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 4 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 5 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 6