Working equations of a circular multimorph piezoelectric micromachined ultrasonic transducer

This paper makes the distinction between the moment and electrical neutral axis location in a circular, simply supported, multimorph piezoelectric micromachined ultrasonic transducer (PMUT) for application to transduction. The derivation applies to an arbitrary n layer stack of piezoelectric and structural materials forming a multimorph. Based on neutral axis location, the plate vibration equation is derived generally and can be applied separately for transmission and receiving modes. From the electrical neutral axis, the charge equation is derived and is related to the location of the neutral axis through an added voltage-dependent term. In governing transducer equations, the voltage dependent added capacitance creates symmetry between the electrical and mechanical domains enabling theoretical calculation of the electrical input impedance, future derivation of equivalent circuit parameters for a multimorph PMUT, and design of high-power ultrasonic imaging arrays.