Bimonthly Report No. 2 March 3, 1963 to May 2, 1963 5549-2-P STUDY AND INVESTIGATION OF A UHF-VHF ANTENNA by A. T. R. M. Adams Kalafus 5549-2-P = RL-2126 Approved by Jn A MZ Lyo John A. M. Lyon &fr, COOLEY ELECTRONICS LABORATORY Department of Electrical Engineering The University of Michigan Ann Arbor United States Air Force Air Force Systems Command Aeronautical Systems Division Contract No. AF 33(657)-10607 Wright-Patterson Air Force Base, Ohio June 1963

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TABLE OF CONTENTS Page LIST OF ILITSTRATI(NS X ABSTRACT vi 1. REPORTS. TRAVEL. AND VISITORS 2. FACTUAL DATA 1 2. 1 Rectangular Cavitv Variational Results I 2. 2. Experimental Verificati on of Variatiolal Data 15 2. 3 Efficiency of Ferrite Loaded Slot AntennL 24 3. ACTIVITIES FOR THE NEXT PERIOD 33 4. SUMMARY 33 REFERENCES 34 DISTRIBUTION LIST 35 iii

LIST OF ILLUSTRATIONS Figure Title Page 1 'a) Loaded rectangular waveguide radiator, (b) equivalent circuit. 2 2 Input admittance of a loaded rectangular waveguide radiator (Fn = 1.0 at cutoff). (a),r=E-= -.0. 4 (b) r =r = 1.5. 5 (c);r =r =2.0. 6 (d) M= E = 2.5. 7 r r re) Ar =r =3.0. 8 (f) = 4.0. 9 (g) A, =e - 5.0. 10 (h) gr =E r 6.0. 11 (i) - = 8.0. 12 r r (j) =e r 10.0 13 3 Dielectric loaded waveguide radiator; (a) front view, (b) side view. 16 4 Slotted dielectric and wedges. 17 5 Mounting of ground plane in Anechoic chamber. 18 6 Dimensions of slotted dielectric insert. 18 7 Experimental verification of variational data. Mor 1, er = 10 (a) Susceptance. 21 (b) Conductance. 22 8 Loss characteristics of ferrite powder material. Cutoff (Fn = 1) at 170 Mcs. 25 iv

LIST OF ILLUSTRATIONS (Cont.) Figure Title Page 9 Efficiency of ferrite loaded rectanglar slot antennas-comparison of theoretical and experimental data. 27 10 Theoretical efficiency of loaded rectangular slot antenna. 28 11 Efficiency of ferrite loaded rectangular cavity slot antenna. (a) d = 4" data taken with H. P. Bridge. 30 (b) d = 4" data taken with PRD S. W. D. 31 (c) d = 9 t' data taken with H. P. Bridge. 32 V

ABSTRACT Data on the aperture admittance of a loaded rectangular waveguide antenna are given and compared with experimental results. Theoretical efficiency data for a loaded rectangular cavity slot antenna is compared with experimental data. With powdered ferrite material presently available. efficiency -s 65 percent. Wit.h solid ferrite material presently available. theoretical results predict '20 percent efficiency. VI

REPtORTS. TRAVEL. AND VISITCRS During 'his period no reports were issued, no travel underTaken. and no one visited the project. 2. FACTUAL DATA 2. 1 Rectangular Cavity Variational Results A stationary expression for the normalized aperture admittance of a loaded waveguide radiator (Fig. 1) was formulated in QPR No. 9 (formula 8, p, 17). The expression was then expanded into the form shown on page 28 of QPR No. 9. the first term of which represents the dominant mode approximation to the aperture field. Dominant Mode Approximat ion y - G + jE 0 4i;. a b 2 - (b - (a- )(k - cos F ab 0 1 a a 10 0 0 -jk A) X.) t (r 2 0 a (I L 7 e ____ (k - ' du d: - 1 -

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-3 - p.r relative pernfwa1bilit.-' 4-, 1adi->._ nmte-ia1, k -material ', a. eum~e (ka at i k frj-e e parce~, a ve nm bei Tn —is double initen —ral has been- evaluated usi~ IBM 7090 computer. Prelimi: aNctaeepseecin BM2 Ax~ch covered t.-ie periociJna 9- oMLe 1963. Si~-ce then'. mre exten.sive data has bee:.- h.,taine ~cii reetc in Fig. 2. Trhe data is sufficientil'. extensive tco allow accurate inlterpolation.,, for intermediate values of b a, pa( and trequency.1 For all the data presenited.~ j is equal to,. However, each figure with a given-1 pL and rma- -be expanded tgie a familof figures for thre same I.L product but different p. ratios. Thi s rrr additional data is obtainedi v,1 multipl-~illw CL —e real andc ima;,-in-ar — part s opf /L (actual). the admittance bv- For inst AceFi.2eca he coneteat p.fgu reV (..: 5, 2) v-, multiplying B anid G by 3. Formulas for~ Larg-e ii p ~dcsrate an100, t e fl>i approximate formulas applw: 2 u (k0 a2 - m12 (k0 b)'3 rG0 (k b)(c- 1) 0 [cp )~.3 a 93 3a I(2 4) (c~+ 3)-2mI}::_. 4 -.. ka. b I k2 a2 _2;r a I1/2-:~ 2 rr

