Nonlinear Equivalent Circuit of High-Power Sandwich Piezoelectric Ultrasonic Transducer

In the theoretical design and analysis of the sandwich piezoelectric ultrasonic transducer, the transducer is considered to be an ideal linear system, where the dielectric, piezoelectric, and mechanical losses are neglected. However, when the transducer is driven at high power, the losses are becoming several times higher comparing them to low signal measurements, and the transducer works in a nonlinear state. In order to predict the performance of the transducer at high power, the nonlinear parameters (complex constants) of the piezoelectric materials are introduced. The corresponding nonlinear equivalent longitudinal wave sound velocity and the nonlinear equivalent longitudinal wavenumber of the piezoelectric ceramics are derived. Then, the nonlinear equivalent circuit (NEC) and the nonlinear resonance frequency equation of the high-power sandwich piezoelectric ultrasonic transducer that related with the losses are deduced. Then, the nonlinear finite element model (NFEM) of the transducer is constructed. The performance parameters of the transducer obtained by the NEC method and the finite element (FE) method are compared with each other, and consistent results have been achieved by two methods. Finally, the contribution of various losses is obtained through theoretical calculation, simulation, and experimental measurement, and the correctness of the theoretical model in this article is verified.