AC transfer function of electrostatic capacitive sensors based on the 1-D equivalent model: application to silicon microphones

Parallel plate electrostatic transducers can be described with the one-dimensional (1-D) lumped model. The one-dimensional approximation based on the elastic, the damping and the inertial force is extended with the electrostatic force (due to the electrical biasing) to model the behavior of electrostatic actuators. In case of sensors, the effect of the external excitation has to be also included. The final equation describing the dynamic behavior of the sensor can only be solved numerically avoiding a compact solution. In this paper the perturbation method applied to solve the equations describing parallel plate capacitive sensors is presented. A compact expression is obtained and applied to model silicon microphones. For the sake of comparison, the silicon microphone is also modeled with the well-known analog equivalent electric circuit, which is extended to take into account the resistor used to bias the microphone. It is shown in which conditions both modeling techniques give equivalent results. However, in front of the traditional equivalent electric circuit, the model based on mass, spring constant and damping coefficient allows taking into account the pull-in instability. Assessment of the modeling method is carried out by experimental measurements on a silicon microphone and previous experimental results reported in the literature. A very good agreement between theory and measurements is obtained.     

Current drive methods to extend the range of travel ofelectrostatic microactuators beyond the voltage pull-in point

When a voltage source drives an electrostatic parallel plate actuator, the well-known pull-in instability limits the range of displacement to 1/3 of the gap. Different strategies have been reported to overcome this limitation. More recently, experimental results have been presented using a capacitor in series with the actuator. Nevertheless, this strategy requires higher voltage than the pull-in voltage value to achieve full range of travel. In order to reduce the operating voltage, a switched-capacitor configuration has been also proposed. In this paper, two different approaches are introduced to control charge in the actuator by means of current driving. Theoretical equations derived for each method show that full range of travel can be achieved without voltage penalty. Both approaches are based on the use of current pulses injecting the required amount of charge to fix the position of the movable plate. Experimental measurements, showing that displacement beyond the pull-in point can be achieved, are in good agreement with the theoretical and the predicted simulated behavior