Lumped element modeling of air-coupled capacitive micromachined ultrasonic transducers with annular cell geometry

Air-coupled capacitive micromachined ultrasonic transducers (CMUTs) based on annular cell geometry have recently been reported. Finite element analysis and experimental studies have demonstrated their significant improvement in transmit efficiency compared with the conventional circular-cell CMUTs. Extending the previous work, this paper proposed a lumped element model of annular-cell CMUTs. Explicit expressions of the resonance frequency, modal vector, and static displacement of a clamped annular plate under uniform pressure were first derived based on the plate theory and curve fitting method. The lumped model of an annular CMUT cell was then developed by adopting the average displacement as the spatial variable. Using the proposed model, the ratio of average-to-maximum displacement was derived to be 8/15. Experimental and simulation studies on a fabricated annular CMUT cell verified the effectiveness of the lumped model. The proposed model provides an effective and efficient way to analyze and design air-coupled annular-cell CMUTs.