A parametric study on design of a microrate-gyroscope with parametric resonance

Parametric excitation for MEMS gyroscopes can provide resonance in both the drive and the sense modes, even with mismatched natural frequencies. In this paper, requirements for such a condition are studied by analyzing the effect of each factor on the steady state amplitudes of the two modes. To develop a general study, the governing equation of the gyroscope is scaled and non-dimensionalized. The resulting governing equation is in the form of a cubic Mathieu equation coupled to a Duffing equation. In the study of the scaled system, for a gyroscope with matched natural frequencies, three sets of optimum designs are obtained. Then, the robustness of parametric excitation for a gyroscope with mismatching modes is shown. As the results indicate, parametric excitation is able to provide high accuracy and robustness for MEMS gyroscopes.