Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Electric Circuits James S Kang California State Polytechnic University, Pomona Australia ● Brazil ● Mexico ● Singapore ● United Kingdom ● United States Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Electric Circuits, First Edition James S Kang Product Director, Global Engineering: Timothy L Anderson Associate Media Content Developer: Ashley Kaupert Product Assistant: Alexander Sham Marketing Manager: Kristin Stine Director, Higher Education Production: Sharon L Smith Senior Content Project Manager: Kim Kusnerak Production Service: MPS Limited Senior Art Director: Michelle Kunkler Cover/Internal Designer: Grannan Graphic Design Ltd Cover Image: Dabarti CGI/Shutterstock.com Internal Images: ©Daumantas Liekis/Shutterstock.com; ©iStockPhoto.com/NesneJkraM; ©iStockPhoto.com/Denis Dryashkin; ©iStockPhoto.com/Zorandimzr Intellectual Property Analyst: Christine Myaskovsky Project Manager: Sarah Shainwald Text and Image Permissions Researcher: Kristiina Paul Manufacturing Planner: Doug Wilke â 2018 Cengage Learningđ ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced or distributed in any form or by any means, except as permitted by U.S copyright law, without the prior written permission of the copyright owner For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Library of Congress Control Number: 2016955676 © 2016 Cadence Design Systems, Inc PSpice® All rights reserved worldwide Cadence and the Cadence logo are registered trademarks of Cadence Design Systems, Inc All others are the property of their respective holders Unless otherwise noted, all items © Cengage Learning ISBN: 978-1-305-63521-0 Cengage Learning 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with employees residing in nearly 40 different countries and sales in more than 125 countries around the world Find your local representative at www.cengage.com Cengage Learning products are represented in Canada by Nelson Education Ltd To learn more about Cengage Learning Solutions, visit www.cengage.com/engineering Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Printed in the United States of America Print Number: Print Year: 2016 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Contents Preface x About the Author 2.6 2.7 xvi 1.1 1.2 1.3 2.8 Introduction International System of Units Charge, Voltage, Current, and Power Independent Sources 2.9 2.10 Dependent Sources 15 1.5.1 Voltage-Controlled Voltage Source (VCVS) 16 1.5.2 Voltage-Controlled Current Source (VCCS) 16 1.5.3 Current-Controlled Voltage Source (CCVS) 16 1.5.4 Current-Controlled Current Source (CCCS) 16 1.6 Elementary Signals 17 1.6.1 Dirac Delta Function 17 1.6.2 Step Function 19 1.6.3 Ramp Function 21 1.6.4 Exponential Decay 23 1.6.5 Rectangular Pulse and Triangular Pulse 24 Summary 27 PrOBLEmS 27 Chapter CirCuit lawS 2.1 2.2 2.3 2.4 2.5 2.11 2.11.1 Simulink 104 Summary 104 PrOBLEmS 105 Chapter CirCuit analySiS MethodS 3.1 3.2 3.3 3.4 3.5 3.6 117 Introduction 117 Nodal Analysis 