9/17/2012
What if resistors are neither in series nor in
parallel?
Delta--Wye
Delta
• Many circuits can be simplified using
three-terminal equivalent networks.
three• These are of the type (Y) wye or tee (T)
and the delta (∆
(∆) or pi (π
(π) networks.
Y - Tee
1
9/17/2012
Delta - Pi
Delta to Wye Conversion
• Each resistor in the YYnetwork 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.
2
9/17/2012
Delta--Wye Chart
Delta
Balanced Networks
• Y and ∆ networks are said to be balanced
when R 1 = R 2 = R 3 = R Y
and when R a = R b = R c = R ∆
• Under these conditions, conversion
formulas become
RY =
R∆
3
R ∆ = 3R Y
Transform the delta network to its equivalent
wye network.
3
9/17/2012
First, transform your
network into its
opposite network.
Second, calculate
the new values for
your network.
Third, erase the old
network.
4
9/17/2012
5