Frequency response of acoustic surface wave filters. I

Abstract

The transfer function of an acoustic surface wave filter is derived from first principles by calculating the current induced on the receiver transducer when an impressed voltage is applied to the generator transducer. By manipulating the equations of motion and the boundary conditions that govern the mechanical and electromagnetic variables, it is shown that the normal component of the electric displacement inside the substrate, and ultimately the surface charge density, can be related to the Fourier transform of the electric potential outside the substrate by means of a dielectric response function. An exact expression for the latter function containing full piezoelectric coupling is deduced, and a numerical prescription given for calculating from it the three important material parameters of the theory—effective relative dielectric constant, effective electromechanical coupling constant, and surface wave velocity. Difficulties associated with solving the mixed boundary value problem for the electric potential outside the substrate are discussed, and an approximate solution is offered. The transfer function calculated within this approximation is related to that obtained from the equivalent circuit model. The phenomenon of the triple transit echo is included in the theory in an empirical way by introducing the reflection coefficient of the transducer as a parameter. The fine structure observed experimentally in the frequency response is explained as an interference effect between the direct wave and the triple transit echo. Frequency response characteristics are calculated for some specific filter designs some of which employ varying finger overlap and varying finger width. There is good agreement between theory and experiment.