History of Saw Devices
IEEE Intl. Frequency Control Symposium, Pasadena, May 1998
David P. Morgan, Impulse Consulting, Northampton NN3 3BG, U.K.
This paper gives a historical account of the development of Rayleigh-wave, or surface acoustic wave (SAW), devices for applications in electronics. The subject was spurred on initially by the requirements of pulse compression radar, and became a practical reality with the planar interdigital transducer, dating from 1965. The accessibility of the propagation path gave rise to substantial versatility, and a huge variety of devices were developed. Passive SAW devices are now ubiquitous, with applications ranging from professional radar and communications systems to consumer areas such as TV, pagers and mobile phones.
The paper describes the extensive work, particularly in the 1970s, to investigate SAW propagation in crystalline media, including piezoelectric coupling, diffraction and temperature effects. This led to identification of many suitable materials. Concurrently, many devices began development, including pulse compression filters, bandpass filters, resonators, oscillators, convolvers and matched filters for spread spectrum. In the 1970s, many of these became established in professional systems, and the SAW bandpass filter became a standard component for domestic TV.
In the 1980s and 90s, SAW responded to the new call for low-loss filters, particularly for mobile phones. With losses as low as 2 dB required (and subsequently achieved) at RF frequencies around 900 MHz, a raft of new technologies was developed. Additionally, for IF filters special techniques were evolved to reduce the physical size needed for narrow bandwidths. Such devices are now manufactured in very large quantities. In order to satisfy these needs, new types of surface wave, particularly transverse leaky waves, were investigated, and materials using such waves now have their place alongside more traditional materials.
Acoustic waves have been used in electronics for many years, notably in quartz resonators which provide high Q-values as a result of the low acoustic losses. Also, delay lines, exploiting the low acoustic velocities, give a long delay in a small space. In 1965, the first surface acoustic wave (SAW) devices were made, introducing exceptional versatility because the propagation path was accessible to components for generating, receiving or modifying the waves. In the subsequent 30 years there has been an explosion in the development of these devices. A huge range of device types have emerged, and they are now ubiquitous in applications ranging from professional radar and communications systems to consumer areas such as TV, pagers and mobile phones. World-wide production stands at hundreds of millions annually. Despite this, the devices are not generally well known, perhaps because they are esoteric components invisible from the outside.
This paper is an attempt at a historical review of the subject, without details of the operation of the devices. The coverage is limited to electronics applications and therefore excludes other areas in which SAW’s are found, namely non-destructive evaluation, seismology, acousto-optics, acoustic microscopes and sensors. The account is biased towards devices, as opposed to phenomena or physics. Some books and special issues are listed at the beginning of the references [1-15].
The reader is asked to bear in mind that history is subjective, and that space contraints enforce the account to be selective. Thus, some ‘favourite’ topics may be found absent. It is planned to post an extended version of the paper on the world-wide web.
We begin by describing initial discoveries which showed that the subject might be practical and useful (Sect. 2, up to 1970). Section 3 describes the period 1970-85, in which the subject developed into practicality and began to demonstrate useful functions in real systems. The period after 1985 has been dominated by demands for high-performance low-loss devices which present special problems, invoking a variety of special solutions. Hence it is convenient to defer this to a new section, Sect.4, which begins with an assessment of the position around 1985. Dates given in the headings are approximate only.
The existence of the basic type of surface acoustic wave, in an isotropic material, was first demonstrated by Lord Rayleigh (J. Strutt) in his 1885 paper , and hence the wave is often called a Rayleigh wave. This straight-crested wave propagates along the plane surface of a half-space, with the particle motion in the sagittal plane (the plane containing the surface normal and propagation direction), and with amplitude decreasing with depth. Rayleigh was interested in the seismic signals observed following a ground shock. He showed that a late component, following the expected signals due to bulk longitudinal and transverse waves, could be explained by the existence of the slower surface wave. The signal could also be relatively strong owing to the wave spreading in two dimensions rather than three.
Subsequently, there was substantial work by other geophysicists with seismic interests. Love’s remarkable treatise , originally published in 1911, includes a study of shear surface waves, with motion perpendicular to the sagittal plane. This wave, called the Love wave, can exist when the half-space is covered with a layer of material with lower bulk shear wave velocity. Love also showed that a Rayleigh-type wave, with sagittal particle motion, could exist in a layered system. Work on this wave at the Earthquake Research Institute, Tokyo, in the 1920s  showed that a series of higher modes could exist. The first higher mode, known as the Sezawa wave, has been used in SAW devices. The many other developments in seismic surface waves are not generally of much relevance to SAW engineers, but the interested reader will find more information in, for example, Brekhovskikh  and Ewing et al .
As for bulk acoustic waves, surface waves were also found useful for non-destructive evaluation, for example detection of cracks near the surface. In this context Viktorov’s book  was an important source. At that time, the commonest methods for generating surface waves were the wedge and the comb, shown in Fig.1. In both cases a bulk wave is generated by a piezoelectric plate transducer and subsequently converted into Rayleigh waves (in both directions in the case of the comb). At this time there were also many other methods, and White’s review  described 24 methods.
These developments were the origin of modern SAW devices. In place of the clumsy wedge or comb transducers, the IDT was a structure that could be fabricated easily by photolithography. A crucial factor was the use of a piezoelectric material, such as quartz or lithium niobate, in which electric and elastic fields are coupled. Thus the propagation medium, the substrate, also plays a part in the transduction process, converting electric signals into acoustic waves and, at the receiver, vice versa. At this stage (1969), the basic elements for SAW were in place:
It was realised that this technology could have a substantial future, since the two-dimensional nature of the device made all points in the propagation path accessible, unlike a bulk wave device. This would confer substantial versatility, since almost arbitrary structures, highly complex if required, could be produced with high precision. Indeed, much of the history of SAW can be seen as an exploration of the functions obtainable by variously-shaped structures on the substrate surface, all fabricated by the same basic process. This line of thinking was reinforced by the concurrent development of integrated circuits, in which the use of a planar technology was enabling a remarkable increase of device complexity, a process still continuing today.
Other early Developments (to 1969)
Court’s paper  noted above appears in a 1969 special issue of IEEE Trans. MTT, which gives a useful snapshot of SAW developement up to that time . As might be expected for a new technology involving waves, there was a notable influence of microwave ideas, reflected in both the analysis techniques and in the applications envisaged. Thus, waveguides had been shown to be effective, amplification of SAW’s using proximity semiconductors was demonstrated, and miniature resonators would be feasible if an efficient SAW reflector could be found. A micro-miniature receiver circuit, with components some 105 times smaller than conventional, might be feasible. Much of this thinking turned out to be impractical though some ideas are still of much interest. The main present application areas, which concern devices consisting of planar components such as IDT’s, did not become clear until later.
SAW waveguides were reviewed by Ash et al  in the above special issue. A variety of ‘topographic’ waveguides, using shaped protuberances or grooves, were shown to be effective. More simply, it was shown that a metal strip on a piezoelectric substrate could guide the wave, and this ‘D v/v waveguide’ is simpler to produce; it has been much used in SAW non-linear convolvers.
To extend the delays obtainable, ‘wrap-around’ delay lines were developed, in which the ends of the substrate were ground into a smooth rounded shape so that the SAW’s could circulate around it. Potentially, these devices could employ waveguides to eliminate diffraction and proximity-coupled semiconductor amplifiers to overcome propagation loss. However, they have not received practical usage.
