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By G. Williams (auth.)

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Example text

Consider the circuit shown in fig. 8(a). Suppose it is necessary to construct its dual. By observation the network has three meshes (A, B, and C); ten branches (1-I 0) and 7 independent nodes (a, b, c, d, e, f and h with reference to the ground node g). The dual network must therefore consists of three independent nodes (A, Band C with reference to a ground node G); ten branches (1-IO) and seven meshes (a, b, c, d, e, f and h with an outer space g). Setting out three nodes A, Band C and a ground node Gas shown in fig.

17(b ). 17 b {b) Illustration of a current source substitution sources can be connected to node c without influencing node c because the same current is fed into and out of the node. Effects of the substitution are to replace one resistanceless current source by two source branches containing resistance and to eliminate a mesh of the original network. Constrained mesh currents It is not always desirable to treat resistanceless sources by source substitutions. Resistanceless current sources may be treated by the topological concept of a constrained mesh current.

4) by multiplying by R and setting IR to be equal to - V. Thus under the conditions that R = 1/G and IR =- V the source branches have the same volt-ampere equation and therefore as far as any external network is concerned they are equivalent and one may replace the other. The equivalence is shown graphically in fig. 14. 14 Source equivalence Thus a voltage source branch consisting of a 10 V source in series with a resistance of 5 Q may be replaced by a current source branch consisting of a 2 A source in parallel with a 5 n resistance.

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