Derivation of COM equations using the surface impedance method

Abstract

The surface impedance method is used for the consistent derivation of coupling of modes equations which describe the interaction of SAW with a periodical system of electrodes of finite thickness. The exact analytic solution of the electrostatic problem in the presence of an arbitrary external electric field for a plane system of electrodes is applied to the calculation of the charge and electric field distributions. Mechanical perturbations are taken into account to first order of the thickness of the electrodes. As a result the scalar self-consistent equation for the electric potential of acoustic waves in the gratings is obtained. For the periodic structure this equation is reduced to the form of COM equations for slowly varying amplitudes. Analytical expressions for all coefficients of the COM equations connecting them with geometrical and material parameters are found. The NSPUDT effect can be considered. Dissipation and energy storage terms can be introduced empirically. The solution of the COM equations is represented in the form of a P matrix with elements written in a convenient form. A simple formula for calculating the location of maximum transducer frequency response is proposed, The balance of energy is considered. Some new relations among the elements of P matrix are found. >