3. Development to 1985
3.1 Propagation and Materials (1970 – 1985)
To be effective, a prime requirement for SAW technology is the availability of one or more substrate materials on which the wave propagation is sufficiently well behaved. Initially, it was not at all clear whether adequate results would be obtainable, and substantial efforts were needed on this topic. The basic needs are listed as follows:
(d) Low temperature coefficient.
(e) Low attenuation
(f) Low dispersion.
(g) Low non-linear effects.
(h) Propagation not much affected by SAW components such as IDT’s.
(i) Minimal degradation due to excitation of unwanted bulk waves.
A remarkable conclusion to be drawn from the early studies is that it is possible to choose a material such that most of the above requirements are easily and simultaneously satisfied – the propagation of SAW’s is, for many practical purposes, ideal. Thus, the SAW designer can often, as a result of the early studies, embark on his task with the knowledge that he will not need to compensate for SAW attenuation, dispersion or diffraction, and that non-linear effects will be negligible at the power levels to be used. However, temperature effects usually need to be considered because a material with many attractive properties may have inadequate temperature stability for some applications, an example being lithium niobate.
A piezoelectric material, which is necessarily anisotropic, is in practice either a crystal or a ceramic. The latter is of limited use because the attenuation of SAW’s on it is generally unacceptable at frequencies above about 50 MHz. There have been a great number of publications studying SAW propagation in anisotropic materials, an extensive topic because the solutions depend not only on the material considered but also on its orientation (the surface normal direction and the wave propagation direction, relative to the crystal lattice). Initially, it seemed that there was no SAW solution for some orientations, but later this was found to be untrue; problems had arisen due to the very complex nature of the numerical methods necessary. In 1968, Campbell and Jones  explained the numerical method for funding SAW solutions, using elastic constants obtained from earlier measurements on the bulk material. They also pointed out that the piezoelectric coupling for SAW’s can be characterised by evaluating two velocities, one for the SAW with a vacuum above the surface (v0), and the other when the surface is covered by a thin metal film which shorts out the tangential electric field but has no mechanical effect (vm). The fractional difference, D v/v º (v0 – vm)/v0, is directly related to the amplitude of surface waves generated by an IDT, as shown rigorously by later theory. In particular, the results showed  that the coupling is strong, D v/v = 2.4 %, for Y-cut lithium niobate with SAW propagation in the Z-direction. This case, known by convention as Y-Z lithium niobate, is one of the most popular choices.
Diffraction of SAW’s, which can be strongly influenced by anisotropy, was first considered theoretically in 1971 by Kharusi and Farnell . They used the ‘angular spectrum of plane waves’ method (ASPW), previously established for optics but here applied for the first time to the anisotropic case. The angular dependence of the SAW velocity gives sufficient information to allow for anisotropy. Various authors investigated, over a few years, several associated topics. Beam steering can occur, so that the SAW energy flow direction is not normal to the wavefronts. In many anisotropic materials, the SAW velocity is approximately a parabolic function of angle, in which case the diffraction pattern becomes the same as that for an isotropic material except for scaling along the main axis; the diffraction can be lesss or more than for the isotropic case. Non-parabolic materials are more difficult to analyse, though the ASPW method still applies. A particular example of this is Y-Z lithium niobate, in which the anisotropy is such that diffraction spreading is substantially reduced – this ‘minimal diffraction’ behaviour is another advantage of this material .
The temperature coefficient of SAW velocity is obtainable by calculating the velocity from elastic constants appropriate for two or more temperatures. However, the temperature coefficient of delay (TCD), which also involves the thermal expansion of the material, is the appropriate parameter for a SAW device. For quartz there is an orientation such that the velocity and expansion effects cancel, giving a TCD of zero at one temperature, as might be expected in view of the AT and BT cuts for bulk waves. The delay is a parabolic function of temperature. The orientation is a 42.75° rotated Y cut, known as the ST-cut, with propagation along X. This case, identified by Schulz et al in 1970 , is essential for many temperature-stable devices such as resonators and oscillators. Later, it was shown  that the ‘turn-over temperature’, at which the TCD is zero, can conveniently be adjusted by changing the cut angle.
Attenuation was shown to be low in many crystalline materials provided the surface is well polished. Experiments [37, 38] bore out the theoretical predictions that the attenuation (in dB) has an f 2 term due to the material viscosity [39, 40], and an f term due to generation of bulk waves in the air [40, 41]. The former is usually dominant, though the total attenuation is often small – for example Y-Z lithium niobate gives about 1 dB/m sec at 1 GHz.
Dispersion is theoretically non-existent, though very small amounts have been found in practice, probably due to surface treatment of the material during preparation. Non-linear effects are also usually insignificant. Early work such as  showed that the former affects the latter. The non-linearity gives rise to harmonic waves which combine to reconstruct the fundamental, but the extent to which this happens can be limited by dispersion (and can be used to measure dispersion). However, this work relates to a free surface and is not so relevant to devices, where the (small) dispersion is mainly associated with SAW components such as IDT’s. Usually, such components are made from aluminium film, which causes little disturbance. This choice was arrived at in the 1960s by examining a variety of film materials, comparing their resisitivity and their effects (attenuation, reflections and velocity shifts) on the SAW’s . With this choice, the components cause little disturbance of the propagation except when intended, as in reflectors for example.
It will be seen from the above that many of the requirements can be investigated using numerical calculations of SAW velocities. A great deal of such work was done in the 1970s to find suitable materials, and it continues to the present day. Extensive theoretical calculations were done by, for example, Farnell  and Slobodnik [37, 38], and the latter published extensive catalogues of SAW velocities in many materials in 1970-74 [45-47]. In addition, much experimental work was done to evaluate for example attenuation, diffraction and non-linear effects , and for this purpose optical probes were widely used [38, 48]. Paying attention particularly to piezoelectric coupling, diffraction effects and temperature stability, a variety of promising material orientations were identified, though not all have been exploited because of practical factors such as cost, size and availability.
A popular alternative to Y-Z lithium niobate is the 128° Y-X orientation, which was shown experimentally to give much less excitation of unwanted bulk waves . Lithium tantalate has intermediate piezoelectric coupling and temperature coefficient, and the X-112° Y orientation gives relatively good temperature stability and low bulk-wave excitation . Zinc oxide films have been investigated since the beginning . Despite their effectiveness for bulk waves the SAW application is more critical, and it was some time before they became common (using glass substrates) in economical TV filters . Recent results demonstrate impressive high-frequency performance, using sapphire substrates . Another promising material, introduced by Whatmore in 1981, is lithium tetraborate . This material has piezoelectric coupling better than that of quartz and a TCD much less than that of lithium niobate. In fact, the TCD is zero at one temperature as for ST-X quartz, though the stability is not so good. The above materials are commonest for practical devices, but many others have been investigated.
The fundamental work on SAW solutions also yielded a new type of surface wave, called the Bleustein-Gulyaev-Shimizu wave after its three independent discoverers [55-57]. This wave is transverse, with particle displacement normal to the sagittal plane, and exists in a piezoelectric material with a diad axis in this direction. The wave ceases to be guided along the surface if the material is not piezoelectric.
3.2 Pulse Compression Filters
As explained earlier, pulse compression was the main driving force behind the initial development of SAW, and the first SAW pulse compression filter was that of Tancrell et al in 1969 , illustrated in Fig.5. In addition to demonstrating a dispersive response, the device was used to compress a 1 m sec chirp pulse to 50 nsec, simulating a pulse compression radar. Conversely, it was also shown that a 1 m sec chirp pulse could be generated by applying an unmodulated 50 nsec pulse to the device. This technique, called ‘passive generation’, was to become a popular method of chirp generation because of the accuracy provided by SAW devices. Soon afterwards, comprehensive theoretical modelling was done , as described below. To determine the electrode positions , we can consider a chirp pulse cos[f (t)] with non-linear phase f (t), and locate the electrodes at places corresponding to uniform phase increments, such that f (t) = np.
