DELTA TO WYE CIRCUITS
In many circuits applications, we encounter components connected together in one of two ways to form a three terminal network: the "Delta", or Δ (also known as the "Pi," or π)
configuration, and the "Y" (also known as the "T") configuration.
a
It is possible to calculate the proper values of resistors necessary to form one kind of network ( Δ or Y) that behaves identically to the other kind, as analyzed from the terminal connections alone. That is, if we had two separate resistor networks, one Δ and one Y, each with its resistor hidden from view, with nothing but three terminals (A,B, and C) exposed for testing, the resistor could be sized for the two networks so that there would be no way to electrically determine one network apart from the other. In other words, equivalent Δ and Y networks behave identically.
There are several equations used to convert one network to the other:
DELTA to WYE transformations:
X = _ BC __
A + B + C
Y = _ AC __
A + B + C
Z = _ AB __
A + B + C
In general:
Rwye = _ Product of adjacent R's in Δ __
summation of all resistors in Δ
WYE to DELTA transformations:
A = XY + XZ + YZ_ B =__XY + XZ + YZ C = XY + XZ + YZ
X
Y
Z
In general:
Rwye = _ summation of cross product in WYE __
opposite R in WYE
With A = B = C = Rdelta = RΔ and X = Y = Z = Rwye = Ry
RΔ = 3Ry or Ry = RΔ/3
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