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and
Eqs.(5.53) and (5.54) reveal that the consistent initial condition of a pe-
riodically switched nonlinear circuit can be obtained from that of its
Volterra circuits. An important advantage of this approach is that
because Volterra circuits are linear, the numerical Laplace inversion
based two-step algorithm can be employed to yield accurate
from
We will come back to this in Chapter 7 in detail when we deal with
the analysis of periodically switched nonlinear circuits.
6. Existence of Dirac Impulses
at Switching Instants
The strength of impulsive voltage or currents generated by the switch-
ing of one switch may be quite large. Such a large current or voltage
may trigger other switches in the circuits that are controlled internally.
It is therefore critical to detect whether a Dirac impulse exists at ev-
ery switching instant in analysis of circuits with internally controlled
switches.
It was shown earlier that the response of circuits in the step immedi-
ately after switching can be decomposed into a consistent initial condi-
tion component, denoted by which is impulse-free, and an incon-
sistent initial condition component, denoted by
mathematically
Because
is continuous, we have
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