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.
Presented in the paper is the design, the simulation, the fabrication and the experiment of a new z-axis resonant accelerometer based on the electrostatic stiffness. The new z-axis resonant micro-accelerometer, which consists of a torsional accelerometer and two plane resonators, decouples the sensing movement of the accelerometer from the oscillation of the plane resonators by electrostatic stiffness, which will improve the performance. The new structure and the sensitive theory of the acceleration are illuminated, and the equation of the scale factor is deduced under ideal conditions firstly. The Ansys simulation is implemented to verify the basic principle of the torsional accelerometer and the plane resonator individually. The structure simulation results prove that the effective frequency of the torsional accelerometer and the plane resonator are 0.66 kHz and 13.3 kHz, respectively. Then, the new structure is fabricated by the standard three-mask deep dry silicon on glass (DDSOG) process and encapsulated by parallel seam welding. Finally, the detecting and control circuits are designed to achieve the closed-loop self-oscillation, to trace the natural frequency of resonator and to measure the system frequency. Experimental results show that the new z-axis resonant accelerometer has a scale factor of 31.65 Hz/g, a bias stability of 727 μg and a dynamic range of over 10 g, which proves that the new z-axis resonant micro-accelerometer is practicable.
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