SAW Bandpass Filter Design Using Hermitian Function Techniques

Hermitian function techniques may be applied t o the design of interdigital transducers (IDT) for arbitrary amplitudeiphase response surface acoustic wave (SAW) bandpass filters. I t is shown that periodically spaced single-finger electrodes may be employed using a synchronous frequency / * which is not harmonically related to frequencies in the passband. The method is demonstrated experimentally for a television intermediate frequency (TVIF) filter with center frcquency f o -44 MHz and synchronous frequency .I* = 55 MHz. I I N I KOI)IICTION N IMPULSE response evaluations as applied to the design of interdigital transducers (IDT) for surface acoustic wave (SAW) bandpass filters, it may be necessary or desirable to obtain the response parameters in a format which can be implemented usingperiodic finger spacing in the IDT. Analytically. this may be necessary when using computational techniques such as may be applied to finite impulse response (FlR) linear phase filters [ l ] , [2 ] . Additionally, pattern generator restrictions in the IDT lithographic fabrication process may dictate the use of periodic finger spacing. This periodicity is readily realizable for symmetric amplitude and accompanying linear phase response through the employment of a synchronous frequency f * (for which the electrode period is half a wavelength) which is equal to the bandpass center frequency f o . Departures from the symmetric amplitude constraint, however, dictate the evaluation of the inverse Fourier transform (IFT) over the required bandpass and an image response that is Hermitian (symmetric amplitude and antisymmetric phase response) about a synchronous frequency in the positive frequency regime, if periodicity of the IDT finger spacing is to be achieved. The IDT apodization function will be geometrically symmetric about impulse response reference time f = 0, however, as long as the phase response is linear. In the synthesis of SAW bandpass filters with nonsymmetric amplitude response, Mitchell and Parker [3] enlployed a synchronous frequency f * = 2f0 and used an overall frequency response function that included a third harmonic bandpass response as the mirror image of the fundamental required response. The “double electrodes” thus obtained from this Manuscript received March 8, 1979. This w o r k H;IS supported in part by an operating grant from the National Rcscarch Council of Canada. M. S. Suthers was with McMaster University, Hamilton, Ontnrio, Canada. He is presently with Bell Northcrn Rcscarch, Ottawa, Ontario, K1Y 4 H 7 , Canadd. C. K . C ~ m p b e l l and J . P. Reilly arc with thc I3cc icdl 1,‘nginccring Department and the Communications Rcscarch Llboratory, Mchlaater University, Hamilton, Ontario L8S 4 L 7 , Canada. synthesis procedure were individually weighted t o provide the desired nonsymmetric amplitude response. I t was noted that the advantageous use of double electrodes for reflection suppression was still preserved, as was the basic disadvantage that their use doubled the required lithographic resolution in the IDT fabrication process. and nonlinear phase responses, it was further shown [4] that such phase responses could be realized using IDT geometries with nonsymmetric apodization functions and double-finger electrodes with periodic spacing, by evaluating the IFT for the bandpass function and its Hermitian image in the negariue frequency regime. The realization of arbitrary amplitude/ phase was additionally detnonstrated by Boege et al. [S] using separately weighted split electrodes, as derived by using a synchronous frequencyf* = 2 f o about which the Hermitian response wzs imaged in the positive frequency domain. In this paper we demonstrate the realization of arbitrary amplitude/phase response for the case where the Hermitian bandpass function is imaged in the positive frequency domain, about a synchronous frequency f * which may have a value other than the harmonic value 2f0. This may be advantageous in the design of IDT geometries for very high frequency bandpass filters, for which a synchronous frequency f * < 2f0 can be employed to ease restrictions set by lithographic resolution for the 1DT fabrication. Additionally, the resulting use of “single” electrodes which are periodically spaced a t a synchronous frequencyf*, which is chosen not to be harmonically related to frequencies in the filter pass band, will serve to suppress spurious signals that would otherwise be caused by reflections from the electrode fingers. To demonstrate this, an example is given here for the response of a TVIF filter with bandpass center frequency fo = 44 MHz, and which employs single-finger electrodes with periodic spacing at synchronous frequency f * = 5 5 MHz. In studies of SAW bandpass filters with symmetric amplitude H E R M I T I A N FUNCTION KELATIONSHIPS Fig. 1 depicts the frequency response characteristic of a bandpass filter with arbitrary amplitude/phase specifications, together with the Hermitian response imaged about some synchronous angular frequency W* = 2nf* in the positive frequency regime. It may be noted that a) either the upper or lower bandpass range can be used to describe the desired filter response and b) for realizability, the entire function will have a Hermitian image aboutf= 0 in the negative frequency regime. Over the bandpass ranges in Fig. 1 , the response relationships 0018-9537/80/’0300-0090$00.75