Time domain modeling in the thickness mode of a piezoelectric transducer and its electrical circuit including time-varying components

Existing models for piezoelectric transducers are generally frequency domain-based. A limitation of these models is that they do not consider the fact that some components of the exciting or receiving electrical circuit can be time-dependent. This can happen when transducers are excited by capacitance discharge via a switch or when the circuit integrates active components such that diodes. In particular, in the case of capacitance discharge excitation, it is well known that the switch output impedance varies according to time. Indeed, its value is high when the switch is off and low when the switch is on. A temporal-based method is presented for the analysis of piezoelectric transducers in the thickness mode and their excitation circuit. A backing material and a matching layer are also considered. This model takes into account time-varying components by means of a step-by-step calculation process. The method has been successfully tested by comparison with measurements of transducer responses using an electrical circuit based on capacitance discharge via a transistor switch.