Exploring Bias-Instability Noise Sources in Quadrature Error Compensation System for Mode-Split MEMS Gyroscopes

In this paper, bias instability (BIS) and angle random walk (ARW) noise sources of quadrature correction for mode-split MEMS gyroscopes are first investigated. We propose a general noise model based on coupling stiffness correction that reveals the transfer mechanism of 1/f and white noise sources. The BIS with a small frequency split is mainly dominated by the electrostatic frequency-tuning voltage noise and that with a large frequency split is determined by the voltage reference noise in the quadrature loop. Due to the electrostatic frequency-tuning voltage noise, the quadrature correction system is unable to compensate for the quadrature error to zero. The BIS with quadrature correction is related to the initial quadrature error and frequency split. We find a good match between the presented model and measurements with an error of less than 15.1%. The simulation and experimental results have indicated that ARW will not be deteriorated by the quadrature compensation system. A MEMS mode-split gyroscope has achieved an ARW of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.029~^{\circ }$</tex-math> </inline-formula>/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd $</tex-math> </inline-formula>h and a BIS of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.08~^{\circ }$</tex-math> </inline-formula>/h under the initial quadrature of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$130~^{\circ }$</tex-math> </inline-formula>/s and the frequency split of 85 Hz with quadrature error compensation. [2025-0014]