Electrostatic regulation of quality factor in non-ideal tuning fork MEMS

This paper presents a method of regulation and maximization of Q-factor in anti-phase driven tuning fork MEMS. Non-symmetric regulation of stiffness in coupled 2-DOF resonators using the negative electrostatic spring effect is shown to adjust the momentum misbalance caused by fabrication imperfections in nominally symmetric structures. Balancing the structure through stiffness matching minimizes the loss of energy through the substrate and maximizes the device anti-phase Q-factor. The approach is experimentally demonstrated using a vacuum packaged SOI MEMS tuning fork gyroscope with initial operational frequency of 2.2 kHz and Q-factor of 0.6 million. By electrostatically tuning stiffness of one of the suspensions, momentum misbalanced caused by the fabrication imperfections was minimized, suppressing anchor loss and increasing the Q-factor to above 0.8 million, attributed to the thermoelastic limit. The experimentally validated analytical model of substrate dissipation is applicable to Q-factor tuning in anti-phase resonators and gyroscopes.