Network analysis (electrical circuits): Difference between revisions

Revision as of 07:45, 31 January 2023

Revision as of 16:54, 12 March 2023

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[[Image:Delta-Star Transformation.svg|right|400px]]

A network of impedances with more than two terminals cannot be reduced to a single impedance equivalent circuit. An {{mvar|n}}-terminal network can, at best, be reduced to {{mvar|n}} impedances (at worst {{math|^''n''[[Binomial coefficient|C]]<submath>\tbinom{n}{2}.</submath>}}]]). For a three terminal network, the three impedances can be expressed as a three node delta (Δ) network or four node star (Y) network. These two networks are equivalent and the transformations between them are given below. A general network with an arbitrary number of nodes cannot be reduced to the minimum number of impedances using only series and parallel combinations. In general, Y-Δ and Δ-Y transformations must also be used. For some networks the extension of Y-Δ to [[#General form of network node elimination|star-polygon]] transformations may also be required.

For equivalence, the impedances between any pair of terminals must be the same for both networks, resulting in a set of three simultaneous equations. The equations below are expressed as resistances but apply equally to the general case with impedances.