Bimonthly Report No. 6 November 2, 1963 to January 2, 1964 5549-6-P STUDY AND INVESTIGATION OF A UHF-VHF ANTENNA by J. E. Herman S. B. Rhee Approved by ohn A. M. Lyon COOLEY ELECTRONICS LABORATORY Department of Electrical Engineering The University of Michigan Ann Arbor 5549-6-P = RL-2130 United States Air Force Air Force Systems Command Aeronautical Systems Division Contract No. AF 33(657)- 10607 Wright-Patterson Air Force Base, Ohio March 1964

TlABLE OF CONTENTS Page LIST F ILLUSTRATIONS it ABS RACT lv 1. REPORTS, TRAVEL, AND VISITORS 1 2. PERIOD ACTIVITIES 1 2. 1 Ferrite Loaded Rectangular Slot Antenna 1 2. 1. 1 Optimization of Ferrite Filled Rectangular Slot Antennas 1 2. 1. 2 Ferrite Loaded Rectangular Slot Antenna With Iris 10 2.2 Log Conical Spiral Antennas 10 2. 2. 1 Large Log Conical Spiral 11 2. 2.2 Small Log Conical Spiral 11 2.3 Equiangular Spiral Antenna 13 2.4 Log Spiral Z i- Zag Antenna 20 3. FUTURE RESEARCH EFFORT 21 3. 1 Equiangular Spiral Antenna 21 3.2 Log Zig- Zag Antenna 21 3.3 Log Conical Spiral Antenna 21 3.4 Magnetic Tuning 21 4. SUMMARY AND CONCLUSIONS 24 APPENDIX A: Radiation Patterns for the Small Log Conical Spiral Antenna 26 APPENDIX B: Radiation Patterns for the Large Log Conical Spiral Antenna 39 ii

LIST OF ILLUSTRATIONS Figure Page 1. IT and bandwidth as a function of.r; for all points, rt " 9, b/a x.3, FN 1.8. (a) Tendency for efficietiiy to have a maximum. (b) Tendency for bandwidth to have a maximum. 4 2. Peaking of radiation efficiency (Aperture transmission coefficient squared). 7 3. Dependence of ILr (optimum) on,rfEr product and physical dimensions of slot (ka/r 1.9). 8 4. Ferrite loading for the large, log conical spiral antenna. (a) Loading with a thin uniform layer, type A material. (b) Loading with a tapered thick layer, type B material. (c) Loading with a uniform thin layer on the bottom half. (d) Loading with a uniform thick layer on the bottom half. 12 5. Ferrite loadings for the small log conical spiral antenna in a cavity. 14 6. Frequency vs. VSWR for the small log conical spiral in a cavity. 15 7. Spiral coordinates. 16 8. Log spiral zigzag antenna, construction details. 22 9. Frequency vs. VSWR for,the log spiral zigzag antenna. 23 A-i to A-12 Radiation Patterns for the Small Log Conical Spiral Antenna 27-38 B-1 to B-16 Radiationi Patterns for the Large Log Conical Spiral Antenna 40-55 iii *I.

ABSTRACT Design criteria for optimal use of ferrites in rectantular slot radiators have been established. Analysis firmly indicates that similar optimization can be achieved for annular slot antennas. Further experiments with log conical spirals have been performed which resulted in extension of frequency range. A log conical antenna taking full advantage of the frequency range of the available ferrite powder'hasbeen made. Final test results on this design will be available shortly. The thickness of ferrite surrounding log conical antenna elements appears to be a negligible factor. An analyticalAtUy of the equiangular spiral which can be adapted to the introduction of layers of ferrite has been completed. Computer results for specific cases are not yet available. Preliminary test data on a log zig-zag antenna using powderdi ferrite are presented, iv

