Out-of-plane motion detection in encapsulated electrostatic MEMS gyroscopes: Principal parametric resonance

Abstract

The impetus of this research is to numerically investigate a measurement method for out-of-plane motion detection in an encapsulated electrostatic MEMS gyroscope. This method is based on a variant of the harmonic detection of resonance (HDR) of the motion-induced current proposed by S. Park et al. [1]. The MEMS device consists of a cantilever microbeam having a paddle at its free end, and is under two simultaneous electrostatic actuations through side-wall and bottom electrodes along in-plane and out-of-plane directions, respectively. In common MEMS gyroscopes, the sense direction lays on the out-of-plane direction, and therefore, it is significant to detect the motion characteristics along this direction. To this aim, the current passing through the bottom electrode is collected. Because the resonance bandwidth for parametric resonance case is much narrower comparing to that of primary and secondary resonances, this motion characteristic is effectively applicable while measurement with ultra-sensitivity is purposed. In this research, it is shown that the out-of-plane resonance characteristics are retrieved through locking on a specific harmonic in the frequency content of the current signal, considering highest sensitivity to harmonic motions. To capture the frequency-amplitude response of the system, a combination of shooting and arc-length continuation scheme is applied to the governing dynamic motion's equations. Some intersections between the stable and unstable solutions branches as such, saddle-node, Hopf, and pitchfork (subcritical and supercritical) bifurcation points, occurring in the system behavior are addressed. Furthermore, for different levels of AC voltage amplitude, it is shown that the variations in the bifurcation points’ position can be figured out from the output current signal, so that this issue is defined as the fundamental basis for current sensing application.