Malocha D.C. Surface Acoustic Wave Filters The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Malocha, D.C. “Surface Acoustic Wave Filters” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
47 Surface acoustic Wave Filters 47.1 Introduction 47.3 Basic Filter Specifications 47.4 SAW Transducer Modeling The SAW Superposition Impulse Response Transducer Model. Apodized SAW Transducers 47.5 Distortion and Second-Order Effects 47.6 Bidirectional Filter Response 47.7 Multiphase Unidirectional Transducers 47.8 Single-Phase Unidirectional Transducers Donald c. malocha 47.10 Coded SAW Filters University of Central Florida 47.11 Resonators 47.1 Introduction A surface acoustic wave(SAW), also called a Rayleigh wave, is composed of a coupled compressional and shear wave in which the SAW energy is confined near the surface. There is also an associated electrostatic wave for a SAw on a piezoelectric substrate which allows electroacoustic coupling via a transducer SAw technologys two key advantages are its ability to electroacoustically access and tap the wave at the crystal surface and that the wave velocity is approximately 100,000 times slower than an electromagnetic wave. Assuming an electro- magnetic wave velocity of 3 x 108 m/s and an acoustic wave velocity of 3 X 10 m/s, Table 47. 1 compares relative imensions versus frequency and delay. The SAw wavelength is on the same order of magnitude as line dimensions which can be photolithographically produced and the lengths for both small and long delays are achievable on reasonable size substrates. The corresponding E&M transmission lines or waveguides would be Because of SAWs relatively high operating frequency, linear delay, and tap weight (or sampling) control, y are able to provide a broad range of signal processing capabilities. Some of these include linear and dispersive filtering, coding, frequency selection, convolution, delay line, time impulse response shaping, and others. There are a very broad range of commercial and military system applications which include components for radars, front-end and IF filters, CATV and VCR components, cellular radio and pagers, synthesizers and analyzers, navigation, computer clocks, tags, and many, many others [Campbell, 1989; Matthews, 1977 There are four principal SAw properties: transduction, reflection, regeneration and nonlinearities. Nonlinear elastic properties are principally used for convolvers and will not be discussed. The other three properties are present, to some degree, in all SAw devices, and these properties must be understood and controlled to meet device specifications. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 47 Surface Acoustic Wave Filters 47.1 Introduction 47.2 SAW Material Properties 47.3 Basic Filter Specifications 47.4 SAW Transducer Modeling The SAW Superposition Impulse Response Transducer Model • Apodized SAW Transducers 47.5 Distortion and Second-Order Effects 47.6 Bidirectional Filter Response 47.7 Multiphase Unidirectional Transducers 47.8 Single-Phase Unidirectional Transducers 47.9 Dispersive Filters 47.10 Coded SAW Filters 47.11 Resonators 47.1 Introduction A surface acoustic wave (SAW), also called a Rayleigh wave, is composed of a coupled compressional and shear wave in which the SAW energy is confined near the surface. There is also an associated electrostatic wave for a SAW on a piezoelectric substrate which allows electroacoustic coupling via a transducer. SAW technology’s two key advantages are its ability to electroacoustically access and tap the wave at the crystal surface and that the wave velocity is approximately 100,000 times slower than an electromagnetic wave. Assuming an electromagnetic wave velocity of 32108 m/s and an acoustic wave velocity of 32103 m/s, Table 47.1 compares relative dimensions versus frequency and delay. The SAW wavelength is on the same order of magnitude as line dimensions which can be photolithographically produced and the lengths for both small and long delays are achievable on reasonable size substrates. The corresponding E&M transmission lines or waveguides would be impractical at these frequencies. Because of SAWs’ relatively high operating frequency, linear delay, and tap weight (or sampling) control, they are able to provide a broad range of signal processing capabilities. Some of these include linear and dispersive filtering, coding, frequency selection, convolution, delay line, time impulse response shaping, and others. There are a very broad range of commercial and military system applications which include components for radars, front-end and IF filters, CATV and VCR components, cellular radio and pagers, synthesizers and analyzers, navigation, computer clocks, tags, and many, many others [Campbell, 1989; Matthews, 1977]. There are four principal SAW properties: transduction,reflection,regeneration and nonlinearities. Nonlinear elastic properties are principally used for convolvers and will not be discussed. The other three properties are present, to some degree, in all SAW devices, and these properties must be understood and controlled to meet device specifications. Donald C. Malocha University of Central Florida
