Shaped combs and parametric amplification in inertial MEMS sensors

In this paper slope-shaped comb are designed, modeled and experimentally verified for electrostatic parametric amplification of micro-displacements. Parametric resonance techniques applied to inertial sensors requires a periodic stiffness modulation, as expressed by the Mathieu equation, and is generally implemented using gap-varying and non-overlapping combs. MEMS vibratory gyroscopes provide the opportunity for applying parametric amplification for both the sensing and driving modes. While gap-varying combs are efficiently used for small displacements (e.g. the sensing mode), larger displacements require a different approach, where slope-shaped combs are a good alternative. Analytical model of slope shaped combs is carried out and compared with experimental characterization of fabricated devices. The analytical model predicts a spring modulation of 0.1%-0.65% spring modulation for 10 V to 40V applied common mode DC bias, and it can be increased for steeper slopes. The parametric amplification operation was experimentally tested using linear differential voltage actuation on the area-varying combs and a phase-synchronised common mode voltage (using a PXIe 1062Q DAQ controller) applied to the left and right shaped combs.