The electrostatic problem for the SAW interdigital transducers in an external electric field. I. A general solution for a limited number of electrodes

An exact solution for finding the surface charge and electric field distributions in interdigital transducers (IDTs) with a limited number N of electrodes is given. It is based on the Keldysh-Sedov solution to the mixed boundary problem of the analytic function theory. The IDT electrodes are placed on the plane boundary between two anisotropic dielectric media. The external electric field may arbitrarily vary along the structure. The solution contains N constants which may be found from the electrodes´ connection conditions. For determining these constants a linear set of algebraic equations is obtained. The coefficients of this system are written in explicit form. The capacitance coefficients for a system of electrodes of different widths are obtained. For illustration purposes systems with one and two electrodes are considered in greater detail. In these cases the external electric field is assumed to vary harmonically along the structure with an arbitrary wavenumber. For one electrode the Fourier transform of the charge distribution is obtained in terms of the Bessel functions. For two electrodes of different widths a simple expression for the capacitance is found. The charge and electric field distributions are represented graphically for several wavenumbers and geometrical sizes of the electrode system. Section I contains a survey, including Russian literature, which is not well known in the west.