Parametric Resonators With a Floating Rotor: Sensing Strategy for Devices With an Increased Stiffness and Compact Design

Abstract

Recently we presented a parametric resonator which is constructed from a double-sided comb-drive transducer with an electrostatically floating rotor. That device had a natural frequency of ~2.3 kHz. In the present study we present a parametric resonator of the same type, but with a natural frequency of ~30 kHz, and a more compact design. The higher frequency is relevant for several applications, and the increased stiffness may contribute to enhancing fabrication yield. However, due to the more compact design, the electrostatic modulation of stiffness is less effective. Because of the drastic reduction of the ratio between modulated stiffness and average stiffness, the new resonator cannot be driven in high-order instability windows, without reverting to excessively high driving voltages. Since it could only be driven in the first instability window, the differential sensing signal is at the same frequency as the driving signal. This makes it difficult to distinguish between motional and feed-through currents. We demonstrate that the 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> harmonic of the differential current is unaffected by feed-through and is therefore preferable for sensing the device response. We show that this higher harmonic component of current, is a unique characteristic of the resonator, and it is not due to a nonlinear mechanical effect, such as Duffing stiffening. [2021-0032]