CMUT design equations for optimizing noise figure and source pressure

The key parameters for the design of a capacitive micromachined ultrasonic transducer (CMUT) cell are the dimensions of the vibrating plate, i.e. plate diameter and thickness, and the gap height. These dimensions together with the magnitude of the dc bias voltage determine the transducer's center frequency, bandwidth, and transmit and receive sensitivity. For a given center frequency, choosing the plate dimensions typically requires a tradeoff between bandwidth and sensitivity. The expected magnitude of the ac excitation and dc bias voltage guides selection of the gap height. Finite element modeling and simulation of the equivalent circuit model help examine these design tradeoffs. However, analytical expressions give better design insight and aid quick evaluation of designs for given specifications. In this work, we develop expressions for transmit pressure and receive noise figure for a circular CMUT cell with bending plate and an ideal parallel-plate CMUT cell. In order to simplify the analysis, we neglect atmospheric pressure, assume a linear spring constant for the plate stiffness, and assume the dc bias voltage to be close to the pull-in voltage. These assumptions are typically valid for CMUTs similar to those designed for medical imaging.