Delta and Wye Circuits

 

In many circuit 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 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 Δ and Y networks behave identically.

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DELTA AND WYE CIRCUITS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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