Acoustic surface wave filters

Acoustic surface wave filters E. DIEULESAINT

and P. HARTEMANN

The main features of interdigital transducers are discussed together with the design aspects which determine the transfer function of Rayleigh-wave filters. Examples of matched, bandpass and rejection filters are given.

Introduction Several articles in ULTRASONICS l,*y3have been devoted to surface waves and particularly to Rayleigh waves. Their general properties as well as the different ways of launching and detecting them have been discussed. For this reason only a brief reminder of the main features of surface waves will be given before describing some applications. The nature of the Rayleigh wave is complex since it consists both of longitudinal and transverse components. The amplitudes of these components decrease according to different laws before fading away at a depth of about one wavelength.4 However, this complexity is balanced by a great advantage: the Kayleigh wave can be easily excited (and detected) by finger transducers which are equivalent to a discrete distribution of ultrasonic sources (or receivers). The relative intensities and phases of these sources are determined by the geometry of the transducer electrodes or, more precisely, by the active length and position of the fingers.5 The effects of interference among the signals emitted by the different ultrasonic generators depend on the shape of the electrodes. Hence, the synthesis of a great variety of transfer functions can be implemented with appropriate transducer geometries.

Transfer function and impulse response of an acoustic Rayleigh-wave filter An elastic wave filter, as any linear time invariant system, can be characterized by its transfer function or impulse response, the two functions being related by a Fourier transform. Since the filter is composed of two transducers its transfer function is equal to the product* of the input transducer transfer function and the output transducer transfer function. Its impulse response is equal to the convolution of the impulse response of each transducer. Let us examine the particular case of a filter with two identical transducers on a piezoelectric substrate, each transducer having N fingers of the same length separated by a constant spacing (Fig.la). A pulse of short duration ~ shorter than the transit time of the elastic waves between two fingers - applied to the input transducer electrodes excites, simultaneously, the (N-l) ultrasonic generators. As the electric field at a given instant has an opposed polarity for two neighbouring pairs of fingers, the emitted acoustic signal is periodic. The spatial period h is 2d if d is the

-_-‘rsibnal

The width of the fingers of most Rayleigh-wave transducers is of the order of a quarter of a wavelength. For frequencies less than 300 MHz the wavelength h, for commonly used materials, is more than 10 pm; the electrodes being readily made by conventional photoetching techniques. For high frequencies (1000 MHz, h = 3 pm) the realization of the transducer fingers requires electronic masking techniques.6*7 This article will describe a number of Rayleigh-wave falters at frequencies less than 200 MHz. Applications of these devices are found in coding, pulse compression and signal filtering. However, before doing so the main characteristics of interdigital transducers, namely the frequency and time responses, will be considered.

The authors are at the Laboratoire d’Acousto&ectricitk, Laboratoire Central de Recherches, Thomson CSF, Domaine Corbwille-BP No 10, 91401 Orsay, France. Paper received 10 July 1972.

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de

-

Acoustic iZ

sianal

signal t

Fig. 1 Filter with identical input and output transducers: a-the periodic acoustic signal is launched when a pulse of short duration is applied to the input transducer, its duration 0 is equal to the transducer length L divided by the Rayleigh-wave propagation velocity V. The amplitude envelope of the output signal is triangular; b-the behaviour of the input and output transducers described by a discrete set of equally spaced generators and receivers

*The output transducer receivers must have appropriate dimensions to receive all the acoustic waves emitted by any of the generators of the input transducer.

