FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFS OH F/6 9/5. AD-Al03 128

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1 k I AD-Al FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFS OH F/6 9/5 PROBLEMS OF THE OPTIMAL CONSTRUCTION OF FERRITE PHASE SHIFTERS -- ETC (Ul JUL 8I A K STOLYAROVP I A NALUN0V END

2 0,FOREIGN TECHNOLOGY DIVISION I~ PFROBLE;I-S OF THE OPTIMAL CONSTRUCTOM OF FERRITE PHASE SHIFTERS WITH RECTANG"ULAR HYSTERES L0 l by A. K. Stolyarov, I. A. Naumov TI iapproved for public release; diztribution unlimited.,,:) Vi "I[ l ii "'_.

3 EDITED TANASLATION FTD-ID(RS)T-/ Ju 818 MICROFICHE NR: FTD-81-C YROBLEMS OF THE PTIMAL ;ANSTRUCTION OF F:RRITE jiase HIFTERS WITH CTA; STERE LOOP Traslte 'A. K.S o brt I. A./ill,.-i..,,i r Antennyd- " THIS TRANSLATION IS A RENDITION OF THE ORIGI. NAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OR EDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED BY: ADVOCATEDORIMPLIEDARETHOSEOFTHE SOURCE AND DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION OR OPINION OF THE FOREIGN TECHNOLOGY DI. FOREIGN TECIHNOLOGY DI VISION VISION. WP.AFB. OHIO. - II II '" "+ 11 F- I j+ II - -+ I '( u mdateit ed ,... =". ' t..

4 U. S. 60ARD ON GEOGRAPHIC NAiMES TRANSLITERATION SY'T7EMT. Block Italic Transliteration Block italic Transliterati. A a A a A, a P p p p R, r b 6 6 B, b C c C c S, s Be V, v T T T m T, t. r i G, g Y y y y U, u 1D, d b F, f E e E i Ye, ye; E, e* X x X x Kh, kh hm C c Zh, zh LA U j Ts, ts Z, z H V V Ch, ch H m l4 U I, i W W LU &m Sh, sh 1 i R a Y, y 11/ aqiuu Shch, ziich HK K, k b 2 % ",7 BA L,l i u Y, y M M.m - b H H H ' N, n 33 j E, e 0 o 0 o O,o k 10 Yu, Yu n n f7 M P, p 1 A N i Ya, ya *ye initially, after vowels, and after b, b; e elsewhere. When written as 6 in Russian, transliterate as y6 or e. RUSSIAN AND ENGLISH TRIGONOMETRIC FUNCTIONS Russian English Russian English Russian Eng..:-!-. sin sin sh sinh arc sh s i.h Cos cos ch cosh arc ch cosh, tg tan th tanh arc th tann ctg cot cth coth arc cth cu.th sec sec sch sech arc sch sech cosec csc csch csch arc csch csch Russian rot lg English curl log.~ - - fl

5 PROBLEMS OF THE OPTIMAL CONSTRUCTION OF FERRITE PHASE SHIFTERS WITH RECTANGULAR HYSTERESIS LOOP A.K. Stolyarov, I.A. Naumov The article gives results of the calculation of a unidirectional waveguide phase shifter, which is presented in the form of ferrite dielectric waveguide magne.tized by a ring magnetic field, the ferrite having an arbitrary thickness. The problem of the propagation of the electromagnetic wave along a two-layer dielectric rod is strictly solved, and the unidirectional effect is found by the perturbation method. A calculation of the waveguide phase shifters with ferrite having a rectangular hysteris loop (PPG) was carried out in work [1]. The phase shifter was presented in the form of a dielectric waveguide covered by a thin layer of ferrite. For practical purposes it is important to examine the more complex system in which the ferrite can have an arbitrary thickness. Examined for this purpose is *,he propagation of a wave along the two-layer dielectric waveguide (Fig. 1), and then calculated by the perturbation method is the unidirectional phase shift under the assumption that the external dielectric cylinder (rdgion II) possesses gyromagnetic properties. The selected method allowed avoiding complex expressions in the form of series for the constant propagation and quite simply analyzing the effect on the magnitude of the phase shift of dimensions and parameters of the dielectric and ferrite cylinders. I