In the 1970s these devices were refined and design methods were improved, including in particular compensation for diffraction. The high-quality reproducible performance of the devices made pulse compression radar a reality. Time-bandwidth products were typically 50 to 500, and the compressed pulse sidelobe rejection typically 25 to 40 dB. The chirps were linear, that is, the frequency of the pulse varied linearly with time. Single-electrode transducers were used initially, but later it was common to use double-electrode transducers to suppress electrode reflections. The substrate was often quartz, chosen for temperature stability, but for some chirp characteristics this would lead to high insertion loss, in which case lithium niobate or tantalate could be used. When SAW devices were used for passive generation (in the transmitter) as well as pulse compression (in the receiver), the two devices (the ‘expander’ and ‘compressor’) were often made as a matched pair mounted in the same package, as this helped to reduce errors due to differences of fabrication or temperature. However, at the present time the generation is often done digitally if the bandwidth is not too large (up to say 20 MHz), as this can be more accurate.
Another development was the use of non-linear chirps as a weighting technique – the frequency-domain amplitude is related to the rate of frequency sweep, and so can be made to vary. This enables the sidelobes to be reduced while maintaining a flat time-domain amplitude, corresponding to the transmitted pulse; in signal processing terms, the receiver is better matched to the transmitter and the output signal-to-noise ratio is somewhat better than in the linear-chirp case. This principle was proposed in 1964 , but it required the performance of SAW devices for its implementation. In 1976, Newton  explored the various design trade-offs, and device results were described by Butler . The non-liner chirp system is more affected by Doppler shifts than a linear chirp, but intermediate waveforms can be designed if necessary. In this and other topics, SAW engineers were the main instigators of radar signal development.
The Plessey AR3D radar (1979) used non-linear chirps in a novel way, in connection with electronic scanning of the radar beam, and had a large non-linear chirp SAW filter in the receiver.
To improve the performance of interdigital devices, the transducers can be slanted so that the wave only needs to pass through relatively few electrodes. This minimises degradation due to electrode reflections . Although double-electrode transducers were soon available to ameliorate this problem, the slanted geometry remained of interest for high frequencies, because it could use relatively wide l/4 electrodes. The device has been developed continually, for example by Potter , and excellent results were obtained recently at 1.5 GHz by Jen .
Interdigital devices become inconvenient if large time-bandwidth products (TB > 1000) are needed. This is because only part of a chirp transducer is active at any one frequency – the remainder is effectively a capacitor connected across the active part, increasing the device insertion loss. For large TB products, the Reflective Array Compressor (RAC) was introduced in 1972 by Williamson and Smith . Here the SAW is launched by a short uniform IDT, reflected through 90° by an array of grooves, reflected again through 90° by another groove array, and finally reaches another short uniform IDT at the output. The groove pitch is graded so that the path length varies with frequency. The device resembles an earlier device, the IMCON, in which bulk waves were reflected by grooves . The IMCON, dating from 1970, used the non-dispersive SH wave propagating in a parallel-sided metal plate. Another precursor was the 1968 demonstration by Sittig and Coquin  of a chirp device using reflection of SAW’s at a graded-periodicity grating, using wedge transducers and giving TB = 540.
The RAC enabled TB products as large as 16,000 to be produced . Also, a shaped metal film could be added between the groove arrays to compensate for measured phase errors, and good sidelobe levels, down to – 45 dB, were achieved. However, it was necessary to vary the groove depths to control the amplitude, making the fabrication time-consuming and therefore expensive.
Signal processing using Chirp Filters
If we consider a radar using linear chirps, it can be expected that a Doppler shift, causing a small shift of the signal frequency, will cause the output pulse to be displaced in time. In view of this, it is not surprising that chirp filters can be used to obtain the spectrum of an applied signal. The method is to multiply the input signal by a linear chirp and apply the result to a chirp filter with opposite dispersion. The output, as a function of time, then gives a scaled version of the spectrum of the input. This was noted by Klauder [22, p.761] and described in detail by Darlington . The system is closely related to Fourier transformation by optical lenses. If the input signal is taken to be CW, the system can be regarded as a method for frequency measurement, and is then called a compressive receiver, with applications including signal measurements for electronic intelligence. The earliest SAW example appears to be that of Alsup et al in 1973 , and it was subsequently developed by for example Atzeni et al, Jack et al  and Moule . For large TB products, many systems have used RAC’s, notably those of Gerard  and Williamson . A recent example is that of Li et al . There are also chirp systems providing variable delay, variable bandwidth bandpass filtering, or chirp filtering with variable time dispersion .
3.3 Bandpass Filters
Following the development of apodisation in pulse compression filters, described above, it was realised that apodisation could also be applied to a transducer with constant electrode pitch in order to control its frequency response, thus enabling it to provide bandpass filtering. This was demonstrated by Hartemann and Dieulesaint in 1969 . Soon afterwards it was realised that the technology was well suited to TV IF filters, the first example being that of Chauvin et al in 1971 , with a 33 MHz centre frequency and about 6 MHz bandwidth. Analysis using both the delta-function model and equivalent networks, allowing for apodisation, was given by Tancrell and Holland .
The apodised IDT, with constant electrode pitch, is a foundational SAW component. Following the delta-function model, it can be regarded as a sequence of equally-spaced sources whose amplitudes (proportional to the electrode lengths or overlaps) can be chosen at will. Now, diffraction and dispersion are often small, and often the electrodes do not disturb incident waves very much. It follows that the spatial shape of the transducer, given by the apodisation, is essentially a scaled version of its impulse response. In turn, the latter is, inevitably, the inverse Fourier transform of the frequency response. Thus a transducer can be designed simply by Fourier transformation of the required frequency response, using the resulting time-domain function to determine the electrode weights. This property was demonstrated by the above authors [76, 77]. It expresses the enormous degree of flexibility available in SAW devices, because any frequency response whatsoever can be synthesised using this principle. There are, of course, practical limitations, but typically many hundred wavelengths are available, giving many degrees of freedom. In practice the device has two transducers, arranged so that the overall response is simply the product of the two transducer responses. Apodisation introduces spaces between each shortened electrode and the opposite bus bar, and these are usually filled with ‘dummy electrodes’ (1971) to improve the uniformity of SAW velocity .
The above design principle can be expressed more rigorously by noting that the frequency response of a source with position corresponding to time t0 is proportional to exp( – j w t0). The transducer, consisting of a regular sequence of these sources, thus has a frequency response of the form
H(w ) = E S n An exp( – jw nt ) .. (1)
where t is the source spacing in time units and An are the source amplitudes, which can be taken to be the electrode lengths or overlaps. The term E is the ‘element factor’, representing the frequency response of each source; this was not known initially, but it could be assumed to be approximately constant. With E constant, equn.(1) is, rigorously, the response of a transversal filter, or finite impulse response (FIR) filter, which had earlier been much studied by designers of digital filters. SAW designers could therefore take advantage of methods for designing digital filters, to optimise parameters such as in-band ripple, skirt width and stop-band rejection. Tancrell  reviewed the position in 1974. A simple approach is to Fourier transform the required frequency response into the time domain (giving a function of infinite length) and then multiply by a finite-length weighting function. This might for example be the Hamming, Taylor or Kaiser-Bessel function, and the performance characteristics of these were compared. However, many early filters were designed using more empirical methods.
