The Generalized Pull-In Condition in Micromachined Voltage Controlled Electrostatic Actuators with a Single Degree of Freedom

A new analytical approach for modelling the pull-in condition of voltage controlled electrostatic actuators (VCEA) with a general single degree of freedom (DOF) and general shape is presented. The presented approach gives a more general view of the pull-in condition in electrostatic actuators. The pull-in condition for an electrostatic actuator is defined in the voltage and degree of freedom plane. Then a general algebraic equation, referred to as the pull-in equation, is derived for the actuator. The solution of this equation directly yields the pull-in condition. Several case studies are then presented and their pull-in characteristics are summarised.