6 IO. Fig. 1. Key: 1) Region 1; 2) Region 11; 3) Region III. For waves of the HFE,. type, the initial fields are recorded in the form: i region III (r/r 2 2.* p2ctkj (pr) sin q II E O i[, CiKj(pr)- KopC2.Ki(pr) Cosq 4Fla K s r (sb) H,= i [AoPCK';(pr) - -O C 2,K (pr)] sin where Yo is the constant of propagation; K'(pr) - the McDonald function and its derivative; Ko=-;p-=v,--K; K,(pr). region II (rl r <r 2 ) E, = g [ BJJ (g 2 r) - B'N 1 (gd')] sin t.. Y, O 2 [BIJ' (gj) + BN, (g2r)] - A IBBJ1 (g,r) + -D.I (g:l ]sin qp (2a) E. f _ IBJ, (g r) + BNt (ggr)) - K 0 gbaj (g 2 r) + I r BDN; (gr)]} cos( 2

7 t1t?0= g' (BJ 1 (.,r) + B4N, QI!r)] cos q) H O I.O g' 18 J (jr)-4-,n,(g 2 r) J - "- e, (1I1, (g 2 r) + 1 r - B3N 1 (gr)]} cosq (2b) H, = i { O g: I B, J; (g 2 r) -4- O 2,N (g 2 r)] -Y-e IB,J, (,r) + + B 4 N, (g 2 r)jj sin i where 2 11(gr),,(gr), N 1 (r), N,(gr) are Bessel functions of the first and second kind and their derivatives; region I (r r 1 ) E,= g2 A1,, (g 1 r) sin 4p O=i A 1 1A (gir) - KO~g 1 AsJI (9 1 r) Co (P~a I (g= 1r) - -LO A 1 J 1 (gr)] sin 9 HO = g2 A.J, (gr) cos q1 (3a) H, ik i g 1 A.! (ger) - -!!- A 2 Jh(g 1 r) ]sin q HO iy9 = giaj(91r E 1 A 1 J 1 g cos q)(b From boundary conditions when r=r 1 and r=r 2, we obtain eight homogeneous equations, from which the relative values of coefficients A, B and C and the propagation constant can be determined. The determinant of the indicated system of equations has the form: i ixogla KO- -i--p - V-. KOthe ikg -, 0 0 It rx '1 o - -2P i KogIsa _ ie ixoi A..- I ri g21 gl p2 y Y i. 0 0 r *-gy 2 0 o ikc~g 2 A -i~gjv - i 2 -p r 0,K rs rt r, o 0 g p 0 o 0 0 1x o : A i~ao KO,F " -- i --) ikopi -A 0H g p 2 1 ) 3

8 where,..- J (ir 71 - A (g,) :.,.) J- :-') _ ' J; ( r ) Jz gil)j, (girl) 'I Ig.r)J (gzr: K, (p(g ir l)(g,) =g. ; (r,) in [2]. The tensor of the magnetic permeability of the ferrite is given The magnitude of the nonreciprocal increase in Ay of the propagation constant is determined by the perturbation method: k 3 (H H" - HHI) ds [, E, H.]dS r~~~~ ~~ Ay= where S is the total area of the cross section throvgh which the electromagnetic wave passes; S 2 - from (1), the area of cross section of the ferrite. Having substituted into equation (5) expressions for fields (2) and (3), and assuming for ferrites with PPG that t4=l, we obtain the final formula for Ay. Part of the integrals entering into the final formula for AV are tabular, and the remaining ones are computed according to the Simpson method. Let us examine the case when the dielectric constants of the ferrite and dielectric are considerably different. that Let us assume zj>e2 ; then at a definite value of r 1 the wave propagation constant Y0 will be greater than Koj/-, and the transverse wave number g 2 will become imaginary. In this case functions Jl(g 2 r) and N (g 2 r) should be replaced in all formulas by functions I (g 2 r) and K (gr), and in the determinant (4) they should be changed to the 1 122~2 opposite signs near terms containing the factor g 2 " A similar change in the formulas in the calculation process should be made in those cases when tz ",, and the transverse wave number g, becomes imaginary.

