Theoretical study of the influence of the electromechanical constants and nonlinear mechanical losses of various piezoelectric materials on their performances in power transducers

Abstract

A simple analytical model is developed in longitudinal resonance mode taking into account the piezoelectric and mechanical constants of the materials as well as a mechanical loss tangent depending on the relative mean strain S : tan/spl delta//sub m/ = tan/spl delta//sub mo/ + /spl alpha/S/sup 2/, where tan/spl delta//sub mo/ is the low power mechanical loss tangent and /spl alpha/ a coefficient characteristic of the non-linearity. For a given acoustical load, the power supplied to the load, the mechanical losses and the maximum internal stress are expressed as a function of the applied electric field at the series resonance frequency for various materials: hard PZT, hard BaTiO/sub 3/ and PMN-PT ceramics and a PMN-PT single crystal. In steady state, the limitation factor would be the loss power for PMN-PT ceramic and single crystal and the maximum stress for hard PZT and BaTiO/sub 3/. In longitudinal mode , the very high compliance s/sub 33//sup E/ of the single crystal goes against it, however, its low acoustical impedance significantly reduces the internal stresses. The hard lead-free BaTiO/sub 3/ could be similar in radiated power to the hard PZT but it should be fed with higher electric fields. The respective influences of tan/spl delta//sub mo/ and /spl alpha/ on the performances are discussed. Finally, some single crystals and textured ceramics seem promising for 31 transducers.