Environmental Engineering Reference
In-Depth Information
ical Laplace inversion is sufficiently accurate over these small intervals.
As long as the time origin is reset to the start of each sub-interval and
the effect of the initial conditions of the circuit at the start of the sub-
interval is accounted for, numerical Laplace inversion will yield accurate
results.
To illustrate this, let us consider the linear time-invariant circuit de-
picted by
where
G
and
C
are conductance and capacitance matrices formulated
using the modified nodal analysis, is the network variable vector,
and
g
is a constant vector specifying the nodes to which the input is
connected.
Laplace transform of
is obtained from
where
The time interval in which we are interested in the behavior of the circuit
is first divided into multiple small sub-intervals of equal width The
first sub-interval is given by (0, The circuit in this sub-interval is
depicted by (4.41). The response of the circuit at
is given by
where
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