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distance between the axes of two adjacent fingers. The total time duration fI of the signal is equal to the length L of the transducer divided by the Rayleigh-wave propagation velocity V, so that &-_-=(N-l)d V V When the elastic signal reaches the output transducer the accompanying piezoelectric field induces an electric voltage whose amplitude increases to a maximum (corresponding to the simultaneous excitation of all the ultrasonic receptors) and then decreases. Hence the impulse response of the filter represented in Fig.la has a time duration equal to 20. Its triangular envelope is symmetrical. It is the autocorrelation function of the impulse response of one transducer. The transfer function of the filter, which is the Fourier transform of this impulse response, is a [(sin x)/x] 2 curve. The relative 3 dB bandwidth is then

Therefore the frequency response characteristic of one transducer has the shape of a (sin X)/X curve. This is not quite correct for the elastic signal emitted by the transducer. Although periodic it does not necessarily vary sinusoidally so the frequency response has other maxima at harmonic frequencies.

b

/ I

I

These results can also be found by another method which consists of representing the input (or output) transducer by a discrete set of infinitely narrow generators (or receptors) located, for example, at the centre of the interdigital spacings as shown in Fig. 1b. This model is useful for sophisticated transducers having fingers of different lengths and variable spacings. The intensity of each source is then proportional to the active length of the fingers. This representation allows one to solve the practical problem of designing a transducer to deliver an imposed impulse response (or transfer function).

I

The location of the generators for a given response such as h (t) = a (t) cos cp(f) can be made at the points xn= Vt, where the instants t,, are such that

cp($J = ml as shown in Fig.2. In fact this sampling can describe many functions as depicted in Fig.3. Therefore it can be predicted that the excitation (by a short pulse) of these 6 generators gives a response which contains not onlv the fundamental, but harmonic frequencies as well.* However, the finger spacing plays a role in selecting the working frequency.

C Fig.2 Geometry of a transducer delivering an imposed impulse response. The imposed impulse response (a) represented by samples (b) at instants t = r,.,, is obtained, in practice, by a transducer with ultrasonic generators located at points x, = V tn. It is assumed that the output transducer (with a few fingers only) has a very large bandwidth

Signal matched filter

a radar system, for example, is given by the maximum of the convolution of the received signal with a replica of the desired signal. The signal matched filter implements this convolution.

It is known 9* lo that the most probable time location of a waveform signal s (t) corrupted by white Gaussian noise in

In the frequency domain, where S (0) is the spectrum of the signal s (t), the matched filter transfer function H(o)

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pulse response is obtained when the receivers of the output transducer are properly spaced and connected. Fig.6 shows the output signal of a filter matched with a pulse modulated by phase reversal according to a pseudorandom code of length 1.5. The duration of the input pulse train is 6 ps and the carrier frequency is 60 MHz. To show how different the output can be when the input signal is not the matched one, a signal identical to the impulse response of the same filter (without time reversing it) has been applied to the input, and the result (Fig.6b) shows that time location is difficult in this case. When the pulse train is amplitude coded instead of phase coded the active lengths of the different receivers of the output transducer are chosen so that the impulse response is also amplitude coded. Filter matched to a frequency signal

modulated

pulse

The impulse response of Rayleigh-wave delay-lines can be frequency modulated with a nearly constant amplitude. The matched filter response to the signal is a time compressed pulse. The structure of the filter is shown in Fig.7 where the variation of the interdigital spacing along the transducer imposes the law for the time variation of the frequency of the impulse response.

b

Two kinds of laws are normally used to vary the frequency of the dispersive delay-lines of radar-system pulse com-

s(t)

Fig.3 Discrete set of generators representing a wave of fundamental frequency (a) and of harmonic frequency (b). The transducer (c) works at the harmonic frequency. The interdigital spacing is equal to a quarter of the corresponding wavelength

f -

is the complex conjugate function so that

of the spectrum S (o),

H(w) = S*(w) In the time domain, subsequently, the filter is h (t) where

the impulse response of

Fig.4 filter

t Lt PY h(t)

Signal s(t) and the impulse response h(f/

of its matched

h (t) = s* (- t) This equation means, as shown in Fig.4, that the impulse response of the matched filter is identical to the pulse obtained after taking the time reversal of the signal s (t). In fact, it is impossible to physically realize the filter without adding a constant delay. Thus a practical matched filter always includes a simple delay-line. The Rayleigh-wave falter can easily be matched with binary or polyphase coded signals or with a frequency modulated radar pulse. Filter matched to a coded pulse train signal Fig.5 shows, as an example, the structure of a filter matched to a binary modulated signal. The phase reversal of the im-

