Frequency-temperature (f-T) behavior for different rotated quartz cuts at high temperatures and their Q-factor estimation

A theoretical study has been carried out for a 20 MHz circular resonator to evaluate the effect of high temperature on the frequency and the Q-factor of the slow (C-) and fast (B-) thickness-shear mode for the SC-cut, SBTC-cut, rotated X-cut and AT-cut using 3-D finite-element method (FEM). We have carried out a frequency spectrum analysis to select the best aspect ratio for each cut angle, based on the separation between the thickness-shear and flexural modes. The best aspect ratio for each cut angle was then investigated for the f-T behavior using the Lagrangian temperature coefficients of elastic constants. FEM results suggest a promising design for a 20 MHz SC-cut resonator which can operate over the temperature range of -50 to 300 deg C.