Two-axis multiple masses resonator with frequency and Q-factor matching

This paper reports a design and experimental results of a two-axis symmetric dynamically balanced resonator based on a triple mass system, whose frequency and Q-factor can be independently tuned. Two dynamically equivalent proof masses are connected by four coupling springs, and four coupling proof masses are implemented between them. The frequency and Q-factor of the anti-phase modes can be tuned independently of each other. The frequency is tuned by electrostatically softening the suspensions stiffness, and the Q-factor is adjusted by controlling the squeeze film damping through the mode coupling between the anti-phase and in-phase modes. The changes of frequency and mode coupling under different DC bias tunings are studied by FEA, which reveals the modification of the suspension stiffness only decreases the frequency and the modification of the inner stiffness of the coupling proof masses exerts a large effect on the mode shape, i.e. Q-factor, while a minor effect on the frequency. The as-fabricated frequency and Q-factor mismatches were evaluated as 5% and 7.7% in a fabricated device, respectively. A large adjustment of the Q-factor by 21% was observed by adding a 27 V DC voltage on the tuning electrodes inside the coupling proof masses, while the frequency was only decreased by as small as 810 ppm. A mode matching was achieved by electrostatic softening the suspensions of both main proof masses. Thanks to the decoupling between frequency and Q-factor, a frequency matching under 10 ppm and a Q-factor matching under 650 ppm were experimentally proved.