Star (y) and delta (a) transformation (or) t and π transformation

STAR (Y) AND DELTA (A) TRANSFORMATION (OR) T AND π TRANSFORMATION

Between three terminals A, B and C, we can connect three resistances (impedances) in two fashions. One is called star connection (y), the other is Delta connection (A). In star connection, one end of each impedance is connected at a point called star point and the remaining three terminals are connected to A, B and C. It is called star connection since it appears like a star.

In Delta connection, the three resistances (impedances) are connected end to end, so as to form Delta shape.

In some electrical circuits, calculations become simpler if it is star connected. In some other problems, Delta connection may enable us to solve it easily. Hence it is necessary to convert given star connection resistances into its equivalent Delta and vice-versa.

The given star and Delta connection of resistances are said to be electrically equivalent, if the resistance between any pair of given terminals is the same. With this assumption, we can derive the expressions for resistances in a star, given delta connected resistances and vice-versa.

(a) Given Resistances in Delta To find Resistance in Equivalent Star

(b) Given Resistances in Star-To-Find Resistance in Equivalent Delta

Multiplying equations (5) and (6), we get