Analytical modelling of electrostatic structures

In order to design or predict the performance of a cylindrical planetary electrostatic motor it is necessary to analyze the torque generated by such a structure. A simple, but sufficiently accurate analytical model is developed for use in design. Conformal mappings used to model the capacitance and torque of the motor as a function of the rotor position, using a quasi-static, two-dimensional approximation. The effect of an insulating dielectric layer on the stator or rotor is evaluated. The approximate analytical models are corroborated using two-dimensional finite element simulations for representative motor geometries. The capacitance of different capacitive encoder structures are analyzed. Encoder structures compatible with silicon micromachining are considered and comprise electrodes with rectangular and triangular grooves. Conformal mappings are used to calculate the maximum and minimum capacitance of these electrode structures. The results of the analysis are corroborated by calculations using boundary integral methods, for chosen encoder geometries