Convergence and Speed Issues in Analog HDL Model Formulation for MEMS

Behavioral simulation using high-level hardware description languages (HDLs) is becoming increasingly relevant for mixed-domain MEMS simulation. In this paper three issues which impact the convergence and simulation time in MEMS behavioral simulations are addressed. First, velocity and displacement are compared for the choice of the across variable in nodal simulation. The through variable is force. Second, three state space implementations of displacement as across variable are compared. Finally, relative scaling of different quantities in order to improve convergence properties is considered with respect to the rotational domain. A minimal equation matrix representation with low condition number using displacement as across variable and scaling of the rotational domain gives the best convergence and simulation time.