THE UNIVERSITY OF MICHIGAN 7848-7-Q STUDY AND INVESTIGATION OF A UHF-VHF ANTENNA Seventh Quarterly Report 1 July 1967 through 30 September 1967 October 1967 Prepared by J. A. M. Lyon, C-C Chen, J. C. Parker and D. L. Smith Approved by _ X..A.M. Lyo, Professor Electrical Engineering Contract No. AF 33 (615)-3609 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 This document is subject to special export controls and each transmittal to foreign government or foreign nationals may be made only with prior approval of AFAL(AVPT), Wright-Patterson AFB, Ohio 45433.

THE UNIVERSITY OF MICHIGAN 7848-7-Q FOREWORD This report, 7848-7-Q, was prepared by the University of Michigan, Radiation Laboratory, Department of Electrical Engineering, under the direction of Prof. Ralph E. Hiatt and Prof. John A. M. Lyon, on Air Force Contract AF 33(615)-3609, under Task 627801 of Project 6278, "Study and Investigation of UHF-VHF Antennas (U)". The work was administered under the direction of the Air Force Avionics Laboratory, Wright-Patternson AFB, Ohio. The task engineer was Mr. Olin E. Horton; the project engineer, Mr. E.M. Turner. This report covers the period 1 July 1967 through 30 September 1967. ACKNOWLEDGE ME NT S The experimental assistance of Mr. U. E. Gilreath and Mr. J. Brooke Hutt is gratefully acknowledged. iii.........

.. THE UNIVERSITY OF MICHIGAN 7848-7-Q ABSTRACT This report covers the work effort on the various tasks of the project for a three-month period. The report goes into considerable detail since it include substantial analysis, computer results, and experimental data. In all of the tasks, substantial progress has been made. However, in one task, a complete reorientation of the work program has been made. Under Task II, on slot arrays, it has been found necessary to simplify the work and also to avoid difficulties with materials. This should allow development of a new array utilizing ferrite filled rectangular slots developed in the prior contract work of this group. l I~~~~~~~~~~~i

- THE UNIVERSITY OF MICHIGAN 7848-7-Q LIST OF FIGURES Figure No. Caption Page 2-1: Antenna 238, A Bifilar Helix Antenna with Shorted Transmission Inductors Used as Loading. 8 2-2: Dimensions of Inductances of Inductance Loaded Antenna. 9 2-3: Coordinate System Assumed for the Helix Antenna. 11 2-4a: Linear Power Patterns of Antenna 238, An Inductor Loaded Bifilar Helix (IE 12 Patterns in the 0 = 0 Plane). 12 2-4b: Linear Power Patterns of Antenna 238, An Inductor Loaded Bifilar Helix (IE 12 Patterns in the 0 = 0 Plane). 0 13 2-5: VSWR of Antenna 238, A Bifilar Helix with Inductance Loading. 14 4-1: Geometry of the Ferrite Tube Antenna. 28 4-2: Linear Power Patterns of the Ferrite Tube Antenna (LE 12 Patterns in the 0 = 0 Plane). 30 4-3: Linear Power Patterns of the Ferrite Tube Antenna (1E1i2 Patterns in the 0 = 900 Plane). 31 4-4: Half-Power Beamwidth Against Frequency of the Ferrite Tube Antenna. 32 4-5: Side-lobe Level Against Frequency of the Ferrite Tube Antenna. 33 4-6: Near Field Measurement, the Relative Amplitude and the Phase of Ep Against the Coordinate Angle 0, Taken at 5 cm from the Feed End of the Ferrite Tube Antenna. 34

THE UNIVERSITY OF MICHIGAN 7848-7-Q List of Figures (Cont'd) Figure No. Caption Page 4-7: Near Field Measurment, the Relative Amplitude and The Phase of Ep Against the Coordinate Angle 0, Taken at 5 cm from the Free End of the Ferrite Tube Antenna. 35 4-8: Near Field Measurement, the Relative Amplitude and The Phase of the Ep Against the Ferrite Tube Axis at 600 MHz in 0 = r/2 Plane. 36 4-9: Near Field Measurement, the Relative Amplitude and the Phase of Ep Against the Ferrite Tube Axis at 900 MHz in 0 = 7r/2 Plane. 37 5-1: Input Resistance R and Reactance X for Folded Dipole Structure where p = 1.0, pa = 1.0. 43 5-2: Input Resistance R and Reactance X for Folded Dipole Structure where p = 1.0, p = 0.8. 44 s a 5-3: Input Resistance R and Reactance X for Folded Dipole Structure where p = 1.0, pa = 0.6. 45 5-4: Input Resistance R and Reactance X for Folded Dipole Structure where p = 1.0, p a = 0.4, 46 5-5: Input Resistance R and Reactance X for Folded Dipole Structure where p = 0.8, p a = 0.8. 47 5-6: Input Resistance R and Reactance X for Folded Dipole Structure where p = 0.8, p = 0.6. 48 i_ __ vi _

THE UNIVERSITY OF MICHIGAN 7848-7-Q List of Figures (Cont'd) Figure No. Caption Page A-1: Solution of the Characteristic Equation for Helix having Core Parameters Cr = 1.00, =1.00; (Air). 53 A-2: Solution of the Characteristic Equation for Helix having Core Parameters e = 3. 77, = 1. 00; (EAF-2 Powder Ferrite Biased into Saturation). 54 A-3: Solution of the Characteristic Equation for Helix having Core Parameters er = 7.88, Pr = 1.00; (Q-3 Ferrite at 150 MHz Biased into Saturation). 55 A-4: Solution of the Characteristic Equation for Helix having Core Parameters er = 22. 0, Pr = 1. 00; (Eccosorb CR at 300 MHz Biased into Saturation). 56 A-5a, b: Solution of the Characteristic Equation for Helix having Core Parameters er = 3. 77, r = 2. 10; (EAF-2 Powder Ferrite). 57, 58 A-6a, b: Solution of the Characteristic Equation for Helix having Core Parameters er = 7.96, f = 12.4; (Q-3 Ferrite at 100 MHz). 59, 60 A-7a, b: Solution of the Characteristic Equation for Helix having Core Parameters r = 7.88, p = 132; (Q-3 Ferrite at 150 MHz). 61, 62 A-8a, b: Solution of the Characteristic Equation for Helix having Core Parameters er = 7. 81, Pr = 14. 3; (Q-3 Ferrite at 200 MHz). 63, 64 A-9a, b: Solution of the Characteristic Equation for Helix having Core Parameters e = 22.0, p r = 4.51; (Eccosorb CR at 300 MHz). 65, 66..................... vii

THE UNIVERSITY OF MICHIGAN 7848-7-Q TABLE OF CONTENTS FOREWORD iii ABSTRACT iv LIST OF FIGURES v I INTRODUCTION 1 II FERRITE LOADED CONICAL SPIRALS 3 2.1 Introduction 3 2. 2 Anisotropic Ferrite Loaded Helix Antenna. 4 2.3 Discrete Inductance Loading 6 2.3.1 Antenna Description 7 2.3.2 Test Results 10 2.3. 3 Conclusions 10 III SLOT ARRAYS 16 IV FERRITE ROD ANTENNAS 17 4. 1 Theoretical Analysis 17 4.2 Experimentation 27 V LOW FREQUENCY FERRITE ANTENNAS 39 5.1 Tuning of Linear Elements Via Magnetic Biasing 39 5.2 Computer Analysis of Multiple Linear Elements 41 VI CONCLUSIONS 49 VII FUTURE EFFORT 50 APPENDIX A: DESIGN CURVES FOR SMALL DIAMETER LOADED HELICES 51 RE FERENCES 70 DISTRIBUTION DD 1473 viii _

THE UNIVERSITY OF MICHIGAN 7848-7-Q INTRODUCTION This report indicates the acomplishment in each of four assigned tasks of this project. A separate section is devoted to each task. Section II describes the work on Task I involving the development of a log conical spiral antenna. Various techniques useful in reducing the size of such an antenna are assessed in this report. For convenience, experiments were confined to the loading of a bifilar cylindrical helix. These results can be transferred to the design of the log conical helix required by this task. Section III covers the effort under Task II which is devoted to the use of physically small slot antennas as elements of an antenna array. In this section, coverage is given to the new work effort which is quite different from what had been previously recorded under this task. Emphasis is now on an arrangement of ferrite loaded slots connected by a coaxial feed system, with the apertures of the slots mounted in a line in a common ground plane. A description of such a three element array is given in the report. In previous work under task II, a waveguide with rectangular slots cut in the broad-face was utilized. Some unsatisfactory results were obtained because the ferrite material used (type Q-3) did not have electrical characteristic as good as those published. This necessitated either going to a much lower frequency, with the attendant difficulties due to the required spacing in the array, or going to a new design utilizing better material. The latter course was chosen, and as a result rectangular slots filled with type EAF-2 material were utilized. This choice will permit the array to be studied in a frequency range from 300 MHz up to 600 MHz which will result in more easily obtained expermental patterns.

i- THE UNIVERSITY OF MICHIGAN 7848-7-Q In Section IV, progress on Task III involving studies of endfire ferrite rod radiators has been described. During this report period, a major part of the effort has been analytical. Also, the important decision has been reached that ferrite rod radiators having only a cylindrical shell are more promising as endfire radiators than solid ferrite cylindrical rod radiators. In addition to analysis, experimentally determined radiation patterns for a ferrite tube antenna are given. Likewise, information is given on experimental measurements of the near field of a ferrite tube antenna. In Section V, the effort under Task IV devoted to new types of ferrite antennas usable down to 30 MHz is discussed. A considerable part of the effort has been on the tuning of linear elements by utilizing magnetic bias. A *computer program study was made on small diameter cylindrical helices utilizing various ferrite material core loadings. The air loaded case was also studied for comparison. For some of the ferrite loading cases, the ferrite has been biased into saturation. Saturated ferrite cores and air core results correspond very well. Studies have also continued on the computer analysis of multi-linear elements. Results on a folded dipole consisting of two similar slow wave elements are presented. The material in Appendix A supplements the coverage given in Section V.

