The impedance method in the theory of surface acoustic waves in periodic structures

Abstract

A method for determining surface impedances of periodic structures is proposed. The method is based on Biryukov’s equation for the surface impedance matrix of an inhomogeneous medium. This nonlinear integro-differential equation relates the impedance matrix with material parameter distributions. A solution of such equation is an alternative approach to boundary-value problems in contrast to the known finite element method. It is demonstrated that this equation in the case of periodic structures is reduced to a system of nonlinear ordinary differential equations of the first order in partial impedances. The developed impedance method is applied to a complex periodic system of elastic electrodes placed on a piezoelectric substrate. By analogy with the well-known function of surface effective permittivity, the infinite matrix of effective permittivity is introduced in an explicit form to characterize the piezoelectric substrate surface loaded by elastic strips. Due to this approach the known complex electromechanical boundary-value problem for calculation of interdigital transducers of surface acoustic waves is reduced to a pure electrical boundary-value problem. Then this last problem is solved by methods of electrostatics in the general case of arbitrary number of different electrodes per periodic cell. As a result, the electrical admittance matrix elements, relating electrode currents with voltages, are obtained. These elements are represented as ratios of dispersion equations’ left-hand side corresponding to various electrode connections. As examples, the frequency dependence of electrical admittances for some important multielectrode periodic cells are calculated.