Bandwidth and noise analysis of high-Q MEMS gyroscope under force rebalance closed-loop control

Abstract

The force-to-rebalance (FTR) closed-loop detection method is commonly used to expand the bandwidth (BW) for micro-electro-mechanical system (MEMS) gyroscopes with low-frequency split and high-quality factors. However, the relationship between the BW and output noise is often incompatible; thus, reducing the detection accuracy of the gyroscope. This paper presents an analysis of the BW and noise spectra under modulation-demodulation FTR gyroscopes. The expressions for the BW and the noise-equivalent rate (NER) spectrum are derived to explore the effects of the loop gain on the BW and NER. It is demonstrated that the gain of the amplifier circuit is maximally transferred to the vibration displacement signal conversion part, which can reduce the output noise without affecting the BW. The simulation and experimental results on the Cobweb-like disk resonator gyroscope show that the derived expressions of BW and NER are correct, and the noise optimization method is effective, which provides an idea for the realization of a high-precision MEMS gyroscope.

Temperature drift suppression for micro‐electro‐mechanical system gyroscope based on vibrational‐displacement control with harmonic amplitude ratio

“…Previous studies [21, 22] suggest that using the force‐to‐rebalance (FTR) closed‐loop detection and quadrature stiffness control mode for the sense mode improves stability. Herein, the expressions for the bias and SF of the gyroscope are $$$$\begin{equation}Bias \approx - \Delta \left( {1/\tau } \right)\sin 2{\theta }_\tau m{\omega }_x\left\| x \right\|\sin ({\varphi }_x)/{K}_{VF},\end{equation}$$$$ $$$$\begin{equation}SF = - 4m{A}_g{\omega }_x\left\| x \right\|\sin ({\varphi }_x)/{K}_{VF},\end{equation}$$$$where τ is the attenuation time constant $$\tau = 2Q/\omega $$, ω is the resonant frequency of the drive or sense mode, Q is the quality factor, m is the mass, $${\theta }_\tau $$ is the damping axis deflection angle, $$\| x \|$$ is the amplitude of vibrational displacement x , $${\varphi }_x$$ is the drive‐mode phase (after phase‐shift compensation, $${\varphi }_x \approx {90}^o$$), $${K}_{VF}$$is the conversion coefficient from voltage to driving force, $${K}_{XV}$$ is the conversion coefficient from vibrational displacement to voltage, and $${A}_g$$…”

“…Previous studies [21,22] suggest that using the force-torebalance (FTR) closed-loop detection and quadrature stiffness control mode for the sense mode improves stability. Herein, the expressions for the bias and SF of the gyroscope are…”

Effect of Quadrature Control Mode on ZRO Drift of MEMS Gyroscope and Online Compensation Method

“…After a one-time circuit phase delay compensation, will be close to ; hence, . In addition, closed-loop control keeps the sense mode relatively stationary, effectively suppresses the influence of frequency splitting, and expands the mechanical bandwidth [ 20 , 25 ]. In other words, when the frequency difference between the two modes is less than the mechanical bandwidth, the sense mode is approximately in the mode-matched state, that is, .…”

“…Equation (18) shows that 2 ZRO is no longer affected by q A , so the bias value and bias stability will be effectively improved. In addition, closed-loop control keeps the sense mode relatively stationary, effectively suppresses the influence of frequency splitting, and expands the mechanical bandwidth [20,25]. In other words, when the frequency difference between the two modes is less than the mechanical bandwidth, the sense mode is approximately in the mode-matched state, that is, A is corrected to a significantly small value.…”

“…Based on previous work on gyroscope closed-loop detection [ 18 , 19 , 20 ], this study compares and analyzes the two quadrature error control modes (Mode I and Mode II) under closed-loop detection. System models of the two control modes were constructed, and the effects of circuit phase delay, quadrature coupling, in-phase coupling, phase of drive, and sense mode on the ZRO were analyzed.…”