Triple Mass Resonator for Electrostatic Quality Factor Tuning

Abstract

In this paper, a triple mass resonator (TMR) with a high capability to independently tune both resonant frequency and quality factor (Q-factor) is reported. An additive oscillating structure is designed into a conventional dual-mass resonator to control the modal shape. The theoretical studies revealed that the amplitude ratio between the outer masses, which mainly determine the Q-factor through the anchor loss, is sensitive to both suspension and inner springs because of mode coupling, while the resonant frequency is only sensitive to the suspension spring. Through this mechanism, the quality factor related to the anchor loss, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{\mathrm {Anchor}}$ </tex-math></inline-formula> , can be adjusted by electrostatic tuning of the inner spring, while the resonant frequency keeps almost constant. On the other hand, the eigenfrequency could be significantly tuned by the electrostatic tuning of the suspension spring. The experimental results showed the Q-factor could be tuned as large as 19% by a DC bias of 15 V at the inner electrode, while the resonant frequency change was only as small as 162 ppm. In contrast, when the DC bias was applied to soften the suspension stiffness, the resonant frequency could be tuned as high as 7023 ppm with Q-factor change of 16%. [2021-0167]