Nonlinear direct and indirect third harmonic generation in piezoelectric resonators by the intermodulation method

Nonlinear characterization in power piezoelectric devices requires a knowle dge of what mechanisms are involved in the nonlinearity. For resonant devic es, it is considered that the origin of these nonlinearities is mechanical, and their effects are: the increase of losses, the shift of the resonant f requency, and the frequency hysteresis. These effects, which can be underst ood by the analysis of the impedance increase near the resonance, can arise from third harmonic generation (second overtone) due to the nonlinearities . This third harmonic can be generated by the cubic terms of the nonlinear constitutive equations (direct contribution), or by the quadratic terms whe n they perform twice consecutively (indirect contribution). The present wor k presents a quantitative evaluation of these two effects, using an intermo dulation method that allows us to know every harmonic generated by the nonl inearity, whether quadratic or cubic. The conclusion of this work is that f or the studied piezoelectric ceramics, with low and high losses, the indire ct effect is negligible compared with the direct contribution, being about 1000 times lower. (C) 2001 American Institute of Physics.