Limitations on the low frequency range of pulsed, thick piezoelectric disks

The objective of this paper is to determine the useful low-frequency limit for transiently-excited thick transducers. The Redwood representation of the Mason equivalent circuit was analyzed for times less than the acoustic propagation time through the transducer. This propagation time, t_T, is the maximum interval available for measuring the pressure pulse radiated from the transducer´s front face. In applications such as finding the frequency dependence of hydrophone sensitivity, the reciprocal of t_T sets an approximate lower limit on the useful frequency range when using the thick-transducer technique. A second low-frequency limit is the reciprocal of the transducer time constant, a quantity arising from the negative capacitance that appears in the transducer equivalent circuit. For common transducer materials and dimensions, these factors set a usable lower limit of 200-400 kHz