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3

RESISTIVE NETWORK ANALYSIS

hapter 3 illustrates the fundamental techniques for the analysis of resistive circuits. The chapter begins with the deﬁnition of network variables and of network analysis problems. Next, the two most widely applied methods— node analysis and mesh analysis—are introduced. These are the most generally applicable circuit solution techniques used to derive the equations of all electric circuits; their application to resistive circuits in this chapter is intended to acquaint you with these methods, which are used throughout the book. The second solution method presented is based on the principle of superposition, which is applicable only to linear circuits. Next, the concept of Thévenin and Norton equivalent circuits is explored, which leads to a discussion of maximum power transfer in electric circuits and facilitates the ensuing discussion of nonlinear loads and load-line analysis. At the conclusion of the chapter, you should have developed conﬁdence in your ability to compute numerical solutions for a wide range of resistive circuits. The following box outlines the principal learning objectives of the chapter. 81

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Chapter 3

Resistive Network Analysis

➲ Learning Objectives

1. 2. 3. 4. 5. 6. Compute the solution of circuits containing linear resistors and independent and dependent sources by using node analysis. Sections 3.2 and 3.4. Compute the solution of circuits containing linear resistors and independent and dependent sources by using mesh analysis. Sections 3.3 and 3.4. Apply the principle of superposition to linear circuits containing independent sources. Section 3.5. Compute Thévenin and Norton equivalent circuits for networks containing linear resistors and independent and dependent sources. Section 3.6. Use equivalent-circuit ideas to compute the maximum power transfer between a source and a load. Section 3.7. Use the concept of equivalent circuit to determine voltage, current, and power for nonlinear loads by using load-line analysis and analytical methods. Section 3.8.

3.1

Network Analysis

The analysis of an electric network consists of determining each of the unknown branch currents and node voltages. It is therefore important to deﬁne all the relevant variables as clearly as possible, and in systematic fashion. Once the known and unknown variables have been identiﬁed, a set of equations relating these variables is constructed, and these equations are solved by means of suitable techniques. The analysis of electric circuits consists of writing the smallest set of equations sufﬁcient to solve for all the unknown variables. The procedures required to write these equations are the subject of Chapter 3 and are very well documented and codiﬁed in the form of simple rules. The analysis of electric circuits is greatly simpliﬁed if some standard conventions are followed. Example 3.1 deﬁnes all the voltages and currents that are associated with a speciﬁc circuit.

EXAMPLE 3.1

Problem

Identify the branch and node voltages and the loop and mesh currents in the circuit of Figure 3.1. a v + R1 _ R2 b v + R3 _ + vR 2 i _ b d ic + vR

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c

R1 + + v _ S ia _

Solution

R4

_

The following node voltages may be identiﬁed:

Node voltages va vb vc vd = v S (source voltage) = v R2 = v R4 = 0 (ground) Branch voltages v S = va − vd = va v R1 = va − vb v R2 = vb − vd = vb v R3 = vb − vc v R4 = vc − vd = vc

Figure 3.1

Comments: Currents i a , i b , and i c are loop currents, but only i a and i b are mesh currents.

Part I

Circuits

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In the example, we have identiﬁed a total of 9 variables! It should be clear that some method is needed to organize the wealth of information that can be generated simply by applying Ohm’s law at each branch in a circuit. What would be desirable at this point is a means of reducing the number of equations needed to solve a circuit to the minimum necessary, that is, a method for...