Environmental Engineering Reference
In-Depth Information
circuit with the input
The circuit in phase is formulated
using modified nodal analysis
where is the network variable vector consisting of nodal voltages,
some branch currents, the charge of nonlinear capacitors, and the flux
of nonlinear inductors; and are the conductance and capacitance
matrices, respectively, containing linear elements and the first-order term
of the Taylor series expansion of the nonlinear elements. The higher
order terms are embedded in the nonlinear function and is a
constant vector specifying the nodes to which the input is connected
in phase Representing the network variable vector of the circuit using
Volterra series expansion
where
is the term of the Volterra series expansion of
Evaluating the above expression at
yields Volterra
series expansion of the initial condition of the circuit
Substituting these results into (7.9) yields,
with the initial condition
where
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