Duality : two networks are said to be dual of each other when the mesh eq’n s of one are the same as node eq’n s for other.
the graph g1 & g2 are said to dual of each
other if the incidence matrix of any one of them is a circuit matrix of other
.thus dual graphs has same no. Of edges
the
dual graphs can be drawn in case of planar graphs . Only planar
networks without mutual inductance have duals.
For mutual inductance
there is no dual relationship.
Conversion properties:
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Original
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dual
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R
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G= 1/R
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L
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C
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Open ckt
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Close ckt
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V
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I
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Voltae source
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Current source
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Kvl
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Kcl
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Node
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Mesh
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Advantage: solution of
on ckt automatically gives sloution of another ckt.