How to reduce the Pull-in Displacement of Parallel-Plate Actuators

In this paper, we show how the pull-in conditions of parallel-plate actuators can be tuned by the geometrical arrangement of multiple electrodes. An analytic model is given allowing to design parallel-plate actuators with a low critical pull-in displacement smaller than 1/3 of the initial electrode gap. Additionally, based on the method of Lagrange multiplicators we derive the optimal electrode arrangement for a series of parallel-plate actuators to maximize the electrostatic force while minimizing the actuators’ footprint.