THE UNIVERSITY OF MICHIGAN 7848-7-Q II FERRITE LOADED CONICAL SPIRALS 2. 1 Introduction The objective of this task is to develop a ferrite filled conical spiral antenna that will cover the 200 to 600 MHz range and be approximately one-third the size of an unloaded conical spiral antenna. The antenna is to have circular polarization with a broad forward directional main beam. The antenna should also be capable of employing both the transmit and receive modes simultaneously. Throughout the course of this contract, emphasis has been placed on size reduction of helix antennas instead of conical spiral antennas. The reasons are three: 1) a helix is a special case of a conical spiral antenna that occurs when the cone angle is 0 degrees; 2) helix antennas are much easier to construct and analyze mathematically; 3) the results of cylindrical helices are directly applicable to conical spirals. Therefore more investigations can be made into reduction techniques with the time and money available. During this report period, emphasis has been placed on two techniques of reducing the size of a helix antenna. The first is by loading with an anisotropic ferrite; the special case of a ferrite biased into saturation by a d-c magnetic field is explored. This special case is one limiting case of tuning the antenna with a d-c magnetic field. (The other limit is an isotropic material.) A saturated ferrite is also the only low loss ferrite material available above about 400 MHz and therefore is itself an interesting ferrite loading. The second technique investigated during this report period is discrete inductance loading, inserting inductances in series with the windings of the antenna. The inductors used were shorted sections of transmission line. Due to a miscalculation in the design of the experimental antenna tested, the predicted results were not obtained. However, the antenna is still very interest

THE UNIVERSITY OF MICHIGAN 7848-7-Q ing because it has the size and shape of a helix antenna, yet operates over almost a 3 to 1 frequency band with a small stop band in the center. 2.2 Anisotropic Ferrite Loaded Helix Antenna. There are several reasons for examining anisotropic ferrite loading in helix antennas. All of these reasons are a consequence of the steady unidirectional magnetic field in the material. First of all, at higher frequencies, a magnetic bias of the ferrite makes a low loss material possible. (Hach, 1966). Second, if a helix is magnetically tuned by adjusting the magnetic field, then the properties of the antenna would be affected by the changes in the characteristics of the material. Third, because a plane wave propagating through a saturated ferrite exhibits circular polarization, precisely the polarization produced by a helix antenna, it may be possible to use anisotropic loading as to mode filter to reduce the high side and backlobes that sometimes result from isotropic loading materials. Because a saturated ferrite can be expected to represent one limit in the range of operation of a magnetic field tuned ferrite loaded antenna, it poses an interesting special case to study. Fortunately, the anisotropy of the permeability tensor of such a material is relatively simple and can be readily predicted by classical electromagnetic theory. The permeability tensor can be described by the following tensor: tPI jlK 0 0 = -jK AU O| 0 0 1 where OyA M 2 2 W -W _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

THE UNIVERSITY OF MICHIGAN 7848-7-Q w z M IC_( o) K - 2 2 W -t 0 and M is approximately Ms, the saturated magnetization (provided the amp0 s litude of the time varying fields is small), y is the gyromagnetic ratio, w is the Larmor frequency and is equal to y B, B0 is the DC magnetic field, 0 and po is the permeability of free space (Collin, 1960). The dielectric constant of the material is the same as when no bias is applied. The permeability tensor, like any tensor, may be transformed to another coordinate system. For the helix antenna, circular cylindrical coordinates are appropriate. Since the transformation matrix from rectangular to circular cylindrical coordinates is: cos 0 sin 0 CR sin 0 cos 0 0 \0 1 then the permeability tensor in the new system is: C cos 0 - jKc sin 0 jK cos0 +pr sin 0 C CR r in - jcos -j sin 0 + p cos 0 0 0 1 which makes the permeability tensor a function of the coordinates. This is true, in general, for any common coordinate system, except rectangular. This dependence on one of the coordinate variables complicates the mathematical solution of any saturated ferrite problem in any coordinate system except rectangular. However, this doesn't make the situation hopeless, and some insight can be obtained by a mathematical analysis.

THE UNIVERSITY OF MICHIGAN 7848-7-Q Details of the mathematical analysis will be given in the final report. The preparation time for this report is insufficient to permit an adequate check of the analysis prior to publication. 2.3 Discrete Inductance Loading If the series inductance of a uniform transmission line is increased, the phase velocity of the wave propagating over the line will be reduced. Since a helix or conical helix antenna can be reasonably approximated by a two wire transmission line having the same wire diameter as the winding of the helix antenna and a wire spacing equal to the diameter of the helix (Rassweiler, 1967) it seems reasonable that if the helix antenna has inductance inserted in series with the winding, then the phase velocity of a wave propagating along the helix, and hence the size of the helix, can be reduced. To check out this theory, a helix antenna was constructed and tested that had additional inductance inserted in series with the winding. The inductances were shorted coaxial transmission line stubs. The object of the experiment was to check out the concept of using inductors made out of shorted sections of coaxial transmission line. If the concept were substantiated, then a ferrite loaded stub would be used. The advantages of ferrite are that smaller stubs could be used for a given inductance and that more stubs could be used per winding, hence making the discrete inductances approximate more closely a distributed inductance. Unfortunately, due to an error in calculating the inductance needed, the inductances inserted were too small, and the hoped for performance was not realized. However, the experimental results were so favorable that they are reported here in the hope that the antenna may be useful to someone else. A backward fire pattern is obtained over almost a 3 to 1 band (475 to 1250 MHz) and the VSWR is close to 3 to 1 with respect to a 50 ohm load over this band,

THE UNIVERSITY OF MICHIGAN 7848-7-Q except for a band of 80 MHz centered around 800 MHz. Yet a helix antenna of the same size would have a center of operation around 710 MHz. 2. 3. 1 Antenna Description The antenna, shown in Fig. 2-1, is a bifilar helix antenna fed at the tip with a hybrid by twin lead consisting of two pieces of RG-58/U coaxial cable on the axis of the antenna. The inductances are inserted every quarter turn, and were designed to produce a 4 to 1 reduction in size assuming the diameter of the two wire line model is the diameter of the helix antenna, and that the diameter of the wire of the parallel wire line is that of the winding of the helix. However, the miscalculation altered this relationship. The formulas used to calculate the inductance needed to accomplished were derived in an earlier report (Lyon et al., 1966) and are restated here: L= Zo/V L' =L/R where R is the multiplicative reduction factor (0.25 in this case), L is the original inductance per unit length, L' the new inductance per unit length, Z~ the characteristic impedance, and V the phase velocity. p The antenna is wound on a 4"ID x 1/16" thick piece of NEMA Grade XXX (Mil-P-3115-PBE) paper phenolic tubing. The pitch angle of the helix is 140 and there are 5 turns on the antenna. The winding was cut at the intervals shown in Fig. 2-2. Part of the dielectric and outer shield was removed, and one end of the remaining part of the shield was soldered to the center conductor to produce the inductor. A helix antenna of this size would have a center frequency of operation of about 710 MHz as can readily be calculated from Fig. 2-3 on page 333 of

THE UNIVERSITY OF MICHIGAN 7848-7-Q FIG. 2-1: ANTENNA 238, A BIFILAR HELIX ANTENNA WITH SHORTED TRANSMISSION INDUCTORS USED AS LOADING. ca-:c:;a~~~~~~~~~~~~~~~~~~~~~~~~~........ r:R ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~j 1 n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.... ~~~" " - "~~~~~~~~~~~` `-` ""~~~~~~~~~~~~~~~~~~~...............~

~I1 End of Winding Fed s til 1.75 -- 6.6cm -C cm M i" -------- 8.45 cm -i FIG. 2-2: DIMENSIONS OF INDUCTANCES OF INDUCTANCE LOADED ANTENNA.

THE UNIVERSITY OF MICHIGAN 7848-7-Q Walter (1965). The antenna described, however, was designed to have a center frequency of operation of 227 MHz, since 910 MHz was assumed to be the unloaded center frequency. 2.3.2 Test Results The radiation patterns taken measuring IE 1 on the 0 = 0 cut as in Fig. 2-3 show the usual backward fire radiation patterns (low back lobe and side lobes, a well developed main lobe) from 475 to 760 MHz and from 840 to 1250 MHz as can be seen in Fig. 2-4. This gives geometrical mean center frequencies of operation of 600 MHz and 1025 MHz respectively, with corresponding bandwidths of 79 percent and 67 percent. Between 760 and 840 MHz, the signal amplitude was so small that it was difficult to record patterns. Those that could be recorded were not satisfactory backward fire helix patterns. The VSWR of the antenna was measured with respect to the input port of the hybrid used to feed the antenna with swept frequency equipment as is indicated in Fig. 2-5. In the lower band, the VSWR was centered around 2.5 with respect to 100 ohms and the variation from this was within + 0. 5 over most of the band. In the high band, the VSWR centered around 3.0 and the variation from this was less than + 0.5 over most of the band. At about 790 MHz the reflection coefficient was almost 1.0. A check of the design indicated that at this frequency, the coaxial stub should be about one-quarter wavelength long, and hence the winding should be effectively open-circuited. 2. 3. 3 Conclusions 1) The transmission line model of the helix antenna presented by Rassweiler (1967) is apparently not quite correct. Assuming that the lower band of operation was caused by the inductive loading and working backwards from its

THE UNIVERSITY OF MICHIGAN 7848-7-Q z R Feed in x-y plane / v I -_y 0.~ I x FIG. 2-3: COORDINATE SYSTEM ASSUMED FOR THE HELIX ANTENNA. 11

THE UNIVERSITY OF MICHIGAN 7848-7-Q 455 460 465 500 550 600 760 780 800 FIG. 2-4a: LINEAR POWER PATTERNS OF ANTENNA 238, AN INDUCTOR LOADED BIFILAR HELIX. (IE 2 Patterns in the 0 = 0 plane.) 12

THE UNIVERSITY OF MICHIGAN 7848-7 -Q 820 840 900 1000 1100 1150 1200 1250 1300 FIG. 2-4b: LINEAR POWER PATTERNS.OF ANTENNA 238, AN INDUCTOR LOADED BIFILAR HELIX. (E 02 Patterns in the 0 = 0 Plane.) 13

THE UNIVERSITY OF MICHIGAN 7848-7-Q 8 3.0 2.C 500 600 700 Frequency (MHz) 8 3.0 2.0 700 800 900 Frequency 8 3.0 2.0 iI 800 900 1000 Frequency FIG. 2-5: VSWR OF ANTENNA 238, A BIFILAR HELIX WITH INDUCTANCE LOADING. 14

THE UNIVERSITY OF MICHIGAN 7848-7-Q frequency range to find the characteristic impedance of the corresponding trans mission line produced a characteristic impedance of 110 ohms. The input impedance of a helix antenna is usually in the range of 100 to 150 ohms. Thus, apparently using the input impedance of a helix antenna in the transmission line analogy correctly predicts the experimental results. 2) Even by itself, antenna 238 is a very interesting antenna. It covers almost the entire frequency range from 475 to 1250 MHz, except for a band of 80 MHz centered around 800 MHz. 3) Series inductance tends to reduce the size of a helix antenna but series capacitive loading will increase the size for a given frequency range of operation. (In the 840 to 1250 MHz range, the stubs were capacitive.) 4) However, the average impedance values measured tend not to support the transmission line analogy. The impedance was higher in the high band and lower in the low band, not the other way around as would be expected from the transmission line relation Z = ALG7. (Note, that in the high band, the capacitance introduced would tend to reduce the inductance in the above formula.)

