Analysis and equivalent circuit for accurate wideband calculations of the impedance for a piezoelectric transducer having loss

Others have analyzed the operation of piezoelectric transducers by defining two complex parameters which have the units of frequency to allow for the effects of loss. The present paper presents an analysis in which this procedure is extended to include harmonics as well as the fundamental frequency. In this extension it is seen that both positive and negative extrema in both the resistance and the conductance occur at a series of harmonics. Equivalent circuits are also presented with examples for both high-Q and low-Q materials showing agreement with these simulations.