High quality factor MEMS gyroscope with whole angle mode of operation

The whole angle (WA) mode of operation for the direct measurement of the angle of rotation is implemented on a high-Q silicon micromachined gyroscope. This paper presents the angle estimation and its associated errors when the WA gyroscope was operating in a free vibration and a closed-loop controlled mode. The high Q-factor, and therefore a large energy decay time constant of the device, enabled the WA measurement of the precession of the vibration pattern for over 30 minutes without energy control loop to sustain the vibration pattern. Taking advantage of the long decay time without the feedback control, rate-dependent errors in the scale-factor were directly observed. For the closed-loop WA operation, the energy, quadrature, and phase-locked loops were implemented and used for feedback control of the device. The control signals were applied to the excitation electrodes of the two orthogonal modes to maintain the amplitude and quadrature errors. In the feedback mode of operation, the WA gyro output was collected for 10,000 seconds at a constant input rate. An angular gain factor of 0.84 was derived from the angle output of the gyroscope with 7 ppm angular gain variation over 1.8 million degrees of continuous rotation.