Reduction of frequency deviations in quartz resonators by electric potentials of plate electrodes

We present a new method in which a direct current (DC) bias field is used to control the resonant frequency of resonator subjected to body forces. The plate electrodes were used to create the DC bias field. Sensing electrodes were used to measure the body forces that cause the acceleration sensitivity. Finite element models were developed using the theory of small deformations superposed on finite initial deformations in Lagrangian formulation. The model results compared consistently well with the measured values for the force sensitivity coefficient K_f of a circular plate subjected to a pair of diametrical forces; hence validating our model for acceleration sensitivity. For our 1 GHz AT-cut quartz plate resonator with the crystal digonal X-axis perpendicular to plate X-axis, the in-plane acceleration sensitivity is negligible, while the Y-axis acceleration sensitivity is maximum. A DC bias field with an appropriate DC bias voltage could yield a reduction in acceleration sensitivity from 10^-10/g to 10^-12/g in the Y-axis