TABLE47 1 Comparison of SAW and E&M Dimensions versus Frequency and Delay, Where Assumed Velocities ar VsAw =3000 m/s and vEM=3 X 10 m/s =300um 1.5m 入1=0.15m lay=1 ns =3 um LEM =0.3 m Delay =10 us =30mm FIGURE 47.1(a) Schematic of a finite-impulse response( FIR) filter.( b)An example of a sampled time function; the envelope is shown in the dotted lines. (c)A SAw transducer implementation of the time function h(t) A finite-impulse response(FIR)or transversal filter is composed of a series of cascaded time delay elements which are sampled or"tapped"along the delay line path. The sampled and delayed signal is summed at a nction which yields the output signal. The output time signal is finite in length and has no feedback. A schematic of an FIR filter is shown in Fig. 47.1 A SAW transducer is able to implement an FIR filter. The electrodes or fingers provide the ability to sample or tap"the SAW and the distance between electrodes provides the relative delay For a uniformly sampled SAw transducer, the delay between samples, At, is given by At= AL/vo where AL is the electrode period and va is the acoustic velocity. The typical means for providing attenuation or weighting is to vary the overlap between adjacent electrodes which provides a spatially weighted sampling of a uniform wave. Figure 47. 1 shows a typical FiR time response and its equivalent SAw transducer implementation. A SAW filter is composed of a minimum of two transducers and possibly other SAW components. A schematic of a simple SAw bidirectional filter is shown in Fig. 47. 2. A bidirectional transducer radiates energy equally from each side of the transducer(or port). Energy not being received is absorbed to eliminate spurious reflections 47.2 SAW Material Properties There are a large number of materials which are currently being used for SAw devices. The most popular gle-crystal piezoelectric materials are quartz, lithium niobate(LiNbO, ) and lithium tantalate(LiTa,O5). The materials are anisotropic, which will yield different material properties versus the cut of the material and the rection of propagation. There are many parameters which must be considered when choosing a given material for a given device application. Table 47. 2 shows some important material parameters for consideration for for of the most popular SAW materials Datta, 1986; Morgan, 1985] c 2000 by CRC Press LLC
© 2000 by CRC Press LLC A finite-impulse response (FIR) or transversal filter is composed of a series of cascaded time delay elements which are sampled or “tapped” along the delay line path. The sampled and delayed signal is summed at a junction which yields the output signal. The output time signal is finite in length and has no feedback. A schematic of an FIR filter is shown in Fig. 47.1. A SAW transducer is able to implement an FIR filter. The electrodes or fingers provide the ability to sample or “tap” the SAW and the distance between electrodes provides the relative delay. For a uniformly sampled SAW transducer, the delay between samples, Dt, is given by Dt = DL/va, where DL is the electrode period and va is the acoustic velocity. The typical means for providing attenuation or weighting is to vary the overlap between adjacent electrodes which provides a spatially weighted sampling of a uniform wave. Figure 47.1 shows a typical FIR time response and its equivalent SAW transducer implementation. A SAW filter is composed of a minimum of two transducers and possibly other SAW components. A schematic of a simple SAW bidirectional filter is shown in Fig. 47.2. A bidirectional transducer radiates energy equally from each side of the transducer (or port). Energy not being received is absorbed to eliminate spurious reflections. 47.2 SAW Material Properties There are a large number of materials which are currently being used for SAW devices. The most popular single-crystal piezoelectric materials are quartz, lithium niobate (LiNbO3), and lithium tantalate (LiTa2O5). The materials are anisotropic, which will yield different material properties versus the cut of the material and the direction of propagation. There are many parameters which must be considered when choosing a given material for a given device application. Table 47.2 shows some important material parameters for consideration for four of the most popular SAW materials [Datta, 1986; Morgan, 1985]. TABLE 47.1 Comparison of SAW and E&M Dimensions versus Frequency and Delay,Where Assumed Velocities are vSAW = 3000 m/s and vEM = 3 2 108 m/s Parameter SAW E&M F0 = 10 MHz lSAW = 300 mm lEM = 30 m F0 = 2 GHz lSAW = 1.5 mm lEM = 0.15 m Delay = 1 ns LSAW = 3 mm LEM = 0.3 m Delay = 10 ms LSAW = 30 mm LEM = 3000 m FIGURE 47.1 (a) Schematic of a finite-impulse response (FIR) filter. (b) An example of a sampled time function; the envelope is shown in the dotted lines. (c) A SAW transducer implementation of the time function h(t)
