A General Equivalent Circuit Model for Piezoelectric Generators

Abstract

This article presents an equivalent circuit model for a piezoelectric generator which can include any number of vibrational modes. First the electromechanical equations are formulated using an assumed mode (for example, the Rayleigh-Ritz method), the mechanical equations are then decoupled by the standard eigenvector approach. A set of single degree of freedom equations are thus produced. The electromechanical coupling terms are modeled in the equivalent circuit using an ideal transformer, or a set of current-and voltage-dependent sources. To validate the equivalent circuit model, the results show excellent agreement with published analytical solutions for the first three vibration modes of a cantilever unimorph generator. The main advantage of the new method is that it can be used to simulate any circuit topology, for which there is no analytical solution, using a standard electronic simulation program. To demonstrate this, the analysis and design of a more complicated diode bridge circuit is presented.