Environmental Engineering Reference
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In the backward step, the Dirac impulse in the input has died out.
Also, the capacitor carried a initial voltage of
The
expression of the output voltage becomes
The integration in the backward step is thus computed from
The area of the impulse is then obtained from
The relative difference between the exact value of the area of the
impulse, which is -5, and that computed from the preceding steps is
only
6.2 Dirac Impulses in Nonlinear Circuits
For nonlinear circuits, the simplest approach to integrate over
the switching instant is the backward Euler formula. As pointed out
in the preceding section that Dirac impulses encountered at
are
represented by a rectangular pulse of width
and height
Eq. (5.55)
can be written as
The integration over the step immediately after switching is obtained
from
If the result is zero when no impulse exists. Otherwise, an impulse
exists and the area of the impulse is quantified by
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