Radiation impedance of an array of circular capacitive micromachined ultrasonic transducers

The radiation impedance of a capacitive micromachined ultrasonic transducer (cMUT) with a circular membrane is calculated analytically using its velocity profile for the frequencies up to its parallel resonance frequency for both the immersion and the airborne applications. The results are verified by finite element simulations. The work is extended to calculate the radiation impedance of an array of cMUT cells positioned in a hexagonal pattern. A higher radiation resistance improves the bandwidth as well as the efficiency of the cMUT. The radiation resistance is determined to be a strong function of the cell spacing. It is shown that a center-to-center cell spacing of 1.25 wavelengths maximizes the radiation resistance, if the membranes are not too thin. It is also found that excitation of nonsymmetric modes may reduce the radiation resistance in immersion applications.