Operation of a high quality-factor gyroscope in electromechanical nonlinearities regime

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This paper describes the operation of a high quality factor gyroscope in various regimes where electromechanical nonlinearities introduce different forms of amplitude–frequency (A–f) dependence. Experiments are conducted using an epitaxially-encapsulated 2 × 2 mm2 quad-mass gyroscope (QMG) with a quality factor of 85 000. The device exhibits third-order Duffing nonlinearity at low bias voltages (15 V) due to the mechanical nonlinearity in the flexures and at high bias voltages (35 V) due to third-order electrostatic nonlinearity. At intermediate voltages (~26 V), these third-order nonlinearities cancel and the amplitude–frequency dependence is greatly reduced. A model is developed to demonstrate the connection between the electromechanical nonlinearities and the amplitude–frequency dependence, also known as the backbone curve. Gyroscope operation is demonstrated in each nonlinear operating regime and the key performance measures of the gyroscope’s performance, angle random walk (ARW) and bias instability, are measured as a function of drive-mode vibration amplitude. We find that low ARW can be achieved even though the gyroscope’s drive mode exhibits large amplitude–frequency dependence, and that bias instability is largely independent of the operating regime.