Quality-Factor Enhancing Locations for Substrate Mounted Resonators

Abstract

An important but often overlooked factor that affects the performance of a meso/micro electro mechanical vibratory sensor is the structural interaction between the sensor's resonator and the substrate on which it is mounted. Situating resonators at node points eliminates this interaction and thereby helps to improve a resonator's quality-factor for a particular mode of vibration. This paper addresses the problem of locating a single degree of freedom spring-mass resonator on a generic cantilever substrate. The loci of natural frequencies obtained when the resonator's mounting location is varied are developed, and the nodal locations are identified. Thereafter a method to obtain these locations from the characteristic equation without solving the associated eigenvalue problem is described. Lookup tables detailing the nodal locations and the corresponding natural frequencies for various resonator parameters are presented. It is found that at these special nodal locations, the magnitude of the power transmitted through anchors is negligible, which ensures minimal structural interaction between the resonator and the substrate.

A frequency split trimming technique for axisymmetric shell structures

“…The practical non-idealities associated with the realization of axisymmetric resonating structures lead to the deterioration of its vibratory properties, such as Q-factor and frequency split (Sharma et al (2020); Anilkumar et al (2020); Zhou and Li (2021)). Several researchers, for instance Fox (1990); Rourke et al (2001); Joachim and Lin (2002); Gallacher et al (2003); Schwartz et al (2009, 2015); Xiao et al (2017), have developed techniques to balance the frequencies of a realized resonator.…”