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- 14 - *. here: C k.) a 0 F V 1 B. Z - - Ir {227-T 2 wAh er-,e: tan h b, a H, 1 4 'log tan (19 + -~ - (s ec O A.j m',, 2 + I1 H1 a- tanl U bI sec & [ 1 -.Cos ilbctn tK b - - do aq ii, + j, Z I1 sec eH [ Cos ( — t )_ - a t a n o a b -i sin ( c~ o a Tm ( 1 2 2 sec to { I - Cos (I" )L I ) i a B (;"L ) 1 — I, 1 The above formulas were Ubried b assuming small angle approximations. for sin (k0 for sin (k and cos (k - c0

-15 - 2. 2 Experimem!al Verit;:i io. of Var iat ion Da A;n experinmenial check onl the vari:.-iional dt. was carried our. using Emerson and Cunming Siyci:st Hi-K with ch;-racterstics ( - l - 10). Equipment used in the experiment is shouwn r r i: Figs. 3 and 4. The 2' x 3' ground plane shown in Fig, 3 was mounted n ithe ground plane at the end of the Anechoic chamnber at the countermeasures laboratory. At the frequencies checked (2 - 4 kMc;. the Anrechoic chamber has very good characteristics. A sketch of the experimental arrangement is shown in Fig. 5. Light absorbing pads were mounted around the 2' x 3' groutnd plane to simulale as nearly as possible an infinite ground plane. Impedance was obtained by conventional slotted-line methods using an X-band slotted line. The geometry of the slotted dielectric insert is shown in Fig. 6. Because of the slot. the geometry differs from the theoretical model. Tapered dielectric wedges were also used (Fig. 4j. Impedance was measured both with and without the wedges inserted. The wedges were used to provide a measurement of the impedance of a geometry corresponding to the theoretical calculations. For the data measured. the impedance falls in a portion of the Smith chart where the constant G curves are very nearly parallel to the constant VSWR circles. Thus G can be determined by the magnitude of the reflection coefficient alone.

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-19 - The taper con:stitutes a;2radtual t.ri sf,:omai.:' fro;m t:e rectarnular dielectric cross section V th ) t —e slo-ttied dielectric crorss secti'f.i and introduces little reflection, at frequencies e tre tlhe taper lenrtlh is appre'iable compared t: the guide v avlelengti-. Near cut ff, t e refletl:iir introduced by the taper may become significait. T:us, at frequencies sli.'gh:tlv a6bove cutoff, tn-e VSWR and G measured sh'oiuld correspon!d to tnat of the t:e.:retical model. Tne value,f B depends,1, the tran:sformation: through te w-edge section. Since the electrical lengthi o(-f the wedg-ed secti:on) is takent into account b — a measurement of minimum position with a short or. the w-ave-uide, it would be expected that a minimum positiorn measuremenlt without the short would give an accurate measurement of the angle of the aperture reflection co,-efficient. The data without wedge represents an accurate measurement of the impedance of a oeometry- differing- firom the theoretical model. The data iith tVle w.edge represents a less accurate measurement of the impedan-ice of a -sgeomet rv identical to th.e teoretical model, with accuracy increasing as frequency, increases. The preset:ne of the sli;t iP the diele tric moaifies the cutoff wlavelength as well as the equivalent circuit of t:he disconltinluitv. Unfortunately, the effect of the slot cannrot be taken into account by perturbation formulas. Th_ b-oundar; co'ditins 3on E at the sides f the t (ur of the slot (surface A of Fig. 6: require continuity of E, while the x

-20 - boundary co-ndi ons at the bottom of the slot (surface B of Fig. 6) require continuity of E. According to perturbation formulas, x these two conditions would tend to change A g in different directions. g Thus the change in A due to the slot is not readily predictable from g boundary conditions. However. we know that guide wavelength has the form: _ 0 A, = --................... where: eff - effective dielectric constantt of the dielectric-guide and air-slot configuration. Two measurements of guide wavelength determine the two unknowns (: eff and f eff c Let ol. 2 /A 2 2 A A. gl g2 Then 1-A 1 - A c 1 A 1- 2 Using this method. f:-m s calculated using several measurements of c guide wavelength. The values variea from 2130 to 2177 Me with an average of 2160 Me. This value was used in plotting FN(Figs. 7(a) and (b)). The theoretical value for cutoff of a waveguide completely filled with dielectric material of dielectric constant 10 is 2080 Me.