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Fig.5 Structure of a binary phase coded pulse matched filter. example corresponds to a pulse coded train of length three

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a single finger pair. The finger number has been reduced as shown in Fig.3, and the working frequency is the 15th harmonic. The compressed pulse given by this filter is shown in Fig.9. The level of the sidelobes (24 dB below the level of the main peak) is imposed by the small compression ratio of about 25. At present the main feasible performance Rayleigh-wave dispersive delay-lines are: a

b

Signal duration : Relative bandwidth: Compression ratio:

characteristics

of

0.5-50 /.ls less than 50% 10-l 000

Bandpass filter Four examples of this class of filter will be given. Quasi-rectangular Fig.6 Filter response for a matched and unmatched signal; a-output signal of a matched filter for a binary phase”pseudo-random coded input pulse of length 15 f+++-++--+-+----) with central frequency 60 MHz (scale: 2 ps per division); b-output signal of the same filter for an input pulse identical to its own impulse response (scale: 2 ps per division)

output

Fig.7 Structure and impulse response of a filter matched quency modulated signal

to a fre-

pression. Firstly, the frequency of the impulse response can be varied linearly with time. The compressed pulse obtained at the output of the filter then has sidelobes 13 dB below the level of the main peak. This difference in levels is not great enough for radar purposes, but it can be increased up to 30 dB for example (with an enlarged compressed pulse) when the active length of the fingers is varied with an appropriate 1aw.l 1 However, in this case the impulse response envelope is no longer rectangular, and the filter is no longer matched with the pulse of long duration and constant amplitude applied to the dispersive line input. Secondly, the frequency of the filter impulse response can be varied with time according to a non-linear law, an Sshaped law for instance. The advantage of this non-linearity is that the sidelobe levels of the compressed pulse are reduced without any mismatching. Unlike the linear weighted case the impulse response amplitude is constant.l* The actual level of the sidelobes is determined by the curvature of the frequency time S-shaped characteristics and depends on the compression ratio. Fig.8 shows such a line on a quartz substrate with a sampled dispersive transducer; each visible line of this long transducer is actually made of

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filter

The impulse response of the device must have the shape of a (sin x)/x curve so that the finger length of the transducer also varies according to (sin x)/x.13 Because of the finite dimension of the transducer, the impulse response of the filter has a limited number of sidelobes. Subsequently, the transfer function presents ripples of the type shown in Fig.10. This transfer function corresponds to an impulse response with three secondary sidelobes on every side of the main peak. A matching network has been used. The central frequency and bandwidth are respectively 3 1 MHz and 6 MHz, and the substrate is quartz. The relative bandwidth of this type of filter is between l-35%, while the insertion losses are presently high (20 dB or more) depending on the substrate and the transducer geometry. Quasi-triangular

Input

transfer function

transfer function

filter

The impulse res onse of this type of filter varies according to a [(sin x)/x] Y law. We have used two filters of this kind, each with a different frequency (28 and 32 MHz) to realize

Fig.8 Filter matched to a frequency modulated signal with one sampled transducer (quartz substrate). The scale is in centimetres

Fig.9 Response of the filter shown in Fig.8 to the matched signal. The frequency time characteristic is S-shaped (scale: 2 @ per division)

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transducer consists of a succession of peaks and the frequency interval between adjacent peaks is equal to the reciprocal of the propagation time between two elementary combs. Thus, the transfer function of a filter presents [(sin x)/x] 2 sh ap e d maxima spaced with an interval frequency Af given by

0

-3 dE The bandwidth for a maximum is about 36 kHz, while a matching network can eliminate the undesirable peaks (Fig. 14). Connecting the two identical filters in series gives a 3 dB bandwidth of 25 kHz.

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Fig.10

Frequency

28

30 32 34 Frequency [MHZ]

response of a bandpass filter.

