Environmental Engineering Reference
In-Depth Information
In the
where
the time origin is shifted from
to
Subsequently, the input is changed to
The
initial condition of the circuit becomes
The circuit in this step
is depicted by
Following the same procedures as those for
we arrive at
Let us examine the properties of (6.11):
If the frequency of the input and the step size
T
are kept un-
changed, and are constant. They only need to be
computed once and can be computed in a pre-processing step prior
to the start of simulation. The computation required in each step is
only one matrix-vector multiplication and one vector addition. The
response of the circuit is obtained at time points of the fixed time in-
terval
T
efficiently. The method is henceforth referred to as
sampled-
data simulation.
The method is exact. No approximation is made in derivation of
the method. In order to obtain the accurate time domain response
of circuits numerically, both and must be computed
to high precision. In Chapter 4 we showed that a high degree of
accuracy can be achieved in computing
and
if the
multi-step numerical Laplace inversion algorithm is employed.
If the circuit has multiple exponential inputs with different frequen-
cies
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