Dissipation in ceramic resonators and transducers

Ceramic resonators in the form of plates and cantilevers are increasingly being used to perform sensing and actuating functions, in addition to their traditional uses as frequency control and selection devices, because of their attractive attributes of low cost and high piezoelectric coupling. Very often the microelectromechanical structures (MEMS) are designed with insufficient attention to the various dissipation mechanisms involved. For piezoceramics, it frequently is unjustified to make simplistic assumptions about how the loss is to be incorporated, because the loss is generally much greater in ceramics than in substances such as quartz and refractory oxides. We consider four dissipation mechanisms that are representable in the constitutive equations, and show, through equivalent network representations, how each separately influences the resonator critical frequencies. The mechanisms are: acoustic viscosity, DC conductivity, dielectric dispersion, and piezoelectric loss. Using plate resonators as examples, we compute the frequency dependencies on the complex piezocoupling factor as functions of harmonic number for thickness field excitation. The traditional Butterworth-Van Dyke equivalent electrical circuit is extended to give a more accurate representation for ceramics, as well as for other materials with high piezoelectric coupling combined with low to moderate values of loss