A new nonlinear coupling of the fundamental and its harmonic overtone thickness shear modes for improvement of resonator Q

Abstract

Ultra high frequency resonators have higher noise levels due to their greater miniaturization and higher power density. This paper proposes a new method using nonlinear acoustic coupling for improving the resonator Q and hence reducing noise levels in third overtone thickness shear resonators. We show an increase in Q of the third overtone mode of thickness when coupled nonlinearly to the fundamental mode of thickness shear. The Q increase and a steep phase-frequency curve will reduce the phase noise of the third overtone resonator. The nonlinear coupling of the fundamental thickness shear mode to the third overtone thickness shear mode was modeled using MATLAB Simulink. 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.