1 -F 7. 2 Measurement Procedures The gain of the test antenna is obtained by adjusting a calibrated attenuator to produce equal receiver levels for both the test antenna and a standard half -wavelength dipole. Corrections to this relative gain figure are made for the mismatch of each antenna to its transmission line, losses that result in the baluns, and losses due to incompatible polarizations. 7, 2. 1 Measurements The set up of the equipment as indicated in the Fig. 7-1 using a standard dipole as the receiving antenna. The power transmitted, attenuator setting and chart level are recorded (Part 1, Appendix C). The dipole is then replaced with the test antenna, and the same power is fed to the transmitting antenna as before. The attenuator is adjusted to give the same chart level as determined in the preceding paragraph. The power transmitted, attenuator setting, and chart level are recorded (Part 2, Appendix C), for both E and H plane patterns of the test antenna. For circular polarization the antenna is rotated 90 on the axis of symmetry for additional E and H plane patterns. The VSWR of the standard dipole at its connector (Part 1, Appendix C) and the test antenna are recorded (Part 2, Appendix C). 7. 2. 2 Calculations If the test antenna is fed with an infinite balun, corrections must be made in both the gain calculation and the measured reflection factor. Attenuation data on cables may be obtained either by direct measurement, or by reference to standard tables. (e. g., Reference Data For Radio Engineers.) If there is significant inefficiency in the standard dipole, the loss must be determined and a correction made in the measured reflection factor. Since the impedance of the standard dipole and the test antenna are usually 131

THE UNIVERSITY OF MICHIGAN 7140-1 -F Recv. Ant. Re(Std. Ant. Trans. Ant. (Std. Dipole) (Arbitrary) (test Ant.) I _ _ Meter Coupler Receiver R. F. or Generator dipole Rectangular 1000 Hz Plotter Osc. FIG. 7-1: EQUIPMENT SETUP FOR EFFICIENCY 132

THE UNIVERSITY OF MICHIGAN 7140-1-F different, the power fed to each antenna is usually different even though the incident powers are identical. The correction factor is the ratio of the dipole power transmission coefficient to that of the test. The power transmission coefficient is one minus the square of the voltage reflection factor. In calculating the gain of the test antenna, the 2. 15db gain of a lossless half wave dipole (constant C in Appendix C) must be added. An extra 3. 01 db must be added for a circularly polarized test antenna because half of the power in a linearly polarized wave is unavailable to a circularly polarized antenna. At this point it is possible for the recorders of the data to make an estimate on the efficiency. The expression d = 3200 is a fairly accurate formula for estimating the numerical directivity, d (Stegen, 1964). The values of 0 and 0 are the half power beamwidths of two orthogonal cuts. If there is rotational symmetry (as there usually is), 0 and 0 have the same value. Using this approximation, efficiency is g x 100. d To calculate the directivity more precisely, a graphical integration of an antenna pattern must be made. If there is a high degree of rotational symmetry in the patterns, only one graphical integration need be performed. If there is significant asymmetry, graphical integrations must be performed on four or more cuts depending on the polarization and patterns. An average of the reciprocals of the directivities calculated for each pattern must be made; the reciprocal of the average is then the value of directivity to be used for calculating the efficiency. To do the graphical integration, Table C-1 of Appendix C may conveniently be used, for either received voltage or power. The directivity, d, is calculated by the formula: 229 U d= (7.1) (width of square in0) (total at bottom of Table C-I, Appendix C) 133

THE UNIVERSITY OF MICHIGAN 7140-1-F where U is the pattern maximum of the power. If the plot is of field strength, U 2 0 0 is used instead of U 0 The formula is an approximation to the exact expression for directivity (Kraus, 1950). 47rU d 2 (7. 2) 2 r r U(O, 0)sindOd0d O O If there is independence of 0, as is often the case, the formula reduces to: 4U 4U 0 o (73) f U(O)sinOde U(/ ) sinO dO 0 0 The integration may be a sum: 4U d -o (7.4) n E U(Oi) sinOi Ai.O If we express Ai. in degrees instead of radians: 4U 229U d o = 360 E U(O) [sinOei Ai0 U(Oi) ini iOA0 134

THE UNIVERSITY OF MICHIGAN 7140-1-F 229U 0 n 1 i=1 Esn IsinI (squares/ao)) (l he ) 229U ~~~~~~~~~o ~~(7.5) n Ai il Ini (quares/Ai) n since all of our AO. are equal. This is the formula stated previously since i=1 sinOi (quares/ ) is the total at the bottom of Table C-1, AppendixC. 135

THE UNIVERSITY OF MICHIGAN 7140-1- F APPENDIX A ENERGY TRANSFER BETWEEN A HELIX AND A FERRITE ROD Studies have been made of continuously excited (i. e. excited over a large portion of the antenna length) traveling wave antennas (Spitz, 1962; Walter, 1965; Weeks, 1957; Rumsey, 1953). Recently, this laboratory began studies of such antennas using ferrite materials. Specifically, a mathematical study of the energy transfer process from the exciter (in our case, a helix) to the ferrite rod (the intended radiating mechanism ) has been made. In a study of energy transfer into a ferrite rod one can start with the proposition that with two transmission lines coupled together, energy fed into one line will be transferred optimally to the second, under certain conditions. The voltage and current differential equations for each of the two transmission lines have been written. A consideration of the coefficients involved in these transmission lines indicates the dependence upon mutual coupling factors. When the second transmission line is to serve as a radiator, it is expected that the energy transferred to this line will be reradiated at the far end in the end fire direction A. 1 Analysis In order to cause a strong coupling between the feeding electric circuit and the receiving ferrite rod the phase velocity of the electric circuit in the axial direction must be adjusted to be approximately the same as the wave phase velocity in the ferrite rod. The phase velocity along the axis of the helix is approximately: vP= csin /I where / is the pitch angle and c is the velocity of light. Treating the helix as a transmission line with distributed L and C, the ferrite slab may be considered to be another transmission line. The arrangement of lines is shown in Fig. A-1. Due to -.... 136

Ferrite Rod Helix 1 1 w ~ ~ ~ ~ ~ I r r r r~~~~%l Aw% V2(x) I (x) 0 Ix (3) FIG. A-i: FERRITE ROD FED BY A HELIX V1. I (x)are voltage and current along helix, 1 2~ I W a e i duc d v lta e a d c rre t a ongfer ite ro V2. 12(x) are induced voltage and current along ferrite rod

THE UNIVERSITY OF MICHIGAN 7140-1 -F the excitation of the helix, there is mutual energy coupling between the helix and the ferrite rod. The circuit equations are Circuit No. 1: Helix dV -d =-ZlIl+Z1212 (A.1) dI dx d= yV1+Y12V 2 (A. 2) Circuit No. 2: Ferrite dV dx =22 21I1 (A.3) dI dx Y2V2+Y21V1. (A. 4) Let Z1=J z/y1, Z2 z2/y2 (A. 5) A. 1, A. 2 and A. 3, A. 4 can be rearranged into the form: d (Vl~Ill -)= (Vl+I1Zl)+z12I2t2Z (A.6) d +I 2Z 2'JZz ~;1 (V 2)+z I (A. 7) |d(V+I2Z2)= z2 (VI2Z 2+z2111Y21Z2 1....____ ~138 —..