absorber Output piezoelectric substrate FIGURE 47.2 Schematic diagram of a typical SAw bidirectional filter consisting of two interdigital transducers. The transducers need not be identical. The input transducer launches waves in either direction and the output transducer converts the acoustic energy back to an electrical signal. The device exhibits a minimum 6-dB insertion loss. Acoustic absorber damps wanted SAW energy to eliminate spurious reflections which could cause distortions TABLE 47.2 Common SAw Material Properties Parameter/Material ST-Quartz YZ LiNbO, 128YX LiNbO, YZ LiTa, O, k2(%) 0.16 C (pf/cm-pair) 3,159 Temp. coeff. of delay (ppm/C) The coupling coefficient, k2, determines the electroacoustic coupling efficiency. This determines the fractional bandwidth versus minimum insertion loss for a given material and filter. The static capacitance is a function of the transducer electrode structure and the dielectric properties of the substrate. The values given in the table orrespond to the capacitance per pair of electrodes having quarter wavelength width and one-half wavelength period. The free surface velocity, vo, is a function of the material, cut angle, and propagation direction. The temperature coefficient of delay(TCD)is an indication of the frequency shift expected for a transducer due to a change of temperature and is also a function of cut angle and propagation direction The substrate is chosen based on the device design specifications and includes consideration of operating temperature, fractional bandwidth, and insertion loss. Second-order effects such as diffraction and beam G eering are considered important on high-performance devices [Morgan, 1985]. Cost and manufacturing tolerances may also influence the choice of the substrate material. 47. 3 Basic Filter Specifications Figure 47.3 shows a typical time domain and frequency domain device performance specification. The basic frequency domain specification describes frequency bands and their desired level with respect to a given reference Time domain specifications normally define the desired impulse response shape and any spurious time responses The overall desired specification may be defined by combinations of both time and frequency domain specifications Since time, h(o), and frequency, H(o), domain responses form unique Fourier transform pairs, given by h(r)=1/2T H(o)e/do (47.1) h(t)e"u dt (47.2) c 2000 by CRC Press LLC
© 2000 by CRC Press LLC The coupling coefficient, k2, determines the electroacoustic coupling efficiency. This determines the fractional bandwidth versus minimum insertion loss for a given material and filter. The static capacitance is a function of the transducer electrode structure and the dielectric properties of the substrate. The values given in the table correspond to the capacitance per pair of electrodes having quarter wavelength width and one-half wavelength period. The free surface velocity, v0, is a function of the material, cut angle, and propagation direction. The temperature coefficient of delay (TCD) is an indication of the frequency shift expected for a transducer due to a change of temperature and is also a function of cut angle and propagation direction. The substrate is chosen based on the device design specifications and includes consideration of operating temperature, fractional bandwidth, and insertion loss. Second-order effects such as diffraction and beam steering are considered important on high-performance devices [Morgan, 1985]. Cost and manufacturing tolerances may also influence the choice of the substrate material. 47.3 Basic Filter Specifications Figure 47.3 shows a typical time domain and frequency domain device performance specification. The basic frequency domain specification describes frequency bands and their desired level with respect to a given reference. Time domain specifications normally define the desired impulse response shape and any spurious time responses. The overall desired specification may be defined by combinations of both time and frequency domain specifications. Since time, h(t), and frequency, H(w), domain responses form unique Fourier transform pairs, given by (47.1) (47.2) FIGURE 47.2 Schematic diagram of a typical SAW bidirectional filter consisting of two interdigital transducers. The transducers need not be identical. The input transducer launches waves in either direction and the output transducer converts the acoustic energy back to an electrical signal. The device exhibits a minimum 6-dB insertion loss. Acoustic absorber damps unwanted SAW energy to eliminate spurious reflections which could cause distortions. TABLE 47.2 Common SAW Material Properties Parameter/Material ST-Quartz YZ LiNbO3 128° YX LiNbO3 YZ LiTa2O3 k 2 (%) 0.16 4.8 5.6 0.72 Cs (pf/cm-pair) 0.05 4.6 5.4 4.5 v0 (m/s) 3,159 3,488 3,992 3,230 Temp. coeff. of delay (ppm/°C) 0 94 76 35 h t H e d j t ( ) = / ( ) -• • Ú 1 2p w w w H h t e dt j t ( ) w ( ) w = - -• • Ú
