A comparative study of one-dimensional models for piezoelectric resonators with mechanical losses

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Abstract
The expression of the electrical input impedance of a piezoelectric resonator can be derived from the piezoelectric constitutive relations and the wave equation, with a rigorous accounting of the internal mechanical losses. Different equivalent circuits, with different levels of approximation, are derived in this paper from the initial expression corresponding to a thickness expander piezoelectric resonator. The final step is the RLC circuit with explicit expressions for the circuit parameters as functions of the material constants. A good understanding of the level of accuracy of these circuits is useful for a better characterization of new piezoelectric materials with high mechanical losses. In this sense, a set of computer programs have been developed in order to evaluate the electrical input impedance according to the different models. A comparison of their level of accuracy is performed taking the initial expression as a reference. In particular, the discrepancies around the fundamental resonance are analysed as functions of kt and Qm.