THE UNIVERSITY OF MICHIGAN 7140-1- F Define the following modes. v+I1Z V+Iz 1 + 1 41 2 + 2 (A. 8) 1+ 4 4J71 2 4J77, There are two modes ( + = forward, - = backward waves) propagating in each circuit. All modes mentioned are a subclassification within the modes existing on each line. Vi= 2Z (Al++A,_) [v 2 / A+A for Circuit No. 1 (A. 9) I 1= c(Ai+ -A )l 7~1 ( V2=22 (A 2++A 2 -for Circuit No. 2 (A. 10) 2 2 2(A2+-A2-) Substituting (A. 8), (A. 9) and (A. 10) into (A. 6) and (A. 7) yields d z-A12 2Y1 2 |dx + 1~= 2/ZlZ 22+ 2- 2 2++A2 |( -/2)A2+= 2 - -A 2A (A +A. (A. 12) dx ~ 1- 2~ 2,ZZ I 1+ 1- ( A 1+ 1 -Next, equations (A. 11) and (A. 12) upon regrouping coefficients can be written, (dx +71)A1+ (2J. +Yz12 Y12 2 Z12 12Z 2 + 11~;1 A 1 3- 2 $-(2 212 (A. 13) zd {Z 21Y211 Y321 2l2 +dx 2 2 2/+= ZZ 2 1+2 2 A1+-(2 2 /2 (A. 14) 139

THE UNIVERSITY OF MICHIGAN 7140-1-F Note that Ai+ means Al+(x). This simplified notation is used from here on. The above equations of specialized forms are the more general set of equations for the coupling of physical systems in terms of modes a1, a2, etc. dal dx =llal+c2a2+c3a3+.. (A. 15) da2 (A. 16) dx C21al+C22a2+23a3+ (A. 16) da3 dx C31al+c 32a2+c 33a3+... (A. 17) Note that each of the above equations applies for each of the lines; the numerical subscript used in these is a mode designation. Now: A1+ = forward mode in Circuit No. 1 A2+ = forward mode in Circuit No. 2 Al- backward mode in Circuit No. 1 A2 = backward mode in Circuit No. 2. From equations (11) and (12) there are four possibilities of coupling among these four modes and these are (1) coupling between AI+ and A2+ (2) coupling between A1+ and A2_ (3) coupling between A 1 and A2+ (4) coupling between Ai_ and A2 The total or net power of the two lines at any plane located a distance x from the origin is given by 140

THE UNIVERSITY OF MICHIGAN 7140-1- F Vl(x)Il'(x) V (x)I'(x) P(x)=Re 2 +Re 2 (A. 18) 2 2 Expressing P in terms of modes, this becomes P(x) =2 AA1+( _(X) 11A1 ( 2+I 1 A22 (x) 2] (A. 19) Evaluating P at x = 0 yields P(O)= 2LAl+()2l -iAl_()12] (A. 20) Consider each of the four possibilities or cases of coupling in turn. Coupling between two forward modes A1+ and A2+ (d (1l) 1+ (1z2 12 1 2 12 12122 (A. 21) Y12 i12/ 21 21 1 21 21 (dx -/zz2Y2)A2+ =(2 2 A1+-( /ZAiZ- 2 A1 - (A. 22) If the following inequality holds true for the greatest power transfer from Line No. 1 to Line 2, Z12+ l2 12 12 y12 1 2 2 ZZ+ 2 21ZZ2 Then equations (21) and (22) simplify as d ___ 12 +12Z 1 2 I( dx I~~Z 1)1+2 (Z;IZr;~12 2 )2+ (A.23) d ( Z21 Y21 ) (A 24) a d)2)A2+= 221 2 + - 2 A 1+ 2 (A.+4) Using the general forms for coupling there results, d d c d 1) 22 and =C (d+jCll)A1-C12A2 ( +jC22)A2-C21A1

THE UNIVERSITY OF MICHIGAN 7140-1- F The above equations are correct for either forward or backward waves. Assume A l+and A2+ vary as e 7x ([+j Cll)A1+ C122+ (A. 25) (T+ j C22)A2+ C21 l+ (A. 26) For a nontrivial solution, the determinant of the above equation must be zero, i. e. C11+Ci22 + 11 ClC22 (A.27) %, et = -j -... (A. 27) Equations (25) and (26) are solved for a pair of values y and y' which apply only for coupling between Ai+ and A2+ modes Al+(x) = PeYX+Qe'X (A.28) If the -y 'Is are imaginary, the coupling is called passive; if they are complex, the coupling is called active. Then the solution for each of the two lines must be A +(x)= PeX+Qe'X (A. 29) 1dA (x) ( A2 (x)= C= dx 1+CA 1+()] (A. 30) C12 Initial conditions are: A +(x)=Ai () (A. 31) A 2+(x)= 0 at x = 0 (A. 32) 2+ The resulting values of the coefficients M and N are, A+() +jl (A. 33) j26 Ai+(0) Fy+ jC] Q = - (A. 34) 142

