Effects of Unequal Electrode Thickness, Location, and Size on Thickness-Shear Mode Quartz Piezoelectric Resonators

We studied thickness-shear vibrations of a rectangular AT-cut quartz plate piezoelectric resonator. The finite element method was used with COMSOL, a commercial software. The plate analyzed had two rectangular electrodes at its top and bottom surfaces near the center, forming a trapped energy resonator. The two electrodes had slightly different thickness, location, or size. The effects of electrode differences on the basic vibration characteristics of the resonator including resonant frequencies and mode shapes were calculated and examined. Results showed that the effects of electrode variations were small but were not negligible, and should be taken into consideration in resonator design.