Mechanical-Thermal Noise in Drive-Mode of a Silicon Micro-Gyroscope

A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system was designed in a Silicon Micro-Gyroscope (SMG). We deduce the system model of closed-loop driving and use stochastic averaging to obtain an approximate "slow" system that clarifies the effect of thermal noise. The effects of mechanical-thermal noise on the driving performance of the SMG, including the noise spectral density of the driving amplitude and frequency, are derived. By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stablility criterion. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.