Broadband parametric amplification for micro-ring gyroscopes

Abstract

Given the fact that MEM gyroscopes can provide a better solution for inertial sensors in terms of size and cost, increasing their performance will remain an important issue in the development of that field. Researchers seek enhancing different performance measures, mainly the bias stability, Angle Random Walk and sensitivity. Nevertheless, different amplification techniques unfortunately decrease the signal to noise ratio (SNR) and thereby decrease the gyroscope’s precision. In this context, parametric excitation methods emerged to have positive effects on both the gyroscope’s sensitivity and SNR, this is based on the fact that the amplification is achieved mechanically.However, parametric amplification is conventionally limited to the resonant frequencies. This limitation affects the efficiency of the control methods used to tune the excitation frequency. This can be, however, overcome by introducing a broadband parametric amplification method. This parametric excitation method is described in this paper in detail. It is based on inducing a modal-coupled phase-shifted parametric excitation in multi-degree of freedom dynamic systems. Using this excitation method the system can be subjected to destabilization on a broad frequency band, i.e. not only at resonant frequencies. In that way the parametric excitation can then offer a negative-damping effect thus mechanically increasing the amplitude and the device’s sensitivity.In this paper, a micro-ring gyroscope is subjected to a bimodal coupled phase-shifted parametric excitation. The system’s differential equations were derived using Hamilton’s principle and discretized using Galerkin’s method. Afterwards, the aforementioned excitation method is applied through a suggested control circuit. The whole system is analyzed by a semi-analytical method, namely, the method of normal forms and verified numerically using the Floquet method. Using the data of a realistic micro-ring gyroscope we could then achieve broadband amplification under certain conditions.