Delta-Wye Conversions

What if resistors are neither in series nor in parallel?

Delta-Wye• Many circuits can be simplified using

three-terminal equivalent networks. • These are of the type (Y) wye or tee

(T) and the delta () or pi () networks.

Y - Tee

Delta - Pi

Delta to Wye Conversion • Each resistor in the

Y-network is the product of the resistors in the two adjacent branches, divided by the sum of the three resistors.

Wye to Delta Conversions• Each resistor in the

network is the sum of all possible products of Y resistors taken two at a time, divided by the opposite resistor.

Delta-Wye Chart

Balanced Networks• Y and networks are said to be

balanced when and when

• Under these conditions, conversion formulas become

RY R3 R 3RY

R1 R2 R3 RYRa Rb Rc R

Transform the delta network to its equivalent wye network.

Examples

Examples First, transform

your network into its opposite network.

Second, calculate the new values for your network.

Third, erase the old network.

Examples

Examples

Examples