Pull-in study for round double-gimbaled electrostatic torsion actuators

This paper reports an analytical study of the pull-in effect in round, double-gimbaled, electrostatic torsion actuators with buried, variable length electrodes, designed for optical cross-connect applications. We find that the fractional tilt at pull-in for the inner round plate in this system depends only on the ratio of the length of the buried electrode to the radius of the plate. The fractional tilt at pull-in for the outer support ring depends only on the ratio of the length of the buried electrode to the outer radius of the ring and the ratio of the ring's inner and outer radii. Expressions for the pull-in voltage are determined in both cases. General relationships are also derived relating the applied voltage to the resulting tilt angle, both normalized by their pull-in values. Calculated results are verified by comparison with finite element MEMCAD simulations, with fractional difference smaller than 4% for torsion-mode dominant systems.