Response correction for SAW filters

A procedure to correct the amplitude of the frequency or the impulse response for signal processing filter based entirely or partly on acoustic surface waves has been described. The method may be applied where the acoustic wave follows different paths inside the component depending on the signal frequency or on the signal time delay in the filter. The method is based on changing the signal phase in an essentially periodic way for instance by etching metal films placed on the surface of the component in order to make correction possible. Laser induced etching can be an efficient way to carry out amplitude correction according to the invention due to the good geometric resolution of this method and because correction of the phase pan of the response can be earned out with the same equipement in accordance with established techniques.

The present invention relates to the correction of the amplitude response 
in the time domain or in the frequency domain for a class of linear, 
reciprocal filters which are based on surface acoustic waves (SAW). The 
signal is carried in the form of a SAW over the surface of the component. 
The SAW will follow a path from an input transducer where the SAWs are 
generated to an output transducer where the SAWs are detected and the 
signal is made available to the user in electric form. Only a part of each 
signal carrying SAW is converted to electric form by the output 
transducer; such part will be referred to part of the useful acoustic 
signal or saw. 
Existing correction methods are based on the fact that the useful acoustic 
signal follows different paths over the component's surface determined by 
the signal frequency if the correction is to be made in the frequency 
domain or dependent on the signal time delay if the correction is made in 
the time domain. 
Correction of the phase response for SAW filter has been done and is being 
done today by the deposition of a metal film which influences the velocity 
of the SAW. After electrical measurement of the component's response, part 
of this metal film may be removed by a deliberate selective etching until 
a correct phase response has been reached as described by V. S. Dolat, J. 
H. C. Sedlacek and D. J. Ehrlich in the paper "Laser direct write 
compensation of reflective array compressors", IEEE 1987 Ultrasonic 
Symposium Proceedings, p. 203-208. 
Correction of the amplitude response for reflector array compressor (RAC) 
chirp filters has been done earlier by the deposition of a resistance film 
(CERMET) which will attenuate the SAW as described in the above Dolat et 
al. paper. After electrical measurement of the response of the RAC filter, 
the attenuating film has been made partially inactive by laser induced 
oxidation until a correct amplitude response has been reached. This method 
requires a strong piezo-electric coupling for the waves in the area where 
the film is located. This is not possible for RAC chirp lines on quartz, 
in particular not if the crystal has a so-called ST-cut. As described by 
M. B. Schulz, B. J. Matsinger and M. G. Holland in the paper "Temperature 
dependence of surface acoustic wave velocity on alpha-quartz"; J. Appl. 
Phys, Vol 41, 2755-2765 orientation of the SAW plane related to the 
crystal axis results in a low temperature dependence of the component, but 
the crystal cut lacks piezo-electric coupling for SAWs in the transversal 
direction where the attenuating CERMET film has to be located. Other SAW 
materials like LiNbO.sub.3 has a sufficient piezo-electric coupling, 
however, it represents a general problem to produce a CERMET film with a 
suitable resistance and a sufficient stability. 
By using the invention, correction of the amplitude response on a time 
selective or a frequency selective basis is obtained by changing the 
substrate surface properties in a deliberate pattern transversely to the 
propagation of the wave to obtain desired SAW velocity changes. These 
velocity changes have to be made in that area of the surface where the 
signal path depends on frequency or on time delay. The resulting change in 
the transfer of the useful signal can be used for amplitude correction of 
the filter response by a procedure of the present invention that will be 
described below. 
A RAC filter, or in principle any other filter, may also be corrected by 
making a cascade connection to a correction filter which has been designed 
to cancel the response errors of the RAC filter to be corrected. This 
method is described in the U.S. Pat. No. 4,857,870: "Method of 
manufacturing a surface wave dispersive filter and a filter manufactured 
in accordance with this method". The additional filter, or the correction 
filter can be integrated with the primary filter on the same 
piezo-electric substrate or on an additional substrate dependent on what 
is the most practical and economic solution. In any case the correction of 
a filter by the design of a particular correction filter will be a rather 
expensive method. 