9 Let us examine the effect of the thickness of the ferrite on the quantity AY. First of all, let us discuss the simplest case when the dielectric constant of the ferrite and the dielectric are identical ( E1= 62). The corresponding calculation curves are given on Fig. 2. From them it is clear that the maximal nonreciprocal effect is reached when r =0, i.e., in a solid ferrite cylinder. The replacement of part of the ferrite by the dielectric [r 1 =O.03; 0.05; 0.1 ),01 changes the nature of the relation.\-i(r~ ; however, the absolute magnitude of the unidirectional [nonreciprocal] phase shift is decreased with an increase in r 1 Therefore, the use of the dielectric with the same permeability as the ferrite can be useful only for control of the shape of the frequency characteristic of the phase shifter. C - - _ " 4'15 Fig. 2. A comparison of curve rl=o on Fig. 2 with results of the precise calculation [4) shows that the maximal unidirectional phase shift takes place in both cases at practically identical diameters (an error of not more than 10%) of the ferrite cylinder; although, from the viewpoint of the approximation theory this case is most unprofitable, since the entire volume of the dielectric undergoes a disturbance. ihis confirms the expediency for using the perturbation method for solving similar problems. 5l

10 Let us now examine the effect of the dielectric on the operation of the phase shifter for which a discusion of curves 3, 4 and 5 is given. At small values of r 1 (r 1:=0.0 0) the value of A-Y is close to that value which corresponds to the solid ferrite cylinder (Fig. 2). With an increase in the diameter of the central dielectric (r,=0.03; 0.04 lot etc.), the magnitude of the differential phase shift is increased and at a certain r I reaches the maximal value. Consequently, for each value there are such dimensions of the dielectric and ferrite at which the greatest activity of the phase shifters is reached. Figure 5 gives the generalized curves according to which the maximally possible magnitude of the phase shift (A majc) for dielectrics with different e can be determined. Just as in the case of a thin ferrite [1], Ay inreases with an increase in 6 of the dielectric. J l - k,4o5a i/ 0,o?O' 'YO EP3 ID, Fig. 3. Fig. i4. An important difference consists in the fact that the unidirectional phase shift reaches a maximum value at the smaller diameter of the ferrite. Thus when l -10 Ay reaches a maximum ata diameter of the ferrite of d 2 0.4l 6 0 and in a thin ferrite tube the

11 maximum is observed when d 2=0.24 X. This denotes that by using the ferrite cylinders of' optimal diameter, it is possible to lower considerably the magnitude of the control current. The use of a dielectric with high C makes it possible to reduce significantly the length of the phase shifter and, consequently, decrease the energy of commutation, the magnitude of which is proportional to the volume of the ferrite. Let us note that owing to an increase in of the dielectric, it is not possible to lower the control current substantially, since the optimal diameter of the ferrite (Fig. 6) is insignificantly decreased with an increase in E of the dielectric , go' '0, ' C J0 Fig. 5. Fig. 6. The curve which determines the wave propagation constant along the dielectric waveguide is plotted on Fig. 6. It indirectly characterizes the correctness of the selected model. As we see, the slowing down of the wave in the optimally fulfilled designs is significant, and, therefore, the metallic walls of the waveguide introduce insignificant corrections into the obtained results. Bibliography I. Stolyarov, A.K., Naunov, I.A. Radiotekhnika i elektronika [Radio Engineering and Electronics], XII, 5, 1967, p Mikaelyan, A.L. Primeneniye ferritov na sverkhvysokikh chastotakh [The Use of Ferrites at Superhigh Frequencies]. GEI [State Power 7

12 Engineering PresL], Nikol'skiy, V.V. Radiotekhnika i elektronika, 1957, No. 2, p Yurgenson, R.R., Teytel'baum, I.G. Collection: Antenny [Antennas], edited by A.A. Pistol'kors, 1966, No. 1, p

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14 DATE FILMED 'Irv.10 DTIC