36

The length of the

fingers of one input transducer electrode varies according to a (sin x)/x curve defined with six sidelobes (three on each side of the maximum). A matching network has been used for the Lsinx)/x transducer

a frequency discriminator. is shown in Fig. 11.

l4 The structure of these filters

The transfer function of each filter is zero at the central frequency of the other. The direct voltages delivered after rectifying by diodes connected at the output of each filter are substracted. So, in our example with a quartz substrate the characteristic is linear over a frequency range of 0.7 MHz, under and above 29.75 MHz; for this frequency the output voltage is zero (Fig.12). The same kind of discriminator with a ceramic substrate at a frequency of 17 MHz has a frequency range of 0.75 MHz and insertion losses of 24 dB. Narrow bandwidth

filter

The bandwidth is proportional to the reciprocal of the duration of the impulse response, provided there is no frequency modulation; to get a narrow bandwidth it is necessary to have a large duration impulse response. This requires a long transducer with many fingers. To reach a 50 kHz bandwidth with a central frequency of 100 MHz, 5 000 equally spaced fingers are needed. This is technologically excessive, however, it can be achieved in a simpler way. We have studied a filter having two transducers, each consisting of a succession of elementary combs with few fingers. The spacing between elementary combs is equal to an integer multiple of the acoustical wavelength which can be different for the input and output transducer.15 An example is given in Fig.13 which shows two identical filters on the same quartz substrate (central frequency f, about 102 MHz). Every visible line corresponds to a single finger pair; the distance between two adjacent finger pairs is 45 and 55 times the wavelength for the input and output transducer. The frequency response of every

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Fig.1 1 Geometry of two filters used to make a frequency discriminator. For each input transducer the finger length varies according to a [(sin x)/xl * law. The central frequency is different for each transducer

Fig.12 Frequency discriminator response (quartz substrate), Horizontal scale: 2 MHz per division; vertical scale: linear

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Fig.13 Two narrow bandwidth substrate. The central frequency spacing of the input for output) filter is 45 wavelengths (or 551.

----

Frequency

-cc

Experimental substrate

specification

limits

measurements

on quartz

filter etched on the same quartz is about 102 MHz, and the elementary transducers of each The scale is in centimetres

Frequency Fig.15

Example

Fig.16

Photograph

[MHz1

of a television if filter frequency

response

-3dB

60

80 FPQqUQfICy

120 [MHz]

140

Frequency response of one filter shown in Fig.13. The Fig.14 bandwidth is about 36 kHz and the horzontal scale shows frequency markers

of a ceramic television filter

Television filter The if image television filters are at present made from conventional discrete components, but theoretical and experimental studies I6 have been conducted for some years to investigate the possibility of using elastic Rayleigh-wave ffiters. The selectivity specifications for the French television standard are shown in Fig. 15. The synthesis of such a filter determines the positions and active lengths of the generators which will produce, within given limits, the frequency response. Experimental results obtained with quartz are also shown in Fig.1 5. Ceramic substrates now under investigation show, when compared with quartz, a double advantage: first, they are cheaper, and second, the losses are lower. Fig. 16 gives an idea of the dimensions of a ceramic substrate filter which is under study. It has losses of about 20 dB. Rejection filter In certain situations some frequencies have to be eliminated. Therefore, there is’a need to realize filters with a precise frequency zero transfer function. Such a transfer function can be implemented with two different delay-lines made on the same substrate (Fig.1 7) and connected in parallel. The amplitude of the transfer function varies as a 1cos x 1curve.

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Input

output

Fig.1 7 Association of two lines working at the same frequency but with different delays constituting a filter which gives a zero output for a determined frequency

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functions. Furthermore, the technology of these transducers, at least for frequencies less than 300 MHz, is quite similar to that for the production of conventional microcircuits. Matched filters as well as tapped delay-lines have been in use in radar systems for a number of years. Despite losses they offer, when compared with conventional filters, several advantages, ie, ease of matching with the signal, simple fabrication, greatly reduced volume, and low cost.

