Radiation impedance of an array of circular capacitive micromachined ultrasonic transducers in collapsed state

Radiation impedance is one of the important parameters in designing efficient and wideband capacitive micro-machined ultrasonic transducer (CMUT) arrays. It determines how much acoustical power is generated in the surrounding medium given the membrane motion. Recently, considerable effort has been put to characterize the radiation impedance of CMUT arrays in conventional uncollapsed regime. However, the radiation impedance of an array of CMUT cells in collapsed state has not yet been investigated. To calculate the array radiation impedance in collapse mode, we first calculate the radiation impedance of a single cell CMUT. For the array case, the mutual impedances between the neighboring cells must also be taken into account. We consider an array of 7, 19, 37, and 61 cells placed in a hexagonal pattern and try to determine the radiation impedance for different degrees of collapse. We find that in the collapsed case the peak radiation resistance value is reached at higher kd values, where k is the wavenumber and d is the center to center cell spacing, compared to the uncollapsed regime.