State-Space Modeling of Nonlinear Electrostatic Transducers and Experimental Characterization Using LDV

Electrostatic speakers and ultrasound transmitters, including capacitive micromachined ultrasound transducers (CMUTs), may be thought of as systems with applied voltage as the input variable and diaphragm displacement and sound pressure as the output variables. These electrostatically actuated systems are inherently nonlinear. Electrostatic pressure is proportional to the square of the applied voltage and is inversely proportional to the cube of the time-varying diaphragm-backplate gap spacing. The squeeze film damping coefficient is also dependent on the time-varying gap spacing. For large diaphragm displacement, strain stiffening of the diaphragm can also affect the transducer dynamics. These nonlinear systems are most commonly driven in a linear regime, whereby the moving diaphragm is biased to an operating point with a large static voltage and a relatively small dynamic signal voltage is superimposed to provide actuation of the diaphragm. In recent work, we have demonstrated advantages of exploiting the full operating range of electrostatic transducers, not restricted to a linear operating regime. Our recent focus has been on using commonly available MEMS microphone structures as airborne ultrasonic projectors at frequencies of up to 100 kHz. Although designed as receivers to work in the audible range, these commercial devices are effective as ultrasound transmitters. A large dynamic input voltage is applied to force the diaphragm to traverse the full diaphragm-backplate gap, typically 2 \(\upmu \) m. Electrostatic pull-in,whereby the diaphragm contacts the backplate,can be exploited as a braking feature to instantaneously eliminate diaphragm ring-down and increase the bandwidth of generated waveforms. Having an accurate model for these nonlinear devices is advantageous. A state-space model based on a segmented diaphragm approach has recently been summarized in prior work. The model is suitable for time-domain simulations of the movement of the diaphragm in response to input drive signals and addresses the nonlinear system aspects listed above. In this work, diaphragm waveforms in response to various input signals are measured using a laser doppler vibrometer (LDV) and compared against simulation results to verify the model’s accuracy.