1, REPORTS TRA ANDqJI VISITORS None 2. PERIOD ACTIVITIES 2. 1 Ferrite Loaded Rectangular Slot Antenna Further deductions and implications have been made concerning the utilization of ferrite material in rectangular slot antennas. Systematic procedures have been obtained which enable the optimum use of the ferrite material for the purpose of improving the efficiency of the antenna or increasing the effective aperture area for a given physical aperture size. Further preliminary analysis indicates that the optimization design procedures can also be applied successfully to rectangular slot antennas. 2. 1. 1 Optimization of Ferrite Filled Rectangular Slot Antennas. Utilizing the variational procedures upon the electronic computer it has been apparent that the irer product is a determining factor in many of the problems of interest. It therefore appears that an important design requirement is to establish the optimum Lr value for a given rer product and a given size of aperture. Another design consideration to be obtained is to establish the proper prEr product for a specific size of aperture. Finally, a third design requirement would be to establish the proper top-to-bottom dimension of a rectangular slot compared to the side-to-stde dimension of the slot when the slot is -1 -

filled with ferrite material. It has been tournd that the radiation efficiency can be maximized by a specit Ic vail e oir occurring in a given CrEr product when applied to a given aperture. The other two optimizations where mentioned above are not true maximum-minimum problems, but result in a monotonic type of variation in each case. However, the knowledge of the variation is helpful in the over-all design problem of such a rectangular antenna. In further consideration of the process of optimizing the value of ir as mentioned for a given MA r product in a given aperture, use is made of a series of computations on a 7090 computer. Details of the variational analysis have been presented in prior Bimonthly Reports Nos. 1 and 2. Some experimental confirmation of the computer results are presented in Bimonthly Report No. 3. From the results in these reports, the fraction of the transmitted power for an infinite wave upon the aperture depends upon IT Ia. The design procedure is then to calculate the maximum value of IT 2. Starting with the result of the previous reports there is the equation -R Y 1..- o = G + j (1) 0 IT1! 1 - IR1 — 4G- (2) 1 +G) +-B' In Eq. 2 let K = G/B. Then for a given physical size of aperture, a

given pr e product and given frequency, K wUl be -onstant since G and B are proportioroal to p T 1K (3) (! - KEB 1 Ba Equation 3 may now be differentiate, witn respect to B. d I T (4) where B /I (5) I + ka From this last equation the maximuml vAlue of IT is obtained: K2 / K2 ITI - - K (6) 1+ 1 + K2 It can be seen from the last expression that the maximum value corresponds to a value of pr which makes B i(k2 Figure 1 shows a plot of IT I and bandwidth as a function of r for the following parametric values: br r b/ a =.3 FN = 1.8

4.. H "1 2 3 4 5 6 7 8 9 Pr -- 10 I 8 I - t i 4 - 1 2 3 4 5 6 7 8 9 r Fig. 1. IT12 and bandwidtn as a function of u; r r F = 1. 8 a) Tendency for efficiency to have a nximumc (b) Tendency for bandwidth to have a maximum.

It is to be noted that the maximum value of ITIa occurs at ir = 6.8 and has been predicted by the equation for B above. However, the maximum value of bandwidth occurs for r = 5. 0. The reason for this is that as Mr increases the electrical length of the cavity increases. This effect tends to decrease bandwidth and leads for a bandwidth maximum at a value of ir slightly less than the Mr value corresponding to maximum IT I. The same reasoning would apply to the problem of maximizing the efficiency since the increase in cavity length will increase the losses incurred. It is very interesting to note according to Fig. 1 the maximum bandwidth is almost double that obtainable for the pure dielectric case (Ar = 1, r = 9). This is supported by the experimental data shown in Table I for the dielectric cavity and powdered-ferrite filled cavity. These antennas are exactly the same size and operate at almost the same frequency. Figure 2 summarizes the information on ITI2 since it is a plot of IT ' versus B with K as a parameter. Every plot of IT I versus Mr such as shown in Fig. 1 will lie along one of the constant K curves. For a given aperture size, prEr product, and frequency, K can be determined from the variational data. Then as ur varies the constant K curves describe the variation of IT I2 and B. Thus, the behavior of IT Ia has a function of Mr can be determined immediately from the curve of Fig. 2. Figure 3 shows the plot of optimum of ur as a function of the product Irer for ka/iI a 1.. It is to be noted that the

Table 1 COMPARISON OF RECTANGULAR SLOT ANTENNAS Size Air loaded Power loaded Solid loaded Dielectric loaded 30" x 7 " x 10" 12" x 3" x 4" 5' x2"x 1." 12" x 3"' x 41" Volume (cu.in.) 2250 144 15 144 BW with Flange BW-No Fla,,-r( VSWR = 3.0 VSWR = 6.0 VSWR = 3. OVSWPR 6. 0 (mc) (mc) (mc) (nic) 64 90 22 50 20 36 19 34 19 32 10 18 8 16 Eff. 90% 65% 30% 85% Dir. (deg) 5 8 5. 0 5.0 5.0 Weight (Ibs) 25. 75 16. 75 3.6 14.5 I { <73 I

I, - l - ITl2 Fig. 2. Peaking of radiation efficiency (Aperture transmission coefficient squared).

