Wave Digital Models of Piezoelectric Transducers for Audio Applications

The number of consumer electronics devices integrating piezoelectric (PE) transducers as flat-panel loudspeakers has recently experienced a steep increase. Being very thin, in fact, PE transducers well cope with the miniaturization process that characterizes the market. However, at the same time, their reduced dimensions cause the sound pressure level to be poor at low frequencies, impairing the overall acoustic response. In this article, we derive novel efficient discrete-time models of PE transducers in the wave digital (WD) domain such that they can be integrated in the future into signal processing algorithms for audio output enhancement. WD filters are, in fact, making headway among audio digital signal processing techniques based on circuit equivalent models thanks to their efficiency, robustness, and accuracy. Starting from circuital representations of the piezo constitutive equations, we derive both lumped and distributed models. In particular, we show how it is possible to implement the frequency-dependent elements characterizing Mason’s model in the WD domain, contrary to what can be done using mainstream SPICE-like simulators. Such WD implementations come in handy for the simulation and fast prototyping of PE systems, paving the way toward the design of model-based digital signal processing algorithms for enhancing the transducer acoustic performance.