Parametric amplification in imperfect capacitive ring-based MEMS gyroscopes using quadratic electrostatic nonlinearity

• Pump voltage distribution orders of 3, 5, 11, 13 generate quadratic nonlinearities • Ideal sense dynamics require drive alignment and nonlinear frequency balancing • Pump voltage phase must be varied when adjusting parametric amplification • Larger parametric amplification suppresses imperfection effects on rate output gain In this paper quadratic electrostatic forces are used to apply tunable parametric excitation to enhance rate-sensitivity in imperfect capacitive ring-based Coriolis Vibrating Gyroscopes (CVG) subjected to electrostatic nonlinearity. Using a mathematical model, implementation is achieved by selecting electrode configurations capable of decoupling the drive, tuning and parametric excitation whilst achieving ideal device performance. For a 16 electrode device operating in the n = 2 in-plane mode it is shown that parametric excitation can be generated by applying a harmonic pump voltage with spatial distributions of m p = 3, 5, 11 or 13. For m p = 3, conditions are obtained for the pump voltage amplitude and phase to achieve nonlinear frequency balancing to trim the CVG at a chosen operating amplitude whilst amplifying the rate output and sensitivity. It is found that the level of imperfection and electrostatic nonlinearity modify the required pump voltage phase, and the phase changes as the pump voltage amplitude is increased to enhance parametric amplification. It is also shown that large pump voltage amplitudes desensitise the rate sensitivity gain to the effects of imperfection. Theoretical results are presented to demonstrate enhanced rate sensitivity, and are validated against results obtained using the finite element method. Results are also presented to investigate the effect of mechanical damping on non-resonant coupling and the pump voltage needed to enhance rate sensitivity gain.