→B2,,—B2"2 FIGURE 47.3 Typical time and frequency domain specification for a SAw filter. The filter bandwidth is Bu the transition bandwidth is B2, the inband ripple is R, and the out-of-band sidelobe level is RI it is important that combinations of time and frequency domain specifications be self-consistent. The electrodes of a SAW transducer act as sampling points for both transduction and reception. Given the desired modulated time response, it is necessary to sample the time waveform. For symmetrical frequency responses, sampling at twice the center frequency, fs 2fo, is sufficient, while nonsymmetric frequency responses require sampling at twice the highest frequency of interest. a very popular approach is to sample at f 4f a The SAW frequency response obtained is the convolution of the desired frequency response with a series of pulses, separated by fs, in the frequency domain. The net effect of sampling is to produce a continuous set of harmonics in the frequency domain in addition to the desired response at fo. This periodic, time-sampled function can be written g(t) an…6(t-t where an represents the sample values, tn=nAt, n= nth sample, and At= time sample separation. The corresponding frequency response is given by G(=∑g(n)n=∑gtn)1x (47.4) where f= 1/At. The effect of sampling in the time domain can be seen by letting f=f+ mf, where m is an integer, which yields G(+ mf, )= G() which verifies the periodic harmonic frequency response. Before leaving filter design, it is worth noting that a SAW filter is composed of two transducers which may have different center frequencies, bandwidth, and other filter specifications. This provides a great deal of flexibility in designing a filter by allowing the product of two frequency responses to achieve the total filter 47. 4 SAW Transducer modeling The four most popular and widely used models include the transmission line model, the coupling of modes model, the impulse response model, and the superposition model. The superposition model is an extension of the impulse response model and is the principal model used for the majority of SAw bidirectional and
© 2000 by CRC Press LLC it is important that combinations of time and frequency domain specifications be self-consistent. The electrodes of a SAW transducer act as sampling points for both transduction and reception. Given the desired modulated time response, it is necessary to sample the time waveform. For symmetrical frequency responses, sampling at twice the center frequency, fs = 2f0, is sufficient, while nonsymmetric frequency responses require sampling at twice the highest frequency of interest. A very popular approach is to sample at fs = 4f0. The SAW frequency response obtained is the convolution of the desired frequency response with a series of impulses, separated by fs , in the frequency domain. The net effect of sampling is to produce a continuous set of harmonics in the frequency domain in addition to the desired response at f0. This periodic, time-sampled function can be written as (47.3) where an represents the sample values, tn = nDt, n = nth sample, and Dt = time sample separation. The corresponding frequency response is given by (47.4) where fs = 1/Dt. The effect of sampling in the time domain can be seen by letting f = f + mfs, where m is an integer, which yields G(f + mfs ) = G(f ) which verifies the periodic harmonic frequency response. Before leaving filter design, it is worth noting that a SAW filter is composed of two transducers which may have different center frequencies, bandwidth, and other filter specifications. This provides a great deal of flexibility in designing a filter by allowing the product of two frequency responses to achieve the total filter specification. 47.4 SAW Transducer Modeling The four most popular and widely used models include the transmission line model, the coupling of modes model, the impulse response model, and the superposition model. The superposition model is an extension of the impulse response model and is the principal model used for the majority of SAW bidirectional and FIGURE 47.3 Typical time and frequency domain specification for a SAW filter.The filter bandwidth is B1, the transition bandwidth is B2 , the inband ripple is R2 and the out-of-band sidelobe level is R1. gt a t t n nn N N () ( ) / / = ×- - Â d 2 2 G f gt e gt e n j ft N N n j nf f N N n s () () () / / / / / = = - - - - Â Â 2 2 2 2 2 2 p p