Extraction of Frequency Dependent Macromodels for Mems Squeezed-Film Damping Effects

In this paper, an efficient macromodel extraction technique for dynamical MEMS gas damping effects is presented. The technique applies an Arnoldi-based model-order-reduction algorithm to generate low-order macromodels from a FEM approximation of the governing equation of the squeeze-film fluidic damping effect, the Reynolds equation. We demonstrate that this approach is more than 100 times efficient than previous approaches, which solve the Reynolds equation using transient finite-element/finite-difference methods. The generated gas-damping macromodels can be easily inserted into system-level modeling packages, such as SPICE, Saber and Simulink, for transient and frequency coupled-domain analysis. We also demonstrated that the simulated results are in good agreement with experimental results for various MEMS devices.