One of the other amplitude correction methods is to correct the depths of 
the reflector grooves after the component has been produced and electrical 
measurements of the response made. This procedure requires a permanent 
masking of the ridges between the grooves. This mask serves as an etching 
mask for the correction etching of the grating without destroying the 
propagation properties of the SAWs in the reflective array. This procedure 
requires a high geometric resolution for the etching process along the 
reflector arrays. An adequate resolution can be difficult to obtain for 
chirp lines with a high chirp rate, that is a small change in the time 
delay per unit frequency. The masking of the ridges has disadvantages in 
that it may result in additional losses and also be a possible source of 
accelerated aging of the component. It has also been difficult to find 
suitable material/etch process combinations for an attractive SAW 
substrate material like LiNbO.sub.3. 
It is therefore desireable to develop new methods for amplitude correction. 
For economic reasons it would be preferable to use the same technology and 
the same equipment for the amplitude correction as is used for the phase 
correction of the response. This property is obtained by the inventive 
amplitude correction method.

The invention and the advantages obtained with the invention will be more 
fully appreciated from the following detailed description when the same is 
considered in connection with the accompanying drawings, in which 
FIG. 1 schematically and in principle shows a reflector array compressor 
"RAC" surface acoustic wave "SAW" chirp filter. 
FIG. 2 schematically and in principle shows a reflector dot array "RDA" 
filter. 
The principal function of a RAC filter as shown in FIG. 1 is that the input 
transducer 1 sends a SAW wave towards an array 2 of reflecting grooves 
which reflects the waves with a 90.degree. change of direction. The high 
frequency signals are reflected close to the input transducer 1 and low 
frequency signal further back into the array. This effect is obtained by 
increasing the distance between the grooves as one goes further away from 
the input transducer. The waves propagate towards an other reflecting 
array 3 which is the mirror image of the first array around the line 
denoted x--x in FIG. 1. This second array reflects the wave towards the 
output transducer as described by A. Ronnekleiv in the paper "Amplitude 
and phase compensation of RAC-type chirp lines on quartz", IEEE 1988 
Ultrasonic Symposium Proceedings, pp. 169-173. Signals with different 
frequency will pass the line x--x at different locations and they will 
also be subject to different delays through the component. The frequency 
dependent delay is the primary function of a chirp filter. 
The "U-structure RDA"-filter as described by L. P. Solie in the paper "A 
SAW filter using a reflective dot array (RDA)", IEEE 1976 Ultrasonics 
Symposium Proceedings, pp. 309-312, is shown in FIG. 2. One difference 
from the RAC-chirp filter in FIG. 1 is that the individual reflectors in 
the arrays 2 and 3 instead of being made as grooves, are made as a string 
of metal dots placed on a straight line. As related to the invention it is 
a more interesting difference that the reflectors of FIG. 2 are 
equidistant along the arrays 2 and 3. This implies that they are all 
effective reflectors in the same frequency range. Hence for the RDA filter 
structure the signals which pass a line x--x will have the same frequency 
range, but obtain different time delays dependent on the location where 
the signals pass the line x--x. 
The invention concerns only correction of the amplitude response. We will 
now establish a relation between phase correction of RAC filters by using 
existing technology and the inventive method for amplitude correction. To 
this end we introduce a periodic change of velocity for the waves along 
the line x--x in the area between the arrays 2 and 3. The period of 
velocity change is L.sub.p and it has a sine shaped function along the 
line x--x shown between the arrays 2 and 3 in FIG. 2. In accordance with 
the aforementioned Volck et al. paper, this change of velocity will result 
in a corresponding change of phase for the waves passing this area. Let W 
denote the width of each of the arrays measured orthogonal to the line 
x--x. If L.sub.p .gtoreq.2 W the result will be a periodic change in the 
phase of the impulse response for the fighter (periodic in time), with 
period T.sub.p =L.sub.p /(2 v.sub.1) where v.sub.1 is the wave velocity 
measured along the arrays 2 and 3 in the x--x direction. If L.sub.p is 
made sufficiently large the result will be a change of phase in the 
frequency response of the filter. This case corresponds to the well known 
method for phase correction of a RAC filter response. The amplitude change 
of the impulse response will be negligible. 
At or close to the range 2 W.gtoreq.L.sub.p .gtoreq.W/2, the magnitude of 
the resulting periodic change of phase for the impulse response will be 
reduced as we reduce L.sub.p. For L.sub.p =W/2 the change of phase for the 
impulse response will be nearly constant and independent of the time 
delay, and approximately equal to the average value of the phase change 
measured along the line x--x. The amplitude of the impulse response when 
L.sub.p is reduced from 2 W will be reduced and stabilized at a level 
given by the amplitude of the periodic phase change when L.sub.p is 
reduced to W/2. A further reduction in L.sub.p will not affect the 
amplitude nor the phase of the impulse response in a significant way 
before L.sub.p is reduced to a size comparable to the wave-length 
.lambda.. If L.sub.p &lt;.lambda. the wave propagation will be that of a 
homogeneous medium. Hence no periodic phase change will occur in the 
output signal and the amplitude response will assume its original value. 
