Lumped-Parameter Equivalent Circuit Modeling of CMUT Array Elements

Abstract

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.

Studying the Effects of Mutual Acoustic Impedance on the Performance of Polymer-Based CMUTs

“…This difference decreases with increased cell spacing. Similar effects were reported in literature, where a shift in center frequency and a reduction in bandwidth was predicted when increasing the cell-to-cell distance in an element (see [40], [16] and [20]).…”

“…More recently, Merrien et. al [20] presented a method to model elements of linear arrays with a single twoport network model. Their approach is based on reducing the degree of freedom of a CMUT element, consisting of multiple cell-columns, to a single piston transducer.…”

Thermal-Mechanical Noise Modeling and Measurements of a Row-Column Addressed CMUT Probe

“…However, noise modeling of an array comprised of hundreds of cells can be tedious [25]. We will show that the two-port network model of a CMUT array element recently published by our group simplifies the noise modeling [26].…”

“…The modeling approach is based on the finite-difference, multiscale method developed by Meynier et al [27] and recently extended to an equivalent two-port network representation of the array element by Merrien et al [26]. The lumped-parameter approach of the array element enables the combination of hundreds of cells into single equivalent impedance terms, hence easier implementation of parasitic components and integration of cascaded two-port networks.…”

“…1. The force associated to the noise input F n is negative because of the chosen convention to represent the array element in receive mode [26].…”