-8 - 10.0 9.0 8.0 *-4 -0a 0. Ti 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0 10 20 30 40 50 60 70 80 90 100 A E r r Fig. 3. Dependence of Ar (optimum) on re product and physical dimensions of slot (ka/in = L 9).

optimum value of Ir decreases with increasing rEr product. In consideration of the problem of the dependence of;rEr on the physical size of the aperture, a check of the computed data for G and B reveals that for a given physical aperture size and frequency different values of;r c yield almost exactly the same values of K. This agrees with the asymptotic expression for 1/K or B/G. This asymptotic expression is valid for large values of u r r. B 1 Fa (1) G 2 I b (k a/n) (7) This latter expression is independent of the;A r product and depends only on the free space electrical size of the aperture K. This implies that a further optimization would yield identical values of IT a. However, the bandwidth would depend not only on IT Ia but also on the rate of change with frequency of the aperture admittance parameters B', BA, and GA. BA and GA are proportional to 1//F7 1 and change very rapidly with frequency near cut-off. The rate of change of B' witt frequency is proportional to the bandwidth ratio plotted in Fig. 1. ThuE all parameters change very rapidly near cut-off and bandwidth improver monotonically as cat-off frequency decreases by Increasing the i rr,> 'Considerig the dependency of the two dimensions the toptam and the Adat d dimension ^th It ip

I observed that K varies approximately as (b/a). In addition, the maximum value of T' approaches 2K for small values of K. Thus, the IT I which was found to be roughly proportional to bandwidth and frequency has now been found to depend upon (b/a)f indicating that the dependents upon the "b" is not very pronounced since it is a square root dependency. 2. 1. 2 Ferrite Loaded Rectangular Slot Antenna With Iris. A further study of appropriate design procedures for maximizing the performance of a rectangular slot antenna using an iris in the aperture plane has been made. The details of the validation of the design procedures are to be found in the final report on rectangular slot antennas utilizing ferrite which is in preparation. However, in the case of slots having irises, the effect of an increase with Mr is to increase the length of the cavity and the optimum efficiency and bandwidth values occur at slightly lower values of r. 2. 2 Log Conical Spiral Antennas As a continuation of the work of the previous period, several different types of ferrite powder loading and their effects on pattern and voltage standing wave ratio (VSWR) were studied. The studies were carried out on the same log conical spiral antennas used previously. Two types of ferrite powders were used during this period and were designated types "A" and "B". Type A powder has the best magnetic Q over the frequency range 100-900 Me but only a limited

quantity is available. Type B powder is of inferior quality but is available in quantity and was used for preliminary tests where radiation efficiency was not a prime consideratio:n. Tis was acceptable for studies of the effects of loading on the radiAdtion patterns of the antennas. 2. 2. 1 Large Log Conical piral. Results obtained by loading the antenna with a thin uniform layer of type A material were reported in BMR No. 5 [Fig. 4(a)]. During this period, type B powder was used to form a tapered thick layer [Fig. 4(b)], a uniform thin layer on the bottom half of the antenna [Fig. 4(c)], and a uniform thick layer on the bottom half of the antenna [Fig. 4(d)]. For each type of loading, radiation patterns were taken for E and E at frequencies of 350 Me, 500 Mc, 700 Mc, and 900 Mc. 0 These are shown in Appendix B. The dimensions of the antenna are as follows: Base diameter 17. 5 cm Apex diameter 5. 0 cm Height 47.0 cm Apex angle 15~ Pitch angle 73~ 2. 2. 2 Small Log Conical Spiral. This antenna was designed according to Dyson's design data. The dimensions are as follows: Base diameter 13. 0 cm Apex diameter 6.0 cm Height 30. 0 cm Apex angle 10~ Pitch angle 73~ J^*n D. Dyson, "The Unidirectional Equiangular Spiral Antenna," IRE h sations on Antenna and Propagation, October 1959, p. 329. **S '*^ ^ -"- J^ L — _

-12 - 1 T I I Ferrite 2 2 Fig. 4a Loading with a thin uniform layer, type A material. Fig. 4b Loading with a tapered thick layer, type B1 material. I I I i 1 " -2 I. r t1 4. e' I Fig. 4c ading with a uniform thin layer on the bottom half. Fig. 4. Ferrite loading for the Fig. 4d Loading with a uniiforn thick layer on the bottom half. large log conical spiral antenua:-.