118 Supernode 142 Mesh Analysis 153 Supermesh 175 PSpice and Simulink 190 3.6.1 PSpice 190 3.6.2 VCVS 190 3.6.3 VCCS 191 3.6.4 CCVS 192 3.6.5 CCCS 193 3.6.6 Simulink 193 Summary 194 PrOBLEmS 194 31 Introduction 31 Circuit 31 Resistor 33 Ohm’s Law 35 Kirchhoff’s Current Law (KCL) 74 Current Divider Rule 82 Delta-Wye (D-Y) Transformation and Wye-Delta (Y-D) Transformation 91 PSpice and Simulink 100 10 1.4.1 Direct Current Sources and Alternating Current Sources 11 1.5 Voltage Divider Rule 2.8.1 Wheatstone Bridge 80 1.3.1 Electric Charge 1.3.2 Electric Field 1.3.3 Voltage 1.3.4 Current 1.3.5 Power 1.4 46 2.7.1 Series Connection of Resistors 53 2.7.2 Parallel Connection of Resistors 58 Chapter Voltage, Current, Power, and SourCeS Kirchhoff’s Voltage Law (KVL) Series and Parallel Connection of Resistors 53 Chapter CirCuit theoreMS 38 4.1 4.2 4.3 208 Introduction 208 Superposition Principle 209 Source Transformations 221 iii Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 iv 4.4 Contents 234 Thévenin’s Theorem 6.3 4.4.1 Finding the thévenin equivalent Voltage Vth 235 4.4.2 Finding the thévenin equivalent Resistance Rth 235 4.5 Norton’s Theorem 263 4.6 4.7 6.3.1 series Connection of Capacitors 390 6.3.2 Parallel Connection of Capacitors 392 6.4 4.5.1 Finding the norton equivalent Current In 264 4.5.2 Finding the norton equivalent Resistance Rn 264 4.5.3 Relation Between the thévenin equivalent Circuit and the norton equivalent Circuit 264 Maximum Power Transfer PSpice 296 300 PrOBLEmS 301 Op Amp Integrator and Op Amp Differentiator 395 6.4.1 op Amp Integrator 395 6.4.2 op Amp Differentiator 397 6.5 284 Inductors 397 6.5.1 sinusoidal Input to Inductor 407 6.6 4.7.1 simulink 299 Summary Series and Parallel Connection of Capacitors 390 Series and Parallel Connection of Inductors 408 6.6.1 series Connection of Inductors 408 6.6.2 Parallel Connection of Inductors 409 6.7 Chapter PSpice and Simulink Summary 416 PrOBLEmS 416 Chapter OperatiOnal amplifier CirCuits 314 5.1 5.2 rC and rl CirCuits 424 Introduction 314 Ideal Op Amp 315 7.1 7.2 5.2.1 Voltage Follower 322 5.3 Sum and Difference 333 5.3.1 summing Amplifier (Inverting Configuration) 333 5.3.2 summing Amplifier (noninverting Configuration) 336 5.3.3 Alternative summing Amplifier (noninverting Configuration) 341 5.3.4 Difference Amplifier 343 5.4 5.5 Instrumentation Amplifier Current Amplifier 347 346 5.7 Analysis of Noninverting Configuration 358 5.7.1 Input Resistance 360 5.7.2 output Resistance 360 5.8 PSpice and Simulink Summary 370 PrOBLEmS 371 363 424 Step Response of RC Circuit 435 7.3.1 Initial Value 438 7.3.2 Final Value 438 7.3.3 time Constant 438 7.3.4 solution to General First-order Differential equation with Constant Coefficient and Constant Input 440 Natural Response of RL Circuit 448 7.4.1 time Constant 450 7.5 Step Response of RL Circuit 459 7.5.1 Initial Value 462 7.5.2 Final Value 462 7.5.3 time Constant 462 7.5.4 solution to General First-order Differential equation with Constant Coefficient and