A multiple Degrees of Freedom Equivalent Circuit for a Comb-Drive Actuator

We present an equivalent circuit of a comb-drive actuator which takes account of mechanical motion in multiple degrees of freedom (DOF). The circuit is derived by a purely theoretical procedure; A lagrange function of the comb-drive actuator is first set up, and following linearization of the Lagrange's equation, results in a linear motion matrix. The obtained linear matrix is then divided into a mechanical matrix, an electrical matrix, and an interacting matrix which is composed of non-diagonal elements and denotes electro-mechanical energy conversion. The mechanical matrix and the electrical matrix are expressed by simple combination of LCR elements, while the interacting matrix is configured by capacitances and dependent source elements. From the equivalent circuit, we can understand interaction, not only between the electrical system and the multi mechanical systems, but also between the different mechanical freedom systems. The equivalent circuit model in the 2DOF system is verified by comparing the experimental result of electrical admittance with simulation, using the developed equivalent circuit, and shows good agreement merely by fitting parasitic capacitance and mechanical resistances. A multi-DOF equivalent circuit is essential when simulating MEMS devices, such as gyro sensors in which at least two-dimensional mechanical motions must be taken in account.