Angularly parameterized macromodel extraction for unconstrained microstructures

In this paper, we present an angularly parameterized model order reduction (APMOR) technique for macromodel extraction of unconstrained microstructures by combining a new, iterated IRS (improved reduced system) method with coordinate transformation theory. The extracted macromodels are encapsulated in the MAST hardware description language and can be exported automatically as components which can be inserted directly into an analog circuit simulator for dynamics simulation. An in-plane micro accelerometer including four variable cross-section folded beams is used to demonstrate the proposed macromodeling method. The folded beams are treated as unconstrained microstructures, and numerical simulation results in a SABER simulator show that the macromodels can dramatically reduce the computation cost while capturing the device behavior faithfully. Compared with FEM results, the relative error is less than 1.4%, while the computational efficiency improves about 22 times. Once the macromodel of one of the folded beams is obtained, the macromodels of all other folded beams can be obtained easily by setting the corresponding angle parameters. With the help of an APMOR technique and the existing model library which is developed in our previous work, the hybrid system-level model of the in-plane micro accelerometer can be constructed rapidly, and the scale factor of the accelerometer is simulated. Compared with experimental results, the relative error is about 8.16%