Wye-Delta Transformations:

 Most of the time we can solve the circuit using our idea of series and parallel connection and ohm�s law or KCL or KVL. But sometimes we encounter some circuit where the formations of elements are neither in series nor in parallel. For example look at the figure of bridge network below:

 

Now look at the following two formations which look like Wye and Delta. These formations usually found in three phase connections, filters, or in matching networks.

  

 (a) Y netwrk (b) Delta Network

 (a) Delta Network

 

 (b) Pie Network

When we analyze a circuit we may find a certain formation to be helpful. And we might want to change one formation into other. Suppose it might helpful for us to work with Wye formation in three phase rather in Delta formation. So we have to know how to transform a Delta network into Wye network.

Delta to Wye conversion:

Look at the figure below:

 

Now for Delta to Wye conversion:

R1 = (Rb . Rc) / (Ra + Rb + Rc)

R2 = (Rc . Ra) / (Ra + Rb + Rc)

R3 = (Ra . Rb) / (Ra + Rb + Rc)

We don�t have to memorize these formulas rather we can easily remember these. Each resistor of the Wye network is the product of the two adjacent resistors of Delta network, divided by the sum of all three resistors of the Delta network.

Wye to Delta Conversion:

Look at the figure again:

Now for Wye to Delta conversion:

Ra = (R1.R2 + R2.R3 + R3.R1) / R1

Rb = (R1.R2 + R2.R3 + R3.R1) / R2

Rc = (R1.R2 + R2.R3 + R3.R1) / R3

We don�t have to memorize this also. The easy way to remember is, each resistor in the Delta Network is the sum of all possible product formation of Wye network�s resistors taken two at a time, divided by the opposite Wye resistor.