Analysis of Electrostatic MEMS Using Energy-Charge Landscape

A common way to analyze electrostatic microelectromechanical systems (MEMS) actuators is to use their energy-displacement landscape. Here, we describe an alternative approach to analyze electrostatic MEMS actuators using their energy-charge landscape. This technique involves coordinate transformation from displacement to charge, thereby formulating the Hamiltonian of electrostatic MEMS actuators in terms of charge. We investigate the use of the energy-charge landscape to analyze static pull-in, dynamic pull-in, and pull-out phenomena. The voltage expressions derived using this method are identical with those derived using the conventional energy-displacement landscape. In addition, we also obtain the expressions for charge under static and dynamic pull-in conditions. This work can aid in the design and analysis of electrostatic MEMS devices. As a case study, the analysis of a feedback capacitor-MEMS actuator system is presented to illustrate the application of the energy-charge landscape.