An Analytical Model for Bandwidth Enhancement of Air-Coupled Unsealed Helmholtz Structural CMUTs

Abstract

Capacitive micromachined ultrasonic transducers (CMUTs) were reported to own high potential in air-coupled ultrasonic applications such as noncontact nondestructive examination and gas flow measurement. The unsealed CMUTs which utilized the squeeze film effect were reported to overcome the narrow output pressure bandwidth of the conventional sealed CMUTs in air operation. This kind of unsealed CMUTs can also be regarded as Helmholtz resonators. In this work, we present the air-coupled unsealed Helmholtz structural CMUTs which utilize both the squeeze film effect and the Helmholtz resonant effect to enhance the output pressure bandwidth. Based on the mechanism of vibration coupling between membrane and air pistons in membrane holes, we propose an analytical model to aid the design process of this kind of CMUTs. We also use finite element method (FEM) to investigate this kind of CMUTs for our analytical model validation. The FEM results show that the significant bandwidth enhancement can be achieved when the Helmholtz resonant frequency is designed close to the fundamental resonant frequency of the CMUT membrane. Compared with the conventional sealed CMUT cell, the 4-hole unsealed Helmholtz structural CMUT cell improves both the 3-dB fractional bandwidth and SPL-bandwidth product around 35 times. Furthermore, it is found that, with more holes under the same hole area ratio or with a smaller ratio of the cavity height to the viscous boundary layer thickness, the Helmholtz resonant effect becomes weaker and thus the output pressure bandwidth decreases.