ELECTRICAL ANTENNA

CHARACTERISTICS

IN GYROTROPIC

L . M. O b o l e n s k i i , Yu. Ya. Yashin

Yu.

OF

A RECEIVING

MEDIA V. C h u g u n o v ,

and UDC 621.396,67

Based on the "generalized" r e c i p r o c i t y t h e o r e m , it is shown that the c h a r a c t e r i s t i c s of a d i pole whose dimensions a r e s m a l l c o m p a r e d with the wavelength coincide in their reception and t r a n s m i s s i o n modes in a magnetically active p l a s m a .

The p r o b l e m of d e t e r m i n i n g the e l e c t r i c a l c h a r a c t e r i s t i c s (impedance, radiation p a t t e r n , effective altitude) of a radiating antenna placed in a magnetically active p l a s m a has been considered r e p e a t e d l y (see, for e x a m p l e , [1-4]). However, in e x p e r i m e n t s a s s o c i a t e d with m e a s u r e m e n t of e l e c t r i c field intensity in the ionosphere at low frequencies or in a l a b o r a t o r y p l a s m a , as well as in a number of other c a s e s , it is n e c e s s a r y to know the c h a r a c t e r i s t i c s of the p r o b e (antenna) operating in the r e c e p t i o n mode. In m e d i a having a s y m m e t r i c a l d i e l e c t r i c - c o n s t a n t t e n s o r , it can e a s i l y be shown on the b a s i s of the e l e c t r o d y n a m i c r e c i p r o c i t y t h e o r e m that the e l e c t r i c a l c h a r a c t e r i s t i c s of the r e c e i v i n g and t r a n s m i t t i n g antennas a r e equal [5]. In g y r o t r o p i c m e d i a the r e c i p r o c i t y t h e o r e m is not applicable in the conventional f o r m , while d i r e c t calculation of the r e c e i v i n g antenna frequently p r e s e n t s considerable difficulties. In the p r e s e n t p a p e r it is shown on the b a s i s of the "generalized" r e c i p r o c i t y t h e o r e m [6], that in the c a s e of a m a g n e t i c a l l y active p l a s m a (neglecting the t h e r m a l motion of the p a r t i c l e s ) the c h a r a c t e r i s t i c s of a short dipole (the dimensions of the dipole a r e much s h o r t e r than a wavelength) in the reception and t r a n s m i s s i o n modes a r e equal. 1. We shall s t a r t f r o m the generalized r e c i p r o c i t y t h e o r e m [6]:

.f .~m (r) E (2) (r, Ho) d r .... Ji' J.'r()2:'l(m E'j) (r, --Ho) dr,

w are htheLF~e i w ] (h1t!~~e' ~are rre a tetehde]bdye~nt hs(letm i~e.s o f l ~hH: ? : t h : = : r U [ a ~ : t h i ~

(i)

firstfield.and second antennas; E(l) and E(2)

Let us write the v e c t o r s j and E in the f o r m J = Jx + ij~ =_ j,)e~Y,

(2)

E = E l + i E 2 = E~e i+= ~ f e i'~,

where J0, E0 are the amplitudes, and Y and #2 a r e the p h a s e s of the c o r r e s p o n d i n g v e c t o r s ; f = f i + i f 2 is the p o l a r i z a t i o n v e c t o r which is n o r m a l i z e d as follows: ( f f * ) = 1. Below it is a s s u m e d that the dipoles are in an illuminated region (i.e., they are within the limits of the radiation pattern), and t h e r e f o r e only homogeneous waves a r e considered. For such waves p r o p a g a t i n g in a m e d i u m d e s c r i b e d by a h e r m i t e d i e l e c t r i c - c o n s t a n t t e n s o r eij , we have the relationship [7] S c i e n t i f i c - R e s e a r c h Radiophysical Institute, Gor'kii University. T r a n s l a t e d f r o m I z v e s t i y a VUZ. Radiofizika, Vol. 12, No. 12, pp. 1776-1779, D e c e m b e r , 1969. Original article submitted June 20, 1967; r e v i s i o n submitted June 6, 1969. 9 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street~ New York, N. Y. 1001t. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

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E(--H0) -- I ( - H o ) r

= f*(H0) r

(3)

The field of a s o u r c e in the wave zone in a given direction may be r e p r e s e n t e d in the f o r m of a quasiplanar wave having an amplitude which depends on distance and a polarization vector which coincides with the polarization v e c t o r of a normal plane wave propagating in the same direction. The amplitude of the field is s y m m e t r i c a l with r e s p e c t to It 0 [7], and t h e r e f o r e Eq. (3) may also be extended to the field of a point dipole in the wave zone. Note that (3) is also valid for a weakly inhomogeneous medium. For a c e r t a i n dipole of length I (l << X, where X is the wavelength in the medium), we have the e q u a tion (4)

j(oz)f(1)*(Ho) = j(o2)f (1) (I-1o) e -iz

where tg X : (jl2)f~2))/(j~2)flI)). The physical meaning of the l a t t e r relationship is obvious. As is well known, a wave propagating in a magnetically active p l a s m a has elliptical polarization. The real and imaginary p a r t s of the p o l a r i z a t i o n vector f (and t h e r e f o r e of the vector f * also) c o r r e s p o n d s to the directions of the two conjugate half-axes (in general, not the principal ones) of this ellipse. Thus, the projections of the e l e c t r i c fields f r o m the polarization ellipses f and f * onto the straight lines coinciding with the dipole axis a r e p h a s e - s h i f t e d relative to one another. This additional shift is determined by Eq. (4). Summarizing, we shall r e p r e s e n t (1) as follows, taking account of (2)-(4):

S dimO :0) E(2) :O) o E(t) exp [i (7o+,bl)+ix]. o exp [i(7~+,~)] d r = jf' dim , Bdr,

