Digital simulation of pulsed ultrasonic waveforms

When modeling or simulating an ultrasonic pulse-echo system it is necessary to know the transducer waveforms that are the input to the system. In general, accurate transducer modeling is complex and waveform calculation is computationally intensive. Because of this, investigators often assume these waveforms to be simple sinusoids, modulated by Gaussian or exponential envelopes. However, these latter type pulses do not properly represent the complex response of modern piezoelectric transducers. In this paper, a simple set of equations is presented which can approximate the behavior of a number of common transducer configurations. In the first step of the procedure, a simple but accurate model is employed to calculate the step responses of quarter-wave-matched and backed piezoelectric transducers, assuming open circuit conditions. Effects of electrical terminations and transmit/receive bandwidth limitations are accounted for, approximately, by cascaded filtering. Emitted pressure waveforms and echo voltage waveforms synthesized by this simple procedure are very similar to measured waveforms from real transducers. Under most conditions, the method is only an approximation because the model erroneously assumes isolation between the electrical and acoustic networks. However, under many conditions the model is sufficiently accurate to predict actual transducer performance.