A generalized impulse response model for SAW transducers including effects of electrode reflections

Closed-form expressions are presented which describe the behavior of arbitrarily weighted SAW (surface acoustic wave) transducers that contain uniform internal reflections. These expressions are based on a coupling-of-modes model of a SAW transducer and are expressed in terms of the Fourier transform of the transducer weighting function with respect to a modified frequency variable. This is the same Fourier transform which forms the heart of the conventional impulse response model. These transforms are easily evaluated using fast Fourier transform (FFT) routines. When the modified frequency variable is mapped back to true frequency, the results are known for all frequencies except a small gap near the center frequency. The response in this gap is easily evaluated numerically using expressions which are also given. The complete three-port model is then presented in terms of a mixed matrix representation in which the acoustic port variables are of a scattering parameter type and the electrical port variable is of a Y-matrix type