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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. An alternative design and operation strategy for resonant gyroscopes delivers faster response while also achieving low levels of noise. These tiny devices measure an object’s rate of rotation, and are commonly used in consumer electronics as well as industrial and automotive applications. Resonant gyroscopes are currently limited by a tradeoff between bandwidth and signal-to-noise ratio, but Mojtaba Hodjat-Shamami and Farrokh Ayazi at the Georgia Institute of Technology have devised a solution to this problem. They employed an eigenmode operation strategy with a thin film piezoelectric-on-silicon resonant gyroscope, and demonstrated that they could routinely achieve mode-matched bandwidths of a few hundred Hertz, with greatly reduced error. This approach could greatly bolster the utility of such piezoelectric devices, but the authors note that a similar eigenmode operation strategy could also broadly optimize performance for other resonant gyroscope designs as well.

This paper presents a quadrature error cancellation technique based on the virtual alignment of the gyroscope excitation and readout electrodes to the actual direction of vibration mode shapes in the presence of fabrication non-idealities. The proposed method which is herein referred to as eigenmode operation, enables modal alignment of all-piezoelectric resonant gyroscopes and along with dynamic frequency matching via displacement feedback obviates the need for submicron capacitive gaps and relatively large DC voltages that are otherwise required for electrostatic mode matching. We demonstrate gyroscopic operation of a 3.1 MHz AlN-on-silicon annulus resonator, which utilizes a pair of high-Q degenerate in-plane vibration modes. The piezoelectric gyroscope shows a large operation bandwidth of ∼150 Hz with a scale factor of 1.6 nA/°/s while operating in air, which greatly relaxes packaging requirements. Eigenmode operation results in ∼35 dB reduction of the quadrature error at resonance.

This paper presents, for the first time, the design, implementation, and characterization of a dynamically mode-matched high-frequency piezoelectrically transduced silicon disk gyroscope utilizing a unique pair of degenerate orthogonal in-plane flexural gyroscopic modes. To eliminate the need for submicron capacitive gaps and large DC polarization voltages that are needed for electrostatic tuning, a linear bidirectional frequency tuning scheme, compatible with all-piezoelectric transduction, is introduced to achieve dynamic mode-matching via active electromechanical feedback. A fabricated 4.34 MHz AlN-on-Silicon 1-mm-diameter solid disk gyroscope supported by a network of peripheral beams was frequency-tuned by 500 ppm (∼2.2 kHz) and achieved a high measured sensitivity of 410 pA/°/s with an effective in-air quality factor of ∼4000, corresponding to a large open-loop operation bandwidth of ∼550 Hz under mode-matched conditions.