System level modeling of microsystems using order reduction methods

In the development of microsystems, Finite Element Method (FEM) simulators are used to investigate the behavior of system components with high accuracy. Generally, FEM simulations are time consuming. System-level models of all components are needed to allow a fast but sufficiently exact investigation of the system behavior to simulate entire microsystems. Typically, microsystems consist of nonelectrical components and electronic circuits. Providing models for electronic components and languages to describe the behavior of nonelectrical subsystems, simulators like Eldo, Saber, and VHDL-AMS simulators become more and more popular in the development of microsystems. For simple structures such as mechanical beams, models of microsystem components can be derived from analytical descriptions. Another possibility to consider more complex structures is to use FEM descriptions to generate models for system simulation. Some FEM simulators like ANSYS allow one to access the numerical values of the system matrices. They are established based on the description of geometry and material data. Usually, these system matrices are very large (10000 up to 100000 system variables or more). For system simulation, models with about 10 up to 100 variables are often required. Therefore, methods for order reduction are applied to derive smaller system matrices. An improvement of an order reduction method based on a projection method is introduced in the paper. Using the reduced systems, behavioral models in languages like MAST, HDL-A or VHDL-AMS can be generated automatically. The method described here was applied successfully to simulate mechanical microsystem components on system level.