-13 - An aluminum cylindrical cavity was made to adapt the conical spiral to flush-mounted operation. Several different types of loading with type A powder are shown schematically in Figs. 5(a) - 5(d). Radiation patterns for each lading were taken for E and E0 at frequencies of 500 Me, 700 Mc, and 900 Mc. These are shown in Appendix A. Figure ishows frequency versus VSWR for the various types of loading for the small log conical spiraL 2. 3 Equiangular rpiral Antenna During the period a mathematical expression for the radiation fields of the equiangular spiral thin-wire (or slot) antenna was found. This expression is adaptable to solution using the IBM 7090 computer if the current distribution and mode of excitation are specified. Consider the planar monofilar spiral shown in Fig. 7, where (r', ') are source coordinates, (r, 0, 0) are field coordinates, and r" r - r' 1. The magnetic vector potential for a thin current distribution in space is 01 l_(1') ejkr" Airr dl'1 (8) spiral where the e wt time depende'.e is understood. In the radiaion field pbase variations are taken ito account by. S r" r G r' stZ 0 coP(0-0'). (9) The equation of the equiangular spiral is

-14 - Air Ferrite Cavity / (5a) (5b) 1" (5c) (5d)j Fig 5. Ferrite loading for small log conical spiral antenna in a cavity.;

Small Log Conical Spiral With Cavity 0 aC: Ca 0 10 9 8 7 6 5 4 3 2 i! I L 400 600 800 1000 1200 1400 1600 Frequency in Me. Fig. 6. Frequency versus VSWR for the small log conical spiral witii cavity.

-16 - Q' z ' I - --- -- Fig. 7. Spiral coordinates

-17 - r' I r a^ (10) whence di' r l/(dr'a^ rj * +1 a T" rO *0 d (11) and f di' r (e' - 1). (12) 0 a= ( The direction of the segment d ' as shown in Fig. is given by A A A si n(V - 0') x + cos(*' - ) y (13) where dr' tanv/' = r - a. (14) Since it is reasonable to assume the antenna impedance satisfies a variational expression, a zero order approximation to the current distribution may be made with only a second order error in the results. The zero order approximation to the current is that of a curved two-wire transmission line with no coupling to surrounding elements. This gives a current depending only on the distance (1') along the line from the feed point, L e., a traveling wave, L(_'). o [eY' + r'e ] I; (Y ' -a+J ) (15)

-18 - where I' is given by (5) and r is the reflection coefficient. Thus the vector potential may be written as A() (r,,0) jr [ e + re "] *+ * r 0. [.-lJ^o sin co(0 - )')] [sin(i/ - 0') x + cos(,' - 0') y] * [ +a r e0 '] do' 0 (16) For total reflection at comes the end of the wire the reflection coefficient be r =e2rL; L r (e'a -1) a+* (17) In spherical coordinates, the radiation field is related to the magnetic vector potential by E -jwA; E -JwA0 (18) where A = A cos + A cos +A sin 0 A = -Ax sin 0 + Ay cos 0. (19) Thus, if A is known the field can easily be found.

-19 - Consider the btfilar spiral with the currents in the two wires out of phase by an angle A at the feed. Then the total magnetic vector potential wil be given by A(r,,0,t) - A(l)(r,,, t) + A(1)(r,0, +, t + ) (20) Thus for balanced excitation (A = w) the total magnetic vector potential is A~I~ ~/10kX + r' A(r,e,0) - - ~ r- er e(...r. aa' o e * {E(-a + rl er' - e ( IF r' (2e~ 0 o a/ l ar V at ~ cos [krO sin 0 cos(0 - 0') e^] ea0' A [sin(V' - 0') cos 0 + cos(P' - 0') sin 0] cos A 0 + [cos(' - 0') cos 0 - sin(*' - 0' sin 0] d. (21) For convenience the following substitutions may be made: z = a0 z = aB at * a 1+- r aa 0 ~a 0

