Mutual radiation impedance for modeling of multi-frequency CMUT arrays

Recently closely packed interlaced capacitive micromachined ultrasonic transducers (CMUTs) with different membrane sizes, on a scale smaller than the acoustic wavelength to mitigate grating lobes, have been introduced for multi-band operation, imaging-therapy, contrast and photoacoustic imaging. An accurate model including the effects of the self and mutual acoustic interactions between CMUT cells for simulating the multi-frequency arrays is necessary. However, the previous works evaluated the effects of the mutual radiation impedance on CMUT arrays with the same membrane sizes. Using the Bouwkamp integral method for integrating the farfield directionality factor of two flexural disks with different sizes, vibrating in phase, series expressions have been obtained for the mutual radiation impedance between two circular radiators of different radii in a rigid plane. Models for the mutual acoustic impedance between membranes of different sizes were validated against previous piston results but extended to flexural disks. The obtained expressions were implemented in an equivalent circuit model of multi-frequency CMUTs. Model predictions of resonance frequencies and displacements closely matched experimental vibrometer measurements of multi-frequency CMUT arrays that were done for low and high frequency transducers.