Electrostatic model for an asymmetric combdrive

This paper presents an analytical solution to the electrostatic actuation of an asymmetric combdrive in out-of-plane and torsional motions. The exact solutions to force in the out-of-plane motion and the integral for torque in the torsional motion are obtained. The dependence of the peak force on the thickness of the movable fingers and the amount of overlap of the combs is given in closed form. Using our model, the shift of the natural resonant frequency due to a dc bias is analyzed. Furthermore, our solution also applies to the in-plane motion of an in-plane interdigitated combdrive. We found that an in-plane interdigitated combdrive generates a constant force within 0.1% when the minimum initial engagement length of the combs is twice the separation gap.