IMPULSE-RESPONSE OF A PIEZOELECTRIC LAYER

The field equations for a piezoelectric layer embedded in an elastic medium have been analysed for the one-dimensional thickness-mode of operation. The force and current response to a voltage pulse excitation has been derived analytically. These solutions can be written as the sum of two parts. The first, known from textbooks, describes a sequence of delta-spikes with spacing T/2; the second is continuous everywhere except the points t = n T/2 (n = 0, 1,...). This second part depends on the value of the coupling factor k(t); it can be ignored for materials with low coupling factors such as quartz (k(t) almost-equal-to 0.1) but it is important for some ceramic materials (e.g. PZT with k(t) almost-equal-to 0.5). It results in very simple formulae for the magnitudes of the discontinuities at the times t = n T/2. The results obtained are valuable for the understanding of the transducer behaviour, especially how the different transfer characteristics for open and short circuit conditions (maxima at f(p) and f(s) respectively) reflect in the time domain. In addition to this analytical results for the magnitudes of the discontinuities can be used as simple test-features for the numerical accuracy of programs for transducer modelling.