In the mid-1970s, optimal design methods were being applied to digital transversal filters , and in turn to SAW filters . In particular, the Remez algorithm [81, 82] enables an arbitrary tolerance to be specified as a function of frequency, as well as the amplitude itself. This remarkable, optimal method not only enables complicated responses to be designed but also enables second-order effects to be compensated. To fully exploit its flexibility, the transducer must have more than two electrodes per centre-frequency wavelength, and typically a double-electrode transducer will be used. Fortunately, this also eliminates electrodes reflections, which could cause severe distortion.
Many bandpass filters also incorporate a multi-strip coupler (MSC). This component, consisting of an array of unconnected electrodes parallel to the SAW wavefronts, was introduced in 1971 by Marshall and Paige [83, 84]. The two transducers in the filter are placed in separate, parallel, tracks, and the MSC transfers the SAW’s from one track to the other. In doing this, bulk waves are not transferred, thus eliminating an unwanted signal which occurs particularly in Y-Z lithium niobate substrates. The MSC also allows the device to be designed with both transducers apodised, giving more flexibility. Several other MSC components will be mentioned later.
Early TV filters were usually made on Y-Z lithium niobate with an MSC, though ceramic substrates for economy were also investigated. The required frequency response would normally be a complicated function, often including a frequency-dependent delay (see e.g. [6 p.207]). The delay variation mimics the behaviour of the conventional L-C filter, which had to be compensated by distorting the signal at the transmitter. Compared with its rival, the L-C filter, the performance of the SAW was not the crucial factor – more important were the small size and the fact that trimming was not necessary. It was a few years before TV manufacturers accepted SAW devices in volume. In this consumer area, cost was the overriding factor, and the device area was soon reduced by using 128° Y-X lithium niobate, which gives low bulk wave excitation and therefore eliminates the need for an MSC. Other substrates now used are  X-112° Y lithium tantalate, piezoelectric ceramics and ZnO on glass. A crucial factor in reducing cost is high-volume production (millions of devices annually), made possible by the simple planar structure and semiconductor-based fabrication techniques. Plastic packages are normally used, and TV filters are made to a wide variety of specifications. Such filters also find their way into VCR’s and DBS receivers.
Simultaneously, there was extensive work on filters for very exacting requirements, notably vestigial sideband (VSB) filters for TV broadcasting equipment. Typically, these have 6 MHz bandwidth centred at 40 MHz, in-band ripple of ± 0.2 dB in amplitude and ± 20 nsec in delay, and skirt width 500 kHz. To realise this, sophisticated designs are needed, usually compensating for diffraction [86, 87] and for circuit effects, i.e. distortion associated with the use of finite terminating impedances. Devices meeting the requirements emerged in the late 1970’s, for example Kodama’s device  using X-112° Y lithium tantalate, though most devices used lithium niobate. These devices are widely used for CATV. Somewhat later, similar filters were developed for digital radio, in which quadrature amplitude modulation (QAM) is used; here each symbol is a pulse whose amplitude and phase can take many values, giving many bits per symbol. The filter requirements for this system are even more demanding than those for VSB. Ganss-Puchstein et al  show examples with ripple as low as ± 0.05 dB for 64-QAM, with bandwidth 20 MHz.
As an alternative to apodisation, Hartmann  introduced ‘withdrawal weighting’, in which selected electrodes are removed from a uniform IDT. This method, much less affected by diffraction, gives excellent results in narrow-band filters. In the 1970s there were studies allowing for the complex electrostatic effects present in the short transducer sections remaining. However, later it was realised that this was unnecessary because the weighting can be done by modifying the electrode polarities rather than physically removing them.
In the 1970s, there was also much work on developing filter banks for applications such as ESM. These could be based on multiple SAW devices , and alternatively Solie  developed an efficient MSC-based method, effectively a frequency-selective beam router.
3.4 Gratings, Resonators and Oscillators
In microwave devices, resonances can be exploited to provide a narrow-band response in a relatively small device. SAW resonators are not quite analogous to this because there is no well-localised method known to provide efficient reflection. However, in 1970 Ash  showed that good reflectivity can be obtained, over a limited bandwidth, by using a regular array of weak reflectors, giving maximum reflectivity when the pitch is l /2. Subsequently, these gratings have usually been composed of aluminium strips (for convenience of fabrication) or grooves (for better performance). A typical resonator would have two gratings, forming a resonant cavity, with two IDT’s in between, one as the input and the other as the output. For temperature stability, quartz would normally be the substrate. In the 1970s there was substantial research on such devices, investigating for example the performance of gratings, optimum positioning of transducers and velocity shifts caused by electrodes or grooves, which could strongly influence the results. In some cases the performance was found to be degraded by the transducers behaving as waveguides, causing unwanted perturbations due to higher modes, and the latter were reduced by incorporating apodisation.
Analysis of gratings was initially done by modelling as a periodic transmission line having sections with alternating impedances, as explained for example by Li and Melngailis . The impedance changes give rise to reflections, and the values needed can be deduced from measurements. Later, first-order analysis of reflection by one strip or groove, in terms of material constants, was derived by Suzuki et al  and independently by Datta and Hunsinger [96, 97]. For a metal strip there are two terms, one arising from electrical effects [95, 97] and significant when D v/v is large, and the other due to mechanical effects [95, 96] and dominant in a weakly-piezoelectric material such as quartz. For a variety of materials, these formulae give reasonable agreement with experimental measurements, notably those of Dunnrowitz  and Wright . The first-order analysis also shows that the SAW velocity in a grating is expected to vary linearly with the normalised thickness h/l . However, measurements revealed an additional (h/l)2 term, which was attributed to stored energy. In early papers, this was represented by adding susceptances to the transmission-line model . Given the scattering behaviour of a single strip, the grating behaviour can be found by algebraically cascading the transmission line sections, though Suzuki  used the coupled-mode (COM) analysis. In either case, there are closed-form formulae for the grating as a whole.
The resonator, consisting typically of either one or two transducers in the cavity formed by two gratings, was described by Staples et al  in 1974, and many others began work almost simultaneously. A major application of the resonator is as the controlling element for a SAW oscillator. For modest requirements the device can be made in one lithographic step, using metal strip gratings. To avoid degradation due to electrode reflections in the transducers, one possibility is to position the electrodes as extensions of the adjacent grating pattern. This ‘synchronous’ design, common since about 1980, produces a skewed frequency response, but this is still acceptable for an oscillator and it avoids the need for a double-electrode transducer with its narrow electrodes. The insertion loss, without tuning inductors, is typically 5 dB.
For high performance, groove gratings are used and the electrode reflections can be minimised by recessing the electrodes into grooves in the quartz surface. Considerable efforts to optimise the performance have included the development of a quartz package, instead of the commoner metal packages, to minimise stresses due to differential expansion. Q-values in the region of 105 are achieved, and the long-term stability can be better than 1 ppm per year . The frequency stability of these devices is comparable to that of bulk wave resonator oscillators when the effects of frequency up-conversion are taken into account, and the SAW devices offer a convenient solution for fundamental mode operation in the range 100 to 2000 MHz.
