F E R R I T E A C O U S T I C M O D U L A T I O N A M P L I F I E R - C O N V E R T E R

G. A. P e t r a k o v s k i i , l~. M. S m o k o t i n , a n d G. N. S t e p a n o v

UDC 621.375.3.7

At the p resen t time relative modulation ampl i f iers (RMA) of e lec t romagnet ic radiat ion in the rad io- f requency and optical regions have been built using va rac to r s [1, 21 and are widely used. Such ampl i f iers have low noise levels, a Large band width and high gain. Amplification in a RMA va rac to r is accomplished by modulating the oscilLations with a pumping signal a c r o s s the nonlinear capacitance of the diode and by subsequent detection or f i l ter ing of one of the side bands of the oscil lation spectrum. It is c lear that a s imi lar pumping modulation of the osci l la t ions cart occur for a fe r r i te sample at fe r romagnet ic resonance due to acoustic vibrat ions [3]. Using such a moduLator as an e lement subjected to a weak ul trasonic signal, it is possible to real ize an acoustic modulation ampLif ier-conver ter [4].

Using an analysis of the Landau--IAfshits equations containing a dissipative t e rm of the Gilbert form, we consider the possibi l i ty of obtaining such an amplification in a ferr i te .

in = -- -~ [mill + ~ lmln], (1)

here 3' is the modulus of the gyromagnet ie ratio, a is the attenuation constant, m = M/IMI is the magnet iza- tion vec tor of the fer r i te .

We take the influence of the eLastic osci l la t ions on the magnetization of the c rys ta l Into account by including the effective field of the magnetoclast ic fo rces in H in the following manner:

time . . . . ~VmeM ' (2)

where Nine is the tensor of the magnetoeLastie forces .

The elast ic displacements Ui ar is ing in the c rys t a l as a resu l t of the acoustic wave are determined in t e r m s of the components of the deformation tensor using the well-known relat ions e i j = (OUi/0xj + 8Uj /Oxi), eli = OUt/Oxi, e tc . . If l inear ly-polar ized shear osci l lat ions, with their displacement along the x axis, propagate into the c rys t a l along the y axis, only exy will be different f rom zero. In the coordinate sys tem shown in Fig. 1 the t e n s o r ~ e will then be diagonal so that

B: OL"x N..,~ = -- A'~ = --- - -

M: Oy

Nit = 0 where ]32 is the magnetoelast ic coupling constant. When standing t ransverse waves are p resen t in the c rys t a l as occurs in experiment , the quantity 0Ux/Oy can be written in the fo rm Uoeos~2t for long wave- length osci l lat ions where U 0 is the amplitude of the acoustic wave, and f~--ee Is I ts frequency. The weak external acoustic signal whose influence on the F1VIR will be calculated is Uo cos f~t.

We solve the problem in the l inear approximation (h << H o) assuming that ~2 << w0, ~ << 1, w e << Wp. For simplicity, we assume also that the sample is in the fo rm of an ellipsoid of revolution p repared f rom an isotropie fe r r i te and that the external homogeneous signal pump h = i heos w t + jh sin wt at a f requency

close to the FMR frequency, w 0 excites only the homogeneous type of precess ion . Represent ing the ef - fective internal field of the c rys t a l in the f o r m

H == i [h cos ,ot - (Nx -1- Nzl),tr. Mx] + j [h sin (,,t -- (Ny q- N~,) 4r. My l 5- tr [Ho - (Nz H- Nz;) 4r.M~l, (3)

where Nx, Ny, Nz are the demagnetizing fac tors , we obtain differential equations for the projec t ions of the magnetization vec tor along the x axis

L. V. Kirenskli Institute of Phys ics , Siberian Department, Academy of Sciences of the USSR. T rans - lated f rom Izvest iya VUZ. Fizika, No. 12, pp. 143-145, December , 1973. Original ar t icle submitted October 30, 1972.

�9 1975 Plenum Publishing Corporation, 227 West 1 7th Street, New York, N.Y. 10011. No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by an)' means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission o f the publisher. A cop), o f this article is available from the publisher for $15. 00.

