Analysis Of Trapped Energy Resonators Research Articles

Transversely varying thickness modes in quartz resonators with beveled cylindrical edges

The equation for transversely varying thickness modes in doubly rotated quartz resonators is applied in the analysis of trapped energy resonators with beveled cylindrical edges. The coefficients appearing in the planar differential operator are written as a sum of a mean or isotropic part plus a deviation. Asymptotic eigensolutions for the nearby isotropic case are obtained for the cylindrical beveled resonator. The resonant frequencies for the actual anisotropic case are obtained from an equation for the perturbation in eigenfrequency from the isotropic solution. A lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. Calculated results are presented for a few beveled AT- and SC-cut quartz resonators and the influence of the radius of curvature of the contour is exhibited.

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.