Theoretical and experimental studies of loss in piezoelectric ceramic resonators

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 a complex frequency, i.e. an exponentially decaying sine wave. Experimental results are presented which corroborate the theoretical analyses