Comparison of Three Automatic Mode-Matching Methods for Silicon Micro-Gyroscopes Based on Phase Characteristic

In this paper, we investigated the method of automatic matching of the resonant frequencies for the decoupled dual-mass
$z$
-axis silicon micro-gyroscopes. The structure of the studied gyroscope is first presented, which features the tuning combs for adjusting the resonant frequency, suppressing the quadrature error, and applying the feedback force. According to the phase characteristic of oscillators, different automatic frequency tuning loops are then designed to match the resonant frequencies of the drive and detection modes. Theoretical analysis is made to display the operation principles. In addition, they are verified and optimized by numeric simulations using the Simulink tool in MATLAB. Finally, by means of Labview Field Programmable Gate Array (FPGA), a digital hardware tool, these loops are tested on a fabricated and packaged gyroscope prototype. By comparison, it is found that when the automatic matching method under the external force is combined with the quadrature nulling method and the Coriolis closed-loop detection, the gyroscope is able to operate under real-time mode matching with a stable and small frequency split below 1 Hz. The performance of the prototype using this tuning method is: 1) the scale factor is 10.91 mV/°/s; 2) the input range is ±120°/s with nonlinearity of 0.1%; and 3) the bandwidth is 32 Hz. The frequency split varies by about 0.15 Hz under the open-loop detection and about 0.26 Hz under the closed-loop detection when the environment temperature changes by 80 °C.