Modal analysis of practical quartz resonators using finite element method.

Finite element simulation has been employed as a promising method in the analysis of piezoelectric active devices. It is desirable to obtain results consistent with experiments for real devices. In this paper, precise geometry models of quartz resonators were generated from direct measurements of practical devices and meshed. Realistic quartz blanks, electrodes, and mountings were included in the models. An application- specified 3-D finite element simulator was developed to perform the modal analysis of realistic crystal resonators. Using the model and simulator, real devices were simulated. Simulation results, including modal analysis and temperature properties, were shown in consistency with experimental measurements. The dependencies of device performance on practical factors were studied.