Design of broadband linear micromachined ultrasonic transducer arrays by means of boundary element method coupled with normal mode theory

In view of the maturity of fabrication processes for capacitive micromachined ultrasonic transducers (cMUTs), engineers and researchers now need efficient and accurate modeling tools to design linear arrays according to a set of technological specifications, such as sensitivity, bandwidth, and directivity pattern. A simplified modeling tool was developed to meet this requirement. It consists of modeling one element as a set of cMUT columns, each being a 1-D periodic array of cMUTs. Model description and assessment of simulation results are given in the first part of the paper. The approach is based on the theory of linear systems so the output data are linked to input data through a large matrix, known as an admittance matrix. In the second part of the paper, we propose reorganization of matrix equations by applying the normal mode theory. From the modal decomposition, two categories of eigenmodes are highlighted, one for which all cMUTs vibrate in phase (the fundamental mode) and the others, which correspond to localized subwavelength resonances, known as baffle modes. The last part of the paper focuses mainly on the fundamental mode and gives several design strategies to optimize the frequency response of an element.