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The theory of eigenmode operation of Coriolis vibratory gyroscopes and its implementation on a thin-film piezoelectric gyroscope is presented. It is shown analytically that the modal alignment of resonant gyroscopes can be achieved by applying a rotation transformation to the actuation and sensing directions regardless of the transduction mechanism. This technique is especially suitable for mode matching of piezoelectric gyroscopes, obviating the need for narrow capacitive gaps or DC polarization voltages. It can also be applied for mode matching of devices that require sophisticated electrode arrangements for modal alignment, such as electrostatic pitch and roll gyroscopes with slanted electrodes utilized for out-of-plane quadrature cancellation. Gyroscopic operation of a 3.15 MHz AlN-on-Si annulus resonator that utilizes a pair of high- Q  degenerate in-plane vibration modes is demonstrated. Modal alignment of the piezoelectric gyroscope is accomplished through virtual alignment of the excitation and readout electrodes to the natural direction of vibration mode shapes in the presence of fabrication nonidealities. Controlled displacement feedback of the gyroscope drive signal is implemented to achieve frequency matching of the two gyroscopic modes. The piezoelectric gyroscope shows a mode-matched operation bandwidth of ~250 Hz, which is one of the largest open-loop bandwidth values reported for a mode-matched MEMS gyroscope, a small motional resistance of ~1300 Ω owing to efficient piezoelectric transduction, and a scale factor of 1.57 nA/°/s for operation at atmospheric pressure, which greatly relaxes packaging requirements. Eigenmode operation results in an ~35 dB reduction in the quadrature error at the resonance frequency. The measured angle random walk of the device is 0.86°/√h with a bias instability of 125°/h limited by the excess noise of the discrete electronics.

Eigenmode operation of piezoelectric resonant gyroscopes