Performance Parameters And Frequency Response Of Cmuts In Transmit, Receive, And Pulse-Echo Operation

Models of electrostatic transducers that assume a constant shape function for the plate's deflection facilitate derivation of closed-form design expressions. This work analyses the static and frequency-response characteristics of capacitive micromachined ultrasonic transducers (CMUTs) using a shape-function based model. This analysis shows that across all CMUT designs of a given plate shape, the CMUT's static parameters vary with bias voltage in the same manner. Normalizing bias voltage by pull-in voltage and plate deflection by gap height enables this result. The static parameters examined are plate deflection, capacitance, transformer ratio, spring softening, and coupling coefficient. As shown here, assuming a basic second-order model of the CMUT, these static parameters along with plate resonance frequency and quality factor describe a CMUT's frequency response. This work specifically examines ideal parallel-plate and clamped circular plate CMUTs, but it extends to other plate shapes with substitution of different expressions for capacitance as a function of plate deflection.