Star-mesh transform

The star-mesh transform (or star-polygon transform) is a mathematical circuit analysis technique to transform a resistive network into an equivalent network with one less node. The equivalence follows from the Schur complement identity applied to the Kirchhoff matrix of the network.

The equivalent impedance betweens nodes A and B is given by:

where ${\displaystyle z_{A}}$ is the impedance between node A and the central node being removed.

The transform replaces N resistors with ${\displaystyle N(N-1)/2}$ resistors. For ${\displaystyle N>3}$, the result is an increase in the number of resistors, so the transform has no general inverse without additional constraints.

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