Harmonic reduction in capacitive micromachined ultrasonic transducers by gap feedback linearization

The nonlinear relationship between the electrical input signal and electrostatic force acting on the capacitive micromachined ultrasonic transducer (CMUT) membrane limits its harmonic imaging performance. Several input shaping methods were proposed to compensate for the nonlinearity originating from the electrostatic force's dependence on the square of the applied voltage. Here, we analyze harmonic generation in CMUTs with a time-domain model. The model explains the basis of the input shaping methods and suggests that the nonlinearity resulting from gap dependence of the electrostatic force is also significant. It also suggests that the harmonic distortion in the output pressure can be eliminated by subharmonic ac-only excitation of the CMUT in addition to scaling the input voltage with the instantaneous gap. This gap feedback configuration can be approximated by the simple addition of a series impedance to the CMUT capacitance. We analyze several types of series impedance feedback topologies for gap feedback linearization. We show that for subharmonic ac excitation, although resistive and capacitive impedances result in a trade-off between input voltage and harmonic distortion for a desired pressure output, harmonic generation can be suppressed while increasing the Pa/V transmit sensitivity for proper series inductance and resistance feedback. We experimentally demonstrate the feedback method by reducing harmonic generation by 10 dB for the same output pressure at the fundamental frequency by using a simple series resistor feedback with a CMUT operating at a center frequency of 3 MHz. The proposed methods also allow for utilization of the full CMUT gap for transmit operation and, hence, should be useful in high-intensity ultrasonic applications in addition to harmonic imaging.