Electromechanical Model of a Longitudinal Mode Piezoelectric Transformer

This paper presents an electromechanical model for a piezoelectric transformer (PT), which is driven at the longitudinal mode. The electromechanical model is established by the coupled equations of motion of the PT, which is derived by the Rayleigh-Ritz method and Hamilton´s principle. The Rayleigh-Ritz method allows us to represent a continuous system by a discrete approximation. Thus, the variational expression of Hamilton´s principle can be used to model the distributed piezoelectric structure for estimating the parameters of the equivalent circuit model of the PT. Furthermore, the equivalent circuit model is used to estimate the electrical characteristics of the PT. Such as input admittance, voltage step-up ratio, output power and efficiency are derived by the equivalent circuit model. Based on the model, the performance of the beam-type PTs can be predicted by the geometrical dimensions and material parameters in the design stage. The validity of the proposed model is experimentally confirmed.