Angularly parameterized macromodel extraction for MEMS structures with large number of terminals

A novel method of the angular parameterized macromodel extraction for the microstructure with a large number of terminals was proposed. First, the macromodel was extracted by combining the block Arnoldi algorithm with the superposition theory for linear systems, and then the equivalent coordinate transformation was applied for angular parameterization of the macromodel. The angular parametrization could avoid the macromodel extraction repeatedly for those microstructures with the same geometry but different initial orientation. A micro programmable grating was used to demonstrate the proposed method. Numerical simulation results show that the macromodel can dramatically reduce the computation cost while capturing the device behavior faithfully. Compared with the FEM results, the relative error is less than 1.3%, and the computational efficiency for transient analysis improves about 45 times.