■' f- ' # LINEAR CIRCUITS TIME DOMAIN, PHASOR, AND LAPLACE TRANSrORM APPROACHES THIRD EDITION Raymond A DeCarlo Purdue University Pen-Min Lin Purdue University Kendall Hunt p u b l i s h i n g c o m p a n y o n o n o Cover image (^^J^ikiaui ^ Used under license from Shutterstock, Inc Kendall Hunft p u b l i s h i n g c o m p a n y www.kendallhunt.cpm Send all inquiries to: 4050 Westmark Drive Dubuque, lA 52004-1840 Copyright © 2001, 2009 Raymond A DeCarlo and Pen-Min Lin Copyright © 1995 Prentice-Hall, Inc ISBN 978-0-7575-6499-4 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright owner r^ Printed in the United States of America 10 O TABLE OF CO N TEN TS Preface vii Chapter • Charge, Current, Voltage and Ohm’s Law Chapter • Kirchhoff’s Current & Voltage Laws and Series-Parallel Resistive C ircu its 51 Chapter • Nodal and Loop Analyses 107 Chapter • T he Operational Amplifier 155 Chapter * Linearity, Superposition, and Source Transform ation 191 Chapter • Thevenin, Norton, and Maximum Power Transfer Theorems 227 Chapter • Inductors and C apacitors 269 Chapter • First Order RL and RC Circuits 321 Chapter • Second Order Linear Circuits 379 Chapter 10 • Sinusoidal Steady State Analysis by Phasor Methods 431 Chapter 11 • Sinusoidal State State Power Calculations .499 Chapter 12 • Laplace Transform Analysis L Basics 543 Chapter 13 • Laplace Transform Analysis II: Circuit Applications 603 Chapter 14 • Laplace Transform Analysis III; Transfer Function Applications 683 Chapter 15 * Time Domain Circuit Response Computations: The Convolution M ethod 763 Chapter 16 • Band-Pass Circuits and Resonance 811 Chapter 17 * Magnetically Coupled Circuits and Transformers 883 Chapter 18 • Tw o-Ports 959 Chapter 19 • Principles o f Basic Filtering 1031 Chapter 20 • Brief Introduction to Fourier Series 1085 In d ex 1119 o n p , o n O o o n n - o o 0 ■ 0 n O n n ^ o PREFACE For the last several decades, EE/ECE departments o f US universities have typically required two semesters o f linear circuits during the sophomore year for EE majors and one semester for other engineering majors Over the same time period discrete time system concepts and computer engi neering principles have become required fare for EE undergraduates Thus we continue to use Laplace transforms as a vehicle for understanding basic concepts such as impedance, admittance, fdtering, and magnetic circuits Further, software programs such as PSpice, MATLAB and its tool boxes, Mathematica, Maple, and a host o f other tools have streamlined the computational drudg ery o f engineering analysis and design MATLAB remains a working tool in this 3'''^ edition o f Linear Circuits In addition to a continuing extensive use o f MATLAB, we have removed much o f the more com plex material from the book and rewritten much o f the remaining book in an attempt to make the text and the examples more illustrative and accessible More importantly, many o f the more diffi cult homework exercises have been replaced with more routine problems often with numerical answers or checks Our hope is that we have made the text more readable and understandable by today’s engineering undergraduates C H A P T E R Charge, Current, Voltage and Ohm’s Law CHAPTER O U TLIN E Role and Importance o f Circuits in Engineering Charge and Current Voltage Circuit Elements Voltage, Current, Power, Energy, Relationships Ideal Voltage and Current Sources Resistance, Ohm’s Law, and Power (a Reprise) V-I Characteristics o f Ideal Resistors, Constant Voltage, and Constant Current Sources Summary Terms and Concepts Problems CHAPTER O B jEC TIV ES Introduce and investigate three basic electrical quantities: charge, current, and voltage, and the conventions for their reference directions Define a two-terminal circuit element Define and investigate power and energy conversion in electric circuits, and demonstrate that these quantities are conserved Define independent and dependent voltage and current sources that act as energy or sig nal generators in a circuit Define Ohm’s law, v{t) = R i{t), for a resistor with resistance R Investigate power dissipation in a resistor Classify memoryless circuit elements by dieir terminal voltage-current relationships Explain the difference between a device and its circuit model ch ap ter • Charge, Current, Voltage and O hm ’s Law ROLE AND IM PORTANCE OF CIRCUITS IN ENGINEERING Are you curious about how fuses blow? About the meaning o f different wattages on Hght bulbs? About the heating elements in an oven? And how is the presence o f your car sensed at a stoplight? Circuit theory, the focus o f this text, provides answers to all these questions W hen you learn basic circuit theory, you learn how to harness the power o f electricity, as is done, for example, in • an electric motor that runs the compressor in an air conditioner or the pump in a dish washer; • • • • a microwave oven; a radio, TV, or stereo; an iPod; a car heater In this text, we define and analyze common circuit elements and describe their interaction Our aim is to create a modular framework for analyzing circuit behavior, while simultaneously devel oping a set o f tools essential for circuit design These skills are, o f course, crucial to every electri cal engineer But they also have broad applicability in other fields For instance, disciplines such as bioengineering and mechanical engineering have similar patterns o f analysis and often utilize circuit analogies W H A T IS A C IR C U IT ? A circuit is an energy or signal/information processor Each circuit consists o f interconnections o f “simple” circuit elements, or devices Each circuit element can, in turn, be