Piezoelectric ceramic materials present a Iow cost alternative to traditional single crystal piezoelectric materials. However, ceramic materials to date have featured significantly larger acoustic losses than those of single crystals, which has limited their application where high Q is a requirement. Acoustic loss in single crystal materials like quartz is sufficiently small such that neglecting loss terms in the constitutive relations has a negligible impact on their solution. However, for piezoelectric ceramic materials such as PZT, the loss terms must be included in any calculations since they have a significant impact on the solution. The inclusion of the loss terms leads to variety of interesting and unexpected behaviors in the piezoelectric resonator which must be understood where the ceramic material is being considered as a replacement for the single crystal. The aim of this work is to explore theoretically and experimentally the behavior of lossy piezoelectric ceramic resonators using PZT as a case study. Acoustic loss is included in the calculations by including acoustic viscosity as the complex component of the elastic stiffness constant. The constitutive relations are the solved for the dispersion relation characterizing the simple thickness modes of plate resonators. The solution has been found to be complex, implying that the device has a complex resonant point. Two equivalent circuit models have been developed to explain this behavior: one approach uses a transmission line model, while the other uses an RLC circuit analog. The simulations have demonstrated that the device looks like an RLC circuit when stimulated by complex frequency, i.e. an exponentially decaying sine wave. Experimental results will be presented which corroborate the theoretical analyses.
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