Lumped-Parameter Equivalent Circuit Modeling of CMUT Array Elements

Design and modeling are key steps in the value chain of Capacitive Micromachined Ultrasonic Transducer (CMUT) arrays. Although CMUT array element models are very powerful, most of them are still limited in their use as tools for electronic design assistance. The electroacoustic equivalent circuits developed are mainly based on a distributed-element approach while lumped-parameter electrical circuits are better suited for electronic software design tools interoperations. To meet this need, the present study aims to implement an electroacoustic equivalent scheme of a full array element, based on a two-port network representation made of lumped-parameters. After an extensive bibliographical review of CMUT models, the new model is set-up from a fully distributed approach using Foldy’s electroacoustic definitions at the element level. Transmit and receive modes are implemented using scalar equations given by the lumped parameters. Moreover, based on a reciprocity analysis, the performance of the complete measurement chain in emission and reception will be defined using the relevant transfer functions. Finally, to help one design CMUT array elements for a given application, a method based on the computation of membranes thickness-size master curves is proposed. The two-port network representation of a full CMUT-based array element allowed by the new lumped-parameter modeling opens a wide range of possibilities regarding array design, electronic integration, operations with acoustic propagation simulation tools and more.