A Technique for the Measurement of Relative Velocity between Parallel Plate Electrodes in Micromachined Structures

Abstract

Numerous applications exist for microstructures that contain two parallel oriented electrodes that experience relative motion. It is often desirable to measure the relative velocity between the two electrodes and then utilize this information. Relative velocity can readily be measured in these types of microsystems if the relative motion of the electrodes is constrained such that the partial derivative of the capacitance between the electrodes with respect to the electrode separation distance is constant, by measuring the current flowing through the time varying capacitor. However, for electrostatic parallel plate actuators and other microstructures that experience similar motion, where the partial derivative of the capacitance between the electrodes with respect to the electrode separation distance is time varying, this technique results in nonlinear distortion in the relative velocity measurement and is therefore not utilized. In this dissertation, this relative velocity measurement technique is applied to electrostatic parallel plate actuator and similar microsystems, and the resulting nonlinearities inherent in this approach are investigated and characterized. It is shown that if the parallel electrodes experience small amplitude relative motion compared to the electrode separation distance at rest, then the nonlinear distortion in the relative velocity measurement is minimal and the total harmonic distortion estimation can be utilized to determine the minimum ratio of the electrode separation distance at rest to the amplitude of relative motion that can be tolerated for a particular application to obtain the required quality level in the relative velocity measurement. It is also shown that this technique accurately detects the direction of relative velocity even if the relative electrode motion is large compared to the electrode separation distance at rest. The results from experimentally validating the theoretical development through the testing of a prototype relative velocity sensor are also presented.