Delay of side pull-in for an electrostatic comb drive model with rotational degree of freedom

Abstract

We analyze the dynamics of an electrostatic comb drive model with one translational and one rotational degree of freedom, and show that an oscillatory voltage profile can significantly delay the onset of the rotational side pull-in instability. The result is facilitated by a simplified capacitance model that restricts the rotation to be small, but allows the translation to be large. The model further assumes that mechanical restoring forces are provided by linear springs, with the rotational spring much stiffer than the translational spring. Under these assumptions, translation and rotation are coupled only by the common input. Choosing the drive voltage to be a periodic puts the rotational dynamics in the form of Hill's equation. The input is restricted to be a piecewise constant bilevel signal, and Floquet theory is applied to compute a map of stabilizing input parameters. The results are validated against hybrid finite-element/lumped parameter simulations, with excellent agreement.