THE UNIVERSITY OF MICHIGAN 7140-1-F where 7'-y= j26 (A. 35) r- -C 2 1 6=/, +I (A. 36) 6=/ C12C21 C 22)2 (A.36) A1I(0) Kt ~ x ~'x (A. 37) A+ j 2 6 B' +jCll)e - (y+jCll)ex (A. 37) 1+ j26 L 11 11 A1+(0) ( CY+jC11) ('y t +j C11) (eX-e') (A. 38) A2+(x)= j26 (A.38) ~2+ j26 C12 Assume that i's are pure imaginary quantities (lossless). Then 7 = -j (+ 6), a' = -j (- 6) (A. 39) where where 13 (C11+C22) (A. 40) 6 + C12C 21 +( 12 2) (A. 41) P 1+ power in Al+(x) mode = 2 A +(x) 2Al+(x)A l+(). 1++1+. 1+ 1 2 P12 1A1+(x)12 1A1+()1 CC 2 sin2 3xJ (A. 42) Define F12 as the power transfer factor between modes Al+ and A2+. 12 11 12= 1 (A. 43) 1 -C 2 C12 C21 143

THE UNIVERSITY OF MICHIGAN 7140-1-F Then the powers in Ai+ and A 2+ are P1+=2 LA1+(x) 2=21 A1+(0) 1- F12Sin2 6x (A. 44) P2+=2[A2+(x12 =2A+(0)2-A1+(x) F sAln+(0)2 F12sin2x x (A. 45) Figure A-2 shows the variation of power on the two lines for the forward mode. Note that power is first transferred from Line 1 to Line 2 beginning at 6 x = 0. Then from 6x = r /2 to 6x = 7r power is coupled back to Line 1. P1+ 21Al+(0)12 P2+ 2F. A1+(0)12 L xIr x FIG. A-2: ENERGY TRANSFER BETWEEN TWO COUPLED LINES. 144 PT- A 0.MW M11r-T M - KCTT1- - -r4TV --- —

THE UNIVERSITY OF MICHIGAN 7140-1-F Comparing equations (15), (16), (23) and (24) yields C11= jZyI (A.46) -I z12 Y12 rz\ z2 C2 = i (A. 48) F (lI- y'zoy2 (A. 49) _K1 2-KZ+12 Y12 12-2.2 2 if Zl= -jWL1 z2=-jWL2 Z 1v-7c'C Y=-jWC1 Y2=-jwC2 z12=-jwM Y12-=-jwN 22 2L 2 where L, C, M and N are line parameters per unit length. Then F = 1 (A. 50) 12 1~i wTL{CF7-w/ C2t)2 1 1+\ 2 / Wmj jM N jLL2//lC' 12 Optimum coupling, F12=, occurs if L C= W 2.' C This means total power transfer occurs...1~~ ~145

THE UNIVERSITY OF MICHIGAN 7140-1-F P1+=2[A lX()2=2[A (0)12 -Lsin (2LL2/ClC2 + ) N/L lx (A. 51) P =2A2 (x)j =21A1+(0) sin (2 +L1L /C C2 + 2 (A. 52) There is very low coupling for Cases (2) and (3) involving, in each case, opposite modes. The coupling for Case (4) involving backward modes only on the two lines, is formulated in the same general manner as Case (1). A. 1 Experiments on Energy Transfer and Radiation The experimental program will be used to confirm the energy transfer conditions prevailing for a ferrite radiator which is fed in a manner corresponding to one transmission line being coupled to another. Certain definitive experiments were run using a spiral transmission line for Line No. 1, and various pitches and diameters of such a transmission were used. Line No. 2 was initially a flat ferrite slab; rods have also been used as described in Section 2. Measurements were used at various spacings of the transmission to the ferrite slab. Radiation from spiral transmission line was not wanted and therefore shielding was introduced so as to make measurements upon the radiation field of the ferrite slab alone. This meant that an objective was to study the ferrite slab as an end fire radiator, knowing that all energy so radiated had to be coupled at the second transmission line from Line No. 1. The results so far have been inconclusive. The coupling was a major problem in initial experiments with the slab. 146

THE UNIVERSITY OF MICHIGAN 7140-1 -F APPENDIX B LOADED HELIX AND CONICAL-HELIX ANTENNAS B. 1 Material Loaded Conical Helix The problem discussed here is the reduction in size of a helix antenna with the addition of cylindrical loading material of arbitrary isotropic p and e. The radiation properties of a conical antenna are almost completely dependent on its active zone, the zone where the near fields are less tightly bound to the cone so that radiation of power can actually occur. This active zone may be described by a minimum of two parameters, the center of the active region and the width of the active region. Most of the theoretical work has been directed at finding the center of the active region of a conical antenna. A shift in this center has been assumed to mean a decrease in size or effective operating frequency of the antenna. Nevertheless, the width of the active zone in a conical antenna is quite large, and if the width of this active zone is not decreased in loading the antenna, then the size of this active zone imposes a limitation in the possible decrease in length of the conical antenna. Recent experimental evidence indicates that active zone width remains constant relative to a wavelength for various loadings (Section II). Additional questions that appear to need answering include the contribution of the loading material (bound currents) to the radiation pattern. A volume integral of the bound currents requires a solution for the fields in the loading material. Also, the losses in the loading material are of great importance. These losses could be computed numerically or theoretically once the fields in the loading material have been computed. A method suggested at the University of Illinois, and is used to some extent to analyze air loaded log conical problems, is to solve the helix problem first. Then, the conical helix is split up into many segments each of which is approximated as a 147

THE UNIVERSITY OF MICHIGAN 7140-1 -F helix. The currents on the wires could then be solved point by point from the feed point by using attenuation, propagation velocities and impedances calculated from the helix solutions corresponding to each segment. The solution for attenuations and fields at each point would show clearly the whole shape of the active region of the antenna. This solution would be done numerically, since the helix solution itself requires a numerical solution in the fast wave or radiation region of operation. B. 2 Loaded Helix Solution The loaded helix problem is solvable if the loading material is assumed in concentric cylinder form, so that boundaries can be represented by a fixed radius. The propagation constant problem is then calculated by matching boundary values. There are two major models for the helix, the sheath helix and the tape helix. B. 2.1 Sheath Helix The sheath helix model is well known in the literature (Pierce, 1950; Watkins, 1958). In addition, the sheath helix has been used to solve for the helix propagation with outside material loading (Tien, 1953; Suhl and Walker, 1954), in all cases for the n = 0 mode. Simple formulas were possible only for the "plane helix" approximation good for large helix diameters. In the bifilar helix case shown below, more general asympotic forms can be used that are good for any sized helix. This helix model assumes an anisotropic conducting layer at the radius of the helix, i. e., conduction only parallel to the helix wires. No mention of the thickness of the wire is made. The sheath helix solution may be then specified in terms of the pitch angle and radius of the helix. The outstanding advantage of the sheath solution is that the spatial modes (the Fourier terms of the fields) describing the helix are not coupled; thus, the relative values of the inside and outside fields may be calculated for each mode independently of all others; in particular, the n = -1 mode that describes backfire radiation from a helix may be studied independently of all other modes. In addition, a hope of closed form solution exists because of 148