The phase change of the impulse response will continue to be constant as a 
function of the signal time delay but may vary with L.sub.p for L.sub.p 
.apprxeq..lambda. or shorter. 
The amplitude change for the impulse response of the filter which occurs at 
a periodic velocity change and which mainly occurs for W/2.gtoreq.L.sub.p 
.gtoreq..lambda., is the basis of the inventive amplitude correction 
method. This effect has not been described earlier and hence not suggested 
used to correct amplitude response. The above V. S. Dolat et al. paper 
describes phase changes over short isolated areas along the line x--x and 
observes that these phase changes can be used for phase correction and 
gives a small local amplitude change. This paper though, does not observe 
that the amplitude changes can be made uniform over large areas of time 
delay for the impulse response or large frequency ranges of the frequency 
response by introducing periodic phase changes with W/2.gtoreq.L.sub.p 
.gtoreq..lambda. along the line x--x of FIG. 1, and they therefore fail to 
observe that these effects can be attractive also for amplitude correction 
of RAC filters. The possibility for amplitude correction can be seen from 
the mode coupling integrals which are to be described in the following 
text, equations 1 and 2. This formalism has not been proposed in the Dolat 
et al. paper. 
To explain the amplitude correction method applied in the frequency domain, 
let us consider the signal amplitude along a curve with coordinate x 
transverse to, but not necessarily orthogonal to the direction of SAW 
propagation in the area where the useful signal will follow different 
paths dependent of the frequency. The line x--x in FIG. 1 will be suitable 
for this purpose. At a given signal frequency let us assume that an 
electrical signal applied to transducer 1 gives a wave amplitude a(x) 
along the curve and that a signal applied to the transducer 4 gives a wave 
amplitude b(x) along the same curve with x denoting the distance from the 
transducer ends of the arrays 2 and 3. The functions a(x) and b(x) are 
functions with complex values where the absolute value represents the 
amplitude of the wave and the phase of the function represents the phase 
of the wave. The expression 
##EQU1## 
represents a mode coupling loss between the two transducers 1 and 4. The 
introduction of a velocity change for the useful SAWs in the vicinity of 
the curve x will change the mode coupling loss. If L.sub.p is large 
compared to .lambda., the effect on the complex wave amplitude will simply 
be a periodic change in the phase as the waves cross the perturbed area, 
.phi.(x), and the mode coupling loss will now become 
##EQU2## 
where exp(j.phi.(x)) is the exponential function of j.phi.(x) and 
j=.sqroot.-1. 
The transmission through the component has now been changed with the ratio 
.vertline.A.sub.2 /A.sub.1 .vertline. in amplitude. By making 
a(x)=[b(x)exp(j.phi.))]* (* denoted the complex conjugate), the maximum 
response of the component is obtained. To reach exactly this value is 
usually of less interest because the functions a(x) and b(x) are difficult 
to find in detail and it is hardly possible to maximize the response at 
several or all frequencies at the same time. On the other hand if .phi.(x) 
has a rapid variation compared to a(x) and b(x) and a mainly periodic 
variation, .phi.(x) may be used to reduce .vertline.A.sub.2 A.sub.1 
.vertline. to obtain a desired amplitude correction. The period of L.sub.p 
should not be made less than approximately one wavelength in the x 
direction because, for the wave propagation perturbation with such a 
periodicity, the waves will mainly see a local average value of the 
propagation parameters. The induced surface perturbations will therefore 
not show up as phase changes of the waves, and the effective .phi.(x) will 
be close to zero and the losses described by eq. 2 and intended to be used 
for amplitude correction according to the invention will disappear. 
The description above indicates that the phase changes occurs in a narrow 
belt transverse to the wave propagation direction. This is not a necessity 
according to the invention in that a wider structure in the direction of 
the signal propagation can be split into narrow belts which are numbered 
from 1 to n. Each of these belts allows an independent application of eq. 
