Environmental Engineering Reference
In-Depth Information
the response of the circuit can be obtained using the principle of
superposition. Note that the zero-input response remains unchanged
as it is independent of inputs. The zero-state response, however,
becomes
where
is the zero-state vector to the input
and
is obtained from
where is a constant vector specifying the connection of the
input source to the circuit and
The complete response is given by
A special case of interest is when corresponding to a unit step
input. The response of the circuit to the unit step input is computed
from
Sinusoidal inputs can also be handled conveniently. For example, if
the response is given by
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