IOOMHz Frequency response of a filter with the same structure as Fig.18 that shown in Fig.1 7. The frequency interval between two adjacent zeros is 3.33 MHz

Different kinds of bandpass and rejection filters have been tested. It has been proved that many transfer functions can be obtained. However, their insertion losses are presently too high and they cannot, as yet, compete with existing devices. Studies are now being directed at increasing the central frequency in order to broaden the bandwidth. This means using electronic masking techniques. In addition, efforts are being made to improve the characteristics of piezoelectric ceramics, in particular the electromechanical coupling factor, the surface state, and the temperature stability. Success in improving ceramic characteristics should make mass production a possibility.

References

‘1 5 6

Fig.19 different

Transversal digital filter. to give

outputs are added

The weighted signals at the the desired function

7 8

The frequency interval between two zeros is equal to the reciprocal of the delay difference of the two lines. Fig.1 8 shows the frequency response of a 100 MHz central frequency filter, the zeros of which are separated by a frequency interval of about 3.3 MHz.

9 10 I1 12

Digital filter

13

Fig. 19 schematically represents a transversal filter using a Rayleigh-wave delay-line. The signal is tapped along the line and the samples obtained are weighted (Q then added (E) to give the desired output signaly (t).17

14 15 16

Conclusion Although the nature of Rayleigh waves is complex, it is comparatively easy to exploit them since the geometry of interdigital transducers allows a great variety of transfer

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17

Stem, E. Microsound components circuits and applications, Ultrasonics 7 (1969) 227 de Klerk, J. Ultrasonic transducers 3. Surface wave transducers, Ultrasonics 9 (1971) 35 Sabine, H., Cole, P. H. Surface acoustic waves in communications engineering, Ultrasonics 9 (1971) 103 FarneIl, G. W. Properties of elastic surface waves, in Physical Acoustics ~015 edited by W. Mason and R. N. Thurston (Academic Press, New York and London 1970) 109 Tancrell, R. H., Holland, M. G. Acoustic surface wave filters, Proceedings of the IEEE 59 (March 1971) 393 Broers, A. N., Lean, E. G., Hatzakis, M. 1.75 GHz acoustic surface wave transducer fabricated by an electron beam, Appkd Physics Letters 15 (1 August 1969) Hartemarm, P., Amodo, C. Rayleigh wave delay-line using two grating array transducers at 2.55 GHz, Electronics Letters 8 (18 May 1972) 265 Atzeni, C. Sensor number minimization in acoustic surface wave matched filters, fEEE Transactions on Sonics and Ultrasonics SU I8 (October 1971) 193 Carpentier, M. Radars: Concepts Nouveaux (DUNOD, Paris) Cook, C. E., Bernfeld, M. Radar Signals (Academic Press, New York and London) Hartemann, P., Dieulesaint, E. Intrinsic compensation of sidelobes in a dispersive acoustic delay-line, Electronics Letters 5 (15 May 1969) Hartemann, P., Dieulesaint, E. Ponderation des lobes secondsires dune impulsion comprimge par une Iigne dispersive a’ ondes dlastiques de Rayleigh, L’Onde Electrique 5 l(June 1971) 523 Hartemann, P., DieuIesaint, E. Acoustic surface wave filters, Electronics Letters 5 (11 December 1969) Hartemann, P., Menager, 0. Rayleigh-wave frequency discriminator, Electronics Letters 8 (20 April 1972) 214 Hartemann, P. Narrow bandwidth Rayleigh-wave fdters, Electronics Letters 7 (4 November 1971) 674 Devries, A. J., Adler, R., Dias, J. F., Wojcik, T. J. Realization of a 40 MHz colour television if response using surface wave transducers on lead zirconate titanate, Ultrasonics symposium (St Louis USA 1969) Squire, W. D., Whitehouse, H. J., Alsup, J. M. Linear signal processing and ultrasonic transversal filters, IEEE ultrasonics symposium on microwave theory and techniques MTT 17 (November 1969) 1020

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