Star Delta Transformation
The transformation from a Star network to a Delta network is simply the reverse of above. We have seen that when converting from a delta network to an equivalent star network that the resistor connected to one terminal is the product of the two delta resistances connected to the same terminal, for example resistor P is the product of resistors A and B connected to terminal 1.
By rewriting the previous formulas a little we can also find the transformation formulas for converting a resistive star connected network to an equivalent delta network giving us a way of producing the required transformation as shown below.
Star to Delta Transformation
The value of the resistor on any one side of the delta, Δ network is the sum of all the two-product combinations of resistors in the star network divide by the star resistor located “directly opposite” the delta resistor being found.
For example, resistor A is given as:
\(A =\frac{PQ+QR+RP}{R}\)
with respect to terminal 3 and resistor B is given as:
\(B=\frac{PQ+QR+RP}{Q}\)
with respect to terminal 2 with resistor C given as:
\(C=\frac{PQ+QR+RP}{P}\)
with respect to terminal 1.
By dividing out each equation by the value of the denominator we end up with three separate transformation formulas that can be used to convert any delta resistive network into an equivalent star network as given below.
Star Delta Transformation Equations
One final point about converting a star connected resistive network into an equivalent delta connected network. If all the resistors in the star network are all equal in value then the resultant resistors in the equivalent delta network will be three times the value of the star resistors and equal, giving: RDELTA = 3*RSTAR