THE UNIVERSITY OF MICHIGAN 7848-7-Q III SLOT ARRAYS Since the last Quarterly Report the effort on the fabrication of a ferrite loaded slot array has been completely reoriented. The work done under this task had previously been concentrated on using a waveguide section with slots cut in one of the broad faces. The material used had been type Q-3 solid ferrite. Unfortunately the electrical and magnetic characteristics of the ferrite were not satisfactory and not in accordance with the published data received by the manufacturer. A new experimental arrangement has now been completed. This consists of three ferrite filled rectangular slots mounted in a metal ground plane. The ground plane is composed of copper screening 5' by 5' in overall size. In the center the metal screening has been replaced by a solid aluminum plate 27" by 20" in size. Three rectangular ferrite filled slots have been mounted on the center line parallel with the long direction of the rectangular plate. That is the H direction of the slots is parallel with the 27" direction of the aluminum plate. The slots are mounted 16 3/16" center-to-center. The central slot corresponds to the center of the ground plate. Each slot has dimensions 5" by 2" by 1 1/2" deep. The 5" dimension corresponds to the direction of the H field. The 2" direction corresponds to the direction of the E field in the aperture. Each slot is filled completely by solid type EAF-2 ferrite. The array of slots just described has been made for operation about a central frequency of 350 MHz. The present status of the array utilizing physically small slot radiator elements is that it is now ready for preliminary experimental testing as an array.....____________ _ ~16.

THE UNIVERSITY OF MICHIGAN 7848-7-Q IV FERRITE ROD ANTENNAS 4. 1 Theoretical Analysis The field components of an isotropic infinite ferrite rod obtained by solving the homogeneous Helmholtz equation subject to the boundary coiditions on the cylindrical surface of the rod for the HEII mode are as follows where the time dependent factor ejwt is understood. Field inside the rod (p < a): H = A J (klP) cos 0 e-j z z i 1 H p LAi (k B(kp) co 0 e-j z P i Jl(klP) 1 1 1EP~kP zE =B. J (k P) sin 0 ej7Z-j E = (k) - Bi k sin p 1 1 _jr (4. 11 E A J(klP) - B. J(k) cos 0 e (4.1) Field surrounding the rod (p > a): H = A H( (k p) cos 0 e-jyz z o n 2......._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1 7

THE UNIVERSITY OF MICHIGAN 7848-7-Q j WE J[ H y(1) jko (1) H A H (k2p) + Bo - H1)(k2P) cosejZ Hp I k2 H- o k E = BOLH() H(kP) 1sin eHz)(kP) E =A - H(1 (k2p) -Bi H1 (k2p) sin 0 ej Z 2 2 inside the rod ' Hi 2 k2 1 k22 AH (k s 0 e- (4.2) Matching the tangential field components gives the roportion of field magnitudes inside and outside the rod as well as the magnitudes of the TM to TE waves (1) A. B. H (k a) 1.~H - 1 k_ 1c o2 e(424) A0 B JI(kla) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _k2 1 8_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

THE UNIVERSITY OF MICHIGAN 7848-7-Q ly 12 i, k k2 A wEl J'1 (kla) we HI(j)(k2a) kl Jl (kla) k2 H() "1 w ~ H11 (k2a) k1 J (kla) k2 H(l)(k a), 2 k1 J (kla) k2 H 1a 1 12 H (k2 a) 1 2 Equations (4.3) and (4. 5) together give the characteristic equation: 22 2 IFa)2 F(1) 2 _ c [J ( 1 + 1 1H (k a) (k a)2 LJ(k a) ia) (k2 H (k a) where X = wavelength in free space, E= E C A graphical solo o q4 de n 2 o9a rn Cgte1 or ution of Eq. (4.6) determine k and k and together with Eq. (4.3) determines 1 2' ________________________ 19 ______1_______k____a___

THE UNIVERSITY OF MICHIGAN 7848-7-Q the propagation constant '. The phase velocity along the longitudinal axis is: V 27f r / - z = 2(r rr (4. 7) c X 2 2 o - C 1 2r r which corresponds to a slow wave for V < c. The computed axial phase velocity for some selected ferrite materials with various diameters has been shown in the previous report, Lyon et al, 1967. The electric and magnetic surface charge densities on the rod surface are: 1 [1 /rCrl 1 2__ 2n au =AJl(kla) sin ke-J1Z e 1i 1 1 jwa k2 *k Xr _ 0 s (4.8) 2 1 1 F 1 Cl2 2__ 2 a = BiJl(kla) j-a (o) 2 cos 0 -Jz In 1 1 1 jwa k2 k2 Pr Er 0 ~ (4.9) These oscillating surface charges on the rod surface are equivalent to the volume electric polarization current and the magnetic polarization current in the rod due to the subatomic displacement of charge centers and charge of spin momenta. The magnitude ratio of au to (x is the same as the ratio of TE to TM waves. In the limiting case with pr = 1, e = 1 both electric and magnetic surface charges vanish. The behavior of a finite ferrod antenna is more or less like a physically thick cylindrical antenna with the volume electric polarization current in ferrod equivalent to the conduction current in metal. A comparison of these two antenna types is given in the following table. 1 _ _ _ _ _ _ _ _ _ _ _ _ __ ~20

THE UNIVERSITY OF MICHIGAN 7848-7-Q Thick Metal Ferrite Rod Cylindrical Antenna Antenna 1 Excitation Voltage Source Field Source 2 Material of Radiator Metal Conductor Ferrite Material 3 Source of Radiation Surface Current Polarization Volume Current 4 Dominant Wave Pattern Standing Wave Traveling Wave At present there is still no exact solution for the field distribution at the junction of the waveguide to the rod and at the end of the rod. To simplify the problem it is assumed that HE mode is traveling along the axis with an attenuation due to radiation and heat loss in the material. The reflection from the end is negligibly small. Maxwell's equation in a homogeneous isotropic material media in the absence of conductance current can be written as: V EH aHl o at + at V x o = a- i-_ ( aE xH = - (E 5E o at o at Pe V-E p Pm V'~ H =-(4.10) Let jeq (=- )aE eq o at -- aH eq '(o~U7 - ~(4.11) Meq_=_( /__- _ o) at '

THE UNIVERSITY OF MICHIGAN 7848-7-Q The radiation field from the ferrod in unbounded free space arises from the magnetic and electric polarization currents in the rod or from the oscillating magnetic and electric surface charges on the rod. The field solution can be represented as the sum of a complementary and a particular solution. The particular solution due to the electric and magnetic polarization currents is E =-V x F - j w A + V (V A) H= V x A - jw F + 1 V (V T) (4.12) 0 j WA0 1 Jeq(r') e- jkr - r A(r) = 41 fJ eqre dv, 4,ff 1 JIr - rtI M (r')e-jklr - r'4 F 1(r) jj e rdv'. (4.13) If only the far field is considered for r >> r': max Jr - r'I = r - r' cost r' cos ~ = p' sin0 cos (0 - 0') + z' cos 0. (4.14) In the radiation zone, the components of the field are therefore given by: 0 i o 0 A -i 0kF E jwp 0 A + j kF 0 (4.15) _E_ = - jao A_ + j kF0 (4.15) 22

THE UNI VERSITY OF MICHIGAN 7848-7-Q E E E"= -= ~ (4.16) H Ho The spherical components of any vector can be obtained from the rectangular components using the relationships: Ve = (V cos 0 + V sin 0) cos 0 - V sin 0 Jx y z V - sin 0 + V cos. (4.17) The rectangular components of the electric field can be obtained by the transformation of coordinates and the relationships of the Bessel functions: | E = E cos 0 - E sin 0 = E sin 0 + E0 cos 0 (4.18) J (kl p) J (k lP) = + J1 (kP) o ki p 11 J2(klP) = - (k lp). (4.19) Thus the field components in rectangular coordinates are: j[Aw,.M + BY -jz E - [i i2 kl J2(kP) sin 2 l ejZ i1 2 Bi2 E ={ - B i J (k p)- [ + J2(kp)cos 0 y 2kE o 1 2k1 23.,._......

