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Circuit Theorems

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Circuit Theorems

Your success as an engineer will be directly proportional to your ability to communicate!

—Charles K. Alexander

Enhancing Your Skills and Your Career

Enhancing Your Communication Skills

Taking a course in circuit analysis is one step in preparing yourself for a career in electrical engineering. Enhancing your communication skills while in school should also be part of that preparation, as a large part of your time will be spent communicating.

People in industry have complained again and again that graduating engineers are ill-prepared in written and oral communication. An engineer who communicates effectively becomes a valuable asset.

You can probably speak or write easily and quickly. But how effectively do you communicate? The art of effective communication is of the utmost importance to your success as an engineer.

For engineers in industry , communication is k ey to promotability . Consider the result of a survey of U.S. corporations that asked what factors influence managerial promotion. The survey includes a listing of 22 personal qualities and their importance in adv ancement. You may be surprised to note that “technical skill based on experience” placed fourth from the bottom. Attributes such as self-confidence, ambition, flexibility, maturity, ability to mak e sound decisions, getting things done with and through people, and capacity for hard work all ranked higher. At the top of the list w as “ability to communicate. ” The higher your professional career progresses, the more you will need to communicate. Therefore, you should regard effective communication as an important tool in your engineering tool chest.

Learning to communicate ef fectively is a lifelong task you should always work toward. The best time to begin is while still in school. Continually look for opportunities to de velop and strengthen your reading, writing, listening, and speaking skills. You can do this through classroom presentations, team projects, acti ve participation in student or ganizations, and enrollment in communication courses. The risks are less now than later in the workplace.

Ability to communicate effectively is regarded by many as the most important step to an executive promotion. © IT Stock/PunchStock RF

Learning Objectives

By using the information and exercises in this chapter you will be able to:

    1. Develop and enhance your skills in using nodal analysis and mesh analysis to analyze basic circuits.
    1. Understand how linearity works with basic circuits.
    1. Explain the principle of superposition and how it can be used to help analyze circuits.
    1. Understand the value of source transformation and how it can be used to simplify circuits.
    1. Recognize Thevenin’s and Norton’s theorems and know how they can lead to greatly simplified circuits.
    1. Explain the maximum power transfer concept.

4.1 Introduction

A major adv antage of analyzing circuits using Kirchhof f’s laws as we did in Chapter 3 is that we can analyze a circuit without tampering with its original configuration. A major disadvantage of this approach is that, for a large, complex circuit, tedious computation is involved.

The growth in areas of application of electric circuits has led to an evolution from simple to complex circuits. To handle the complexity, engineers over the years have developed some theorems to simplify circuit analysis. Such theorems include Thevenin’s and Norton’s theorems. Since these theorems are applicable to linear circuits, we first discuss the concept of circuit linearity. In addition to circuit theorems, we discuss the concepts of superposition, source transformation, and maximum power transfer in this chapter. The concepts we de velop are applied in the last section to source modeling and resistance measurement.

4.2 Linearity Property

Linearity is the property of an element describing a linear relationship between cause and effect. Although the property applies to many circuit elements, we shall limit its applicability to resistors in this chapter. The property is a combination of both the homogeneity (scaling) property and the additivity property.

The homogeneity property requires that if the input (also called the excitation) is multiplied by a constant, then the output (also called the response) is multiplied by the same constant. For a resistor, for example, Ohm’s law relates the input i to the output v,

v=iR(4.1)v = iR \tag{4.1}

If the current is increased by a constant k, then the voltage increases correspondingly by k; that is,

kiR=kv(4.2)kiR = kv \tag{4.2}

The additivity property requires that the response to a sum of inputs is the sum of the responses to each input applied separately . Using the voltage-current relationship of a resistor, if

v1=i1R(4.3a)v_1 = i_1 R \tag{4.3a}

and

v2=i2R(4.3b)v_2 = i_2 R \tag{4.3b}

then applying (i1 + i2) gives

v=(i1+i2)R=i1R+i2R=v1+v2v = (i_1 + i_2)R = i_1R + i_2R = v_1 + v_2

\n(4.4)

We say that a resistor is a linear element because the voltage-current relationship satisfies both the homogeneity and the additivity properties.

In general, a circuit is linear if it is both additive and homogeneous. A linear circuit consists of only linear elements, linear dependent sources, and independent sources.

A linear circuit is one whose output is linearly related (or directly proportional) to its input.