Modeling and verification of the double frequency effect using a MEMS device

Abstract

The derivation, verification, and implication of the nonlinear dynamic and frequency response of electrostatic actuator due to the double frequency effect (DFE) were reported in this study. In particular, an extra mode called half mode was observed and measured in various studies. However, a complete in-depth discussion of the effect was not reported in the past. In the present study, a second-order dynamical equation was adapted firstly to model the dynamic and frequency response of electrostatic actuator where typical harmonic input signal with a dc bias was used. Secondly, by solving the equation, complex waveform in dynamic response and an extra half mode in frequency response due to the double frequency effect can be observed and discussed. To verify the simulated result, an electrostatic driving device was fabricated using PolyMUMPS(C) process. Note that in frequency response, when dc bias is equal to the amplitude of ac signal, simulated and experimental results indicated that the amplitude of half mode was one-fourth of first mode.