THE UNIVERSITY OF MICHIGAN 7848-7-Q {-j IAy - Bw EL JA(kp ly + Bw1p)cos 20 i H = ( 1 2 x o2kl o 1 2k ( 21T j[AiY +Bi we YH = 2k1 1 J2(klP) sin 20 e (4.20) Substitute Eq. (4.20) into Eqs. (4. 11) and (4. 13) and perform the integration by using Eq. (4.14) and Bessel-Fourier series ejkp' sin 0 cos ( - 0') = J (kp' sin 0) a~~o00 + Jn (kp' sin 0) cos n (p - 0') (4.21) n = 1 and the Lommel integral formula x I = x j (ax) Jn(ox) dx x (ax) 8 J (OX) n (n X)J (x) d 2 + 2 2 n ax n J (x) - J (ax) (4.22) n, ax n( Thus the vector potential components in rectangular coordinate are: j (1- eo) xA 8kI1 [A WZE l + Bi'Y] I2(kl) sin 20 f(r) f(0) x 8kl + i A = 2 A.w A B y I (k 8k1 L1 Io 1(kl) -[A. wi1 + Biy] I2(kl) cos 2 0 f(r) f(8) 24

THE UNIVERSITY OF MICHIGAN 7848-7-Q (c - E ) A 4 Bi(k1) sin 0 f(r) f(0) z 4 i F- i ~l '1 -2 BAiT - Bi.E1 Io(k + [Ai y + B.wl I2(k1) cos 2 0 f(r) f(0) F=- 1 FA.A + B.wE I2(k) sin 2 f(r) f(0) y 8k i1 i 21 w(1 - o ) F = 1 o A I (kl) cos 0 f(r) f(0) (4.23) z 4 ill where e-j k r f(r) = r f(6e):= j (kcos 0 - -1] k cos 0 -y a I (k) = | pJ (k p) J (kp sin 0) dp 1 1 a Ii(k1) =| p Jl(klP)J (kp sin 0) dp 2I(k) 2 PJ2(k1p) J2(kp sin 0) dp. Substituting Eq. (4.23) into Eq. (4.17) gives the spherical components of the vector potential A and F.....____- _______ 25

THE UNIVERSITY OF MICHIGAN 7848-7-Q A i A J (21I0 s AWH - BylI (k ) cos ) A0 8k f(r) f(0) sin 2 B2i 0I(k1 ) o [ 8k 1 i ( 1) + j2klB i I 1(k) sin 0 + [Aiw + B I2(k1) cos 0 j W(E1 E) 02[Aw W. B1;Io(k A = 8k f(r) f(0) cos 2 A - B 1 (k) [AiWp + Bi I2(kl)1 F- ~ul-~Uo)1 y s -B 'WE I(k)cos 0 O = 8k f(r)f(0) os2 - B Io 1)O o + j 2klAi Il(k1) sin+ [AiY +B.iWEc I2(k ) cos 0 F= 8k f(r) f(0) sin 2 AY - Bi WE I0(k + AiY + BiWEl J I2(k1 (4.24) Thus the radiated field is. obtained by substituting Eq. (4.24) in (4. 15) E= f (r) f() sin CA[2 (AiwP 1-BiTY)Io(kl) cos 0 + j 2klBiIl(k1) sin0 + (Awi + Bi y)I2(k1) cos] +C 2 (Ai - Bi.w E)IO(k1)+(AY +Biw1)2 1] (4.25) F__ _ _ _ _ _ _2__ 26 _

THE UNIVERSITY OF MICHIGAN 7848-7-Q E = f(r)f(O) cos CA L2(Aiwi1 -BiY)I (k 1 i 1 + B )I2(k + CF [2(Ay - B.wE 1(k1) cos -j 2 k1 Ai Il(k ) sin 0 -(A.iy+Biwtl) I2(k ) cos 0 (4.26) where k2( c1) l k2(r k 2(E 1) nk 2(, -1) r r C = A -8 k F 8k 1 1 ~ In case when, = f' then C = O and the radiated field reduces to the pattern of a dielectric rod antenna. It is observed that the magnitude (B.) of the TM component of the hybrid mode should be as small as possible in order to lower sidelobe level and increase the directivity in the endfire direction. 4. 2 Experimentation In the analysis of the ferrite rod wave guide it is seen that an increase in the permeability lp or the permittivity e of the ferrite rod has the effect of increasing the propagation constant along the axis. This may be the cause of increasing the numbers of side lobes and its levels. In order to obtain end-fire narrow beam patterns it is preferable to have an axial propagation constant nearly equal to the free space propagation constant. Experimentally it appears that a cylindrical shell of ferrite will serve as well for a surface waveguide as the solid rod. As shown in Fig. 4-1 a cylindrical ferrite shell was used instead of a solid ferrite rod since there was insufficient ferrite material. EAF-2 ferrite powder with p = 2.2, e = 3.8 was inserted be17 r tween two fiber glass tubes with a 6 inch and a 5 inch diameter respectively.,_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2 7

900 Metal Feeding Cap EAF-2 Ferrite PowderH 1800a X0 0cm cm Feeding dipole 0 15 ~FicmI I 45 cm 7 70 ~~~~~~~~~~~cm 2 O. D. =15 cm I. D. =12.5- cm T I =45 cm Length of feeding dipole 12 cm FIG. 4-1: GEOMETRY OF THE FERRITE TUBE ANTENNA.

- THE UNIVERSITY OF MICHIGAN 7848-7-Q One end of the tube was fitted tightly into a metal circular cylindrical cavity having 6 inches in depth. Excitation was by a symmetrical dipole inserted from the base of the cavity and mounted diametrically. In this way. the ferrite radiator has a 1/2 inch shell layer, 6 inches of outer diameter, 18 inches of length and has a 45 degree conical shape with a tapered free end. The radiation patterns in the E-plane and in the H-plane are presented in Figs. 4-2 and 4-3 from 400 MHz to 1150 MHz. It should be pointed out that the TEl mode cutoff frequency of the cylindrical guide without the loading of the ferrite tube is 1170 MHz. Below this cutoff frequency the radiated field is weak; it is difficult to detect it accurately at the far field zone. The patterns shown in the Figs. 4-2 and 4-3 show the effects of adding the ferrite tube. In the normal operation region above cutoff the directivity is more than 15 db above an isotropic source. The measured half power beamwidth and the side lobe level are plotted against frequency in Figs. 4-4 and 4-5. It is seen from the graph that the side lobes are more prominent in the H-plane than in the E-plane which is expected due to the asymmetric field distribution of the HE mode in the ferrite tube. Also it can be observed that the side lobe level is more than 4 db down from the main lobe. The near field distribution along'the outer surface of the ferrite tube has been measured by using a probe moving axially and along the circumference. Figures 4-6 and 4-7 show the E - distribution against the coordinate 0 taken at 2 inches from the feed end and 2 inches from the free end respectively. The E field is observed to be sinusoidal around the circumference and the p sudden change of phase at 0 = 7r /2 and 0 = 37r /2 is to be expected. Figures 4-8 and 4-9 show the E - distribution along the tube axis at 600 MHz and 900 MHz. The observed pattern using a voltage probe appears to be standing _____________________ ~29 _

THE UNIVERSITY OF MICHIGAN 7848-7-Q d = 0.2X d = 025X d = 0.3X I = 0. 6X I = 0. 75X 1 = 0. 9X 400 MHz 0 500 MHz 0 600MHz 0 d= 0.35X d=0.4k d= 0.45X o 0 0 700 MHz =- 1. 05X 800 MHz A = 1.2X 900MHz = 1. 35X o o 0 d = 0.5X d = 0. 525X d = 0. 55X 1000MHz I = 1. 5X 1050 MHz I = 1. 575X 1100MHz = 1.65X FIG. 4-2: LINEAR POWER PATTERNS OF THE FERRITE TUBE ANTENNA (IE 12 Patterns in the 0 = O Plane). 30

THE UNIVERSITY OF MICHIGAN 7848-7-Q d = O.2X d O. 0.25X eI =0.6X.75. 400 MHz 500 MHz 600 MHz d = 0.35X} d =0.4X d = 0.45X 1. 05X~ 1= 1.2XO = 1.35X0 700 MHz 800 MHz 900 MHz d =0.5X d = 0.55X d = 0.575X o I =. 5A | = 1.65X O = 172X 1000 MHz 1100 MHz 1150 MHz FIG. 4-3: LINEAR POWER2PATTERNS OF THE FERRITE TUBE ANTENNA (IE I Patterns in the 0 = 90~ Plane). 31

THE UNIVERSITY OF MICHIGAN 7848-7-Q 20~ 30 40 d 500 600 70 p 0 - - 80 X 900 3 woo /~1000P/ E-Plane Patterns (0 = 0O) 110 -- H-Plane Patterns (0 - 90~) 1200 - I I, I, I m I I, I I, I 400 500 600 700 800 900 1000 1100 d = 0.2X d = 0.3X d = 0.4X d = 0.5X = 0. 6X~ = 0.9X~ 0 = 1.2X0 I=1.5X f (MHz) FIG. 4-4: HALF-POWER BEAMWIDTH'AGAINST FREQUENCY OF THE FERRITE TUBE ANTENNA. 32

0r E-Plane Patterns (0 = 0~) -2 ----- H-Plane Patterns ( = 90 ) -4 8 -6 -8 "o -10 0,, - \ r~~~~ % -12 0c -1 - 1 4 cD -la~~~~~~~~~~~~~~~~~~~~~r \ ~~~~~~~~~~~~I c. -160f (MHz) FIG. 4-5: SIDE-LOBE LEVEL AGAINST FREQUENCY OF THE FERRITE 400 500 600 700 800 900 1000 1100AN d = 0.2X d = 0.3X d = 0.4X d = 0.5X ~ 0 O 0 0 ' f (MHz) FIG. 4-5: SIDE-LOBE LEVEL AGAINST FREQUENCY OF THE FERRITE TUBE ANTENNA.

f - 600 MHz - ' Relative Amplitude of E x x Relative Phase of Ep 1.2 1500 Z Angle 0 ^ Q) Q ~~~~~~~~~ ~~~~~~~~.8 ~~500. -1.2 -100 "Q 0 -1500 2n /2 0 r/2 3or /2 Angle 0 -— > FIG. 4-6: NEAR FIELD MEASUREMENT, THE RELATIVE AMPLITUDE AND THE PHASE OF Ep AGAINST THE COORDINATE ANGLE, TAKEN AT 5cm FROM THEZ FEED END OF THE FERRITE TUBE ANTENNA.

f = 600 MHz:~~~~~~~~~~~~~~~~ Relative Amplitude of E X~~X Relative Phase of E P 1.2 - 150 -_~~~~~~~ x ------. o0 1. 0 100 0 >.8 -x 0 c -.6 ~~~~~~~~~~~~~~~~~00 0 7Z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C C 0 c..2 -100 I 0 - 150 ~ -7r /2 ~0 7r /2 7t 3wr/2 Angle 00- ' FIG. 4-7: NEAR FIELD MEASUREMENT, THE RELATIVE AMPLITUDE AND THE PHASE OF E AGAINST THE COORDINAGE ANGLE 0, TAKEN AT 5 cmZ ~EE IOTEEREU ATp FIG. -TH EA FIEED IESRMNTOF THE FERILTIE AMLTUBE ANDTHENA