Constant Input 464 7.6 7.7 Solving General First-Order Differential Equations 476 PSpice and Simulink 488 Summary 494 PrOBLEmS 495 Chapter Chapter CapaCitOrs and induCtOrs 6.1 6.2 7.3 Analysis of Inverting Configuration 351 5.6.1 Input Resistance 354 5.6.2 output Resistance 354 Introduction 424 Natural Response of RC Circuit 7.2.1 time Constant 428 7.4 5.5.1 Current to Voltage Converter (transresistance Amplifier) 348 5.5.2 negative Resistance Circuit 349 5.5.3 Voltage-to-Current Converter (transconductance Amplifier) 350 5.6 413 Introduction 379 Capacitors 380 6.2.1 sinusoidal Input to Capacitor 389 379 rlC CirCuits 8.1 8.2 505 Introduction 505 Zero Input Response of Second-Order Differential Equations 505 8.2.1 Case 1: overdamped (a v0 or a1 2Ïa0 or z 1) 507 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 ConTEnTS 8.2.2 Case 2: Critically Damped (a v0 or a1 2Ïa0 or z 1) 509 8.2.3 Case 3: Underdamped (a , v0 or a1 , 2Ïa0 or z , 1) 510 8.3 Solution of the Second-Order Differential Equations to Constant Input 545 8.6 Step Response of a Series RLC Circuit 549 8.6.1 Case 1: overdamped (a v0 or a1͞2 Ïa0 or z 1) 550 8.6.2 Case 2: Critically Damped (a v0 or a1 2Ïa0 or z 1) 552 8.6.3 Case 3: Underdamped (a , v0 or a1 , 2Ïa0 or z , 1) 553 8.7 Step Response of a Parallel RLC Circuit 566 8.7.1 Case 1: overdamped (a v0 or a1 2Ïa0 or z 1) 567 8.7.2 Case 2: Critically Damped (a v0 or a1 2Ïa0 or z 1) 569 8.7.3 Case 3: Underdamped (a , v0 or a1 , 2Ïa0 or z , 1) 570 8.8 8.9 General Second-Order Circuits PSpice and Simulink 600 Summary 603 PrOBLEmS 604 638 Impedance and Admittance 9.5.1 Resistor 639 9.5.2 Capacitor 640 9.5.3 Inductor 642 9.6 9.7 9.8 9.10 Phasor-Transformed Circuit 644 Kirchhoff’s Current Law and Kirchhoff’s Voltage Law for Phasors 649 Series and Parallel Connection of Impedances 652 Delta-Wye (D-Y) and Wye-Delta (Y-D) Transformation 656 PSpice and Simulink 661 Summary 664 PrOBLEmS 664 Chapter 10 analySiS of PhaSor-tranSforMed CirCuitS 668 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 Introduction 668 Phasor-Transformed Circuits 669 Voltage Divider Rule 669 Current Divider Rule 672 Nodal Analysis 676 Mesh Analysis 678 Superposition Principle 681 Source Transformation 683 Thévenin Equivalent Circuit 686 10.9.1 Finding the Thévenin Equivalent Voltage Vth 687 10.9.2 Finding the Thévenin Equivalent Impedance Zth 687 580 8.9.1 Solving Differential Equations Using Simulink 600 8.9.2 Solving Differential Equations Using PSpice 601 10.10 10.11 Norton Equivalent Circuit Transfer Function 692 689 10.11.1 Series RLC Circuits 701 10.11.2 Parallel RLC Circuits 707 10.12 Chapter PhaSorS and iMPedanCeS 9.1 9.2 9.5 9.9 8.5.1 Particular Solution 545 8.5.2 Case 1: overdamped (a v0 or a1 2Ïa0 or z 1) 546 8.5.3 Case 2: Critically Damped (a v0 or a1 2Ïa0 or z 1) 547 8.5.4 Case 3: Underdamped (a , v0 or a1 , 2Ïa0 or z , 1) 548 RMS Value 620 Phasors 624 9.4.1 Representing Sinusoids in Phasor 627 9.4.2 Conversion Between Cartesian Coordinate System (Rectangular Coordinate