A SAW oscillator can also be realised using a delay line, with the output fed back to the input via an amplifier. In fact, the first SAW oscillator, produced in 1969 by Maines et al , was of this type; it was put forward as a method for determining the substrate temperature coefficient, since frequencies can be measured very accurately. The Q-factor of a delay line is essentially its length in wavelengths, typically a few hundred and therefore much less than that of the resonator. However, this is not necessarily a disadvantage. Analysis of the short-term stability [101, 103] shows that the input power level is an important factor. For the resonator the high Q-factor magnifies the internal power level, so that the input power must be more constrained in order to avoid damage to the electrodes. In fact, the two devices can give similar performance , though the resonator is of course more compact and needs less input power.
The resonators considered above can also be regarded as narrow-band bandpass filters but their sharply peaked responses, corresponding to an L-C filter with only one pole, are not attractive. For multiple-pole designs, with potential for flatter passbands, a wide variety of methods for coupling single-pole devices were investigated in the 1970s . However, these were not popular for various reasons such as critical fabrication, narrow bandwidth capability or poor stop band rejection. Later, we describe the transverse-coupled resonator, an effective solution to this problem.
3.5 Convolvers and Spread-Spectrum Devices
This Section is concerned with devices for correlation of coded waveforms such as PSK, as used in spread-spectrum communications, and in particular with programmable devices. The popularity of the topic in the 1970s is illustrated by the fact that about a quarter of the 1976 Special Issue of Proc. IEEE  is devoted to it.
Mixing of contra-directed SAW’s was first observed in 1969 by Svaasand , using a quartz substrate. The non-linear effect is however much stronger in lithium niobate, and the convolution process was first verified in this material by Quate and Thompson  using bulk waves, and by Luukkala and Kino  using SAW’s with the arrangement of Fig.6. In view of earlier remarks that non-linear effects are usually insignificant in SAW devices, the deliberate use of them here is at first sight perplexing. However, the non-linearity is indeed weak, causing little perturbation of the input waves; it turns out that although the output signal has a very low power level, it is sufficient to ensure that thermal noise does not appreciably degrade the correlation process.
The efficiency is nevertheless of considerable concern, and in 1974 narrow beam widths of about 3l were used, increasing the power density and hence the strrength of the non-linear interaction [108, 109]. The sensing electrode thus became a D v/v waveguide, with the added advantage that the beam was well guided. With the addition of ground electrodes on the surface adjacent to the guide, the device was much more efficient . The bilinearity factor, defined by C = Pout – Pin1 – Pin2 (with the powers in dBm), was C » – 71 dBm. Many later devices were similar, though usually with SAW’s in two waveguides and a subtracting arrangement to reduce spurious signals , and bilinearity factors improved by a few dB’s. Special methods were used for generation of narrow SAW beams, namely a multi-strip beam compressor , waveguide horns , chirp transducers  and transducers with curved electrodes . Typical devices would have 100 MHz bandwidth and 16 m sec interaction length, capable of correlating waveforms with time-bandwidth products up to 1600. In 1981 it was shown that the device could be characterised by a two-dimensional frequency response, and this facilitated measurement of the spatial uniformity of the device [ 6, 113].
For better efficiency, a variety of devices exploited electronic non-linearity in semiconductors. It was known in the 1960s that SAW’s in lithium niobate, for example, could be amplified by a drift current of electrons in an adjacent semiconductor (silicon) . To avoid unwanted propagation loss, it was necessary to maintain a small gap of thickness comparable to the wavelength between the semiconductor and the substrate. In the early 1970s it was shown that, with waves generated at each end of the lithium niobate, non-linearity in the semiconductor gave convolution action with improved efficiency [115, 116]. Bilinearity factors in the region of C » – 60 dBm were obtained [116, 117]. An alternative device used a zinc oxide film on a silicon substrate [116, 118], in which case an air gap is not necessary, though the fabrication of the ZnO film is a complex matter. Recent devices of this type have used the Sezawa wave (the first higher Rayleigh wave mode) because it can give stronger piezoelectric coupling, and gave very high efficiency with C = – 41 dBm . These acoustoelectric devices are also capable of other functions including signal storage and optical scanning, as discussed by Kino .
Another approach to correlation of waveforms such as PSK is the tapped delay line, in which the taps are short transducers with polarities (0 or 180° ) corresponding to the code. These devices originated in the 1960s . It was soon realised that programmable filters could be realised by arranging external circuitry to switch the phase of the output from individual taps [121, 122]. A recent device of this type  had amplitude as well as phase programmability, and was demonstrated as an adaptive notch filter to reject CW interference in a communication system.
It was recognised in the early days that these devices were limited by the space and complexity of the bond wires for individual taps. To overcome this, integration of the SAW and semiconductor components was envisaged, and this aim has prompted research work for many years. For example, Hagon  demonstrated in 1973 a 64-tap filter on aluminium nitride, with switching circuitry in silicon, both materials being in the form of films on the same sapphire substrate. Later, Hickernell  demonstrated an integrated programmable 31-tap device in silicon, using MOSFET’s as taps (not requiring piezoelectricity), and with a ZnO film for the IDT. Recently, another technology has emerged, the acoustic charge transport (ACT) device in which an unmodulated SAW propagates along a (piezoelectric) GaAs substrate and packets of charge are transported in the potential wells associated with the SAW [126, 127]. Zinc oxide is needed for the SAW transducers, but the charge packets can be sensed by electrodes, much as in a CCD. A fully integrated technology would appear to have much potential, allowing circuits to incorporate the delays obtainable with SAW’s, but to date there does not seem to be a practical realisation.
3.6 Transducer Analysis (1965–1985)
This topic is vital to SAW devices, and indeed often encompasses the analysis of a device. Because of its importance, it has been pervasive throughout the history of SAW. The complexity of IDT behaviour on a piezoelectric substrate is enough to justify the use of several different approaches concurrently. Thus, simple approximate methods are convenient to use and may serve as the basis for the inverse process of transducer design. Complex, comprehensive methods predict details with more accuracy, as needed for sophisticated devices, and give insight into factors limiting performance.
In the 1960s there were many initial attempts, such as those of Coquin and Tiersten , Joshi and White  and Skeie . Emtage had an approach somewhat related to modern COM analysis. These works laid some useful groundwork but their complexity, and the limitation to unweighted single-electrode transducers, made them not very suitable for device analysis.
One reason for the complexity here is the presence of electrode reflections. The electrode pitch in a single-electrode transducer is l /2 (at the centre frequency), so that reflections from all the electrodes are in phase. This can cause substantial distortion, as shown in the experimental and theoretical study of Jones et al . The double-electrode transducer, introduced in 1972 by Bristol et al , virtually eliminates this problem by using an electrode pitch of l /4, so that electrode reflections cancel in pairs. Subsequently, all devices requiring high performance (e.g. VSB bandpass filters) have used transducers of this type or similar. Hence, for many purposes a theory that ignores electrode reflections is acceptable.
The simplest approach is the approximate ‘delta-function’ model of Tancrell and Holland , which envisages a localised source at each edge of each electrode. A localised source can be represented by a spatial delta function, hence the name. To accommodate apodisation, the sources are considered to be present only where electrodes of different polarity overlap. Excitation is analysed simply by adding the waves generated by the sources, ignoring the presence of other electrodes (thus excluding electrode reflections). This method gives excellent value in that a straightforward calculation yields a great deal of information about the response. Consequently, the method is still used to the present day. The main limitation is that the transducer impedance is not obtainable, thus excluding evaluation of the device insertion loss and the circuit effect (i.e. distortion associated with terminating impedances).
