An integrated program of vibrations of quartz crystal plates with mindlin plate theory for resonator design

Abstract

The theory and method have been extensively studied for the design of quartz crystal resonators, and Mindlin plate theory is widely used. As most research were aimed to solve specific problems of vibrations, there is no application program for the design. An integrated program based on Mindlin plate theory for the AT-cut quartz crystal resonators have been developed in our study, because AT-cut quartz crystal is the most popular cut for resonators. The functions include how to determine the optimal size of crystal plate and the configuration of electrode according to known relations. Then we are going to add to the program on how to calculate the electrical parameters of quartz crystal resonators with the consideration of dissipation. In the program, we can obtain dispersion relation, frequency spectra, frequency-temperature relation and so on, which can provide essential references for the design. All the analyses can provide the device performance parameters such as mode, frequency, frequency-temperature relation, which are useful to evaluate the effect of different parameters and optimal design. Consequently, we can avoid time-consuming trial and error steps in the process of design and establish the foundation for computational simulation and optimization.