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-'. 9') - t., Tigures (aad7b h'tersults of tire experime-'fal check. The experimental ard theoretical values of F show iooa ag~reement, the experimental dlata- 'w 'ith wBecwme falling ve-rv close to the tbeo~)..etical values. Tc~e resUlt' fil. G-) also appear to be acc.~urate, althoughi it is somewvhat more difficult to) o.btain a.,.- accu(-,mate c pri. Te experimental data ibo1n-i Figure?(b is slotteca assuming, a I:~,sless sample. If thj-,e atten.-)uation. is take,,, itraclm' h a measurement i tInc sample shttci te experimie,,tal datak app:,ac~eS.e t enetical data. Howeer, ome efiemet in 7-lique are necessarv oesr accurate attenuati-,,.n. measi-,reme-t s. Further tests ~xill be ariaout frvalues 4 '4 4 land 16.

-24 - '. 3l EffLiU emx::o, ut FerrTe Loaded Slot Anlt.l-ennl. The efficiency of a loaded rectangular cavity slot antenna was analyzed in BMR No. 1. Using the analysis for one of the simpler cases (probe:-ear aperture. low losses, magnetic losses only), theoretical data for efficiency w:a s calcul- ted aInd compared with experiment. From BMR No. 1 (pae 27) Magnetic volume losses only Efficiency - PL i t — PR PL 2d (k2 a - 27 sin 2 1 LR L a (1 - irn 2 k2 a2 - 2 (1 -JR k a? 2 9 where d - length of cavity R - complex aperture reflection coefficient ( k2 aR -" 10 -- - -aUsing the above formula, theoretical efficiency data was calculated for two cases, i -: = 3 and!; - c - 10. d was calculated using theoretical aperture admittance data (BMR No. I Table No. II). Figure 8 shows L'"/ '1' data for the ferrite powder material used in t: e experiments.

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06 - Figure 9 shows theoretical awc experimental data for the ferrite powder loaded rectangular cavity antenn,. Figure 1i0 shows theoretical data on01 for, ( 10. using the same;, ' data. The efficiency was measured using reflection techniques as described in QPR No. 10 and Ref. I. The tests were made in the anechoic chamber of the countermeasures laboratory. The rectangular cavity slot antennas was mounted in the large ground plane at one end of the anechoic chamber. Four aluminum "hats" of different sizes were alternately placed over the antenna and bolted to the ground plane. The impedance measurements with the four hats lie on a circle on the Smith chart. The efficiency. as defined in Ref. 1. is equal to 2 D1 D2 (D1 + D2) ( - D32 R2 ) where D1 = longest distance from Z to the eage of the circle. D2 = shortest distance from Z to the edge of the circle. 2 a D3 = distance from Z to center of the Smith chart. 3 a R - radius of the Smith chart. Z = impedance of the antenna in free space. a For the measurement of 2'. light lossy pads were placed on the ground plane and a large and a large (10' x 10') array of lossy pyramids was was placed in front of the antenna in order to reduce reflections as much as possible. Smith chart plots are shown in Fig. 11. Efficiency is calculated directly

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frm IK pb tsa h he, C ~ Fe7d ta'i> it"IC)~edi oss Efi i en c measu:eme-l~s ea -et a k e at 31 Meca a 2-a' Mc. r esults f or tru smple thl-eo-retical mno el sh~vx~~o ao-reemne:t between theor". an.d experiment. The lo-w f reriue cl case (22? Mc) Shows a 12'reate-r aiceiextra thle Knign frequencv case (31VF Mc,. Hloowever, thne expeirimet-~al acata fcW 1,1 22, Mc is less reliab~le, as is i, diaed- FiL. 1 1 (C,. Thne ti~eoretical dat a '4' Fig.,,- 10 P -ciie,4es effic-ien-cies 4i at-o(ut 20 per c-,,A. for a1 stolid ferrite material. E x -pe v rim n s V'. Pr a so1id!rt anin r newa iefce' me asiur em"' I s'Il he maaie fora f ur iFceck oni th-e the'-r-v,

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-33 -3. ACTIVITIES FOR THE NEXT PERIOD Two graduate students have been added to the project to aid in an investigation of loaded tran veling wave antennas. Emphasis will be placed upon the spiral and the log conical antennas. Further checks will be made on the theoretical variauonal data shown in this report. Impedance and efficiency characteristics of solid ferrite loaded and dielectric loaded rectangular cavity antennas will be investigated. 4. SUMMARY Extensive data on the aperture adm+ttance of a loaded rectangular waveguide radiator is given. An experimental check shows good agreement between theory and experiment. This basic data is used in calculations of bandwidth., resonant frequency. and efficiency. Theoretical and experimental values of bandwida'h and resonant frequency have been compared in previous reports Theoretical and experimental values of efficiency are compared in this report. Agreement between theory and experiment is good. showing promise for design methods based on this combination of variational techniques and Smith chart calculations.

-3 4 -RL FERENCES 1. Interim Engineer1-ing Repof` oi,-, Mil~la u e, Zero-Drag. Fi-oadbludlc. Tirr.'thle Cavity An'enn,-as'. IJul;%v o pteber 1953, o' ~V01~ aon Researcl 1n InsiT4-u-e. ContraCt No AF3fb d5