Environmental Engineering Reference
In-Depth Information
The input
is connected to the sub-circuit
of phase
only
and is disconnected from the sub-circuit
outside phase
This is
consummated by making use of the window function
defined
earlier.
The effect of the initial voltage (charge) of the capacitors and that of
the initial current (flux) of the inductors of the sub-circuit must be
accounted for as they have an impact on the behavior of the circuit
in phase
The voltage (charge) of the capacitors and the current (flux) of the
inductors at the end of phase must be extracted so that they will
not affect the behavior of the sub-circuits in subsequent clock phases.
The circuit matrices of each sub-circuit are obtained by applying ap-
propriate matrix stamps introduced in the preceding sections to each
circuit element. In implementation, the matrix stamps of each type of
elements are coded as functions with element type, element values, and
their electrical connections as input parameters of the functions so that
the overall circuit matrices can be formulated in an automated manner.
where is the input of the circuit whose connection in phase is
specified by the constant vector is the window function for
the input, is the network vector in phase which may contain
nodal voltages, branch currents, the charge of nonlinear capacitors, and
the flux of nonlinear inductors. is the linear conductance matrix
whose entries are made of linear elements and the linear portion of non-
linear elements, is the linear capacitance matrix in phase whose
entries are from linear capacitors and inductors; is a nonlinear
vector containing all nonlinear terms of the Taylor series expansion of
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