2. 0 x 180 0 1. 6 120 0J 1.4 Z 600 1. 2 X 60r CD~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C Tb i. O O ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~CD 03C1) 1. 0 ~~~~~~~~~~~~~0 X ~~~~~~~~~~CD -;I W 0~~~~~~~~~~~~~~~~~ > 8 -600 f =f600 MHz Nk(CD Q) 6 0 -120 t Relative Amplitude of E C120 V..4...WX.-.WX- 'Lm...r. pC-D Relative Phase of E cD XIIX X P -180 0.2, -10 0 10 20 30 40 Along the Metal W all in cm t Along the Ferrite Rod Surface in cm FIG. 4-8: NEAR FIELD MEASUREMENT, THE RELATIVE AMPLITUDE AND THE PHASE OF THE E AGAINST THE FERRITE TUBE AXIS AT 600 MHz IN ~ = r/2 PLANE. p

f = 900 MHz - Relative Amplitude of E P X ---x Relative Phase of E H p 180~ 0 1. 6 x —x x.2 120 600 a0 F. 2 9 N F E. a) ~~~~~~ ~~ -60~~~~~~~.~~ -600 Along the Metal Along the Ferrite Rod Surface in cm Wall in cm FIG. 4-9: NEAR FIELD MEASUREMENT, THE RELATIVE AMPLITUDE AND THE PHASE OF 4j x~

,, THE UNIVERSITY OF MICHIGAN 7848-7-Q waves rather than traveling waves, probably because the conical cap free end and the short length ferrite tube form a resonance cavity. The continued investigation using experimental effort will be described in the next report. The exact mechanism governing the radiation properties of the tube antenna is not yet fully understood. It is hoped that the near field measurements will help to clarify the arguments among the existing theories. However, experimentally it has been found that the ferrite material used offered better guiding properties than the dielectric material..................__________ 38......................._______

THE UNIVERSITY OF MICHIGAN 7848-7-Q v LOW FREQUENCY FERRITE ANTENNAS The objective of this task is to investigate the design feasibility of new types of ferrite antennas that are usable at frequencies as low as 30 MHz. An effort has been made to identify realistic applications of ferrite loading to linear radiating elements. Accordingly, the investigation has focused upon applications which improve the performance of antennas that are relatively small. The range of sizes considered is 0. 1X < 2h < 0. 5X, where X = free space wavelength, and h = element half-length. The low end was chosen so as to avoid severe supergain limitations in element performance, while the high end was considered to be a practical size limit for a loaded 30 MHz element. Moreover, the detailed discussion is limited to center fed (or ground plane imaged) elements which support standing wave current distributions. 5.1 Tuning of Linear Elements Via Magnetic Biasing Some inherent advantages of applying static biasing fields to material loaded multiple linear elements were discussed in Section 5.1 of the Sixth Quarterly Report, (Lyon et al, 1967). Section 5.2 of the same report described some magnetic biasing experiments which used small diameter material loaded helices as the linear slow wave structure. The interesting results of these experiments, combined with promising theoretical implications, has motivated a more thorough study of this particular slow wave structure. To this end, rather extensive design curves for small diameter core loaded helices have been prepared, and appear in Appendix A along with the details of the mathematical origin. An underlying assumption of isotropic core material is implied by the mathematics, so that strictly speaking the results are rigorous only for the unbiased structure. However, since saturation of the ferrite core ____________________________________. 3 II -......

THE UNIVERSITY OF MICHIGAN 7848-7-Q material represents a limit on the tuning range of magnetic biasing, the theory discussed in Section II was applied to obtain approximate results for this limit. As an approximation, a helix filled with a ferrite material biased into saturation by a DC magnetic field can be assumed equivalent to one filled with only a dielectric material of the same dielectric constant as the ferrite. This approximation is deduced by noting that the magnetic properties of a ferrite biased into saturation do not effect the wave number of the wave equation for electromagnetic waves inside such a material. By assuming that there is no variation of the field in the 0 direction for the helix (which is not the case for anisotropic loading), the characteristic equation becomes identical to the isotropic loaded case with the relative permeability of the material identically unity. This approach yields a rough idea of the phase velocity reduction for a biased loading. To establish the reduction in phase velocity, obtainable with ferrites that are available in our laboratory, the computer program described in Appendix A was used to obtain graphical solutions of the characteristic equation. Plots were made for the following core loadings: 1) Air, 2) EAF-2 ferrite powder, 3) Indiana General Q-3 ferrite at 100 MHz, 150 MHz, and 200 MHz, and 4) Eccorsorb CR at 300 MHz. Eccorsorb CR is an Emerson and Cuming Microwave absorber having fairly low electric and magnetic loss properties at the frequency of interest. In certain instances two plots were made for each loading so that the results could be read with greater resolution. The solution of the characteristic equation for an air core is given in Fig. A-1 for purposes of comparison with the loaded results. Figures A-2 through A-4 depict the approximate results when the indicated ferrite loadings are biased into saturation. ___ __ __ __ __ ___ __ __ __ __ _ 40

THE UNIVERSITY OF MICHIGAN 7848-7-Q The results for a saturated core and an air core are seen to be nearly identical. Figures A-5a,b through A-9a,b depict rigorous results for the same ferrite loadings without magnetic bias. A substantial reduction in phase velocity is seen to occur for a given helix pitch angle. Intermediate values of bias field should produce phase velocity reductions between the no bias and saturation bias cases. For small helix pitch angles, the sheath helix is an excellent approximation to the physical problem, and close agreement between theoretical and experimental phase velocity reduction factors can be expected. At the larger helix pitch angles, the theoretical model would be more closely approximated by using multifilar windings connected in parallel at the feed. To date, good agreement between theoretical and experimental results has been obtained for the unbiased loadings. Since fields of sufficient intensity to saturate the ferrite have not yet been generated in the project laboratory, the accuracy of the graphs for the saturated core awaits experimental verification. 5.2 Computer Analysis of Multiple Linear Elements A generalized analysis of two parallel linear elements was presented in Appendix A of the Fourth Quarterly Report, (Lyon et al, 1967). That analysis is the foundation from which ideas for several interesting design concepts are being exploited. Although the formulation was complete, rather limited numerical information was presented for the impedance associated with the symmetric excitation mode. This limitation was eliminated by the addendum which appeared in Appendix B of the Sixth Quarterly Report, (Lyon et al, 1967). This appendix developed the symmetric mode impedance of a small diameter helical slow wave structure. The formulas are also valid for describing the effects of material loading inside the helix, and are representative of the effects ob

THE UNIVERSITY OF MICHIGAN 7848-7-Q tainable from other slow wave structures. Due to the general utility of these results, they were put into a convenient graphical presentation to facilitate usage. The addendum material in Appendix B of the Sixth Quarterly Report, along with the previously developed formulation in Appendix A of the Fourth Quarterly Report, has been incorporated into a general computer program. The computer program is useful as a diagnostic tool in designing meaningful experiments. In addition results from existing experiments can readily be compared to theory by inserting into the program the appropriate parameters of the experiment. At present the program calculates the input impedance Zi =R + jX to a structure composed of two parallel linear slow wave structures with various lumped impedance terminations. The structure and associated nomenclature were specified in Appendix A of the Fourth Quarterly Report. Computer results for the particular case corresponding to a folded dipole formed of two similar slow wave elements are presented in Figs. 4-1 through 4-6. The slow wave elements characterized were small diameter helices having symmetric and asymmetric mode phase velocity reduction factors of p and Pa' respectively, a length to thickness ratio of 55, and an asymmetric mode characteristic impedance of 250 ohms. As the figures clearly show, some interesting variations in impedance behavior result from different combinations of ps and Pa. Figure 4-1 illustrates the input impedance for an ordinary open wire folded dipole since ps = Pa = 1.0. Figure 4-3 illustrates an interesting negative reactance slope behavior near kh = 7r /2 when p = 1.0, p = 0.6. This structure may be realized by placing dielectric material between two linear conducting elements, thereby affecting only the asymmetric phase velocity reduction factor as is the case for TV "twin-lead" cable. 42

THE UNIVERSITY OF MICHIGAN 7848-7-Q 600- R 500 400 300 200 10 0j 0. 5 1.0 1. 5 2.0 kh 2.5 800 - X 600 - 400 200 0 I I 0.5 1.) 1.5 2.0 kh 2 5 -200 - -400 - -600 - -800 FIG. 5-1: INPUT RESISTANCE R AND REACTANCE X FOR FOLDED DIPOLE STRUCTURE WHERE p = 1.0, p = 1.0. 43

THE UNIVERSITY OF MICHIGAN 7848-7-Q 600 R 500 - 400 300 200 100 0 0.5 1.0 1.5 2.0 kh 2.5 800 X 600 - 400 - 200 - C, I I 600 5 0. 5 1.0 1.. 0 kh.5 -200 - -400 - -600 - -800 FIG. 5-2: INPUT RESISTANCE R AND REACTANCE X FOR FOLDED DIPOLE STRUCTURE WHERE p = 1.0, p = 0.8. 44

THE UNIVERSITY OF MICHIGAN 7848-7-Q 600 R 500 - 400 - 300 - 200 - 100 0 0.5 1.0 1.5 2.0 kh 2.5 800 - 600 - 0.5 1.0 1.5 2.0 kh 2.5 -200 -400 -600 -800'FIG. 5-3: INPUT RESISTANCE R AND REACTANCE X FOR FOLDED DIPOLE STRUCTURE WHERE p = 1.0, p = 0.6. 45

THE UNIVERSITY OF MICHIGAN 7848-7-Q 600 R 500 400 300 200 100 0.5 1.0 1.5 2.0 kh 2.5 800 600 400 200 0.5 1.0 1.5 2. 0 kh 2.5 -200 -400 -600 -800 - FIG. 5-4: INPUT RESISTANCE R AND REACTANCE X FOR FOLDED DIPOLE STRUCTURE WHERE p = 1.0, p = 0.4. 46

