# DELTA to STAR conversion Formula with {FREE PDF} & STAR to DELTA

A Delta to star conversion is a “pi” model circuit to a “T” model circuit conversion. Similarly, star to delta conversion means “T” model to “Pi” model conversion. This makes a more straightforward calculation and analysis of the complex circuit. Also, we will see a Delta to star conversion formula with the FREE pdf.

What will I learn?

## What is the Delta connection?

A pi model in the network is known as a DELTA connection. This contains three elements in the circuit. In short, those elements may be Resistor, capacitor, or Inductor. The triangular symbol denotes a delta connection,  Δ (delta).

## What is the star connection?

A “T” model in the network is a STAR connection. This also contains three elements in the circuit. Those elements may be the same as in the delta connection. The “WYE” symbol denotes a star connection, Y (star).

## Delta to STAR conversion

A delta to star conversion converts a “pi” model to the “T” model. Delta to Star conversion has the following formula:

S_1 = \frac{D_1D_2}{D_1+D_2+D_3}
S_2 = \frac{D_2D_3}{D_1+D_2+D_3}
S_3 = \frac{D_3D_1}{D_1+D_2+D_3}

Here S1, S2, and S3 are impedances of the branches of the star converted circuit that should be placed with respect to the D1D2, D2D3, and D3D1.

Conclusively, if we have the delta network of the same impedances and we want to convert it to star network then divide the impedance by 3(using the above formula). Trick to remember delta to star conversion is: DELTA (5 letters) and STAR(4 letters).

If same impedances available, to convert from delta to star (5-4 letters) divide by 3.

## Star to Delta conversion

A star to delta conversion converts the circuit from the “T” model to the “pi” model. Lastly, we can say that for a star to delta conversion, the branch of the delta model will be the sum of the adjacent branches divided by the opposite branch. Below is the Star to delta conversion formula:

D_1=  \frac{S_1S_2+S_2S_3+S_3S_1}{S_3}
D_2=  \frac{S_1S_2+S_2S_3+S_3S_1}{S_1}
D_3=  \frac{S_1S_2+S_2S_3+S_3S_1}{S_2}

Here S1, S2, and S3 are impedances to the branches of the star circuit. Whereas the D1, D2, and D3 are the impedances of the branches of the Delta circuit.

If same impedances available, to convert from star to delta (4-5 letters) multiply by 3.

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