These deficiencies were overcome by the equivalent network models introduced in 1969 by Smith et al . Here, the IDT was modelled as an array of bulk wave transducers. Accurate equivalent networks for the latter had already been established, and they could be cascaded to simulate an IDT. For simplicity, the electric field generated by the electrodes was assumed to be either vertical or horizontal, leading to the ‘crossed-field model’ or ‘in-line field model’ respectively. Unlike the crossed-field model, the in-line model predicts electrode reflections. However, it was later concluded that the crossed-field model corresponded more closely to reality, with reflections included if necessary by incorporating transmission lines with impedance discontinuities . Although physically unrealistic, this model includes all the basic phenomena present, which are capacitance, transduction, propagation and reflection, though appropriate parameters need to supplied from either experimental experience or more basic theory. Tancrell and Holland  applied the method to apodised and chirped transducers.
An important parameter is the piezoelectric coupling constant, k2. For bulk wave transducers this is unambiguously defined, and by analogy the value for a SAW IDT was expected to be approximately k2» 2 D v/v. Values in this region were obtained from measurements on various substrates. Most authors now define k2 = 2 D v/v. The present author concluded [ 6, p.153] that the appropriate value was k2 = 2.25 D v/v, though the difference is not be very significant practically.
Hartmann’s ‘impulse model’  provided a simpler approach, extending the delta-function method to give, for example, transducer impedances. Like many other theories, this made use of the fact that the acoustic susceptance Ba of a transducer is the Hilbert transform of its conductance Ga, as first noted by Nalamwar and Epstein .
A major advance was Ingebrigtsen’s introduction of the effective permitivity e s(b) in 1969 . Taking all the quantities to vary as exp( jb x), this is defined by
Although inconvenient in some cases because of computational complexity, the above approach also leads to useful approximate results. Milsom showed that G(x), the surface potential due to a line of charge, could be expressed as a sum of electrostatic, SAW and bulk wave terms. The SAW term has the form G s.exp( – jk0|x|), where G s is a constant. Also, Ingebrigtsen  proposed that, for Rayleigh waves, e s would be approximately proportional to (b – k0) / (b – km), giving the pole and zero noted above. From this it can be shown [ 6] that G s is proportional to D v/v, thus justifying the earlier use of this parameter as a measure of the piezoelectric coupling . The Ingebrigtsen approximation was also used in the analysis of SAW propagation in a regular array of metal strips , using Floquet expansions with the fields expressed as summations of Legendre functions. The width of the predicted stop band is consistent with the electrode reflection coefficient deduced later by Datta .
Ignoring the bulk-wave Green’s function, as is often valid, the remaining SAW and electrostatic terms still lead to some complexity because they involve electrode reflections. However, the latter are often small because, for example, double-electrode transducers are used or D v/v is small. To exclude reflections, the analysis can be cast in an approximate ‘quasi-static’ form [ 6, 141]. This shows that the SAW amplitude generated by an IDT is proportional to the Fourier transform of the electrostatic charge density, which also gives the capacitance. In fact, the role of the electrostatic solution had been recognised from earlier work in the 1960s, and an algebraic solution for the single-electrode transducer, involving elliptic integrals, was derived in 1969 by Engan . This was the first analysis to show how the coupling, and the relative levels of the harmonics, depend on the metallisation ratio a/p. Later, Peach  derived algebraically the charge density obtained when a voltage is applied to one electrode in a regular array. This function, essentially the element factor for one electrode, can be used to synthesise the response for many types of transducer using superposition. Numerical electrostatic calculations have also been used extensively, initially by Hartmann and Secrest  in connection with end effects. Smith’s work  is also notable, and a recent account is given by Biryukov et al .
It should be noted that none of the above theories include mechanical loading, a complex subject which will be mentioned later.
3.7 Low-loss Filters (to 1985)
Throughout the history of SAW, the problem of obtaining good performance with low insertion loss has been a major concern. The problem arises because well-matched IDT’s reflect the waves strongly, giving unwanted multiple-transit signals which are usually unacceptable. To avoid this, most early filters (and all high-performance filters) had quite high insertion losses, typically more than 20 dB. Resonator filters afford one solution, but only for very small bandwidths.
As far back as 1969, Smith et al  used a tuned auxiliary IDT to reflect the unwanted ‘backward wave’ from an IDT, giving a device with reduced loss and small ripple. This principle still survives in some present devices, in the form of a reflective grating added to an IDT.
In 1972, Lewis  demonstrated a ‘three-transducer device’, in which a symmetric output transducer was situated between two identical outer transducers, both connected to the input. The output transducer receives waves with the same amplitude on both sides, and in this situation it does not reflect if it is electrically matched. Thus, reflections are suppressed and the minimum loss is ideally 3 dB. A related device is the ring filter of Fig.7, in which waves generated (in both directions) by the input transducer are transferred to an adjacent track, with propagation directions reversed. A central output transducer receives these waves and, again, gives no reflection if it is electrically matched. Here, the minimum loss is ideally 0 dB. The waves can be transferred between the tracks by a multi-strip (MSC) trackchanger incorporating a 3 dB coupler and and two mirrors . However, the earliest ring filter  used a simpler MSC arrangement, and Brown  developed further modifications. Recent devices used an adapted multi-strip trackchanger which also suppresses the stop band, and achieved a 1 dB insertion loss .
A simpler solution was the ‘single-phase unidirectional transducer’, or SPUDT, introduced in 1982 by Hartmann . Asymmetry was introduced by depositing additional metallisation on alternate electrodes of a double-electrode transducer. When a voltage was applied, this transducer generated waves preferentially in one direction, and it could be electrically matched to minimise acoustic reflections. The disadvantage of additional metallisation (which required accurate alignment to an existing pattern) was overcome by new types of SPUDT, notably the group type of 1983  and the DART (Distributed Array reflection Transducer) of 1986 . The group type uses IDT’s alternating with reflective gratings, while the DART consists of asymmetric cells incorporating wide reflector electrodes. In all these SPUDT’s, internal reflections are introduced deliberately, with an asymmetry such that waves launched in one direction are reinforced. The principle had, in essence, been anticipated much earlier in a transducer demonstrated by Hanma and Hunsinger , though this is not popular now because it incorporates l /16 electrodes. Another SPUDT is the floating-electrode UDT, or FEUDT, introduced in 1984 [158, 159].
Yet another possibility is a simple single-electrode transducer fabricated on an asymmetric substrate. Demonstrated by Wright in 1985 , this simply uses a substrate orientation with asymmetric mechanical properties, such as ST-X+25° quartz, and is called a ‘natural SPUDT’, or N-SPUDT. Although it seemed surprising that a symmetric transducer could be directional, earlier analyses had shown that the phase of the electrode reflection coefficient could be affected by the substrate orientation [95, 96], and Thorvaldsson  showed that this could account for the N-SPUDT effect. However, this UDT is of limited applicability because the ‘forward’ direction is determined by the substrate.
4. Recent Devices (1985–1997)
Summarising the above, the period 1970-85 saw the establishment of the basic elements of SAW technology – materials, propagation effects, analysis of transducers and gratings, design techniques – and the development of a wide variety of devices meeting exacting performance requirements. The technology had been set up and shown to be effective. Much of this effort (with the notable exception of the TV filter) was in response to military and professional requirements, particularly in radar and communications, with emphasis on optimising the performance. In contrast, the post-1985 period was driven more by consumer requirements, particularly for mobile phones, where cost, insertion loss and size were more important than before. It is therefore convenient to review the position at this point.