THE.UNIVERSITY OF MICHIGAN 7848-7-Q 600 R 500 - 400 - 300 - 200 - 100 - 0 0.5 1.0 1.5 2.0 kh 2.5 800 X 600 - 400 20 0.5 1. 0 1.5 2.0 kh 2. 5 -2 0 --400 - -600_ -800 FIG. 5-5: INPUT RESISTANCE R AND REACTANCE X FOR FOLDED DIPOLE STRUCTURE WHERE p = 0.8, p = 0.8. 47

THE UNIVERSITY OF MICHIGAN 7848-7-Q 600 R 500 400 300 200 100 0.5 1.0 1.5 2.0 kh 2.5 800 x 600 400 200 0 0.5 1.0. 5 2.0 kh 2. 5 -200 -400 -600 -800 FIG. 5-6: INPUT RESISTANCE R AND REACTANCE X FOR FOLDED DIPOLE STRUCTURE WHERE p = 0.8, p = 0.6. s 48

THE UNIVERSITY OF MICHIGAN r 7848-7-Q VI CONCLUSIONS Both analysis and experiments have verified that a log conical spiral antenna can be reduced substantially in size. The present methods available, which have been investigated experimentally, are such as to assure the success of designing a log conical spiral antenna operable in the range from 200 to 600 MHz with a reduction in size. Although it is not anticipated that anisotropic loading will be utilized in the final design of this antenna, this type of loading does appear to be worthy of future study. It has been decided to utilize a slot array of only three ferrite filled rectangular slots for establishing the feasibility and usefulness of the suggested concept. If there appear to be substantial advantages in this small array, including a reduction in near field effects due to small size of elements, then it is expected that justification can be extended to larger arrays. It can be definitely concluded that the utilization of ferrite loading material for end fire rod antennas produces satisfactory results if the ferrite loading material is used in the form of a cylindrical shell. The experimental results confirm that such ferrite tube antennas have superior performance to ferrite rod antennas. The study of ferrite loaded antennas down to 30 MHz has given considerable emphasis to the tuning of such antennas utilizing magnetic bias. For reasonably small size antennas in this frequency region, the radiating elements must certainly be of the highly tuned type. Therefore, in order to achieve reasonable coverage in frequency, it appears necessary to use either multiple tuning or continuously variable tuning, such as represented by magnetic bias. 49

'. THE UNIVERSITY OF MICHIGAN 7848-7-Q VII FUTURE EFFORT In the next few weeks, a decision must be made as to which manner of loading is most appropriate for size reduction of the log conical spiral antenna. Quite aside from the physical outline size, it is important to maintain a reasonable weight for the final design. A choice must be made among the various alternative methods of loading which have been studied so far. It is expected that the analytical work on ferrite tube radiators will be completed during the next report period. A careful study of the correctness of the analytical work will be made through a comparison of radiation patterns obtained both analytically and experimentally. In the future, all of the effort on this task will be on the ferrite tube rod radiator, which has a hollow airspace in the center of the core. In the next few weeks, the array of three ferrite loaded rectangular slots will be thoroughly tested experimentally to obtain its actual radiation pattern. These tests will be performed on the roof-top antenna range. It is expected that pattern measurements will be made in a fairly narrow range of frequencies centered about 300 MHz. Supplementing these pattern measurements, there will be work done on the driving point impedance of each of the three slots. Effort will then be made to take this information and extend it to the prediction of driving point impedances of slots arranged in a still larger square array. A careful comparison between experimental and theoretical results for elements useful down to 30 MHz will be completed. This should establish the accuracy of the mathematical techniques developed, and add support to the useful applications indicated by the study. _ _ _ _ _ _ _ _ __ W50 -

THE UNIVERSITY OF MICHIGAN 7848-7-Q APPENDIX A DESIGN CURVES FOR SMALL DIAMETER LOADED HELICES In designing a small diameter helix to function as a linear slow wave structure, it is essential to know the dependence of the phase velocity reduction factor (X /X) upon the helix pitch angle (Q). This information may be obtained from the solution to the characteristic equation for a sheath model of a helical transmission line. The characteristic equation for an arbitrary isotropic material loading in the helix core was derived by Li (1958) in his doctoral thesis. For a small diameter helix, the characteristic equation is 22 + u(ka)2 n(nka) 2cot2 - 2(ka2 2 n (2 2 k 7L2 rc(ka)2 {n(2/ka) -y 2 2 2 where k = 13 - /, is the wave number in the longitudinal direction,: is t I0 the free space wave number, "a" is the radius of the helix, / is the pitch angle of the sheath winding, and y is Eulers constant (0. 5772157). (Note: Li's notation is used only throughout this appendix. The notation appearing on subsequent figures is consistent with both this appendix and the remainder of the report.) A computer program was written for the IBM 7090 computer at the University of Michigan Computing Center in Fortran II that would solve the characteristic equation and plot the required pitch angle (sb) vs 3 oa for a family of specified phase velocity reduction factors. With the slight modifications that are indicated by comment cards, the main program may be used on any computer system compatible with Fortran II. The subroutine that does.....~ 551 -

THE UNIVERSITY OF MICHIGAN 7848- 7-Q the plotting, however, calls on many local subroutines to use the IBM 763/789 plotter and is not compatible with other systems. Nevertheless, both the main program and the subroutine are included in the event that they may be useful to others wishing to solve the characteristic equation for other ferrites. Solutions to the characteristic equation for a number of different core loadings are graphed in Figs. A-1 through A-9. The loadings are characterized by the relative permittivity (e ) and permeability (p ) of the core material. The materials which the Er and fpr represent are stated in parentheses. While various engineering implications relating to the core material are discussed in Section 4. 1, a few mathematical observations will be stated here. Li pointed out that little phase velocity reduction beyond that of an air core (e =t = 1) r r is obtained with just dielectric loading of small diameter helices. This is illustrated in Figs. A-1 through A-4, where the relatively minor effect of increasing just e is seen to be more prominent for larger values of 27ra/X and smaller values of X /X. On the other hand, the utilization of ferrite loading g to increase p results in a substantial phase velocity reduction for a specified helix pitch angle. The effect is illustrated in Figs. A-5a,b through A-9a,b, where two scales have been used to facilitate accuracy............__ ~52

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 I g 0.8 22 0.7 20 18 0. 6 16 14 0. 5 0)~~~~~~~~~~0. 4 10 60. 3 4 ~~~~2+o~~~~~~~~~0. 2 0.0 O..o _ e, 0 0.01 0.02 0.03 0.04 0.05 2 7ra/X (Radians) FIG. A-i: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS e = 1.00, /u = 1.00; (Air). 53

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 22 Ag/X=0. 8 0.7 20 18 16 14 12.j./' 0.4 bB10 6 0..10.0 0.03 0.04 0.05 2wr a/X (Radians) FIG. A-2: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS e = 3.77, p = 1.00; (EAF-2 Powder Ferrite Biased into Saturation). 54

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 22 Xg/X=0.8 0.7 20 18 16 14 1204 10 0.0 0.01 0.02 0.03 0,04 0.05 2w a/X (Radians) FIG. A-3: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS c = 7. 88, ur = 1. 00; (Q-3 Ferrite at 150 MHz Biased into Saturation). 55

'(uoJrpJn:uS ~ouP pas1e.a: ZHWI 008:e UD qjosoooa) 00 '1 = atr '0 g= _z3 SI:L\VMI uVd tqOOD DNIAVH XIrI3H IOJ NOILVfln~ DILSIlIXtLD5VVHD 3HL JO NOIJLflOS:t-V '0DIJ g0'0 ~ 0'0 00'0 O0' 0 TO 0'0 I - I. I...'AZ 010 9 "1 91 NVI1I AIIAN 311

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 - 22 20 18 16 Q 12t 10 8 0. 1. 6 4 2 0 I. I! 0.0 0.01 0.02 0.03 0.04 0.05 27 a/X (Radians) FIG. A-5a: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS Er = 3.77, /ur = 2.10; (EAF-2 Powder Ferrite). 57

THE UNIVERSITY OF MICHIGAN 7848-7-Q 80 70 60 50 /X 40 0. 8 b30 0. 0. 6 20 1 _0. 5 20 10 ~/~ ~~~~~~~~0.3 10 0/ 0.2 0.1 00. 0.01 0.02 0.03 04 0. 5 21w a/X (Radians) FIG. A-5b: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS er = 3. 77, /r = 2.10; (EAF-2 Powder Ferrite). 58

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 / 22 Xg/X= 0.3 20 / 18 16 14 i 0.. 12 10 bL 6 4 2 0.0 0.01 0 002 0.03 0 04 0 15 2w a/X (Radians) FIG. A-6a: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS er = 7.96, /ur = 12.4; (Q-3 Ferrite at 100 MHz). 59

THE UNIVERSITY OF MICHIGAN 7848-7-Q 80 i 70 60. 8 0.7 50 0. 6 O9~~~~~~~~~~ 405 0 30 0. 2 20 10 0.0 0.01 0.02 0 03 0.04 0.05 27r a/X (Radians) FIG. A-6b: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS Er = 7. 96, ur - 12.4; (Q-3 Ferrite at 100 MHz). 60

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 C 22, X g/X 0.3 20 - 18 - 16 14 12 - 4 0 - 0 I I I 0. 0 0.01 0.02 0.03 0.04 0.05 2wr a/X (Radians) FIG. A-7a: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS er= 7.88, /r = 13. 2; (Q-3 Ferrite at 150 MHz). 61

g9 '(ZHA OiT wl lla;a g-b0) fa'a1 = r '88 'L = S) SI3JaIVVcd 3lOO DNIAVH XI)arH Oi NOILVflba DIJLSI:3hILDYVVYHO aHiL dO NOIdLfYIOS:qL-' 'DI CIO 0 T00 '0 0 '0 '0 0 0'O 0D,1.I I I I 01.0::'-" —'-"- ~ =* '01.. Lo/. 1.. I/ 0 E i.0'0 /'0 X/ X 0O ~I ----' - '0 t. 'O, 'o i i I I I I 08 NVO:IHDI~:I X&I$1t~AINl itH&

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 xg/X = 0.3 22 g 0. 2 20 18 -16 -T 14 12 { _. 10 8 - 2 -0 t. I t 0.0 0.01 0.02 0.03 0.04 0.05 2w a/X (Radians) FIG. A-8a: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS cr = 7.81, /~r = 14.3; (Q-3 Ferrite at 200 MHz). 63

