Mechanical and Electrical Noise in Sense Channel of MEMS Vibratory Gyroscopes.

Xukai Ding,Jia Jia,Yang Gao,Hongsheng Li

doi:10.3390/s17102306

Abstract

This paper presents a theoretical analysis of mechanical and electrical noise in the sense channel of micro-electromechanical systems (MEMS) vibratory gyroscopes. Closed-form expressions for the power spectral density (PSD) of the noise equivalent rate (NER) of gyroscopes in the open-loop and the force-rebalance operations are derived by using an averaged PSD model and an equivalent transfer function. The obtained expressions are verified through numerical simulations, demonstrating close agreements between the analytic and the numerical models. Based on the derived expressions for the PSD of the NER, the impacts of the modal frequency split, quality factor, and the gain of the feedback forcer, as well as the gain of the signal conditioning circuit, on the gyroscope noise characteristics are theoretically analyzed. In addition, the angle random walk (ARW) and the standard deviation of the NER are also discussed through the PSD models. Finally, the effects of the loop closing, the mode matching, and the gain of the feedback forcer on the PSD of the NER were verified via a MEMS vibratory gyroscope with a tunable modal frequency split.

Highlights

Gyroscopes based on micro-electromechanical systems (MEMS) technologies have great advantages of small size, low power consumption, low cost, and batch fabrication over their traditional counterparts
In the force-rebalance noise model, the noise sources are separated from the closed-loop, and the modulation–demodulation process in the closed-loop is linearized by the equivalent transfer function
The noise characteristics of MEMS vibratory gyroscopes were evaluated by a silicon tuning folk micro-gyroscope with a tunable modal frequency split, previously reported in [15]

Summary

Introduction

Gyroscopes based on micro-electromechanical systems (MEMS) technologies have great advantages of small size, low power consumption, low cost, and batch fabrication over their traditional counterparts. The noise model in [5] includes both the mechanical noise and the electrical noise, the feedback architecture of the force-rebalance operation in the study is not a typical one. We obtain closed-form expressions for the power spectral density (PSD) of the mechanical and the electrical NER in a typical force-rebalance architecture by using an averaged PSD model and an equivalent transfer function of the modulated–demodulated sense axis. In the force-rebalance noise model, the noise sources are separated from the closed-loop, and the modulation–demodulation process in the closed-loop is linearized by the equivalent transfer function By this approach, the closed-loop noise model can be transformed into an open-loop one and, the analysis method used in the open-loop model can be applied.

Model of Sense Channel in MEMS Vibratory Gyroscopes

Open-Loop Noise Model

Force-Rebalance Noise Model

Angle Random Walk and Standard Deviation of Noise Equivalent Rate

Experiments and Results

Conclusions