1.7.4: Thévenin’s and Norton’s Theorems Revision: June 11, 2010 215 E Main Suite D | Pullman, WA 99163 (509) 334 6306 Voice and Fax Doc: XXX-YYY page 1 of 12Copyright Digilent, Inc. All rights reserved. Other product and company names mentioned may be trademarks of their respective owners.N/A Consider the two interconnected circuits shown in Figure 1 below. The circuits are interconnected at the two terminals a and b, as shown. Our goal is to replace circuit A in the system of Figure 1 with a simpler circuit which has the same current-voltage characteristic as circuit A. That is, if we replace circuit A with its simpler equivalent circuit, the operation of circuit B will be unaffected. We will make the following assumptions about the overall system: •Circuit A is linear •Circuit A has no dependent sources which are controlled by parameters within circuit B •Circuit B has no dependent sources which are controlled by parameters within circuit A Overview In previous chapters, we have seen that it is possible to characterize a circuit consisting of sources and resistors by the voltage-current (or i-v ) characteristic seen at a pair of terminals of the circuit. When we do this, we have essentially simplified our description of the circuit from a detailed model of the internal circuit parameters to a simpler model which describes the overall behavior of the circuit as seen at the terminals of the circuit. This simpler model can then be used to simplify the analysis and/or design of the overall system. In this chapter, we will formalize the above result as Thévenin’s and Norton’s theorems . Using these theorems, we will be able to represent any linear circuit with an equivalent circuit consisting of a single resistor and a source. Thévenin’s theorem replaces the linear circuit with a voltage source in series with a resistor, while Norton’s theorem replaces the linear circuit with a current source in parallel with a resistor. In this chapter, we will apply Thévenin’s and Norton’s theorems to purely resistive networks. However, these theorems can be used to represent any circuit made up of linear elements. Before beginning this chapter, you should be able to: After completing this chapter, you should be able to: • Represent a circuit in terms of its i-v characteristic (Chapter 1.7.3) • Represent a circuit as a two-terminal network (Chapter 1.7.3) • Determine Thévenin and Norton equivalent circuits for circuits containing power sources and resistors • Relate Thévenin and Norton equivalent circuits to i-v characteristics of two-terminal networks This chapter requires: •
1.7.4: Thévenin’s and Norton’s Theorems page 2 of 12 Copyright Digilent, Inc. All rights reserved. Other product and company names mentioned may be trademarks of their respective owners. Figure 1. Interconnected two-terminal circuits. In chapter 1.7.3, we determined i-v characteristics for several example two-terminal circuits, using the superposition principle. We will follow the same basic approach here, except for a general linear two- terminal circuit, in order to develop Thévenin’s and Norton’s theorems.
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- Thévenin's theorem, Voltage source, Norton's theorem, rth, Current Source, Series and parallel circuits