Electrostatic correction of structural imperfections present in a microring gyroscope

This paper describes a procedure for identifying mass and stiffness imperfections present in a microring gyroscope. In general mass and stiffness imperfections will be present as a result of fabrication variances and will contribute to mistuning of the gyroscope. Both mass and stiffness imperfections are treated as perturbations of the ideal isotropic mass and stiffness. The mass and stiffness perturbations are combined to form a structural imperfection, which is shown to be determinable from Nyquist plots of the frequency response functions. An analysis of electrostatic "tuning" is presented and demonstrates that the nonlinear negative spring component produced from a particular arrangement of capacitive electrodes is capable of removing such structural imperfections. If uncorrected the structural imperfections would otherwise result in anisoinertia and anisoelasticity. A comparison between the theoretically predicted tuning voltage and the experimentally derived value is made and shown to be in agreement. The major advantage of electrostatic tuning is that it may be implemented on-chip during operation thus providing active tuning. This is in contrast to the trimming techniques employing laser ablation or focussed ion beam, which may only be done prepackaging.