Convolution at Microwave Frequencies in Yttrium Iron Garnet

J. H. Collins, J. D. Adam, and J. M. Owens

Citation: AIP Conference Proceedings 10, 150 (1973); doi: 10.1063/1.2946831

View online: http://dx.doi.org/10.1063/1.2946831
View Table of Contents: http://aip.scitation.org/toc/apc/10/1
Published by the American Institute of Physics
150

CONVOLUTION AT MICROWAVE FREQUENCIES IN YTTRIUM IRON GARNET

J H Co]]ins, J D Adam and J M Owens

University of Edinburgh, Edinburgh, Scotland

ABSTRACT

Convolution in real time of two oppositely directed travel] dug

magnetostatic waves of angular frequency, ~ , has been observed in
YIG rods, plates and epitaxial films at microwave frequencies~ The
multiplication process occurs through the gyromagnetic precession as
in earlier frequency doubling experiments in ferriteso The necessar#
spatial integration and output at 2 ~ , is obtained either by a single
turn coil or a distributed inductor, depending on the geometry of the
YIG sample, with its axis being along the direction of the bias
field o

Detailed convolution experiments have been performed at L and

S-band frequencies on single short pulses, single long pulses and
double pulses utilising magnetostatic waves in YIG plates of non-
ellipsoidal geometry~ Observed bilinearity factors can be as high
as I0-2(mW)-I in contrast with values of less than lO-5(mW) -I avai-
lable from interacting travelling waves via the electroacoustic
anharmonicity in Lithium Niobateo Device d~namic range is predicted
to be in excess of 80 dBo Magnetostatic wave convolution has also
been demonstrated in epitaxial YIG films~

INTRODUCTION

Acoustic waves have recently been used to perform convolution,

utilising either bulk or surface waves on a variety of materials,
relying on acoustoelectric anharmonicity in ferroelectrics or on the
piezoelectric electron-phonon interaction in semiconductorslo In
this paper we describe in more detail a highl~ efficient convolution
process, previously reported briefly for rods~o2,using magnetostatic
volume waves propagating in single crystal Yttrium Iron Garnet plates

PRINCIPLES OF OPERATION

In 1956, Ayres et al3 demonstrated, in ferrites, that applica-

tion of rf magnetic fields ( ~ , ~ ) at a frequency ~ , transverse to
a z-directed magnetic bias field" generates a frequency doubled, 2 ~ ,
magnetisation component along the bias field~ The frequency doubling
arises from the intrinsic non-linear products in the equation of
motion:

dt
- Y(~x Tb (I)
which analytically yield a small signal variation in the z-directed
magnetisation of:
 151

-Ms (&2 + hy 2)
m (2)
z H. 2 _ ( ~ / y ) 2
3.

where hNM denotes the saturation magnetisation, ~ the internal

magnetic ~ield, ~ , the signal angular frequency and Y the gyro-
magnetic ratio.

The frequency doubling concept may be extended to travel l~ng

waves~ Two oppositely directed magnetostatic waves are launched by
fine wire couplers at each end of a YIG plate (Figure I )o These
waves have associated hx and ~ and ~patially dependent wave numbers,
-k and +k, and interact throug~ equation 2, when spatially overlap-
ping~ The product m z is at twice the signal frequency (2~) and has
k = 0 by conservation of momentum~ This z-directed double frequency
component of the rf magnetisation is coupled out by a single turn
coil, which also performs spatial integration over a band of k vectozs
due to the non-ellipsoidal geometry~ For epitaxial YIG geometries,
which are essentially lellipsoidal' and have fixed k values through-
out their propagation, the spatial integration must be performed by
an inductor distributed along the propagation path~ Convolution is
possible only with volume magnetostatic modes, since spatial overlap
does not generally occur with oppositely directed surface magneto-
static waves due to their field displacement nature~ For the plate
magnetised in its plane, the 2 ~ signal is coupled out by a single
turn coil surrounding the central plane of the YIG plate, Figure lao
The normally magnetised plate, whether in bulk or epitaxial YIG,
allows planar operation with input fine wire couplers and the output
coupling loop arranged as shown in Figure Ibo

The output power Po at 2 ~ and the input powers, P1 and P2 at

are related theoretically through a bilinearity factor C, defined by:

Po = C~176 exp ( ~ ) (3)

where x is the attenuation rate of the magnetostatic waves in dB/
psec, t is the two port magnetostatic delay and ~ and L^ are the
input transduction losses~ Expresslons for ~land Cl , for the in-
plane and normally magnetised plates respectively, 5f thickness S,
are given by:

16 I:Ls ( ~.rrMs )2 2
(2)

16RL (4#Ms)2 o [(u/Y)2 -Hi2~/n~ 2

(5)
152

where R and R~ denote the output impedance and the load resistance
at 2 w ~espectlvely, and Bi equals ~ + 4~Mso

EXPERIM]~ TAL RESULTS

Experiments have been performed on a flux grown bulk YIG plate

of dimension ( ~ W and S lying along ~ I ~ , ~12~ andS107 axes) of
13o5 x 3o8 x 1o2 mm respectively~ Convolution for the in--plane mag-
netised plate (Figure la) was investigated at a signal frequency of
I GHz o When a rectangular signal pulse of 0.2 ~sec duration was
applied to one of the fine wire couplers, using the other fine wire
as an output coupler, two port magnetostatic delays were observed
with attenuation rates of 25 dB/~sec with an untuned double trans-
duction loss of 38 dB (ie ~ = ~ = 19 dB)o Single time coincident
pulses were then applied to both inputs and the convolved 2 GHz out-
put, which was coupled out by the fine wire loop, observed~ It was
found that on rem~oval of either of the input signals the 2w output
dropped below the level of detectibility~

Untuned double transduction loss in the normally magnetised

case at 2 GHz was 56 dB (~ = L2 = 28 dB) and attenuation rates were
25 dB/~sec, as before~ On application of two time coincident input
pulses at 2 GHz a cenvolved output from the coupling loop was obse-
rved at 4 GHz.

