estimation of oscillation period/switching time for electrostatically actuated microbeam type switches

the undamped dynamic response of step-voltage driven parallel-plates, cantilever, and fixed–fixed type electromechanical switches is numerically investigated. in each case, application of energy technique yields the threshold values of the amplitude and the applied voltage beyond which the oscillatory motion of the movable electrode ceases to exist. these critical values are identified as the dynamic pull-in parameters of the corresponding microactuator model. for all three microactuator configurations, empirical expressions for the switching time and oscillation period are developed. these empirical relations are applicable over a wide range of applied voltage, and the estimates obtained using the proposed empirical relations correlate very well with the previously published results. furthermore, the phase portraits of these actuators have been thoroughly investigated in order to examine the role of static pull-in point in a dynamic setting and also to propose the design rules to build faster microswitches.