Analysis of temperature adaptability for frequency control loop for silicon micromechanical gyroscope

It's generally agreed that using a PLL-based frequency control loop for a silicon micromechanical gyroscope the drive frequency can track the natural frequency precisely in any condition. To verify it, an analysis of its frequency tracking ability in varying temperature condition is presented. Firstly the dynamical analysis of the drive mode is presented and its phase-frequency relation is obtained. By analyzing the PLL-based frequency control loop the phase condition for frequency tracking is established. Then the simulation for the relation between the phase drift with temperature of the displacement readout circuit and the drive frequency of the gyroscope is carried out under the fixed phase condition. It shows that the frequency error will increase when the phase drift of the displacement readout circuit is increasing. Finally an experiment is carried out with a digital-analog mixed PCB based on FPGA, which is designed to simultaneously measure the drive frequency, natural frequency and phase drift of displacement readout circuit in temperature ranging from 5°C to 50°C. The results show that the phase of the displacement readout circuit drifts with temperature, and the error between natural frequency and drive frequency is proportional with the phase drift. Thus in order to keep the frequency tracking accuracy in different temperature the compensation for the phase condition must be employed.