?-Y and Y-? conversions

kiran

?-Y and Y-? conversions

In many circuit applications, we encounter components connected together in one of two ways to form a three-terminal network: the "Delta," or ? (also known as the "Pi," or ?) configuration, and the "Y" (also known as the "T") configuration.

It is possible to calculate the proper values of resistors necessary to form one kind of network (? 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 ? and one Y, each with its resistors hidden from view, with nothing but the three terminals (A, B, and C) exposed for testing, the resistors 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 ? and Y networks behave identically.

There are several equations used to convert one network to the other:

REVIEW:
"Delta" (?) networks are also known as "Pi" (?) networks.
"Y" networks are also known as "T" networks.
? and Y networks can be converted to their equivalent counterparts with the proper resistance equations. By "equivalent," I mean that the two networks will be electrically identical as measured from the three terminals (A, B, and C).
A bridge circuit can be simplified to a series/parallel circuit by converting half of it from a ? to a Y network. After voltage drops between the original three connection points (A, B, and C) have been solved for, those voltages can be transferred back to the original bridge circuit, across those same equivalent points.

Cheers!

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?-Y and Y-? conversions