1750

~L.~, u[lm]

J - z l ~ / d

x:o~i] F i g . I. Directions of the m a g n e t i c f i e l d s a c t i n g on the s a m p l e : h) a m - p l i t ude of the m i c r o w a v e pump f i e l d , I4_0) m a g n i ~ d e of the c o n s t a n t m a g -

ne t i c f i e ld .

;k, + 2~ m~ + ~,o I l + :7 co~ ~t ) ,n.,. == ~ t~ co~ ,,,t, ~ (4)

w h e r e

~'o = "; l / & ! - ( N _ - - N z l 4:Mzj, N . ~= N x ~ N y , 2~ = 2~,'.'o,

3,,,c B., l ~p (~' + ~c) - - = = - - - , ~ " c = " - - : - 4 : M U o , " - ; * : . . . . . ~ ' s . v = ' i h . 2 % ' 3'I'-' 2 o,~

Equation (4) deseribes the oscil lations of a l inear osci l lator whose reasonanee f r e q u e n c y e x p e r i e n c e s small "s low" oscil- lations about some equilibrium position and in form corresponds to the equation solved in [5]. In the same way as done by l~et - rakovskli el. al. [5], we solve Eq. (4) by the Krylov--lBogolyubov method in the form given by i~Ittropol'skii [6]. For the alternat- ing amplitude b and phase ~ of the oscillations in the magnetiza-

l ion which have s m a l l d e v i a t i o n s f r o m t h e i r s t a t i o n a r y v a l u e s in the p r e s e n c e of the e x t e r n a l a c o u s t i c s i g n a l

~ c , we ob ta in the e x p r e s s i o n s (5)

= : Fsin (o_t : ~), ~7 = ~ ,gsi~ (c,t + ~)

w h e r e

1 - : g = -- ,,,,, 6-, -- ,,') ~ t~:- t.:- -t- I6",, ..... V- + ~,-~ -- !:F!

4

5 =- - - % 0 2 : - ~,~)I,2 {4~;- -q-" + l~',, " ~ + ~'~ -- ~.~]2} #

[ ~ .Q2 4 - ~2 4 - (m , , - - ~ , ) "

t g ~ = - - I( '". . - o,)-" i ~2 ._ ,.51. ' . . . . . . 2~ ~' t g '.-, ,~ o-' 4- V-' - - (,,,,, - - '..~)~

F r o m the r e l a t i o n s o b t a i n e d i t i s c l e a r tha t the o s c i l l a t i o n s of m x a r e d e s c r i b e d in t e r m s of a m o d u l a t i o n both in a m p l i t u d e and p h a s e . The m a x i m u m v a l u e s of the a m p l i t u d e of the s ide bands of the o s c i l l a t i o n s p e c t r u m due to the a m p l i t u d e and p h a s e modu la t i on a r e e q u a l to:

a) fo r the c a s e of s m a l l f r e q u c n c i e s , ~2 << ( 1 / 2 ) I y I A H

to o o) c ~ tof f tO c

, l~m == ~ ' iT;Z~; ~ , A f r o . . . . ,1~7-- ,

b) for the case of hlgh frequencies, ~2 >> (I/2)}yl AH

- " A d d , n = . . . . . �9 .Jam ~o': ' �9 4~c2

In order to make a comparison of the values Aam and Afm it should be noted that the use of the phase modulation is more effective. We introduce conventional expressions for the gain in order to estimate the amplification properties of the system:

A r:t cog Ka ---- 4 : -~-Aam M, K f : t= - f ' hc M , w h e r e h c = - - 7 . . i "

A c a l c u l a t i o n of Kf f o r an y t t r i u m f e r r i t e in the low f r e q u e n c y c a s e with 4~rM = 1750 G, h = 5 . 1 0 - 3 0 e , A H = 0.5 (De g i v e s Kf ~ 100 which v e r i f i e s the p o s s i b i l i t y , in p r i n c i p l e , of c r e a t i n g a r e a c t i v e modu la t i on a m -

p l i f i e r u s ing a f e r r i t e .

