Nonlinear measurement of piezoceramic resonators by the intermodulation method

The high signal characterization of piezoceramic devices when working in resonance shows alterations of the linear behavior because large strains are involved. However, it is difficult to know if these alterations are produced by quadratic or cubic nonlinear contributions, independently if the nonlinearities are caused by elastic or piezoelectric contributions. The cubic nonlinear terms produce nonlinear signals at harmonic frequencies ω and 3ω (where ω is the excitation frequency), so they modify the impedance and the characteristic resonance parameters (shift the resonance frequency f_s, and decrease the quality factor Q). The quadratic nonlinearities generate signals at frequencies 2ω and 0ω directly, and can generate, indirectly, nonlinearities at frequencies ω and 3ω, for example when the signals of frequencies ω and 2ω are combined. A measurement method is proposed which consists of exciting the resonator with two signals with close frequencies ω_A and ω_B near the resonance frequency, and making the measurement of the nonlinear intermodulation (IM) signals. This method allows the simultaneous measurement of both the quadratic and the cubic nonlinearities (direct and indirect), with different resonator impedances, and to obtain the dependence between the excitation current (or strain) and the nonlinear intermodulation level. The measures allow us to value which nonlinear effect is dominant, the direct third order or the indirect second order