Environmental Engineering Reference
In-Depth Information
continue integration after switching. Instead,
or
(imme-
diately after switching) must be used.
iii)
Impulses generated at switching instants may trigger the switching of
other switches that are controlled by internal variables of the circuits.
Numerical algorithms that compute from and the detec-
tion of the existence of impulses at switching instants are the focuses of
this chapter.
2. Numerical Laplace Inversion Based
Two-Step Algorithm
It was shown in Chapter 4 that numerical Laplace inversion is a high-
order numerical integration method that yields the accurate time domain
response of linear circuits. An important advantage of this approach is
that it is capable of handling both the impulses and discontinuities that
can not be handled by conventional numerical integration methods in
the time domain.
To illustrate this, consider the circuit shown in Fig.5.1. The output
voltage of the circuit is given by
Its time-domain response is given by
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