Resonator Q increase and noise reduction in third overtone thickness shear resonators

Abstract

Ultra high frequency resonators have higher noise levels due to their greater miniaturization and higher power density. This paper investigates a new method using nonlinear acoustic coupling for improving the resonator Q and hence reducing noise levels in third overtone thickness shear resonators. For trapped energy resonators such as the AT-cut quartz resonators the fundamental and third overtone thickness shear modes are well behaved. At high drive levels, the fundamental mode may be described by a Duffing equation that has a nonlinear cubic term in displacement. This cubic term in displacement has a third overtone thickness shear frequency component that could be used to improve the Q of third overtone thickness shear resonator. The coupling of the Duffing equation for the fundamental thickness shear mode to the third overtone thickness shear mode was solved using a MATLAB Simulink model. At higher drive levels, the mechanical nonlinearities of the fundamental mode will drive the third overtone thickness shear mode if its resonant frequency is sufficiently close to three times the fundamental thickness shear frequency. This nonlinear coupling will improve the Q of the third overtone thickness shear mode by as much as 15-fold. The Q increase is dependent on (1) frequency matching of the third overtone mode to three times the fundamental mode, (2) the drive level of the fundamental mode, and (3) the relative phase of the fundamental drive to the third overtone drive.