(5)

where B denotes a c e r t a i n amplitude factor. 2. Below we shall a s s u m e that the i m p r e s s e d antenna, tf it is likewise assumed that the intensity the dipole c r o s s section, one may go over f r o m Eq. p r o c i t y t h e o r e m for two antennas in a magnetically t h e o r e m was given, for example, in [8] in a s i m i l a r

li ,,.

emf is applied to a c e r t a i n given small segment of the of the i m p r e s s e d field is uniformly distributed over (5) to the following f o r m of the electrodynamie r e c i active p l a s m a (for an isotropic medium the r e c i p r o c i t y form):

(6)

= ---=" B e ~ , 121

where $'1 and ~'2 are the emfs applied to the first and second dipoles; I12 is the amplitude of the c u r r e n t which is produced in the first dipole by the field of the second; [21 is the amplitude of the c u r r e n t in the second dipole induced by the field of the first.* The quantity 7?denotes a certain additional phase d e t e r mined by Eq. (5), and its specific f o r m is not essential for the subsequent analysis. Making Use of (6) and then proceeding as is done in the m a j o r i t y of monographs on antenna theory (see, for example, [5]), we obtain the relationship Ik(Zkq-Z~ ~) e", ................... E J T e k F k ( % O, 0,)

N = consi

(7)

where I k and E k are r e s p e c t i v e l y the c u r r e n t at the dipole t e r m i n a l s and the projection of the electric field onto the direction of the dipole in the reception mode. All of the remaining p a r a m e t e r s of (7) r e f e r to the antenna in the t r a n s m i s s i o n mode: hek is the effective dipole height; F k is a c e r t a i n function which c h a r a e t e r i z e s the directivity p a t t e r n and the orientation of the dipole relative to H 0 (01 is the angle between the dipole and the external magnetic field); Z k is the impedance between the dipole t e r m i n a l s (k = 1,2,...,m is the dipole number). Since the quantity N will be the same for any dipole r e g a r d l e s s of its orientation relative to H0, it is obvious that N is a universal constant. *All of the quantities indicated above apply to the antenna c r o s s section considered.

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3. The equality of the input impedance Zak of the antenna when it operates in the reception and t r a n s mission modes may be demonstrated using the superpos[tion principle and the t h e o r e m concerning an a c , tire two-port (Thevenin's theorem) [9].* Let us note that the only assumption included in this p r o o f concerning the media surrounding the antenna is their tinearity. Using this fact, one may write the e x p r e s s i o n s for Z k + Zak in Eq. (7) in the f o r m Zk(re)~_ Za(re) .~ Ek(re)Ite k(re) F k(re) Ik(re)

(8)

Substituting (8) into (7), we obtain (..h~(re)Fr~ / = A1 exp (i'%). \he(tra) Ftra /

(9)

Since N is a universal constant, one may use the simplest case, in which both dipoles are situated in a vacuum, to determine it (this can easily be understood if the r e c i p r o c i t y t h e o r e m for dipoles in a weakly homogeneous p l a s m a which e m e r g e s into a vacuum at some distance f r o m the first p a i r of r a d i a t o r s is a p plied consistently). Then, s i m i l a r l y to the way in which this was done in [10], it may be shown that N = 1. With allowance for this, it follows immediately f r o m Eq. (9) that he(re)k = he(tra)k, Fre k = F t r a k exp(iPk), i.e., the effective lengths of a short dipole are equal in the reception and t r a n s m i s s i o n modes, while the radiation patterns differ only by a phase factor. For short linear antennas the phase factor is unessential. The difference between the radiation pattern of the receiving antenna and that of the t r a n s m i t t i n g antenna by a phase factor may be explained as follows. Assume that a t r a n s m i t t i n g antenna which is oriented in a specific way relative to H 0 and is excited by some stipulated amplitude c r e a t e s a field having the a m plitude 9 , the polarization 3r and the phase q~ at a certain point in space. Let us place an identical t r a n s mitting antenna at the reception point (its orientation relative to H 0 and its i m p r e s s e d c u r r e n t are the same). Then the radiation field of this antenna at the initial point coincides in amplitude with ~, but differs in polarization and phase. In o r d e r to achieve complete coincidence of the field, it is n e c e s s a r y to change the orientation of the radiating (or receiving) dipoles. In conclusion, the authors thank V. L Talanov for his discussion. LITERATURE 1. 2. 3. 4. 5.

CITED

T . R . Kaiser, Planet. Sp. Sci., 9, 639 (1962). V . P . Piati and H. Well, Radio Sci., 69, 291 (1965). H. Staras, IEEE T r a n s . and P r o c . , Al~-12, 695 {1964). Yu. V. Chugunov, Izvestia VUZ. Radiofizika, 1._ll, No. 1, 50 (1968). G . Z . Aizenberg, Shortwave Antennas [in Russian], Gos. [zd. Liter. po Vopr. Svyazi i Radio, Moscow,

(1962). 6. 7. 8. 9. i0.

V.L. Ginzburg, Propagation of Electromagnetic Waves in a l~lasma [in Russian], GIFML, Moscow (1960). Yu. Ya. Yashin, Izvestia VUZ. Radiofizika, 9, No. 6, 1108 (1966). E.L. Feinberg, Propagation of Radio Waves along the Earth's Surface [in Russian], Izd. AN SSSR, Moscow (1961). L.A. Bessonov, Theoretical Foundations of Electrical Engineering [in Russian], Izd. Vysshaya Shkola, Moscow (1962). A.L. Drabkin and V. L. Zuzenko, Antenna-Feeder Devices [in Russian], [zd. Soy. Radio, Moscow

(1961).

*V. L Talanov kindly directed our attention to this fact.

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