Accurate Radiation Impedance Analysis for CMUT Design

The transducer resonance frequency is a key parameter for the field of ultrasound. The resonance frequency in vacuum is well understood, and an analytical expression for the center frequency in immersion was derived by Lamb in 1920 Hi, however this expression has limited validity. Importantly, the model fails to cover plate aspect ratios needed by imaging requirements and met by recently fabricated medical Capacitive Micromachined Ultrasonic Transducers (CMUTs). Based on the equation of motion a new expression for the resonance frequency in immersion is derived. The influence of the immersion medium is included via the radiation impedance, which is approximated using the well-known Taylor expansion, yielding results similar to Lamb's. For precision at smaller aspect ratios, this work proposes using the Fade approximant instead. Comparing the frequency ratio to FEM simulations, the Pade approximant shows a fourfold reduction in error from 12.0% to 3.0%.

Automated summary

This article introduces the importance of the resonance frequency of ultrasound transducers in the field of ultrasound, and proposes a new expression for deriving the resonance frequency in immersion. By considering the influence of the immersion medium, an approximation of the radiation impedance is obtained using the Taylor expansion, and the use of the Fade approximant is suggested for higher precision at smaller aspect ratios.