THE UNIVERSITY OF MICHIGAN 7140-1 -F the existence of only one mode in any calculation. The k-3 diagram is a well known and important tool in the description of the propagation of any periodic structure. A typical k-13 diagram, shown in Fig. B-1, is basically a plot of frequency on the vertical axis and phase shift per cell on the horizontal axis. The two 450 lines describe the propagation of backward and forward plane waves in free space. The line labeled C is the plot of the solution of /31 versus k for a typical helix. It is known from coupled wave theory that waves having nearly the same propagation constant tend to couple their energy back and forth very efficiently. Thus, it is expected and well known that, when the helix characteristics of k versus 1 match those of a backward free space wave, the energy will be coupled efficiently from the helix to a radiating free space wave (the "active" region). Therefore, the region E and F shown in Fig. B-1 is called the radiation or fast wave region. In addition, it can be shown that the power in the n = -1 mode for backward waves is completely predominant over all other modes in this region. This justifies studying only the n = -1 mode for backward wave propagation with axial radiation. The calculations being performed are "free mode" solutions without mention of the relative amounts of different modes obtained from a more difficult "source" solution. The n = -1 mode is then assumed the predominant mode excited by whatever source is used. B. 3.1. a Full Core Loaded Sheath Helix. The TE and TM modes necessary to describe the sheath helix electric (e, E) and magnetic (h, H) fields are given for the n mode by, Inside Outside e =aI (B.1) E =AK (B. 5) e= aC I+bC2I' (B. 2) E =AC K+BC K' (B.6) h = bI (B. 3) H = BK (B. 7) z Z h = aC5I' + bC I (B.4) = AC K' + BC K (B.8) 149

- THE UNIVERSITY OF MICHIGAN 7140-1 - F ka k0a cot 4 k-k= -2 -1 O fla cot4, FIG. B-1: I k - 3 DIAGRAM OF BIFILAR HEINX 150

THE UNIVERSITY OF MICHIGAN 7140-1 -F where: all constants and fields are understood to be for the n mode (i.e. en' an, ~~~jwt-jI~z~~'znz I (y r)) and have a e j z factor omitted n n IK = I (y r), K (ny r), modified Bessel functions of the first and second kinds re spectively; the primes are derivatives with respect to argument. th - = 3 is propagation constant along helix axis for the n mode k = 27 f/c where f is frequency and c is the speed of light 2 -Z-2 th 7= -k AE =y for the n mode. 2 2" th P=.. -k =r n for then mode At and e are the relative permeability and dielectric constants, respectively, of the loading material. C k(Y,r n', ', ) are well known constants of the separation of variables method, (Watkins, 1958) given by: -no -no C = o1 2 2 32 4 yr n (B.9) o -n~ jC=o -n/ C _ -noC C 5 C 6 y2r 7 F 8 F2r where Ao0, e are the MKS permeability and permittivity of free space; respectively, The boundary conditions The standard el = E 11 = 0 (B. 10) hll =Hll (B. 11)

THE UNIVERSITY OF MICHIGAN 7140-1-F or, rewritten E = e = 0 (B.12) z z (B. 13) 0 Z 0e He cotz 0= 0 (B.14) e3 + e~ cote /-0 3 0 h + h cot -H -H cot 0 =(B.15) z 0 z0 where = helix pitch angle a = helix radius //, refer to parallel and perpendicular field components relative to the conductor direction The fields are shown are understood to be at the point on r = a These four boundary conditions give four homogeneous equations in five unknowns a, b, A, B, 13 for a given k, /i, e for each mode independently. Upon eliminating a, b, A, B (or setting the determinant of the boundary condition equations equal to zero), an equation for 1, the propagation constant of the n mode, is obtained; K' a)In(ya) 1 [y2a22nacot 2 (B. 16) K n(a)In(ya) C 2k 2y a4co2 nn k y a cot 0 where K'( a) I' (ya) Y n n K ( a) I (ya) C = n n (B. 17) 1 n( a) 3 n F2a2-noacotq p K n(a) r3 In(,ya) a -nyacot 152

THE UNIVERSITY OF MICHIGAN 7140-1 -F Since C > 1 as c, p - 1, Eq. (B. 16) approaches the well known sheath determinantal equation in air. (Watkins, 1958). The material loading effects are entirely contained in the constants C, y, and r. For the simple slow wave case, where >>k, - y 'r (if P, e are not too large), the constant C becomes, K' I n n K I' 2 n n C n (B. 18) K' I 1 n n /L K I' n n where Bessel function arguments are understood. By an investigation of the asymptotic forms for Bessel functions for large n, K'I lim n n -- 1 for any argument (B. 19) n --->oo K It nn Studies by many helix investigators such as Sensiper (1951), Watkins (1958), and this laboratory have shown the asymptotic products are fairly accurate for n>1 for any argument, especially for large arguments. Using this approximation, and 1 T = Wr, the determinantal Eq. (1) becomes KTI'h _V [12aa -n acot 2 n n (B. 20) KI 222 2 2 n n (C k a )3 a cot where Bessel function arguments (3 a) are understood, and 2 1+c C =1 (B.21) — +1 153

THE UNIVERSITY OF MICHIGAN 7140-1-F The constant C has been grouped with (ka), the frequency-size parameter, to show immediately that for a given Oa, an increase in C causes a decrease in k a for the equation to be satisfied. Thus as / or e are increased, the frequency of radiation (or size) radiation is decreased. The slope of the k-3 diagram, Fig. B-i, is thus reduced with loading to line D, by the multiplicative factor -- 1 C 1-+- e (B. 22) C 1+c which will be used as a nominal "reduction factor" throughout this report. Equation (4) has been obtained from the sheath model and used by others (Suhl and Walker, 1954; Hair, 1964) for the effect of dielectric loading on sheath helices intended for traveling wave applications, For the n = 0 mode, it was necessary to assume the radius of the helix very large, called the "plane helix". The important difference in this case is that the n = -1 mode is of interest and, because of the bifilar winding, the n = 0 mode is not present. The "large n" asymptotic approximation can then be used for n a 1, independent of the argument (helix size). The solution so far, has not actually been for the radiation region (E and F in Fig. B-1), since slow waves were assumed, restricting the region of operation away from the k = -1 line of radiation. Actually, in order to be valid, the restriction is imposed >> k FI7' by the slow wave assumption that Thus, for fairly high JR~ the equation breaks down practically everywhere. The reduction factor is thus only valid in the slow wave region for moderate J L E'. 154

