A hybrid system-level modeling and simulation methodology for structurally complex microelectromechanical systems

We present a hybrid system-level modeling and simulation methodology by combining numerical macromodels with parameterized lumped-element behavioral models for structurally complex microelectromechanical systems (MEMS). We decompose the MEMS into several functional components. For those components with complex geometry and boundary conditions, we model them using numerical macromodels, whereas for those with simple geometry, we model them using parameterized lumped-element behavioral models. Both models are represented by the same syntax and similar equation forms to ensure the compatibility. Afterward, the hybrid numerical macromodels and parameterized behavioral models are inserted into the same simulator and then interconnected to each other according to the original topography of the MEMS for system-level simulation. As one of the key technologies of the proposed methodology, macromodeling has been improved in two aspects. First, macromodeling for the component with dynamic boundary condition is achieved by combining modal analysis with a novel iterated improved reduced system method. Second, angular parameterization for the components with the same geometry but different initial orientation is achieved by the matrix coordinate transformation. A $z$-axis micromachined gyroscope is used to demonstrate the proposed methodology. Simulation results show that the method can efficiently support the design for structurally complex MEMS.