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.

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Thermal-Mechanical (T-M) noise is a natural phenomenon occurring in Capacitive Micromachined Ultrasonic Transducers (CMUT). T-M noise is a value of great interest because it is linked to the minimal detectable pressure of a transducer and can also serve as a convenient characterization tool. Indeed, the general behavior of a CMUT array is translated through its T-M noise which does not require any external applied source to be assessed. However, T-M noise is difficult to measure, often time requires a dedicated measurement chain and is mostly based on spectrum analyzers in a carefully controlled environment. In this paper, we present a temporal technique to characterize the T-M noise of CMUT-based arrays with a commercially available amplifier and a digital oscilloscope. The approach is applied to an air coupled Row-Column Addressed (RCA) matrix array, for which the elements cannot be measured with traditional microprobes systems. This task is performed using a Printed Circuit Board (PCB) dedicated to the characterization of RCA arrays and designed to drive rows and columns individually. Noise Power Spectral Density (PSD) modeling of the complete measurement chain is achieved using a lumped-parameter model of the RCA array element and using the amplifier gain, electrical impedance, and noise characteristics. Measurements obtained with the signal analyzer and the temporal method are in good agreement with the model. The presented characterization technique can be extended to other micromachined ultrasonic transducer probe architectures, technologies, and amplification systems.