Analysis of trapped energy resonators with circular electrodes

A simple theoretical model of trapped energy resonators with circular electrodes utilizing monoclinic crystal plates is presented. The effects due to ana nisotropic slowness curve for guided thicknesswaves in piezoelectric plates are included in this model so that it can be generally applied to the rotated Y-cut plates of quartz, LiTa03, or LiNb03. The theory is based on the "angular spectrum of plane waves" representation of two-dimensional thickness-wave solutions in the vicinity of the cutoff frequencies. Experimental measurements of resonant frequencies, vibrational patterns, and motional inductances on AT-cut quartz resonators are provided, and it is shown that calculations based on the theory are in excellent agreement with the results of experiments.