Wi th the a i m of v e r i f y i n g the t h e o r e t i c a l p r c m i s e , an e x p e r i m e n t a l s tudy of a m o d e l of an a c o u s t i c a m p l i f i e r - - c o n v e r t e r u s ing a f e r r t t e wi th A H = 3 0 e was c a r r i e d out. The a m p l i f i e r c o n s i s t e d of an input d e v i c e , a m o d u l a t o r , and a d e m o d u l a t o r . The m o d u l a t o r was a hol low r e s o n a t o r c o n s i s t i n g of an e n c l o s e d p i e c e of t h r e e - c e n t i m e t e r w a v e - g u i d e with an induc t ive coup l ing a p e r t u r e in which a 1.2 m m s i n g l e - c r y s t a l s p h e r e of y t t r i u m g a r n e t was p l a c e d n e a r a c a v i t y wa l l a t the an t inode of the h i g h - f r e q u e n c y f i e ld h. The inpu t dev i ce c o n s i s t e d of a f u s e d - q u a r t z rod (sound conduc to r ) in which t r a n s v e r s e e l a s t i c o s c i l l a t i o n s we re e x c i t e d a t a f r e q u e n c y of 1.5 MHz by a q u a r t z t r a n s d u c e r bonded to the end face of the s a m p l e . The s p h e r e was p o l i s h e d p a r a l l e l to [110] c r y s t a l l o g r a p h i c p lane fo r b e t t e r a c o u s t i c cons t an t .

A c o n s t a n t m a g n e t i z i n g f i e l d H 0 was a p p l i e d p e r p e n d i c u l a r to the n a r r o w wa l l of the m i c r o w a v e r e - s o n a t o r a long with a l i n e a r l y - p o l a r i z e d m i c r o w a v e f i e l d whose magn i tude c o r r e s p o n d e d to the l i n e a r p o r t i o n of the one of the s l o p e s of the f e r r o m a g n e t i c r e s o n a n c e . E l e c t r o m a g n e t i c o s c i l l a t i o n s g e n e r a t e d by a

1751

microwave k lys t ron gene ra to r , p a s s e d through a f e r r i t e i so la to r , an at tenuator , and a c i r cu la to r to the input of the resona to r . Acoust ic osc i l la t ions were applied to the f e r r l t e sample and because of the change in the f e r r o m a g n e t i c resonance conditions due to the change in the magne toe las t i c coupling, mic rowave osclUat ions re f lec ted f r o m the r e s o n a t o r were modulated at the f requency of the acoust ic signal. The r e - f lected signal f r o m the r e s o n a t o r p a s s e d through the c i r cu la to r to the a demodula tor using a de tec to r head with a D-405 type de tec tor whose output was t r a n s f o r m e d and ampli f ied and connected to a m e a s u r i n g de- vice. A V6-1 se lec t ive m i c r o v o l t m e t e r s e rved to m e a s u r e the output s i g n a l

The gain of the ampl i f i e r was de te rmined by compar ing the voltage a t the de tec tor of the f e r r i t e a m p l i f i e r - - c o n v e r t e r with the voltage a r i s ing at the quar tz t r ansduce r bonded to the acoust ic conductor with the same ampli tude of e las t ic osc i l la t ions as that a r i s ing in the y t t r i um garne t single c rys ta l . Such m e a - s u r e m e n t s of the gain in our c o n v e r t e r model gave a value of 26 dB for a pump g e n e r a t o r power of 10 mW.

The 26 dB gain is not the m s x i m u m value poss ib le . The gain can he inc reased by inc reas ing the power of the pump osc i l la t ions and the se lect ion of f e r r i t e c r y s t a l cha r ac t e r i s t i c s .

1. 2. 3. 4. 5. 6.

L I T E R A T U R E C I T E D

V. N. Detinko and A. S. Pe t rov , Izv. VUZ SSSR, Fizlka, No. 3, 14 (1966). I. R. Biard, P roc . IEEE 51, 327 (1963). F. V. Lisovsldi and Ya. A. Monosov, Radiotekhaika i F.lektronika, 7, 1328 (1967). G. A. Pe t r akovsk i i and E. M. Smokot im, Avtorskoe Svedete l ' s tvo , No. 332529 (1/VII) (1970). G. A. Pe t r akovsk i i , A. S. Pe t rov , and V. A. Tabar in , Izv. VUZ SSSR, Fizika, No. 1, 138 (1970). Yu. A. Mi t ropol ' sk i l , P r o b l e m s in the Nons ta t ioaary Theory of Osci l la t ions [in Russian] , Nauka, Moscow (1964).

1752