Initially, to d~onstrate the convolution action three types of

signal were applied to both input couplers and the 2~ output
observed. Both plate configurations were used with similar results
which are: (a) a single rectangular input pulse with T( t, where T iS
the input pulse length and t is the two port magnetostatic delay,
gave a triangular 2w output pulse of base width approximately 2T ;
(b) a single rectangular input pulse with T ~t, gave a symmetrical
trapezoidal output pulse with rise and fall times equal to half the
propagation delay; and (c) a double pulse with T ~(t and pulse
spacing ~Ach less than t gave three triangular output pulses of
base width approximately 2T separated by half the pulse spacing, the
centre pulse being approximately twice the amplitude of the other
two~ These results demonstrate the correct autocenvelution charac-
teristics for the three types of inputs studied.

Further detailed measurements were performed to characterise the

process in both normmlly and in-plane magnetised plates with short
rectangular input pulses. Figure 2 shows the square law beh~viour
of the convolved output, Po, as a function of the input power with
PI = P2, in conformity with equation (3), for the in-plane magnetised
plate at I GHz. Also shown is a plot of Pout versus PI for a two
port magnetostatic delay pulse demonstrating the absence of satura-
tion and non-linear effects up to 17 dBm input.

Figures 3 and 4 show respectively for the in-plane magnetised

plate and normally magnetised plate, the experimental variation of
the magnetostatic two port delay (w), the delay of the convolved
 153

output (2w) and the b~]inearity factor C as a function of bias field~

Note that the delay of the convolved output is always half of the
magnetostatic two port delay. Further that b~l~nearity factor C
increases with increasing delay in both cases which is consistent
with equations (4) and (5), since the magnetostatic delay for a
backward volume wave in an in-plane magnetised plate ~ oo when
w/y= Hi and the delay of the forward~ volume wave in a normally mag-
netised plate ~co when w/y= (BiHi)~o Inclusion of loss in
equations (4) and (5) results in a finite ~ of C occuringzwhen
w/y = ~ for the in-plane magnetised plate, and whenW~ = (B= ~.)~ for
the normally magnetised plate. ~

The theory presented describes satisfactorily the observed

experimental behaviour of the convolved output. However, the output
impedance ~ and the effects of energy focussing must be determined
before accurate comparisons are feasible~ The above effects have
also been observed in non~slly and in-plane magnetised epitaxial YIG
films with comparable efficiency.

Convohtion utilising magnetic wave interactions is provem here

to be a highly efficient process~ For a C factor of 10-~(mW) -I , with
efficient matching of the input transducers(4), output levels up to
-10 dBm should be achievable for input signal levels of 5 d ~ o Thus,
the device dynamic range is inherently in excess of 80 dBo

ACKNOWL~DG~EN T

The single crystal YIG plate used in the experiments described

was lent by I~ H Dotsch of Phillips Forshungslaboratoriu~, Hamburg,
GMBHo

REFERJ~CES

I o P Das, M N Araghi and W C Wang, "Convolution of signals using

surface-wave delay lines , Appl P~fs Lett, ~
9 1,
4, pp 152-154,
1972, contains references relevant to the surface acoustic wave
studies o

2o J D Adam, J H Collins and J M Owens, "Convolution with magneto-

static waves in a YIG rod", Electronics Letters 8, 9 pp 229-230,
1972 o

o W P &yres, P H Vartanian and J L Melchor, "F~equency doubling in

ferrites", J Appl Phys, 27, 2 pp 188-189, 1956.

o J D Adam, J H Co]]ins and N Rubino, "Electromagnetic matching

considerations for YIG delay lines", Proc IEEE ~ pp 1373-1375
(August 1968)o
154

P0ut P0

(dBm dBm)

-80

_A_2~
(a)

-30- --70
H
SL ~ 7l~ K

f~nnT//P- k
-20- --60
_A_2~
(b) I I
+20 +10 0
Fig I Magnetostatic plate
Convolver Configurations Po (d Bm)
Fig 2 Square Law Behaviour
of Convolved Output (N case)
DELAY = 1 GHz C
C I DELAY
(~SEC) rnWF (~SFC)
1.5 ./. 1.5

\
//I/
1.0 I'0 I03
\
164

0.5 - / 0.5 _ 164

/
- 165
i l

0 I I G5
300 310 32( 1500 1520 1540
H(Oe) H(Oe)
Fig 3 Delays and C versus Fig 4 Delays and C versus
Field (// case), ur= 1 GHz Field ( • case), w-= 2 GHz