THE UNIVERSITY OF MICHIGAN 7140-1 -F However, previously discussed, it has been shown by the University of Illinois (Klock, 1961; Dyson, 1965; Maclean, 1962) that the actual fast wave solution for helices in air may be approximated by extrapolating the slow wave solution by a straight line on the k-13 diagram into the fast wave radiation region. In addition, the tape helix solution has been shown, for narrow tape helices in air, to approach the straight line k-1, k a = sinj (B. 23) Oa and for conical helices, k a sin cose (B.24) a where 0H is the half cone angle. These solutions are good approximations in both slow and fast wave regions of unloaded helices. Finally, sheath solutions phase velocity have always been close to tape solutions. Therefore the decrease in k- | slope, computed for the slow-wave, loaded, sheath helix, was applied to the narrow tape solution for the loaded helix and conical helix and extrapolated from the slow wave region into the radiation region. In addition, the ka corresponding to k = -,3 was computed (Hong, 1965). Thus, the k-1 diagrams for the loaded sheath helix (with some narrow tape approximations in addition) have slopes, Helix ka _ sin___ (B. 25) Oa c ka sino coseo Cone k - (B. 26) Oa C The line D in Fig. B-1 indicates a typical k-, diagram for a loaded helix. 155

THE UNIVERSITY OF MICHIGAN 7140-1-F If the intersection of the k-1 line is assumed the point of backfire radiation, then the frequency —radius parameter for the helix in backfire radiation is; (Hong, 1965) 1 + - 1+~1+ +cos b Helix k a (B. 27) 0 1+ 1 + + sin 1 + co Cos cosO Conical k a = (B. 28) Helix 0 1 1 +, sinbcosO which shows the size or frequency reduction, R, to be expected due to loading 1+ ka (loaded) 1+c o) R - ka (unloaded) (B. 29) 1+1 +.1/ (sinocosO) For the small sinicoxO usually encountered Al 1I 1 + e C In conclusion, a determinantal equation for the full core loaded sheath helix has been solved for a slow wave approximation to the reduction factor caused by loadin. An extrapolation into the fast wave region gives an approximate helix antenna 156

THE UNIVERSITY OF MICHIGAN 7140-1-F reduction. Exact numerical calculations of Eq. (B-16) are in progress. B. 3. 1.b Inside-Layer Loaded Sheath Helix. The inside-cylindrical-layerloaded sheath helix problem is exactly the same as the full-core loaded sheath helix except that hybrid (combined TE and TM) modes must be used to describe the fields in the cylindrical loading at the helix-air boundary. These modes are expressed by matching the boundary fields at the interface of the air-core and the loading cylinde (r = a). The problem gets very complicated, so that at the outset, we assume T" e 0~~~ n.th The fields at the helix-air interface (r = a) for the n mode are, Inside Outside e = a(I+C K) (B. 30) E = AK (B. 34) z 9 z e = aC (I+C K)+bC 2(I'+C 10K') (B. 31) E0 = AC K+BC K' (B. 35) h = b(I+C OK) (B. 32) H = BK (B. 36) z 10 z H = aC 5(I' + C K')+bC 6(I+ C 10K) (B. 33) H= AC K' +BC K (B. 37) where, C -- C8 are defined in the earlier section, I, K = I (F a), Kn(r a) are modified Bessel Functions of order n corresponding to the n thmode The constants Cg and C10 represent the solution for the hybrid modes in the loading cylinder, _I KF,/ 9C K | lat r-=b (B. 38) C9 K [1Q K- 5KI 157

THE UNIVERSITY OF MICHIGAN 7140-1-F 10 K [] at r = b (B.39) where it is stressed that here the Bessel function arguments ( rb) in the last two equations use the radius of the inside air core, b, since the boundaries conditions for the hybrid modes are stated there. Matching boundary conditions at the helix-air interface as before, and eliminating the four constants a, b, A, and B,one obtains a determinantal equation for 3, K'I' - [32a2- n3acot (B.40) (B. 40) KI (C 2k2a2)132a2cot2 e where the constant C for layer loading is p K I'+C K' 10 The constant C is similar to C for the full core loading, with additional factors that carry the layer thickness. Using the large order asymptotic approximations as discussed in the full core section for the n = -1 (backfire) mode, as well as large argument approximations; the constant Ce may be simplified to 2 l+eC 11 I 21C (B.42) e 1 1 158

THE UNIVERSITY OF MICHIGAN 7140-1-F where 1+ E exp [-2(a-b (B.43) C (B. 43) 1 1 -(1 — exp [-2(a-b 1 + exp [-2(a-b - (B.44) 121 -1 exp -21(a-b)] The asymptotic approximations employ the additional assumption in this case that (1 a) and (13b) are fairly large (>5), which is true for the large 3 (> 10) found in slow wave regions, if a and b are not small. The factors C11 and C12 determine the "effectiveness" of c and p, respectively; Fig. B-2 plots these functions which allow quick estimates of the effect of layer versus full core loading. The constants C11 and C 12 may be seen to approach 1/e or 1/p, respectively, as thickness (b - a) approaches zero; this behavior is correct, since then C -> 1 and the determinantal equation approaches the classic sheath helix solution in air. For (b- a) large, C11 and C12 approach 1, which is correct since then Ce becomes the full-core loading factor. Notice that the / in the abscissa of Fig. B-2 is a function of the "effectiveness". Thus, this curve is not an explicit solution for the layer thickness. Nevertheless, the effect of thick layers (effectiveness = 1, where 1 is almost unchanged from the fully loaded case, may be quickly seen. For e or lP < 5, the effectiveness is over 90 per cent when f(a - b) > 1.5. This may be related to layer thickness, since 27 3(a-b) i (a-b). (B.45) XCs inq (a-b) 159

