Receive-Noise Analysis of Capacitive Micromachined Ultrasonic Transducers

This paper presents an analysis of thermal (Johnson) noise received from the radiation medium by otherwise noiseless capacitive micromachined ultrasonic transducer (CMUT) membranes operating in their fundamental resonance mode. Determination of thermal noise received by multiple numbers of transducers or a transducer array requires the assessment of cross-coupling through the radiation medium, as well as the self-radiation impedance of the individual transducer. We show that the total thermal noise received by the cells of a CMUT has insignificant correlation, and is independent of the radiation impedance, but is only determined by the mass of each membrane and the electromechanical transformer ratio. The proof is based on the analytical derivations for a simple transducer with two cells, and extended to transducers with numerous cells using circuit simulators. We used a first-order model, which incorporates the fundamental resonance of the CMUT. Noise power is calculated by integrating over the entire spectrum; hence, the presented figures are an upper bound for the noise. The presented analyses are valid for a transimpedance amplifier in the receive path. We use the analysis results to calculate the minimum detectable pressure of a CMUT. We also provide an analysis based on the experimental data to show that output noise power is limited by and comparable to the theoretical upper limit.