Hierarchical Representation and Simulation of Micromachined Inertial Sensors

A circuit-level methodology for simulating micromachined inertial sensors based on a hierarchical representation of microelectromechanical systems (MEMS) is presented. In the NODAS methodology ( N O dal D esign of A ctuators and S ensors), microaccelerometers and microgyroscopes are designed as netlists of general-purpose micromechanical beams, plates, electrostatic gaps, joints, and anchors and evaluated using lumped-parameter behavioral models. The on-chip displacements and global position of each micromechanical element have been separated in the netlist, enabling application of translation and rotation of the chip while simultaneously providing access to on-chip displacements for position sensing and electrostatic actuation. Simulations of static displacements and modal frequencies of a cantilever beam, a crab-leg accelerometer, and a symmetric vibratory-rate gyroscope agree to within 2% of finite-element analysis when using the minimal number of elements. Simulation of a 16 kHz vibratory-rate gyroscope system with dual transresistance sense amplifiers illustrates the ability to perform systemlevel mixed-domain simulation.