Comparison of the Mason and KLM equivalent circuits for piezoelectric resonators in the thickness mode

The parameters of the KLM and Mason´s equivalent circuits in the thickness mode are presented to include dielectric, elastic and piezoelectric loss. The models are compared under various boundary conditions with and without acoustic layers to the analytical solutions of the wave equation. We show that in all cases equivalence is found between the analytical solution and the KLM and Mason´s equivalent circuit models. It is noted that in order to maintain consistency with the linear equations of piezoelectricity and the wave equation care is required when applying complex coefficients to the models. The effect of the piezoelectric loss component on the power dissipated in the transducer is presented for loaded and unloaded transducers to determine the significance of the piezoelectric loss to transducer designers. The effect of the piezoelectric loss on the insertion loss was found to be small