An Analytical Model for Capacitive Pressure Transducers With Circular Geometry

This paper derives an analytical model of a capacitive pressure transducer based on equations for deflection and fundamental mode shape of a clamped circular plate. The derived model enables efficient large-signal electromechanical simulations and calculation of an equivalent circuit. The model shows good agreement with finite element analysis and experiments. The spring-mass-damper system used in the model is calculated for uniform, anisotropic, and layered plate materials. A cubic spring constant captures large plate deflections. Use of the clamped-plate shape function leads to a simple expression for capacitance as a function of deflection and to closed-form equations for pull-in voltage. Comparison of the model with finite element analysis for several air-coupled capacitive micromachined ultrasonic transducer designs shows better than 10% agreement for deflection, resonant frequency, and pull-in voltage. The model also compares well with characterized devices. The analytical model could be further improved with additional damping sources and methods to model a compliant plate boundary.