Environmental Engineering Reference
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[33], two-graph [34, 5], and modified nodal analysis are most cited. The
equivalent-circuit approach represents switched capacitor networks with
a set of building blocks that have known characteristics. This approach
is effective for small switched capacitor networks only. Transmission ma-
trix approach maps the building blocks of switched capacitor networks
to a set of matrices so that the networks can be analyzed conveniently.
It is effective for networks of small size. Signal-flow diagram approach
makes use of Mason's rule [35] to yield the transfer function from a given
input node to an arbitrary output node. This approach provides many
insights of the operation of networks, it, however, is not particularly
convenient for computer analysis of switched networks.
Modified nodal analysis (MNA), an extension of the nodal analysis,
has been used extensively in analysis of electrical networks since its emer-
gence in 1970s [36]. For ideal switched capacitor networks, due to the
existence of impulsive currents at switching instants in these networks,
nodal charge conservation law is used at switching instants [37, 28]. This
approach possesses many advantages over other formulation methods in-
cluding [38] :
Ease in circuit formulation. MNA formulation inherits the intrinsic
advantages of Tableau formulation in circuit formulation [39]. The
MNA formulation for arbitrarily large circuits is straightforward. No
manipulation of equations is necessary.
Branch voltages and many branch currents are eliminated in MNA
formulation as compared with Tableau formulation, leading to much
smaller circuit matrices.
Circuit matrices are sparse. The sparsity of circuit matrices enables
the use of sparse matrix solvers to significantly reduce the cost of
computation.
Convenience in calculating parameter sensitivity [5].
Time derivatives of independent sources are never needed.
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