An analysis of the frequency-temperature relations of SC-cut quartz crystal plates with the Lee plate theory

The analysis of high frequency vibrations of piezoelectric crystal plates at the thickness-shear modes are of great importance in resonator design. In addition to fundamental issues like the vibration frequency, practical needs on the effects of complication factors such as the electrodes and temperature fluctuation are also required to be available for the optimal selection of structural parameters. With the modified Lee plate equations and thermal field considered, the frequency-temperature relations which are essential in the quartz crystal resonator development have been investigated. As we have found, the frequency change from the Lee plate theory in the operation range of a quartz crystal resonator is consistent with predications of Mindlin plate theory. We now are able to design resonators with the choice of Mindlin or Lee plate equations based on individual choices.