100 90 80 I 70 -p, = 2 60 40 =3 tn ~ 40,E=80.1I.2.3.4.5.7 1.0 2.0 3.0 Layer Thickness P(a-b) FIG. B-2: EFFECTIVENESS OF 1 OR e VERSUS LAYER THICKNESS

THE UNIVERSITY OF MICHIGAN 7140-1-F which gives, a-b =.015X The thicknesses of loading tested were in the range.006 -.02X with. 02X layers behaving approximately as full core. The calculation for very thin layers would need a trial and error procedure (since 3 is changed drastically), or a regrouping of Eq. B. 41 and more approximations. Further calculations of thickness effect are planned. B. 3. 2 Tape-Helix Solution The tape helix solution was originally done by Senseper (1951). The model consists of a very thin, narrow, conducting tape. In the case of the loaded tape helix, a cylinder of loading material is placed inside or outside or surrounding the tape. In this case, the solution is considerably more complex since all the spacial modes contribute to the propagation constant of any one mode. Nevertheless, several slow wave solutions have been performed for the loaded tape helix. One solution (Shestopalov, 1961) agrees with the full core sheath solution for the effect of e in the slow wave region. It is necessary to distinguish between the slow wave and fast wave solutions since the slow wave solutions may be obtained relatively easily by using expressions and simplifications that heavily depend upon the fact that the phase velocity of the wave is much slower than that of free space, especially the assumption that 3 is real. These solutions are valid in the slow-wave region and of great use in the traveling wave tube problems theywere usually solved for. Nevertheless, they are sometimes used to describe radiation characteristics of a helix in the fast wave region where the assumptions appear to have little or no validity. Work done by the University of Illinois (Dyson's, 1964; Klock, 1963) shows that, both experimentally and theoretically, the fast wave solutions for air-loaded helices tend to follow approximately a straight line into the fast wave region from 161

THE UNIVERSITY OF MICHIGAN 7140-1-F the slow wave region. These theoretical results are based on a numerical calculation allowing complex values of i, rather than the slow wave analytical solutions assuming real /3. The analytical solution for real values of 3 results in the trajectory of the k-3 solution that bends downward, as shown in Fig. B-1, the right hand part of line C (dotted). The solution avoids the so called "forbidden" region by assuming no radiation. Thus the solution for real 3 gives the incorrect solution in the case of an open helix for both real and imaginary 3. A present study is an attempt to numerically solve for the propagation constant of loaded helix in the fast wave region by digitally calculating the zeros of the characteristic equation with complex /3, including an attenuation constant, assumed due to radiation. This attenuation constant will give attenuation per cell for the various helix segments approximating the conical antenna. It is hoped that by this attenuation constant, the width of the active region may be estimated as well as the center of the active region. The digital calculations are not yet completed. They will be included in a technical report later this year. 162

THE UNIVERSITY OF MICHIGAN 7140-1-F APPENDIX C EFFICIENCY FORMS DATA AND WORK SHEET Test Antenna No. Date Frequency (MHz) By Transmitting Antenna No. Standard Antenna No. Temperature Part 1. (Standard Antenna) 1. Power Transmitted 2. Attenuator Setting 3. Chart Level 4. VSWR Part 2. (Test Antenna) 1. Power Transmitted 2. Attenuator Setting 3. Chart Level 4. VSWR Part 3. (Loss for Infinite Balun Feed) Number of Feet of Coax Attenuation in db/100 ft. Note: See pages 614, 615 of Reference Data for Radio Engineers, 4th Edition, International Telephone and Telegraph Company, (1956). -,,~~~ ~163

THE UNIVERSITY OF MICHIGAN 7140-1 -F A = Attenuation in db = a = Attenuation (numerical) = Antilog (-0) rm = Reflection Factor (measured) - + 1 - =t = True Reflection factor = a[ = m Part 4. (Loss of lead cable to dipole) Please do calculations in the remainder of this page.....- 164

THE UNIVERSITY OF MICHIGAN 7140-1 -F Part 5. (Calculation of Gain) 1 - r 2 V = VSWR Correction factor = 10 log 1 2 test where F and F are the corrected reflection factors. dipole test G = Gain of the test antenna in db = C +Atest Adipole V Ltest Ldipole where C = 2.15 db for a linearly polarized test antenna and 5.16 for a circularly polarized test antenna and L is the sum of the cable, balun, and hybrid test losses between the connector and the tip of the test antenna, and L is the loss dipole calculated for the dipole. g = Gain (numerical) = Antilog = Part 6. (Optional Check) 32, 600 00 - g r7 gd x 100 = per cent Part 7. (Calculating Directivity and Efficiency) U = Height of pattern maximum expressed in number of squares = 229 U d 0 (width of square in ) (total at bottom of Table C-l) = Efficiency = 9 x 100 = per cent 165

THE UNIVERSITY OF MICHIGAN 7140-1 -F TABLE C-i: GRAPHICAL INTEGRATION o o 0o o Range Number of Squares Under Number of Squares Under SineO Result (degrees) Curve (for E plot only) Power Plot or Square of 4 for E Plot 0-12 0.1045 12- 24 0.326 24- 36 0. 500 36 - 48 0.670 48 - 60 0.810 60 - 72 0.914 72 - 84 0.979 84 - 96 1.000 96- 108 0.979 108 -120 0.914 120- 132 0.810 132- 144 0.670 144 -156 0.500 156- 168 0.326 168 -180 0.1045 180 - 168 0.1045 168 - 156 0.326 156 - 144 0.500 144 - 132 0.670 132- 120 0.810 120 - 108 0.914 108-96 0.979 96 - 84 1.000 84 - 72 0.979 72 - 60 0.914 60 - 48 0.810 48- 36 0.670 36 - 24 0.500 24 -12 0.326 12 - 0 0.1045 O Total 166

THE UNIVERSITY OF MICHIGAN 7140-1 -F ACKNOWLEDGE MENTS The help of Terry B. Lewis and U. Edward Gilreath for their excellent laboratory measurements and many original ideas is gratefully acknowledged. 167

