Effects of Non-Ideal Frequency Splits on Linear Parametric Resonance in MEMS Mode-Split Gyroscopes

This paper illustrates effects of non-ideal frequency splits on linear parametric resonance using triangular parallel-plate area-varying capacitors in the sense mode of mode-unmatched MEMS gyroscopes for the first time. Differing from previously reported ideal cases with no frequency splits in fully mode-matched gyroscopes, even sub-hertz frequency splits between the drive mode and sense mode can strikingly decrease amplified gain. Furthermore, the best parametric phase for maximal gain depends on frequency splits and are not any more π/2 or 3π/2. Also, the boundary conditions are derived with the frequency mismatch. Results demonstrate that the frequency mismatch alters characteristics of parametric resonance compared to those in ideal mode matching case. This work indicates that using parametric resonance in the gyro sense mode cannot ignore frequency splits and should try to combine with real-time mode matching via electrostatic stiffness tuning.