A perturbation method for calculating the capacitance of electrostatic motors

Recent advances in micromachining technology have made possible the fabrication of a number of electrostatic devices, including variable capacitance micromotors. These variable capacitance micromotors employ one or more sets of conducting plates that act as capacitors. An accurate estimate of the capacitance between these sets of plates for various configurations is necessary to design and simulate such devices. Capacitance calculations can be performed using a variety of methods, including finite element techniques. An efficient method of calculating the capacitance is to reduce the problem to a set of integral equations that are then approximated by a set of algebraic equations. This method was previously used to calculate the capacitance of a linear micromotor with an infinite set of conducting lands on both the rotor and the stator, which introduces spatial periodicity that greatly simplifies the problem. Recent micromotor designs, however, employ only a few sets of conducting lands per phase, which makes it unclear if the previous results can be applied. In this paper, a new perturbation method for solving the integral equations and thereby estimating the capacitance is presented. This method does not make the assumption of infinite sets of conducting lands to introduce spatial periodicity. The perturbation method is computationally efficient and can be used for any design, including those that use very few repeated sets of conducting lands. The results obtained by this method are compared with the previous results which include experimental data. Finally, the method is extended to rotary micromotors and to three dimensional problems.