E.P. 155.3: Electricity and Magnetic Circuits I
Lecture 18
March 15th, 2005
Norton’s Theorem
Reading:
Boylestad’s Circuit Analysis, 3rd Canadian Edition
Chapter 9.4, Pages 252 - 256
Assignment:
Assignment #9
Due: March 24th, 2005
E.P. 155.3: Electricity and Magnetic Circuits I
Norton’s Theorem
Any two terminal linear bilateral dc network can
be replaced by an equivalent circuit consisting of
a current source and a parallel resistance.
a
=>
IN
RN
b
This allows us to replace arbitrarily complex circuits
(or parts thereof) with a simplified equivalent circuit. The
simplified circuit is called the Norton equivalent circuit or
just the Norton equivalent.
In doing this, we can simplify any subsequent analysis
we do with respect to the two terminals.
March 15th, 2005
Norton’s Theorem
2
E.P. 155.3: Electricity and Magnetic Circuits I
In order to accomplish this, use the following
procedure:
1.
Identify the two terminals that the external
circuit connects to.
Note: the external circuit is usually referred
to as the load on the portion of the circuit
being replaced.
2.
Remove the portion of the circuit that you are
going to replace with its Norton equivalent.
3.
Determine the short circuit current, ISC,
between the two terminals of the circuit to be
replaced. This current is the Norton current,
IN.
4.
Determine the resistance, RN, between the
two terminals of the circuit to be replaced.
Note that in order to do this the circuit must
be “dead”. This means that all sources in
the circuit must set to zero.
5.
Draw the Norton equivalent circuit with IN
and RN.
IN
March 15th, 2005
RN
Norton’s Theorem
3
E.P. 155.3: Electricity and Magnetic Circuits I
Note that there is a relationship between the Thévenin
equivalent and the Norton equivalent since they are duals
(i.e., complementary).
RTH = RN
E TH = I N R N
IN =
ETH
RTH
Since they are related usually you choose either the
Thévenin equivalent circuit or the Norton equivalent circuit
atter which one) and switch from one to the
other. Most engineers choose the Thévenin equivalent.
Why??
March 15th, 2005
Norton’s Theorem
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E.P. 155.3: Electricity and Magnetic Circuits I
Example #1:
Replace the following circuit with its Norton
equivalent. What is the value of the current through RL?
Check your answer against the same circuit given in
the Thévenin Theorem notes to see if the relationships
between the two circuit equivalents hold.
2Ω
10V
a
2Ω
1Ω
RL
b
March 15th, 2005
Norton’s Theorem
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E.P. 155.3: Electricity and Magnetic Circuits I
Example #2:
Replace
equivalent.
the
following
circuit
with
its
Norton
a
2Ω
6Ω
3Ω
4Ω
4A
12V
b
March 15th, 2005
Norton’s Theorem
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