THE UNIVERSITY OF MICHIGAN 7848-7-Q 80 70 =0.9 I 0. 8 60 0. 7 50 o. 5 40 0)[D~~~~~~~~~~ ~0. 4 bD 30 0. 3 20 10 0.0 0.01o 0. 0.0.03 0.'04 0.05 2wr a/X (Radians) FIG. A-8b: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS Er = 7. 81, Mr = 14.3; (Q-3 Ferrite at 200' MHz).64 64

THE UNIVERSITY OF MICHIGAN 7848-7-Q 24 Xg/X = 0.5 22 0. 4. 20 18 16 i4 /) o -- --— 10i- 8 2 0.0 0.01 0.02 0.03 0.04 0.05 27r a/X (Radians) FIG. A-9a: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS er = 22.0, p = 4.51; (Eccosorb CR at 300 MHz). r 65

THE UNIVERSITY OF MICHIGAN 7848-7-Q 80 I I I 70 60 50 30 0. 5 O. 4 20 0.6 ~~~~~~~~~~~~10 ~ ~ ~ 0 i I - I 0.0 0o.01 0.02 0.03 0.04 0.05 2i a/X (Radians) FIG. A-9b: SOLUTION OF THE CHARACTERISTIC EQUATION FOR HELIX HAVING CORE PARAMETERS cr = 22.0, pr = 4.51; (Eccosorb CR at 300 MHz). 66

....t b~~~~~~~~~~~~~~~~~;D/ ' - a;iME..NSION P.51 (};r;\~~~~~~~~~~~~~~~~450),S~~~~~~~~~~~~~~~~~~~~~~~ # CI T T NR!JI~kYY., AND TAPEPR 6JtikE..OU.TPUTI TAP.E OFJHE UN.IY ER SIT.Y. $F C_. MICHIGAN SYSTE_ ^........ 10 'REEAD INPUTf -,TA P E' 7,20, RELMU, RELEPS. -. 20- -: *: n<FORMAT (2 E 10. 0O) -___ -'. 2a1 W-::WFRITE OUTPUT TAPE 6,22,RELMURELEPS: _ —__-___ 263 JR =1.... 26.:2-:., f:O RM:3: —H:1 T-H:.'.........E'..... A:..... 8. ' -...._ —." I-::i0: 5010 -52 H X, BET A(i O )*rA........ AND P S I AR E PRa I NT ED aOUT IN TH. oR DER..); -.....45 ':W'TE OUTPU JAPE 6,46 -60. AE I:.:A.:XKA E2-.::0l BA*2 ).-. 0 C.SO.RT-IS. A:: LOCAL FUNiCTION FOR CALCULATINNG THE SOUARE ROOT. rTXKA=SORT (XKAE2) E C E LOG ISA LCAL FUN O FOR CALCULATING THE NATURAL LOGRITHM. C- ' E....".... -, ~...,.'?'. 25:LINES:'.'.; P INTE.:..S..:'I'S:.A::'..LOCAL FUNC. C........../ ~..... r.. - - r,....,, ' ~ ~ — L i R E S 1 ' i.11

80 BRACK=ELOG(2.'0/XKA). 90 8bRACK=BRACK-0.5772157 100 CT2PSI=(2.0O*XKAE2*"BRACK*(2.0+(RELMU*XKAE2*BRACK)))/(RELMU*(BOA**'2) 1*(2.0+(RELEPS'X XKAE2*BRACK))) 110 COTPSI=SORT(CT2PSI) C ATAN IS A LOCAL FUNCTION FOR CALCULATING THE ARCTANGENT. '. C... - 120 PSI(I)=ATAN(1.0/COTPSI) 130.'PSI(I)=PSI(I)/(1.74.5329E-2).. 135 X(I)-B'OA-... 136 'IF (J-5) 153,140,140. ' 140, WRITE OUTPUT.TAP'E 6, 150,R,BOA, PSI(I).. 150 FORMAT (1P3E20.8).co 15 2 J= 0.' 153 J=J+1 155 I=I+1 0 160 BOA=BOA+O.001 170 IF (BOA-0.05) 50,50,180 180'. R=R+O.1 190o IF (R-0.99)40,195,195 195. CALL GRAPH (X,PSI) ) 200 GO TO 10 END 2 5 ''L INES.PRI NTE D l l~~~~~~~~~~~

C THIS SUBROUTINE DOES THE GRAPH USING THE CALPLOT SUBROUTINES.. (',, PLTX)(X IS NOT CALLED FOR SINCE 8.5 INCHES OF GRAPH PAPER IS SUFFICIENT. C PSCALE IS NOT CALLED FOR SINCE TH1E SCAL- E FACTORS 'ARE K-iNOWiA pRIORI. C THESE APRIORI VALUES ARE FED INTO PLTOFS. C, SUBROUTINE GRAPH (BOAPSI) DIMENSION PSI(450),' BOA(450)'. C C CSTATEMENiT 10 SPECIFIES THE RELATIVE ORIGIN. C 10 CALL PLTOFS(O.O,O.'01, O,10.o,10.0',i.O) C C S:TATEMENT 30 DRAWS Ai'!DI LABELS THE X AXIS. 35 DOES THE UPPER X AXIS,. Z C 40 DRAWS.AND LABELS THE Y AXIS. <45- DOES THE RIGHT Y AXIS. C 30 CALL PAXIS(i.-O1. O,1H,H-1,-5.00.0,00,001,1.0) 35 CALL P-AXIS( 1.0o,9.O, 1H,-1,-5.O,00,00.0,1, 1.0 ) 40' CALL PAXIS(1.0,1.O,1H,1,-8,09.0,00.0, 10:.0,.2) 45- CALL PAXIS(6.,0-10,1H,1,-8.0,90..0,0.0,010. 00,.2) C o 0C SICE THE NORMAL MODE OF PLOTTINGIS LIEA-RECTAGUAR THE MODE NEED NOT BE - C DEFINED. C50 PLOTS PSI VS. BETA(O)*A USING A SOLID LINE, '. 0 C PRSTER, PONRST, AND POFRST ARE CALLED TO PREVENT PLOTTING OUTSIDE r C THE DESIRED PLOTTI-IG REIGON. C 47 SWT=PRSTE1(lO1.Ot5.0,8.0) 48 SWT=PONRST(O) 50 0 0 60 i=.,9 1 9 55 K=1+(I-1)5- 0 ' 60 CALL PLINE..OA(K).PSI(K),50,1,O0,i) 65 SWT=POFRST(O) c ~ - '' C 70 INDICATES THE PLOTTING IS ALL FINISHED. C 70 CALL PLTEI\D t80 RETURN END __. 39- LINES PRINTED

, THE UNIVERSITY OF MICHIGAN 7848-7-Q REFERENCES Collin, Robert C. (1960) Field Theory of Guided Waves, McGraw-Hill Book Company Inc., New York. Fradin, A. Z. (1961), Microwave Antennas, Pergamon Press, London. Hach, R.C. (1966), Conductron Corporation, Private Communication with one of the Authors. James, J.R. (1967), "Theoretical Investigation of Cylindrical Dielectric Rod Antennas," Proc. IEEE, 114, pp. 309-319. Kiely, D.G. (1953), '"Dielectric Aerials;" Methuen Monograph. Li, T. (1958), "The Small-Diameter Helical Antenna and its Input-Impedance Characteristics, " Doctoral Thesis, Northwestern University. Lyon, J.A.M., N.G. Alexopoulos, G.G. Rassweiler, D.L. Smith, J.C. Parker, W.W. Parker and P.R. Wu (1966), "Study and Investigation of a UHF-VHF Antenna, " The University of Michigan Radiation Laboratory Report No. 7848-2-Q. UNCLASSIFIED. Lyon, J.A.M., G.G. Rassweiler, N.G. Alexopoulos, J.C. Parker, D.L. Smith and P.R. Wu (1967), "Study and Investigation of a UHF-VHF Antenna," The University of Michigan Radiation Laboratory Report No. 7848-4-Q. UNCLASSIFIED. Lyon, J.A.M., C.C. Chen, E.S. Greene, J.C. Parker, and D.L. Smith (1967), "Study and Investigation of a UHF-VHF Antenna, " The University of Michigan Radiation Laboratory Report No. 7848-6-Q. UNCLASSIFIED. Rassweiler, G. G. (1967), "Helical and Log-Conical Helical Antennas Loaded with an Isotropic Material, " Doctoral Thesis, also The University of Michigan Radiation Laboratory Report No. 7848-3-Q. (November, 1966) UNCLASSIFIED. Walter, C. H. (1965), Traveling Wave Antennas, McGraw-Hill Book Co., New York. Wolff, E. A. (1966) Antenna Analysis, John Wiley and Sons, Inc., New York......._ _ _ _ _ _ __ ~70..

