General one-dimensional treatment of the layered piezoelectric resonator with two electrodes

Abstract

A general transfer matrix description of arbitrarily oriented layered piezoelectric structures is presented. Except for the restriction to two electrodes, it is the most general one-dimensional treatment possible. The description is derived as an exact solution of the fundamental differential equations and the boundary conditions at the terminating surfaces and at the electrical port. It allows the calculation of the electrical admittance appearing between the electrodes for any frequency, as well as the determination of the entire resonance frequency spectrum using only simple matrix multiplications. It covers the general case of multimode excitations and its coupling results. Thus it is not restricted to a single displacement direction and can be used for the rigorous analysis of layered structures containing, e.g., doubly rotated Y-cut quartz crystals.