2 to find a desired effect of the phase change .phi..sub.n (x) in belt No. 
n as a factor of (A.sub.2 /A.sub.1).sub.n, where the transmission 
properties for the belts 1 to n-1 has been included in the computation of 
the related attenuation functions. The total correction will be the 
product of all N sequential corrections. It is obvious that the amplitude 
correction can be different for two different frequencies only to the 
degree that the useful SAW follows two different paths through the 
component or alternatively are influenced in different ways by the SAW 
material perturbation in an area common to the signals at the two 
different frequencies. 
It is of practical interest to observe that if for two subsequent 
corrections for the same component .phi.(x)=.phi..sub.1 (x)+.phi..sub.2 
(x) where .phi..sub.1 (x) and .phi..sub.2 (x) both are periodic functions 
but the functions have no common harmonics (in particular important for 
the lower harmonics), the two contributions to the amplified reduction 
factors (see eq. 2) will be independent of each other. 
We have so far discussed amplitude correction of the frequency response of 
a component. In principal the same procedure can be used for amplitude 
correction of the impulse response of a component. For an impulse response 
amplitude correction it is required that signals which have different 
delays through the components will pass the component by more or less 
different paths. 
To obtain a good correction for the impulse response it is preferable that 
the total frequency response of the component is relatively narrowband and 
that the major band limitation occurs outside the area where the 
correction is carried out. To obtain a fairly simple description of the 
method, band limited signal will be assumed which means that the phase 
change of the signal in the correction area is reasonably well defined. 
Once again let x be a coordinate transverse to the wave propagation 
direction, and let y be a coordinate along the wave direction. a(x, y, 
.tau.) is the complex wave amplitude caused by an impulse of the input 
coupler 1 after a time .tau. and b(x, y, .tau.) the corresponding 
amplitude caused by an impulse to the output coupler 4 in FIG. 2. In this 
case the impulse response of the component at a time .tau. will be 
proportional to, wherein n is a time parameter which for a given 
contribution to the convolution integral (3) gives the time delay seen by 
the wave through the impulse response a(x,y,.eta.) 
EQU .intg..intg..intg.a(x,y,.eta.)b(x,y,.tau.-.eta.)dxdyd.eta. (3) 
It is a consequence of equation 3 that by imposing a variable phase shift 
.phi.(x) for the waves around a given y-coordinate of the material it is 
possible to influence the amplitude of the impulse response here in the 
same way as described above for the frequency response. Amplitude 
correction of the impulse response is therefore possible. 
For those cases where a description with a frequency independent phase 
shift function .phi.(x) for the correction is too coarse, it is possible 
to use a more exact description of the wave propagation effects of the 
changes based on time delay or frequency dispersive time delay. Also for 
this more detailed description the effect on amplitude may be found with 
good accuracy from expressions of the form shown in eq. 3. If the impulse 
response correction has to be accurate over a wide frequency band, the 
frequency spectrum of the time delays used when weighted with the 
amplitude of a and b according to eq. 3, should give a flat frequency 
response across the desired band at the same time as it reduces the 
amplitude in a desirable way. 
FIG. 2, in which the same reference numerals as before have been used to 
denote corresponding parts: shows a "U"-structure "RDA"-filter that is 
well suited for amplitude correction of the impulse response according to 
the invention rather than frequency response. 
The local changes of the velocity which must be introduced in the wave 
propagation to use the amplitude correction methods described above, may 
be obtained by placing thin films of metal or other suitable materials on 
the surface of the component in the area suited for correction. The films 
will change the wave velocity by shortening electric fields generated due 
to piezo-electric coupling and/or by loading the surface mechanically. The 
films may be patterned by standard photolithographic techniques. It is of 
interest to note that as noted in the aforementioned Dolat et al. paper, 
molybdenum, Mo, and some other materials (Si, Ti) may be etched by laser 
induced processes to obtain a desired change of the pattern without 
disassembly and wet processing of the components. It is also possible and 
from an acoustic point of view equally effective to deposit patterned 
films either by the usual photolithographic methods or by locally 
stimulating deposition of a film from a gas by laser light. Several 
applications of this technique are described by D. Bauerle in the book 
"Chemical Processing with Lasers", Volume 1 of Springers series in 
Material Sciences. (ISBN 3-540-17147 -9, Springer, Berlin, 1986). 
The amplitude correction according to the invention will result in 
undesirable changes of the signal phase. The practical problem associated 
with this is minor, because the phase can be corrected by established 
techniques such as those disclosed in the above Dolat et al. paper, which 
may be carried out with the same production equipment as before.