THE UNIVERSITY OF MICHIGAN 7140-1-F REFERENCES Adams, A. T. (1964), '"The Rectangular Cavity Slot Antenna with Homogeneous Isotropic Loading,"'The University of Michigan Cooley Electronics Laboratory Report No. 05549-7-T. Allen, J. L. (1964), "Array Antennas: New Applications for an Old Technique, " IEEE Spectrum, 1, pp. 115-130. Bevensee, R. M. (1964), Electromagnetic Slow Wave Systems, John Wiley and Sons, New York. Bulgakov, B.M., V.P. Shestopalov, L.A. Shiskin and I.P. Yakimenko (1960), "Symmetrical Surface Waves in a Helix Waveguide with a Ferrite Medium," Radio. i. elek., 5, pp. 102-119. Bulgakov, B. M., V.P. Shestopalov, L.A. Shiskin and I. P. Yakimenko, (1961), "The Irreversible Propagation of Waves in a Helix Waveguide Placed in a Ferrite Medium," Radio Eng. and Electronics, 4, pp. 118-134. Chatterjee, J.L. (1953), "Radiation Field of a Conical Helix," J. Appl. Phys., 24, pp. 550-559. Cheo, B.R. (August, 1965), "Radiating Slots on a Dielectric Filled Waveguide," New York University, Bronx, New York, Technical Report 400-118. Dyson, J.D. (May, 1965), "The Characteristics and Design of the Conical LogSpiral Antenna, " University of Illinois Technical Report, AFAL-TR-65-124. Hair, H.H. (December, 1964), "Development of Helical Phase Shifters," General Electric Company, Final Report prepared for MIT Lincoln Laboratories. Hong, S. (2 September 1965), "Size Reduction of Bifilar Helical Antennas by Loading with Magnetic-Dielectric Material," The University of Michigan Radiation Laboratory, Memo 07260-504-M. Jasik, H. (1961), Antenna Engineering Handbook, McGraw-Hill, New York, 9. Jones, H.S., Jr. (1965), "Dielectric-Loaded Waveguide Slot Arrays," USAMC Harry Diamond Laboratories Technical Report TR-1269. Kay, A. F. (May, 1956), "Mutual Coupling of Shunt Slots in the Broad Face of Rectangular Waveguide," Scientific Report No. 3, TRG, Inc., AD98799.... 168

THE UNIVERSITY OF MICHIGAN 7140-1-F Knott, E.F., V.V. Liepa, T.B.A. Senior, "A Surface Field Measurement Facility' Proc. IEEE, 53, pp. 1105-1107. Kornhauser, E.T. (1951), "Radiation Field of Helical Antennas with Sinusoidal Current," J. Appl. Phys., 22, pp. 887-891. Kraus, J.D. (1950), Antennas, McGraw-Hill, New York. Larson, R.W. and V. M. Powers (January, 1966), "Slots in Dielectrically Loaded Waveguide, " Radio Science, 1, No. 1, pp. 31-35. Louisell, W.H. (1960), Coupled Mode and Parametric Electronics, John Wiley and Sons, New York. Lyon, J.A. M., et al (1965), "Study and Investigations of a UHF-VHF Antenna," The University of Michigan Radiation Laboratory Report 5549-1-F, AFAL-TR65-64. Lyon, J.A. M., et al (July, 1965), "Study and Investigation of UHF-VHF Antennas," Interim Engineering Report, U.S.A. F. Contract AF 33(615)-2100, The University of Michigan Radiation Laboratory Report No. 07140-1-T. Oliner, A.A. (January, 1957), "The Impedance Properties of Narrow Radiating Slots in the Broadface of Rectangular Waveguide, " Part I and II, Trans. IEEE, AP-5, pp. 4-20. Patton, W. T. (1963), "The Backfire Bifilar Helical Antenna, " The University of Illinois Technical Antenna Laboratory, Report No. 61, AD289084. Pierce, J.R. (1950), Traveling Wave Tubes, D. vanNostrand, Inc., New York. Radio Corporation of America (1963), "Hexagonal Magnetic Compounds, "RCA Report No. 8, AD420336. Ramo, S. and J. R. Whinnery (1953), Fields and Waves in Modern Radio, John Wiley and Sons, New York, pp. 351, 370 and 371. Ramsay, J.F. and B.V. Popovich (1963), "Series-Slotted Waveguide Array Antennas," IEEE International Conv. Record, Pt. 1, pp. 30-55. Reference Data for Radio Engineers, (1956), 4th Ed., International Telephone and Telegraph Company, New York. 169

THE UNIVERSITY OF MICHIGAN 7140-1 -F Rumsey, V.H. (1953), "Traveling Wave Slot Antennas, " J.Appl. Phys., 24, pp. 1358-1365. Shestopalov, V.P., A.A. Bulgakov and B. M. Bulgakov (1961), "Theoretical and Experimental Investigations of Helix-Dielectric Aerials," Radio. i. elek., 6, pp. 159-172. Spitz, E. (1962), "A Class of New Type of Broadband Antennas," Electromagnetic Theory and Antennas, URSI Symposium, Copenhagen, (Ed. E. C. Jordan) Stegen, Robert J. (July, 1964), "The Gain-Beam-Width Product of an Antenna," Correspondance, Trans. IEEE, AP-12, pp. 505-6. Suhl, H. and Walker, L.R. (July, 1954), "Topics in Guided Wave Propagations Through Gyromagnetic Media;' Bell Sys. Tech. J., 33, pp. 939-986. Thourel, L. (1960), The Antenna, John Wiley and Sons, New York. Tien, P.K. (1953), "Traveling Wave Tube Helix Impedance," Proc. IRE, 41, No. 11, pp. 1617-1623. Walter, C. H. (1965), Traveling Wave Antennas, McGraw-Hill, New York. Watkins, D.A. (1958), Topics in Electromagnetic Theory, John Wiley and Sons, New York. Whiteside, H. (October, 1962), "Electromagnetic Field Probe;"' Harvard University Cruft Laboratory, Report No. TR-377. Weeks, W. L. (1957), "Coupled Waveguide Excitation of Traveling Wave Slot Antennas, " University of Illinois, Technical Report No. 27. Yakimenko, I. P. and V.P. Shestopalov (1962), "An Experimental Investigation of a Helix Ferrite Waveguide, " Radio Eng. and Electr. Phys., 7, pp. 1047-1054. 170

UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA- R&D (Security claesificeatlon of title, body of abstract andc indexing annotation must be entered when the overall report is classified) 1. ORIGINATING ACTIVITY (Corporate author) Za. REPORT SECURITY C LASSIFICATION The University of Michigan Radiation Laboratory L Unclassified Department of Electrical Engineering 2b. ROJP 3. REPORT TITLE Study and Investigation of a UHF-VHF Antenna 4. DESCRIPTIVE NOTES (Type of report and inclusive date.) Final Report - February 1965 through February 1966 5. AIJTHOR(S) (Last name, first name, initial) Lyon, John A. M., Alexopoulos, Nicholas G., Chen, Chao-Chun, Kazi, Abdul M. Rassweiler, George G., Smith, Dean L., and Wu, Pei-Rin 6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS April 1966 170 39 8a. CONTRACT OR GRANT NO. S4. ORIGINATOR's REPORT NUMBER(S) AF 33(615)-2102 7140-1-F b. PROJECT NO. 6278 c.Task 627801 S b. OTHER RI PORT NO(S) (Any other nimber thet may be alsigned Task 627801 d. AFAL-TR-66-101 10. AVA ILABILITY/LIMITATION NOTICES.. Qualified requestors may obtain copies of this report from DDC. Distribution of this report restricted in accordance with US Export Act. DOD Dir. 203.4 AFR400-10 and should not be disseminated to OTS. 11. SUPPi EMENTARY PNOTES 13. IP1QSORINiG MI-ITARY ACTIVITY Air Force Avionics Laboratory AVWE Research and Technology Division, AFSC Wright-Patterson AFB, Ohio 45433 13. ABSTRACT This report indicates some of the advantages of usingferrite loading in a number of types of traveling wave antennas. Studies have been made on ferrite loaded helices and ferrite loaded log conical antennas. For a given frequency of operation it has been found possible to reduce the diameter of each of these types of antennas by a factor of approximately 55 - 70 per cent. Some variation in performance as a function of the amount of loading or thickness of the ferrite layer was observed. Near field probing techniques were used to show that ferrite loading changes the position of the active region on the log conical spiral. Likewise, near field probing shows that a particular region is active at a lower frequency when when ferrite loading is applied to a helix. The effects of ferrite loading on the log zigzag type are also indicated. Relatively high efficiencies have been obtained for the ferrite loading of helices and log conical spirals. The power limitation occasioned by the use of ferrite loading for the rectangular slot antenna has been examined. For rectangula slots loaded with powdered EAF-2 ferrite designed to operate at 300 MHz it is estimated that an average or cw power limit is less than 50 watts average. DD 1 JN 4 1473 UNCLAFI ED Security Classification

UNCLASSIFIED Security Classification 14. LINK A i LINK B LINK C KEY WORDS ROLE WT ROLE WT ROLE. WT Antennas UHF-VHF Ferrite Loading Techniques INSTRUCTIONS 1. ORIGINATING ACTIVITY: Enter the name and address imposed by security classification, using standard statements of the contractor, subcontractor, grantee, Department of De- such as: fense activity or other organization (corporate author) issuing (1) "Qualified requesters may obtain copies of this the report. report from DDC." 2a. REPORT SECURITY CLASSIFICATION: Enter the over- (2) "Foreign announcement and dissemination of this all security classification of the report. Indicate whether "Restricted Data" is included. Marking is to be in accord- report by DDC is not authorized." ance with appropriate security regulations. (3) "U. S. Government agencies may obtain copies of this report directly from DDC. Other qualified DDC 2b. GROUP: Automatic downgrading is specified in DoD Di- users shall request through rective 5200. 10 and Armed Forces Industrial Manual. Enter the group number. Also, when applicable, show that optional, markings have been used for Group 3 and Group 4 as author- (4) "U. S. military agencies may obtain copies of this ized. report directly from IDC. Other qualified users 3. REPORT TITLE: Enter the complete report title in all shall request through capital letters. Titles in all cases should be unclassified. If a meaningful title cannot be selected without classification, show title classification in all capitals in parenthesis (5) "All distribution of this report is controlled. Qualimmediately following the title. ified DDC users shall request through 4. DESCRIPTIVE NOTES: If appropriate, enter the type of _i," report, e.g., interim, progress, summary, annual, or final. If the report has been furnished to the Office of Technical Give the inclusive dates when a specific reporting period is Services, Department of Commerce, for sale to the public, indicovered. cate this fact and enter the price, if known. 5. AUTHOR(S): Enter the name(s) of author(s) as shown on 11. SUPPLEMENTARY NOTES: Use for additional explanaor in the report. Enter last name, first name, middle initial. tory notes. If military, show rank and branch of service. The name of the principal author is an absolute minimum requirement. 12. SPONSORING MILITARY ACTIVITY: Enter the name of the departmental project office or laboratory sponsoring (pay6. REPORT DATE. Enter the date of the report as day, ing for) the research and development. Include address. month, year; or month, year. If more than one date appears on the report, use date of publication. 13. ABSTRACT: Enter an abstract giving a brief and factual summary of the document indicative of the report, even though 7a. TOTAL NUMBER OF PAGES: The total page count it may also appear elsewhere in the body of the technical reshould follow normal pagination procedures, i.e., enter the port. If additional space is required, a continuation sheet shall number of pages containing information, be attached. 7b. NUMBER OF REFERENCES: Enter the total number of It is highly desirable that the abstract of classified reports references cited in the report. be unclassified. Each paragraph of the abstract shall end with 8a. CONTRACT OR GRANT NUMBER: If appropriate, enter an indication of the military security classification of the inthe applicable number of the contract or grant under which formation in the paragraph, represented as (TS), (S), (C), or (U). the report was written. There is no limitation on the length of the abstract. How8b, &, & 8d. PROJECT NUMBER: Enter the appropriate ever, the suggested length is from 150 to 225 words. military department identification, such as project number, te subproject number, system numbers, task number, etc. 14. KEY WORDS: Key words are technically meaningful terms 9a ORIGINATOR'Sr, REPORT NUMBER),: Enter the, oor short phrases that characterize a report and may be used as 9a. ORIGINATOR'S REPORT NUMBER(S): Enter the offi- index entries for cataloging the report. Key words must be cial report number by which the document will be identified selected so that no security classification is required. Identiand controlled by the originating activity. This number must fiers, such as equipment model designation, trade name, military be unique to this report. project code name, geographic location, may be used as key 9b. OTHER REPORT NUMBER(S): If the report has been words but will be followed by an indication of technical conassigned any other report numbers (either by the originator text. The assignment of links, rules, and weights is optional. or by the sponsor), also enter this number(s). 10. AVAILABILITY/LIMITATION NOTICES: Enter any limitations on further dissemination of the report, other than those UNCLASSIFIE D Security Classification