On the lateral instability analysis of MEMS comb-drive electrostatic transducers

TL;DR

This paper analyzes the lateral instability of MEMS comb-drive transducers, deriving analytical and numerical solutions for critical voltage considering translation and rotation effects, including special operation modes.

Contribution

It provides the first comprehensive analysis of lateral pull-in instability considering combined translation and rotation, including anti-phase and Bennet's doubler configurations.

Findings

Critical voltage depends on translational and rotational stiffness.

Translational offsets and angular deviations affect stability.

Anti-phase and Bennet's doubler modes are analyzed for the first time.

Abstract

This paper investigates the lateral pull-in effect of an in-plane overlap-varying transducer. The instability is induced by the translational and rotational displacements. Based on the principle of virtual work, the equilibrium conditions of force and moment in lateral directions are derived. The analytical solutions of the critical voltage, at which the pull-in phenomenon occurs, are developed when considering only the translational stiffness or only the rotational stiffness of the mechanical spring. The critical voltage in general case is numerically determined by using nonlinear optimization techniques, taking into account the combined effect of translation and rotation. The effects of possible translational offsets and angular deviations to the critical voltage are modeled and numerically analyzed. The investigation is then the first time expanded to anti-phase operation mode and Bennet's doubler configuration of the two transducers.