A complete analytical model for square diaphragm capacitive sensor with clamped edge

Capacitive Pressure Sensors have been among the most promising MEMS in recent years due to its inherently low power consumption, higher reliability and better performance. A complete analytical model is necessary to accurately determine the effects of sensing variables on the sensor. In this paper, a mathematical model is developed for square diaphragm capacitive sensors, which includes analytical equations for load-deflection characteristic, pull-in voltage and critical distance at pull-in and capacitance. The work is different from the previous ones in the way that it adopts a direct method to solve the governing equations of deflection which gives the load-deflection characteristic without involving any numerical aid and accounts for both small and large deflection. Again, the numerical integration for capacitance calculation has been replaced by an approximate analytical model which reduces the computational effort comparably. Comparison with experimental data reveals excellent accuracy of the model.