Calculation of equivalent parameters in CMUT 1-D theoretical model

It´s always difficult to model the real 3-D capacitive micromachined ultrasonic transducer (CMUT) because of the nonlinearity and filed coupling. An alternative solution is to build a 1-D equivalent model which is enough to acquire the desired behavior of CMUT. However, it´s hard to obtain the 1-D equivalent parameters of the real 3-D CMUT. This paper proposes such a theoretical model to calculate the 1-D equivalent parameters of a CMUT with circular membrane. To derive this model, a reduced-order model is used to approximate the shape of the circular membrane under the electrostatic force and fluid pressure. With the obtained pull-in voltage and natural frequency, several reasonable assumptions are made to calculate the 1-D equivalent parameters. Finally, a typical example is given for the validation of our model. The results obtained by the proposed model are compared to those by 3-D FEM simulation. The good agreements show that the 1-D equivalent parameters attained by our proposed model can be used to build a 1-D equivalent model.