thought o f as an ener gy or signal/information processor For example, a circuit element called a “source” produces a voltage or a current signal This signal may serve as a power source for the circuit, or it may rep resent information Information in the form o f voltage or current signals can be processed by the circuit to produce new signals or new/different information In a radio transmitter, electricity powers the circuits that convert pictures, voices, or music (that is, information) into electromag netic energy This energy then radi ates into the atmosphere or into space from a transmitting antenna A satellite in space can pick up this electromagnetic energy and trans mit it to locations all over the world Similarly, a T V reception antenna or a satellite dish can pick up and direct this energy to a T V set T h e T V contains circuits (Figure 1.1) that reconvert the information within the received signal back into pictures with sound FIG U RE 1.1 Cathode ray tube with surrounding circuitry for converting electrical signals into pictures Chapter • Charge, Current, Voltage and O hm ’s Law CH A RGE AND CU RREN T CH A R G E Charge is an electrical property o f matter Matter consists o f atoms Roughly speaking, an atom contains a nucleus that is made up o f positively charged protons and neutrons (which have no charge) T he nucleus is surrounded by a cloud o f negatively charged electrons Th e accumulated charge on 6.2415 x 10’^ electrons equals -1 coulomb (C) Thus, the charge on an electron is -1 X 10-19 C Particles with opposite charges attract each other, whereas those with similar charges repel The force o f attraction or repulsion between two charged bodies is inversely proportional to the square o f the distance between them, assuming the dimensions o f the bodies are very small compared with the distance o f separation Two equally charged particles meter (m) apart in free space have charges o f C each if they repel each other with a force o f 10“^ c^ Newtons (N), where c = x 10^ m/s is the speed o f light, by definition The force is attractive if the particles have opposite charges Notationally, Q will denote a fixed charge, and q or q{t), a time-varying charge Exercise How many electrons have a combined charge o f -5 x 10 C? AN SW ER; 333,3 ,5 Exercise Sketch the time-dependent charge profile q{t) = (l-^ ^ C, ? > 0, present on a metal plate M ATLAB is a good tool for such sketches A conductor refers to a material in which electrons can move to neighboring atoms with relative ease Metals, carbon, and acids are common conductors Copper wire is probably the most com mon conductor An ideal conductor offers zero resistance to electron movement Wires are assumed to be ideal conductors, unless otherwise indicated Insulators oppose electron movement Common insulators include dry air, dry wood, ceramic, glass, and plastic An ideal insulator offers infinite opposition to electron movement C U R R EN T Current refers to the net flow o f charge across any cross section o f a conductor T he net move ment o f coulomb (1 C) o f charge through a cross section o f a conductor in second (1 sec) produces an electric current o f ampere (1 A) The ampere is the basic unit o f electric current and equals C/s The direction o f current flow is taken by convention as opposite to the direction o f electron flow, as illustrated in Figure 1.2 This is because early in the history o f electricity, scientists erroneously believed that current was the movement o f only positive charges, as illustrated in Figure 1.3 In metallic conductors, current consists solely o f the movement o f electrons However, as our under standing o f device physics advanced, scientists learned that in ionized gases, in electrolytic solu c h ap ter • Charge, Current, Voltage and O hm ’s Law tions, and in some semiconductor materials, movement o f positive charges constitutes part or all o f the total current flow One Ampere of Current " One ; ; Cloud o f \ se co n d ^ | 6.24x10’® later i ; k electrons J Boundary FIG U RE 1.2 A cloud o f negative charge moves past a cross section of an ideal conductor from right to left By convention, the positive current direction is taken as left to right One Ampere of Current One Coulom b One of positive 'second later charge Boundary FIGURE 1.3 In the late nineteenth cenmry, current was thought to be the movement of a positive charge past a cross section of a conduaor, giving rise to the conventional reference “direction of positive current flow.” Both Figures 1.2 and 1.3 depict a current o f A flowing from left to right In circuit analysis, we not distinguish between these two cases: each is represented symbolically, as in Figure 1.4(a) The arrowhead serves as a reference for determining the true direction o f the current A positive value o f current means the current flows in the same direction as the arrow A current o f negative value implies flow is in the opposite direction o f the arrow For example, in both Figures 1.4a and b, a current o f A flows from left to right 1A -1A > < (a) (b) FIG U RE 1.4 A of current flows from left to right through a general circuit element ... water to flow in a pipe or a hose? W ithout pressure from either a pump or gravity, water in a pipe is still Pressure from a water tower, a pressured bug sprayer tank, or a pump on a fire truck... retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright owner r^ Printed... right; (e) line segments joining C H A R G E A N D C U R R EN T PRO BLEM S ( 0,0 ), ( 0,1 ), ( 2,1 ), ( 2,- 1 ), ( 5,- 1 ), ( 5,1 ), ( 6,1 ), ( 6,2 ), ( 7,2 ), ( 7,- 2 ), ( 8,- 2) 1.Consider the diagram o f Figure P I.la