.DISTRIBUTION LIST AF33(615)-3609 Proj. 07848 Destination Number of Copies Adams-Russell Company Library - Antenna Section 280 Bear Hill Road Waltham, Mass. 02154 1 Aero Geo Astro Security Officer Edsall and Lincolnia Blvd. Alexandria, Va. 1 Aerospace Corporation Robert C. Hansen 2400 E. E1 Segundo Blvd. Los Angeles, Calif. 90045 1 Cutler-Hammer Division, Airborn Instruments Labs. Librarian - Antenna Section Walt Whitman Road Melville, L.I., New York 11729 1 All Products Company Mr. James Buzbee Mineral Wells, Texas Americal Electronic Laboratories, Inc. Antenna Section Box 552 Lansdale, Pa. 1 Andrew Alfred Consulting Engineers Librarian - Antenna Section 299 Atlantic Ave. Boston, Mass. 02110 1 AVCO Res. and Adv. Development Division Research Library 201 Lowell Wilmington, Mass. 01887 1 AVCO Electronic and Ordnance Division Technical Library 2630 Glendalndale-Milford Road Cincinnati, Ohio 45241 1 Bell Aircraft Corporation Technical Library - Antennas Buffalo, New York 14205 1 Bell Telephone Laboratories Inc. Technical Reports Library Room 2A165 Whippany, New Jersey 07961 1

AF 33(615)-3609 Proj. 07848 Bendix Radio Division Technical Library - Dept. 462-4 East Joppa Road Baltimore, Md. 21204 Bendix Research Laboratories Technical Library 20800 10 1! Mile Road Southfield, Michigan 48076 Boeing/Wichita - Antenna Systems Staff Unit Technical Library 3801 South Oliver Wichita, Kansas 67201 Boeing Aerospace Division Technical Library - Antenna and Radomes Box 3707 Seattle, Washington 98124 1 Bunker-Ramo Corporation, Defense Systems Div. 8433 Fall Brook Avenue Canoga Park, California 91304 1 Canoga Electronics - Advanced Programs Dept Box 2086 Canoga Park, California 91306 1 Chance-Vought Aircraft, Inc. BuAer Representative Technical Library - Antenna Section Box 1500 Arlington, Texas 75222 Collins Radio Research Division Technical Library 5200 C NE Cedar Rapids, Iowa 52406 1 Collins Radio Corporation Dr. Robert L. Carrel - Antenna Section Dallas, Texas 75207 1 Dalmo Victor Company Technical Library - Antennas 1515 Industrial Way Belmont, California

AF 33(615)-3609 Proj. 07848 Domre and Margolin, Inc. Technical Library - Antenna Section 29 New York Avenue Westbury, L.I.,N.Y. 11591 Douglas Aircraft MSSD Technical Library Antenna Section 3000 Ocean Park Blvd. Santa Monica, Calif. 90406 1 Dynatronics, Inc. Technical Library - Antennas Hwy 17 and 92 N. Castlebury Orlando, Florida 1 Electronic Communications Research Division Technical Library 1830 York Road Timonium, Md. Emerson and Cuming, Inc. E. J. Luoma 869 Washington St. Canton, Masso 02 021 1 Fairchild Aircraft and Missiles Division Technical Library - Antennas Hagerstown, Maryland 1 Fairchild Hiller Corporation Technical Library 1455 Research Blvd. Rockville, Md. 20850 1 General Dynamics/Convair Technical Library - Antennas Grants Lane P.O. Box 748 Fort Worth, Texas 76101 1 General Electric Electronics Laboratory Technical Library Electronics Park Syracuse, New York 13201 1 General Electric Light Military Electronics Dept. 901 Broad Street Utica, New York 13503 1

AF 33(615)-3609 Proj. 07848 General Electric General Engineering Laboratory Building 371, Room 478 Schenectady, New York 12305 General Electronics Laboratories, Inc. Technical Library - Antennas 18 Ames Street Cambridge, Mass General Precision Laboratory Technical Library - Antennas 63 Bedford Road Pleasantville, N. Y. Goodyear Aircraft Arizona Division Antenna Department Box. 85 Litchfield Park, Arizona 85340 1 Grumman Aircraft Engineering Corporation Technical Library - Avionics Engineering South Oyster Bay Road Bethpage, N. Y. HalliUcrafters Company Technical Library - Antennas 4401 West Fifth Avenue Chicago, nlinois 60624 Hoffman Laboratories, Inc. 4501 North Arden Drive El Monte, California 91734 Hughes Aircraft Corporation Technical Library - Antennas Centinela and Teale Streets Culver City, California 90232 Hughes Aircraft Communications and Videosonics Div. Antenna Section 1901 West Malvern Avenue Fullerton, California ITT Federal Laboratories Technical Library - Antennas 500 Washington Ave. Nutley, N. J. 07110

AF 33(615)-3609 Proj. 07848 Laboratory for Electronics, Inc. Antenna Department 1079 Commonwealth Avenue Boston, Mass. 02115 1 Ling-Temco-Vought Military Electronics Div. Librarian - Antennas 1200 Jupiter St. Garland, Texas- 1 Litton Systems, Amecom Division Technical Library - Antennas 1140 E. W. Highway Silver Spring, Md. 20910 1 Lockheed Marietta Division South Cobb Drive Marietta, Georgia 30061 1 Lockheed Electronic and Armaments System Office P. O. Box 551 Burbank, California 91503 1 The Martin/Denver Division Headquarters Antenna Iboratory Mall Nr. T-0453 P. O. Box 179 Denver, Colorado 80201 1 The Martin/Orlando Company Technical Library - Microwaves Box 5837 Orlando, Florida 1 The Martin/Baltimore Company Technical Library - Antennas Baltimore,-Md. 21203 1 Maxon Electronics Corporation,Sunrise Highway Great River, L. I., New York 11739 1 McDonnell Aircraft Corporation Technical Library - Antennas Box 516 St. Louis, Missouri 63166 1 Melpar, Inc. Technical Library - Antennas 3000 Arlington Blvd. Falls Church, Va. 22047 1

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.AF 33(615)-3609 Proj. 07848 RCA Missile and Service Radar Division Manager, Antenna Engineering Skill Center Marne Highway Moorestown, New Jersey 08057 1 Rantec Corporation Librarian - Antenna Labtory 24003 Ventura Blvd. Calabasas, California 91302 1 Raytheon Equipment Division Library - Mr. J. Portsch P. 0. Box 520 Waltham, Mass. 02154 1 Raytheon Missile Systems Division Research Library Hartwell Street Bedford, Mass. 1 Raytheon Space and Information Systems Div. 528 Boston Post Road Sudsbury, Mass. 1 Sanders Associates Librarian - Antennas 95 Canal Street Nashua, New Hampshire 1 Sichak Associates. Mr. W. Sichak 518 Franklin Ave. Nutley, New Jersey 1 HRB Singer Corporation Attn: Library - Antennas Box 60, Science Park State College, Pa. 16801 1 Southwest Research Institute Librarian - Antenna Laboratory 8500 Culebra Road San Antonio, Texas 78206 1 Space Technology Laboratory Research Library One Space Park Redondo Beach, California 90278 1

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AF 33(615)-3609 Vkoj. 07848 AFCRL C. J. Sletten CRD L G Hanscom Field Bedford, Mass. 01731 2 AFETRL - Technical Library Patrick AFB, Fla. 32925 1 AFMDC - Technical Library Holloman AFB, New Mexico 88330 1 APGC, Hq. 3208 Test Group Eglin AFB, Fla. 32542 1 ASD - ASEP B. Brooks Wright-Patterson AFB, Ohio 45433 1 RADC - EMATA, Griffiss AFB, New York 13442 1 RADC EMLT-1 Griffiss AFB, New York 13442 1 RADC EMIAD - R F Davis Griffiss AFB, New York 13442 1 SEG - SEAEM Mr. Mulligan Wright-Patterson AFB, Ohio 45433 1 SEG - SEACC Y. E. Stahler Wright-Patterson AFB, Ohio 45433 1 SEG - SEPIE Wright-Patterson AFB, Ohio 45433 1 AFSC - SCSE Andrews AFB, Wash. D. C. 20331 1 RTD - RTGS Bolling AFB, Washington, D. C. 20332 1 Hq, USAF, AFRDR, Lt. Col. B. Lieber Washington, D. C. 20330 1 Hq, USAF AFXSAI, Air Battle Analysis Center Dep. Dir. Plans for War Plans Washington, D. C. 20330 1 RTD RTHR Bolling AFB, Washington, D.C. 20332 1 FTD TD-EE Wright-Patterson AFB, Ohio 45433 1

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AF 33(615)-3609 Proj. 07848 Cornell Aeronautical Laboratory Research Library Buffalo, New York 14221 1 University of Illinois EE Res. Laboratory Engineering Experiment Station Urbana, Illinois 1 Air Force Avionics Laboratory AVWE-3 Wright-Patterson AFB, Ohio 45433 5 +reproducible Defense Documentation Center Alexandria Virginia 22314 20 + card 163 + reproducible

Unclassified Security Classification DOCUMENT CONTROL DATA - R & D (Security classification of title, body of nbstract anJ inldhdexlng innlotatioon nlut be entered when the overall report i. classified) 1. ORIGINATING ACTIVITY (Corporate author) Za. REPORT SECURITY CLASSIFICATION iThe University of Michigan Radiation Laboratory, Dept. of Unclassified Electrical Engineering, 201 Catherine Street, 2b. GROUP Ann Arbor, Michigan 48108 3. REPORT TITLE Study and Investigation of a UHF-VHF Antenna 4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Seventh Quarterlv Report 1 July 1967 through 30 September 1967 6. AUTHOR(S) (First name, middle initial, last name) Lyon, John A.M., Chen, C-C, Parker, J.C. and Smith, D.L. 6. REPORT DATE 7it. TOTAL NO. OF PAGES 7b. NO. OF REFS October 1967 12 8a. CONTRACT OR GRANT NO. O9a. ORIGINATOR'S REPORT NUMBER(S) AF 33 (615)-3609 7848-7-Q b. PROJECT NO. 6278 C. (h. OTHER REPORT NO(S) (Any other numbers that may be assigned Task 627801 tisre d. 10. DISTRI BUTION STATEMENT. DISTRIBUTION STTEMENT Qualified requestors may obtain copies of this report from DDC. This document is subject to special export controls and transmittal to foreign governments or foreign nationals may be made only with prior approval of AFAL(AVPT), Wright-Patterson AFB, Ohio 11. SUPPLEMENTARY NOTES 1T. SPONSORING MILITARY ACTIVITY Air Force Avionics Laboratory AVWE Research and Technology Division, AFSC _ Wright-Patterson AFB. Ohio 45433 13. ABSTRACT This report covers the work effort in the various tasks of the project for a three-month period. The report goes into considerable detail since it includes substantial analysis, computer results, and experimental data. In all of the tasks, substantial progress has been made. However, in one task, a complete reorientation of the work program has been made. Under Task II, on slot arrays, it has been found necessary to simplify the work and also to avoid difficulties with materials. This should allow development of new array utilizing ferrite filled rectangular slots developed in the prior contract work of this group. DD FORM 1473 UNCLASSIFIED Si'cu rilyn (7I..ss1 i i i 1i c.,I

UNCLASSIFIED Security Classification 14. KE WRSLINK A LINK B LINK K EY WO RDS. R O L E WT WROLE WT R OLE W Y ANTENNAS FERRITE LOADING TECHNIQUES PHYSICALLY SMALL ANTENNAS UNCLAS5WpjF j __

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