A general multi-mode lumped equivalent circuit model for circular cMUT cells

In this work, we present a general multi-mode lumped equivalent circuit model for an arbitrary excited circular cMUT cell operated in a small signal regime. It can be considered as a model extension of the modal analysis based equivalent circuit model already presented in [1]. In order to derive this model, a comprehensive description of the radiation impedance by the Bouwkamp's impedance theorem [2] is provided. Comparing with other existing lumped equivalent circuit models, this model can simulate a wide frequency range, i.e., containing those harmonic modes, response of cMUTs under an unconventional excitation. A case study based on a half electrode excited circular cMUT cell is presented, and frequency response results from the modelling are well validated by COMSOL simulation. Potentially, this method can also handle the problem of a group of cMUT cells.

I. Introduction

Capacitive Micromachined Ultrasonic Transducers (cMUTs) are considered as alternatives of their piezoelectric counterparts. In the past two decades, the major interest on cMUTs is their promising applications in ultrasonic diagnosis [3]. cMUTs will be mainly operated in the vicinity of the fundamental mode. Recently, there is an increasing interest of cMUTs in various types of applications, such as ultrasonic therapy, bio or chemical sensing, harmonic imaging and a potential enabler of acoustic manipulation. You et al., utilized asymmetrically excited cMUTs for super resolution ultrasonic imaging, showing an interesting prospect of the unconventional cMUTs [4]. Based on these facts, there is still plenty of room at the frequency region of harmonic modes or the applications of unconventional cMUTs. These emerging applications require a more generalized model which can handle the harmonic mode responses of cMUTs or cMUTs excited in the unconventional conditions. However, researches about the modelling of cMUTs operated in these unconventional conditions are still very limited. Christiansen et al., [5] discussed the modal radiation patterns of a circular plate, which can be considered as a transmission simulation of a cMUT cell operated in a gaseous medium. However, cMUTs are always operated with a medium load, a more practical model is still desired.