Electric Circuits and Signals

Nassir H. Sabah

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351835756
• Edition: 1
• Topic: Tecnología e ingeniería
• Subtopic: Ingeniería eléctrica y telecomunicaciones

Solving circuit problems is less a matter of knowing what steps to follow than why those steps are necessary. And knowing the why stems from an in-depth understanding of the underlying concepts and theoretical basis of electric circuits. Setting the benchmark for a modern approach to this fundamental topic, Nassir Sabah's Electric Circuits and Signals supplies a comprehensive, intuitive, conceptual, and hands-on introduction with an emphasis on creative problem solving.

A Professional Education

Ideal for electrical engineering majors as a first step, this phenomenal textbook also builds a core knowledge in the basic theory, concepts, and techniques of circuit analysis, behavior, and operation for students following tracks in such areas as computer engineering, communications engineering, electronics, mechatronics, electric power, and control systems. The author uses hundreds of case studies, examples, exercises, and homework problems to build a strong understanding of how to apply theory to problems in a variety of both familiar and unfamiliar contexts. Your students will be able to approach any problem with total confidence. Coverage ranges from the basics of dc and ac circuits to transients, energy storage elements, natural responses and convolution, two-port circuits, Laplace and Fourier transforms, signal processing, and operational amplifiers.

Modern Tools for Tomorrow's Innovators

Along with a conceptual approach to the material, this truly modern text uses PSpice simulations with schematic Capture® as well as MATLAB® commands to give students hands-on experience with the tools they will use after graduation.

Classroom Extras

When you adopt Electric Circuits and Signals, you will receive a complete solutions manual along with its downloadable resources supplying additional material.

1

Circuit Variables and Elements

Overview

Physically, an electric circuit is an interconnection of circuit elements of various types, such as sources of electric energy, resistors, capacitors, and inductors. In the presence of sources, current flows in different parts of the circuit, and voltages appear at the terminals of circuit elements. The circuit is described by a circuit diagram that specifies how the circuit elements are interconnected and on which are shown the values assigned to these elements. For each type of circuit element, voltage and current are related in a particular way that is characteristic of the given type. In the case of ideal resistors, for example, the voltage across a resistor and the current through it are related by Ohm’s law.

A discussion of electric circuits logically begins with the definitions of the two basic circuit variables, namely current and voltage, and their relation to electric energy and power. It is emphasized in this discussion that the two fundamental laws of conservation of charge and conservation of energy must be satisfied in any valid electric circuit. Ideal circuit elements are also considered in this introductory chapter. Voltage sources, current sources, and resistors are presented in some detail. Capacitors and inductors are only briefly introduced at this stage in preparation for Chapter 5 on the sinusoidal steady state. A discussion of their general behavior is postponed to Chapter 11. The chapter ends with concluding remarks on the assumptions made in basic circuit theory.

Learning Objectives

• To be familiar with:
  • The general nature of electric resistance in metals
  • The nature of the assumptions made in basic circuit theory
• To understand:
  • The basic circuit concepts of current, voltage, and power
  • How power absorbed or power delivered by a circuit element is related to the assigned positive directions of current through the element and voltage drop or rise across the element
  • The attributes of independent and dependent, ideal voltage sources and ideal current sources
  • The attributes of an ideal resistor, Ohm’s law, and the power dissipated in a resistor
  • The attributes of an ideal capacitor and an ideal inductor, their voltage—current relations, and the energy they store

1.1 Electric Current

Definition: Current is the rate of flow of electric charge.

To illustrate this definition and derive an expression for current, consider a stream of charged particles moving with a velocity u m/s, each particle carrying a positive charge of e coulombs (Figure 1.1.1). For simplicity, it is assumed that the stream is of uniform cross-sectional area A m², and that the concentration of particles and their velocity are uniform throughout. In an infinitesimal time dt, the charge dq that crosses a given plane xx′ is that contained in the disk of volume Audt m³. Multiplying this volume by the concentration n of the particles per cubic meter, and by e, gives dq = Aunedt. According to the preceding definition, the current i equals dq/dt. Hence,

i=dqdt=Aune⁢(1.1.1)

When charge is expressed in coulombs and time in seconds, current is in amperes (A). The following should be noted:

1. The dimensions of the quantities in Equation 1.1.1 are:
   A=Cs=m2.ms.particlesm3.Cparticle
   Quantities on the RHS cancel out between numerators and denominators, leaving C/s. It is helpful to check the dimensions of all defining relations so as to gain a better appreciation of the quantities involved.
   

   FIGURE 1.1.1
   Flow of electric charges in a conducting medium.
2. Unlike charge, which has only magnitude and sign, current is, in general, a vector quantity that has both magnitude and direction. By convention, and for purely historical reasons, the direction of current is considered as that of motion of positive electric charges. In Equation 1.1.1, e is positive, so that i has the same sign as u. If the particles are negatively charged, e is negative, and the direction of i is opposite that of u.
3. In the presence of an electric field, positive and negative charges experience forces in opposite directions. As a result, positive charges move in the direction of the electric field, whereas negative charges move in the opposite direction. However, the direction of current is the same for both positive and negative charges because, in the case of negative charges, the signs of both e and u in Equation 1.1.1 change simultaneously.

Current Carriers

In metals, current carriers are predominantly conduction electrons, which have sufficient energy to detach from their parent atoms, becoming free electrons within the crystal. These electrons are able to acquire a mean drift velocity in the presence of an applied electric field, as explained more fully in Section 1.7. In some solids, such as semiconductors, current can also be carried by what are effectively positive charges, or holes. In conducting (or electrolytic) solutions, conduction is by means of positively charged ions (cations) or negatively charged ions (anions). In gases, current carriers could be positively charged ions, negatively charged ions, or electrons.

Example 1.1.1 Drift Velocity in a Copper Wire

A copper wire 2...

Table of contents

• Cover
• Half title
• Supplementary Resources Disclaimer
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Prologue: Solving Circuit Problems
• Foreword: Historical Landmarks, Nature, and Relevance of Electric Circuits
• Units, Symbols, Acronyms, and Abbreviations
• 1 Circuit Variables and Elements
• 2 Basic Circuit Connections and Laws
• 3 Basic Analysis of Resistive Circuits
• 4 Circuit Simplification
• 5 Sinusoidal Steady State
• 6 Linear and Ideal Transformers
• 7 Power Relations and Circuit Measurements
• 8 Balanced Three-Phase Systems
• 9 Responses to Periodic Inputs
• 10 Frequency Responses
• 11 Duality and Energy-Storage Elements
• 12 Natural Responses and Convolution
• 13 Switched Circuits
• 14 Two-Port Circuits
• 15 Laplace Transform
• 16 Fourier Transform
• 17 Basic Signal Processing Operations
• 18 Signal Processing Using Operational Amplifiers
• 19 Electric Circuit Analogs of Nonelectrical Systems
• Appendix: Reference Material
• Bibliography
• Index