In this work, an approach to the design of broadband thickness-mode piezoelectric transducer is pre- sented. In this approach, simulation of discrete time model of the impulse response of matched and backed piezoelectric transducer is used to design high sensitivity, broad bandwidth, and short-duration impulse response transducers. The effect of matching the performance of transmitting and receiving air backed PZT-5A transducer working into water load is studied. The optimum acoustical characteristics of the quarter wavelength matching layers are determined by a compromise between sensitivity and pulse duration. The thickness of bonding layers is smaller than that of the quarter wavelength matching layers so that they do not change the resonance peak significantly. Our calculations show that the −3 dB air backed transducer bandwidth can be improved considerably by using quarter wavelength matching layers. The computer model developed in this work to predict the behavior of multilayer structures driven by a transient waveform agrees well with measured results. Furthermore, the advantage of this this model over other approaches is that the time signal for optimum set of matching layers can be predicted rapidly

In the paper there has been made an advantage of the non-classical operational calculus to determination of the response of the certain discrete time-systems. The Z-transform is often used to analysis of the stationary discrete time-systems. However, the use of the Z-transform to determination of the response especially of the non-stationary discrete time-systems is doubtful or may cause complications. This method leads to differential equations of n-th order of variable coefficients, whose solutions are very difficult or impossible. The non-classical operational calculus can be used to analysis both of the stationary and non-stationary discrete time-systems. The presented method with the use of the Heaviside operator soon leads to the target without unnecessary differential equations.