Network Reduction: Star–Delta Transformation Because of its shape, the network shown in Figure is called a T (tee) or Y (wye) network. These are different names for the same network.

Star-Delta The network shown in Figure is called 𝜋 (pi) or Δ (delta) because the shapes resemble Greek letters 𝜋 and Δ. These are different names for the same network.

Rule 1: The resistance of any branch of a Y network is equal to the product of the two adjacent sides of a Δ network, divided by the sum of the three Δ resistances.

Rule 2: The resistance of any side of a Δ network is equal to the sum of the Y network resistance, multiplied in pairs, divided by the opposite branch of the Y network. Find Rt at terminals a and d.

Step 2: Now, we can redraw the Y circuit as a Δ circuit and reconnect it to the original circuit.

Y – Δ REDRAWN CIRCUIT

STEPS TO SIMPLIFY REDRAWN CIRCUIT

Source Transformation Source transformations are easy to perform as long as there is a familiarity with Ohms Law. If there is a voltage source in series with an impedance, it is possible to find the value of the equivalent current source in parallel with the impedance by dividing the value of the voltage source by the value of the impedance. The converse also applies here: if a current source in parallel with an impedance is present, multiplying the value of the current source with the value of the impedance will result in the equivalent voltage source in series with the impedance. A visual example of what is being done during a source transformation can be seen in Figure

Remember V=I.Z Figure . An example of a DC source transformation. Notice that the impedance Z is the same in both configurations.