Initial development of SAW’s was greatly helped by three factors already present – suitable materials (lithium niobate, quartz), photolithography and computing (for device analysis, design, and mask pattern generation). These have always been crucial to SAW development. Optical lithography, originally spurred by integrated circuit requirements, was also basic to other technologies starting about the same time, namely CCD’s, integrated optics and bubble memories. Around 1970, line width capabilities were in the region of 1 m m, limiting SAW devices to about 1 GHz. In present manufacturing, 0.4 m m lines are feasible using non-contacting optical steppers projecting a reduced image. Devices with sub-micron lines were in fact made quite early using electron-beam fabrication , demonstrating device feasibility at high frequencies, though this method is not suitable for volume manufacturing.
The success of SAW devices can be attributed to several key factors:
(d) Excellent accuracy and reproducibility arise from the precision of photomask generation machines and the reproducibility of crystalline substrate materials.
(e) Complex designs, exploiting the versatility, are feasible because of sophisticated numerical analysis and design techniques.
(f) Single-stage lithography is well suited to mass production of low-cost devices, with many devices per wafer.
The progress of the subject is illustrated by the reviews of Williamson  in 1977 and Hartmann  in 1985. Williamson listed 45 distinct species of SAW device, with 10 of them well established in practical systems. Thirty-seven government systems used SAW devices, particularly matched filters, bandpass filters and delay lines. Prices ranged from $1.50 to $10,000. Hartmann listed 29 types of SAW device in use in systems, again with many military applications, including radar, ESM, ECM and ECCM. In addition, the move towards consumer applications was already evident, including pagers, cordless phones and VCR’s, as well as TV IF filters. The practical significance of SAW was shown by the fact that many systems designers were already relying on performance standards unobtainable by any other technology.
In the Soviet Union, and in eastern European countries, there was also substantial SAW development, but awareness of this among western scientists was restricted because of the limited communications between the two blocs. However, most at least of the topics mentioned above were pursued in the east, in particular the TV filter. Useful reviews of work in Siberia and in eastern Europe were given in 1991 by Yakovkin [165a] and Buff [165b], respectively.
In the post-1985 period, consumer applications, particularly mobile and cordless phones, demanded low-loss compact filters, including RF filters with losses of 3 dB or less. In addition to the development of many new device types, this requirement has led to the use of novel types of wave. We therefore consider these waves before describing the devices.
This section is mainly concerned with bandpass filters. Other topics, such as pulse compression and convolvers, continued to be of interest, but they appeared less in the research literature because the main principles were established earlier.
4.2 Transverse Waves and New Materials (1975–1997)
The devices considered earlier have all used piezoelectric Rayleigh waves, for which the particle displacement is in or close to the sagittal plane and the velocity is less than that of the slowest bulk wave. However, in many materials there are special orientations giving solutions with shear displacement (normal or almost normal to the sagittal plane), and often with higher velocities. Several of these have practical advantages over Rayleigh waves for some situations and have become widely exploited, particularly in response to the strong demand for low-loss RF filters for mobile phones, described below. The topic originated around 1970, but it is convenient to consider it here because the applications are quite recent.
In 1977, Lewis  demonstrated that bulk shear waves could be used in rotated Y-cut quartz, with propagation normal to X. These ‘surface-skimming bulk waves’ (SSBW) were shown to have amplitude proportional to x –1/2. This was expected because, as for a shear horizontal wave in an isotropic material, the displacement was practically parallel to the surface and the boundary conditions were predicted to have little effect. Orientations close to BT-cut and AT-cut respectively gave good temperature stability (much better than ST-X quartz) and a high velocity (5100 m/s) attractive for high-frequency devices. To reduce the propagation loss, Auld et al  showed (initially using an isotropic material) that the wave could be trapped at the surface by means of a grooved grating. In later studies using AT-cut quartz, the grating was provided simply by the transducer electrodes or metal strips. The wave was called a ‘surface transverse wave’ (STW), and was used in resonators . Avramov’s work on resonator design showed that, in addition to enabling the frequencies to be increased, STW resonators could handle power levels higher than their SAW counterparts, giving improved short-term stability when used to control oscillators .
Leaky wave solutions were first identified in X-cut quartz by Engan et al in 1967 . They have velocities higher than that of the slowest bulk wave. The term ‘leaky wave’ refers to a theoretical solution in which the wavenumber is allowed to be complex, so that the amplitude decreases as exp( – a x). The attenuation can be very small, negligible in practical terms. Useful leaky waves were found in rotated Y-cuts of lithium niobate in 1970  and of lithium tantalate in 1977 [166, 172], and these are reviewed in . Propagation is in the X-direction. Compared with SAW, these waves offer higher piezoelectric coupling, higher velocity and higher power handling, and consequently they have been widely used in low-loss RF bandpass filters. The velocity is higher than that of the slow bulk shear wave. For lithium tantalate, the attenuation varies with the cut angle and becomes practically negligible at about 36° , for a free or metallised surface. In lithium niobate, negligible attenuation requires an angle of 41° for the free-surface case, or 64° for the metallised case. Despite this distinction, both cuts have been successfully used in low-loss devices.
Roughly speaking, transducers and gratings behave on these materials almost as if the waves were conventional Rayleigh waves. However, detailed studies in the 1980s revealed a complex picture. In 36° Y-X lithium tantalate there is in fact a SSBW solution in addition to the leaky wave. On a free surface these waves have almost identical velocities and they are difficult to distinguish, but for a metallised surface the leaky wave velocity is reduced and the waves can be distinguished. The SSBW amplitude theoretically decays as x –1/2 for small x and x –3/2 for large x . The x –1/2 variation has been seen experimentally, as has the exponential decay of the leaky wave . It seems that these complications do not affect practical devices much, perhaps because the devices use transducers rather than free or metallised surfaces. However, spurious signals, possibly associated with the SSBW, have been seen in impedance element filters . A similar situation occurs in 41° Y-X lithium niobate [175, 177].
In the last few years there has been renewed interest in the search for leaky surface wave solutions . New cases found include several longitudinal types, in which the displacement is almost parallel to the wave vector. In particular, 47° Y-cut lithium tetraborate, with propagation normal to X, gives a very high velocity of 7000 m/s with D v/v = 0.7 %, and this has been used in a 1.5 GHz filter .
Returning to Rayleigh waves, recent work has seen the development of diamond as a SAW material [179, 180]. Diamond can be grown as a film on a silicon substrate, with a ZnO layer on top to provide piezoelectric coupling for IDT’s. The high SAW velocity, in the region of 6000 m/s, is attractive for high frequencies, as demonstrated by practical filters .
4.3 Modern Low-loss Filters (1985 – 1997)
Mobile phone applications call for I.F. filters with bandwidths of typically 50 to 500 kHz, and with low loss. For these, the design of DART’s was investigated [181, 182], recognising in particular the complication that both transduction and reflection can be weighted (usually by withdrawal weighting). Filters consisting of two DART’s could give excellent performance, with for example 200 MHz centre frequency, 1 MHz bandwidth, 9 dB loss, 55 dB triple-transit suppression and 60 dB stop band suppression . However, now there was a new problem in that narrow-band devices were too large for pocket-sized applications.
A more compact arrangement is obtainable using multi-track DART filters [182, 184], in which output signals due to direct SAW transits are cancelled; the output arrives only after reflection at the output DART’s and, in some cases, at a central grating. Fig.8 illustrates a two-track device with gratings. These arrangements increase the number of frequency-selective stages involved, and therefore reduce the bandwidth for a given device length. Another development [185, 186] was the ‘Z-path filter’ of Fig.9, in which the wave from an input SPUDT is reflected by an inclined grating into a second track, where it is again reflected by a another grating and finally received by the output SPUDT.
