The electrostatic problem for the SAW interdigital transducers inan external electric field. I. A general solution for a limited numberof electrodes

摘要

An exact solution for finding the surface charge and electricnfield distributions in interdigital transducers (IDTs) with a limitednnumber N of electrodes is given. It is based on the Keldysh-Sedovnsolution to the mixed boundary problem of the analytic function theory.nThe IDT electrodes are placed on the plane boundary between twonanisotropic dielectric media. The external electric field maynarbitrarily vary along the structure. The solution contains N constantsnwhich may be found from the electrodes' connection conditions. Forndetermining these constants a linear set of algebraic equations isnobtained. The coefficients of this system are written in explicit form.nThe capacitance coefficients for a system of electrodes of differentnwidths are obtained. For illustration purposes systems with one and twonelectrodes are considered in greater detail. In these cases the externalnelectric field is assumed to vary harmonically along the structure withnan arbitrary wavenumber. For one electrode the Fourier transform of thencharge distribution is obtained in terms of the Bessel functions. Forntwo electrodes of different widths a simple expression for thencapacitance is found. The charge and electric field distributions arenrepresented graphically for several wavenumbers and geometrical sizes ofnthe electrode system. Section I contains a survey, including Russiannliterature, which is not well known in the west