In-Plane-Sensing Analysis of Comb-Like Capacitive Micro-Machined Ultrasonic Transducers (CMUTs) Using Analytical Small-Signal Model and FEM

In this work, capacitive micro-machined ultrasonic transducers (CMUTs) were developed into comb-like shapes to make these comb-like shaped structures work for sensing in-plane vibrations of ultrasonic guided waves. On this basis, an analytical small-signal model, which is mainly a combination of the forced vibration theory and the simplified parallel-plate capacitor model, was proposed to satisfy the requirements of theoretical design. Through the proposed model, the in-plane-sensing behaviors of a comb-like CMUT cell can be predicted, including vibrating velocity, output current, and sensitivity. Compared with the results calculated from the finite element method (FEM) simulation, it was found that the static state and the frequency-domain results of the analytical small-signal model agree well with those of FEM simulations if the used first natural frequencies of these two methods are identical. Considering the fringing field capacitance could further improve the accuracy of the analytical small-signal model. At last, influences of some external parameters, i.e., dc bias voltage, air damping, and input in-plane displacement, on the sensitivity of a comb-like CMUT cell were discussed by the analytical small-signal model and FEM simulation. Relevant results reveal the way to design a comb-like CMUT and indicate the conditions when the analytical small-signal model is accurate. Our work develops the theory on the in-plane-sensing comb-like CMUT and is expected to be combined with the theory on the previous out-of-plane-sensing CMUT to realize 3-D-CMUT for sensing 3-D guided waves.