Radio-frequency requirements for mobile phones have also prompted a variety of novel SAW techniques. Because of the relatively wide bandwidth, typically 30 MHz, leaky waves on lithium tantalate or niobate are normally used. The low-loss requirement is more urgent here since, for a receiver front end, it bears strongly on the signal-to-noise ratio. Also, centre frequencies of 900 MHz and above make designers reluctant to use electrodes any narrower than those of single-electrode transducers, so the complication of electrode reflections has to be accepted. An early idea was the interdigitated interdigital transducer (IIDT) described by Lewis in 1972  and demonstrated by him in 1982 . The device, Fig.11, consists of a regular sequence of transducers connected alternately to the input and output. This scheme received much attention in the 1980s [186, 190], and Hikita , for example, obtained 4 dB loss at 830 MHz with 30 MHz bandwidth and 50 dB stop band rejection, using a 36° Y-X lithium tantalate substrate. Related devices [186, 191] have used two tracks coupled using self-resonant IDT’s, and sometimes reflective gratings at the ends to reduce the loss.
Impedance element filters (IEF’s) use SAW components connected electrically, with no acoustic interaction, in a manner reminiscent of ladder filters using bulk wave quartz resonators. This principle was used by Lewis and West  in 1985. Hikita et al [196, 197] used banks of single-electrode transducers in which electrode reflections cause the response to be sharply peaked, so that they behave like resonators. They also demonstrated a duplexer, that is, a pair of filters for direct connection to the antenna, with the receiver filter suppressing the transmitter band and vice versa. Starting in 1992, another type of IEF used SAW resonators, each consisting of a single-electrode transducer between two gratings . With a simple design approach, two or more resonators with different resonant frequencies can be combined to give a response with a low-loss passband, though the stop band rejection is somewhat limited. Losses of 2 dB were achieved at 840 MHz, with 35 MHz bandwidth. Within a few years, production of such devices reached tens of millions per year. A 2.5 GHz filter gave 100 MHz bandwidth and 3 dB insertion loss . For improved stop band rejection, a balanced bridge arrangement has been used .
For RF applications the power handling capacity has been a concern, since powers in the region of 1 W are sometimes needed. The SAW filters were found to be limited by migration of the aluminium electrodes. In the 1980s there were many studies of this, and substantial improvement was obtained by adding a small proportion of copper to the aluminium, as shown for example by Hikita .
4.4 Recent Analysis (1980–1997)
Various analytic techniques developed up to about 1980 were more or less adequate for the times, as described above. However, later there were more demands on the analysis because of new device developments. Notably, ‘conventional’ devices such as VSB filters were being applied to more demanding specifications, calling for more accurate analysis; many new devices included internal reflections in the transducers, as seen above; and new modes – leaky waves and STW – were being widely applied.
One consequence was the extension of earlier theory to allow for two-dimensional behaviour, for example, allowing the charge density to vary in two directions. For application to dot arrays, Huang and Paige developed a 2-D electrostatic analysis  and a 2-D Green’s function  in 1982 and 1988, respectively. The Green’s function is essentially the potential generated by a point charge on the surface of an anisotropic piezoelectric dielectric. Techniques of this type were also applied to transducers, recognising that the electrostatic charge density on the electrodes is distorted near the ends . Visintini et al  applied these concepts to the analysis of sophisticated wide band filters for digital radio systems, incorporating an ASPW synthesis.
Returning to the 1-D case, a convenient way of incorporating internal reflections into transducer analysis has been the coupling-of-modes (COM) method, complementing the earlier network model. The approximate COM method envisages forward- and backward-propagating waves with slowly-varying amplitudes, represented by coupled differential equations. Coupled-mode theory originated with microwave work in the 1950s, but its first use in SAW seems to be that of Suzuki’s work in 1976 on gratings . For SAW transducers, the extension to include the necessary transduction terms was done by Koyamada and Yoshikawa , and physical justification was given by Akçakaya . The COM approach is notable for yielding algebraic expressions for all the required scattering properties (conversion, reflection, admittance) of a unweighted transducer . The analysis depends on only a few parameters, governing transduction, reflection, velocity and attenuation. For complex transducers, such as DART’s, it is feasible to deduce these from experimental measurements, without considering the complexities of the underlying physics .
Early analysis of strip reflection coefficients, mentioned above, was complemented in the 1980s by rigorous numerical calculations using the finite element method (FEM), particularly by Koshiba . Calculation of the stop band width of a grating yields the strip reflection coefficient, assuming that the latter does not vary much with frequency. Moreover, for transducer analysis, the application of this method to both the short-circuit and open-circuit cases gives in addition the transduction parameter [210, 211]. In this way, COM parameters have been deduced for IDT’s using leaky waves on lithium tantalate and niobate . In contrast to the SAW case, the transduction parameter is found to depend on the electrode thickness. Another application of FEM was Ventura’s analysis, with experimental verification, for the familiar case of reflection of SAW’s by Al strips on ST-X quartz . This showed that the reflection coefficient was substantially larger than that given by earlier theory of Datta  when the metallisation ratio exceeded 0.5.
Rigorous analysis of SAW transducers with irregular electrodes is very complex. Hashimoto  used a boundary element method (BEM), incorporating the electrostatic and SAW Green’s functions, to analyse a FEUDT with floating electrodes. For general one-dimensional problems with finite electrode thickness, involving mechanical effects, a generalised Green’s function can be used . This relates, at the surface, the 3 components of displacement and the potential to the 3 components of traction and the charge density. It is therefore a 4´ 4 matrix of functions. Ventura et al  applied these ideas, with FEM and BEM, to SAW device analysis. In these papers, the charge density on a electrode is assumed to have the form p(x)/Ö (a2 – x2), where p(x) is a simple polynomial and the edges are taken to be at x = ± a. This form is helpful because it gives the correct behaviour at the edges; it was introduced by Smith and Pedler in the 1970s .
Analysis methods for leaky waves and STW’s have been mainly restricted to uniform gratings and single-electrode transducers. These waves behave in a manner more complicated than SAW’s, in that the film thickness is more significant, and conversion to bulk waves occurs at and beyond the upper edge of the stop band. Hashimoto  has analysed a metal grating using the effective permittivity, with mechanical loading added using FEM. The numerical results were fitted to an empirical formula deduced by Plessky , from which the COM parameters for transducer analysis can be deduced. This allows the COM parameters to vary with frequency, in particular to model the loss due to bulk wave radiation. This approach has been applied to device analysis for both leaky waves on 36° Y-X lithium tantalate  and STW’s on quartz .
SAW technology, with the advantages noted in Section 4.1, is eminently suitable for linear analogue devices. Within this area, the versatility is so great that the devices cover almost all the functions imaginable – bandpass filters, pulse compression filters, resonators and so on. This has all been achieved since the IDT emerged in 1965, and the devices have demonstrated steadily-improving reproducible performance with, when needed, cost effectiveness associated with single-stage lithography. The subject is also packed with many fascinating physical topics, involving almost all the phenomena that waves in anisotropic media might exhibit. And new innovations are still occuring today.
As stated earlier, key ‘background’ requirements are piezoelectric materials, lithography and computing. This author would like to add a fourth factor – the hard work and dedication of an international band of very proficient people who had the inspirations, delved into the analysis, conducted experimental tests and finally made the devices perform useful functions. The progress achieved is staggering, and will surely fascinate anyone with a technical disposition. It has been a privilege to be involved in it.
It is a pleasure to acknowledge helpful comments made on the manuscript by C.S.Hartmann, M.F.Lewis and V.Plessky.
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