A theoretical model of an electrostatic ultrasonic transducer incorporating resonating conduits

This article considers a theoretical model of an electrostatic transducer with resonating conduits connected to the cavities in the backplate. A one-dimensional (in space) model is proposed so that the inverse problem of optimising the design parameters of the device for a desired output is not computationally prohibitive. The mathematical model is described based on matching the acoustic impedances at each interface of the device. The resulting ordinary differential equation is solved to give the frequency domain response of the system and the pressure output at the membrane. Derivation of the electrical impedance, transmission voltage response (TVR) and reception force response (RFR) is also provided. The model is implemented to compare a standard device (no conduits coming from the cavity) with a device with one conduit coming from the cavity. The model output is collated with experimental data and then used to analyse the maximum pressure output for various cavity and conduit dimensions. The results show a significant dependence of the device performance on the cavity and conduit dimensions. The incorporation of fluid filled conduits onto the cavities in the backplate significantly increases the pressure output as well as the transmission and reception sensitivities. The results show that a practical transducer design could be achieved by suitable choices of device geometry and the physical properties of the materials employed.