System) and Polar Coordinate System 629 9.4.3 Phasor Arithmetic 635 Zero Input Response of Parallel RLC Circuit 530 8.4.1 Case 1: overdamped (a v0 or a1 2Ïa0 or z 1) 532 8.4.2 Case 2: Critically Damped (a v0 or a1 2Ïa0 or z 1) 532 8.4.3 Case 3: Underdamped (a , v0 or a1 , 2Ïa0 or z , 1) 532 8.5 9.3 9.4 Zero Input Response of Series RLC Circuit 511 8.3.1 Case 1: overdamped (a v0 or a1 2Ïa0 or z 1) 513 8.3.2 Case 2: Critically Damped (a v0 or a1 2Ïa0 or z 1) 513 8.3.3 Case 3: Underdamped (a , v0 or a1 , 2Ïa0 or z , 1) 513 8.4 9.2.1 Cosine Wave 615 9.2.2 Sine Wave 618 PSpice and Simulink Summary 721 PrOBLEmS 722 718 615 Introduction 615 Sinusoidal Signals 615 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 v vi ConTEnTS Chapter 11 aC Power 11.1 11.2 11.3 11.4 11.5 733 Introduction 733 Instantaneous Power, Average Power, Reactive Power, Apparent Power 733 Complex Power 739 Conservation of AC Power 749 Maximum Power Transfer 752 Power Factor Correction (PFC) PSpice and Simulink 767 Summary 770 PrOBLEmS 770 881 PrOBLEmS 881 the laPlaCe tranSforM Introduction 778 Three-Phase Sources 778 778 Balanced Y-Y Circuit 782 12.3.1 Balanced Y-Y Circuit with Wire Impedance 786 792 Balanced Y-D Circuit 12.4.1 Balanced Y-D Circuit with Wire Impedance 796 12.5 Balanced D-D Circuit 12.6 Balanced D-Y Circuit 801 14.4 813 12.6.1 Balanced D-Y Circuit with Wire Impedance 816 PSpice and Simulink Summary 825 PrOBLEmS 825 821 MagnetiCally CouPled CirCuitS 829 Introduction 829 Mutual Inductance 950 PrOBLEmS 951 CirCuit analySiS in the s-doMain 829 Dot Convention and Induced Voltage Summary Chapter 15 13.2.1 Faraday’s Law 830 13.2.2 Mutual Inductance 831 13.2.3 Mutual Inductance of a Second Coil Wrapped Around a Solenoid 833 13.3 835 15.1 15.2 Equivalent Circuits 848 Energy of Coupled Coils 853 Linear Transformer 855 Introduction 954 Laplace-Transformed Circuit Elements 954 955 15.2.1 Resistor 955 15.2.2 Capacitor 956 15.2.3 Inductor 957 15.3 Laplace-Transformed Circuit 958 15.3.1 Voltage Divider Rule 958 15.3.2 Current Divider Rule 961 13.3.1 Combined Mutual and Self-Induction Voltage 838 13.4 13.5 13.6 914 14.5 Solving Differential Equations Using the Laplace Transform 942 14.6 PSpice and Simulink 947 Chapter 13 13.1 13.2 Inverse Laplace Transform 14.4.1 Partial Fraction Expansion 923 14.4.2 Simple Real Poles 925 14.4.3 Complex Poles 928 14.4.4 Repeated Poles 934 12.5.1 Balanced D-D Circuit with Wire Impedance 805 12.7 Introduction 886 Definition of the Laplace Transform 887 Properties of the Laplace Transform 891 14.3.3 Frequency Translation Property 895 14.3.4 Multiplication by cos(v0t ) 898 14.3.5 Multiplication by sin(v0t) 899 14.3.6 Time Differentiation Property 900 14.3.7 Integral Property 902 14.3.8 Frequency Differentiation Property 904 14.3.9 Frequency Integration Property 907 14.3.10 Time-Scaling Property 908 14.3.11 Initial Value Theorem and Final Value Theorem 910 14.3.12 Initial Value Theorem 910 14.3.13 Final Value Theorem 912 12.2.1 negative Phase Sequence 781 12.4 886 14.3.1 