approximated model [9] in which rectifier devices are not considered
(RI C removed and RII C short-circuited). This model uses a Laplace-domain expression to analyse the response of the electrical driver according to the parameters of Fig. 1 and certain probe characteristics. Neglecting ZL ðZL RShÞ and considering the probe with its cable as a parallel network Rp Cp (only during this VT calculation phase), a linear expression can be obtained for VT depending on the amplitude Hv and switching time s of the step function and the other
parameters detailed in Fig. 1:In (3), Rp is the inverse of the maximum conductance in
the loaded transducer. The time response VTðtÞ could be
computed from the complex frequency response derived
from (2).
Since possible effects from the rectifier devices R
C
have not been considered, expression (2) is valid only
until the first zero-crossing of the spike. This reduces the
application of this driving model to not very narrow
spikes (low-MHz range); moreover it is not very
appropriate for analysing VT when fine details must be
considered. For this reason we proposed another model
in [10], based on an equivalent network integrating the
whole transmitter, for an accurate simulation of driving
responses. It integrates the real effects of all the components
in Fig. 1 with a version of the Mason–Redwood circuit for the piezoelectric section of the transmitter. In order to analyse, with this equivalent network, possible non-linear influences on the transmitter voltage VTðtÞ, we have used the same driving scheme as in [10]. The components involved are of plug-in type and can be removed for different experiments. As an example of the magnitude of these influences, Fig. 2 shows the experimental and computed waveforms obtained when the two rectifier sets R C are removed in the driving scheme of Fig. 1. The high-amplitude oscillations of the C-LSh
resonant circuit cause a harmful lengthening of the spike from typical time-durations when R C are present (roughly signed with the shaded zone). This experiment was made with the driver configuration used for resistive load in [10], but here loading with a tuned probe of 6 MHz of nominal frequency through a l m long coaxial cable. In this case, the internal ‘‘real’’ HV step function, loaded by the probe, descended from 82 to 2 V in 7 ns.