kt m krt 0 B J -J /i Go r' e r (22) o r The pattern may be found for a0 oora0 v cut. For the 0 o cut, Eq. 21 becomes A(r,, o) = Bea e(a'a + Jj*) e( ')(2e - z)] (23) cos [k' sin a cos e] e [sin(' - ) cos 0 0 - cos(' - 0] dz Equation 23 gives a set of integrals which may easily be evaluated by numerical methods on the computer. Whence, the magnitude and phase of the field components may be tabulated for each set of parameters. The application of this method to a ferrite loaded antenna presents a difficult boundary value problem. However, it is hoped that a thin layer loading may be simulated by merely assuming the current propagates in a "slow-wave" mode, i. e., by assuming B = vi k. A computer program has been written and test data are being run. It is hoped that a full set of theoretical and experimental curves will be available for inclusion in the next bimonthly report. 2 4 Log Spiral Zig-Zag Antenna A log zig-zag antenna was designed to take advantage of its reduced volume with frequency independent characteristics similar to

-21 - those of the log conical spiral. The dimensions used are shown in Fig. 8. An initial test of the VSWR for a 1/4" thick uniform layer of type A powder was made and compared with the air loaded case (Fig. 9). 3. FUTURE RESEARCH EFFORT 3. 1 Equiangular Spiral Antenna A continuing effort will be made to obtain theoretical and experimental patterns of the equiangular spiral, including the case with a thin ferrite load. 3.2 Log Zig-Zag Antenna During the next period, the effects of loading on beam pattern will be observed. Also a cavity will be constructed so that the antenna may be adapted to flush mounted operation. 3. 3 Log Conical Spiral Antenna A successful conclusion is anticipated for the experimental investigation of the log conical spiral. Investigation of the theoretical problem will continue. 3.4 Magnetic Tuning A model of the solid ferrite-filled rectangular cavity-slot antenna delivered to WPAFB is currently being constructed for use in determining the effects of strong magnetic bias on the radiation properties

-22 - I i I I T Fig. 8. Log spiral zigzag antenna construction details.

-23 - Log-Spiral Zigzag Antenna 3 Cfl 10 &9 -8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 - Ferrite filled -—. Air filled - -- --- I I I 4 200 400 600 800 1000 Frequency in Mc Fig. 9. Frequency versus VSWR for the log spiral zigzag antenna.

of the antenna. Preliminary measurements previously reported indicate that the resonant frequency of the cavity may be varied by introduction of a magnetic field across the antenna. This has the effect of varying the permeability of the ferrite material. In particular, the ferrite becomes anisotropic in the presence of a magnetic field. 4. SUMMARY AND CONCLUSIONS A study of design procedures for ferrite-filled rectangular slot antennas has resulted in an optimal design requirement corresponding to the proper selection of the value of relative permeability for the highest radiation efficiency of the antenna. A further study of an available variational analysis of the annular slot antenna shows that the same optimization of radiating efficiency can be made for the annular slot using ferrite. Best results on pattern, bandwidth, and radiation efficiency of a log conical spiral antenna can be obtained with a uniform loading of ferrite powder, although the thickness of the ferrite layers on each side of the conductor does not appear to be of great influence. So far major changes in radiation pattern have not been observed using ferrite. It is believed a more detailed analysis and testing program may show frequency regions where directivity increases and also frequency regions where this directivity may decrease. The latter is anticipated to some extent because of the miniaturization accomplished through the use of ferrite. Other workers have observed increased directivity of a helical

antenna using a hollow dielectric circular cylinder as a core. Since, to date, only preliminary work performed loading of the equiangular spiral and the log zig-zag antenna, no conclusive results have been obtained,

- 26 - APPENDIX A RADIATION PATTERNS FOR THE SMALL LOG CONICAL SPIRAL ANTENNA

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38 200 -I 6() ' 70 4 1 IN 14 F" V 4 34 14 3 I.. A. I..:1", 1 V4, A 0* Pr0 1 80' 1,o I 900 1600 200,3 I5G 2100 A. - - - -- - i It jgmall K7 1' 2 1w 230* w dw4kd%*. Li, - I F i,...,, '.. ,. - - - -1 - - - -. --. -.. i 4 i i. - - -.. I I '.. i ft 7ddtlw!! I I I I I IL-A- q.. -F-R jT -I"Wlr 11 40 0 I I I I I 2W. 2w 50 3o' AVA ~V, I - k air~ I V, - q.., 11 if. 144. -. 'B

-39 - APIPEL.INDLX IA IA\DIATION PATTEtNIN FOR THE LA,;-x2RG E. LOG i, A L SP R AL t, ANTE, NNA

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