Linearity Property (Superposition Principle) 893 14.3.2 Time-Shifting Property 894 three-PhaSe SySteMS 12.3 879 Chapter 14 Chapter 12 12.1 12.2 865 PSpice and Simulink Summary 14.1 14.2 14.3 756 Ideal Transformer 13.7.1 Autotransformer 874 13.8 11.5.1 Maximum Power Transfer for norton Equivalent Circuit 756 11.6 11.7 13.7 15.4 15.5 15.6 Nodal Analysis 964 Mesh Analysis 971 Thévenin Equivalent Circuit in the s-Domain 980 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 ConTEnTS 15.7 15.8 Norton Equivalent Circuit in the s-Domain 990 Transfer Function 997 16.6.3 Phase Response 1102 16.6.4 Series RLC HPF 1102 16.6.5 Parallel RLC HPF 1104 16.6.6 Sallen-Key Circuit for the Second-order HPF 1105 16.6.7 Equal R and Equal C Method 1108 16.6.8 normalization 1109 16.6.9 Unity Gain Method 1110 16.6.10 normalization 1111 15.8.1 Sinusoidal Input 998 15.8.2 Poles and Zeros 999 15.9 Convolution 1020 15.9.1 Commutative Property 1021 15.9.2 Associative Property 1021 15.9.3 Distributive Property 1021 15.9.4 Time-Shifting Property 1021 15.10 Linear, Time-Invariant (LTI) System 16.7 1037 Bode Diagram 1040 15.11.1 Linear Scale 1040 15.11.2 dB Scale 1041 15.11.3 Bode Diagram of Constant Term 1044 15.11.4 Bode Diagram of H(s) s 1000 1044 15.11.5 Bode Diagram of H(s) 100ys 1045 15.11.6 Bode Diagram of H(s) sy1000 1046 15.11.7 Bode Diagram of H(s) 104y(s 100)2 1047 15.11.8 Complex Poles and Zeros 1059 15.12 Simulink 1064 PrOBLEmS 1064 Chapter 16 firSt- and SeCond-order analog filterS 1074 16.1 16.2 Introduction 1074 Magnitude Scaling and Frequency Scaling 1075 16.2.1 Magnitude Scaling 1075 16.2.2 Frequency Scaling 1076 16.2.3 Magnitude and Frequency Scaling 1078 16.3 16.4 16.5 First-Order LPF 1079 First-Order HPF 1081 Second-Order LPF 1084 16.5.1 Frequency Response 1085 16.5.2 Magnitude Response 1085 16.5.3 Phase Response 1086 16.5.4 Series RLC LPF 1087 16.5.5 Parallel RLC LPF 1088 16.5.6 Sallen-Key Circuit for the Second-order LPF 1090 16.5.7 Equal R, Equal C Method 1092 16.5.8 normalized Filter 1093 16.5.9 Unity Gain Method 1098 16.6 Second-Order HPF Design 1100 16.6.1 Frequency Response 1101 16.6.2 Magnitude Response 1101 1113 Bandpass Filter 1120 16.7.7 Equal R, Equal C Method 1122 16.7.8 normalization 1123 16.7.9 Delyiannis-Friend Circuit 1125 16.7.10 normalization 1126 16.8 Second-Order Bandstop Filter Design 1129 16.8.1 Frequency Response 1130 16.8.2 Magnitude Response 1130 16.8.3 Phase Response 1132 16.8.4 Series RLC Bandstop Filter 1132 16.8.5 Parallel RLC Bandstop Filter 1134 16.8.6 Sallen-Key Circuit for the Second-order Bandstop Filter 1136 1062 Summary Second-Order Bandpass Filter Design 16.7.1 Frequency Response 1113 16.7.2 Magnitude Response 1113 16.7.3 Phase Response 1116 16.7.4 Series RLC Bandpass Filter 1116 16.7.5 Parallel RLC Bandpass Filter 1118 16.7.6 Sallen-Key Circuit for the Second-order 15.10.1 Impulse Response 1038 15.10.2 output of Linear Time-Invariant System 1038 15.10.3 Step Response of LTI System 1039 15.11 vii 16.9 Simulink 1147 Summary 1148 PrOBLEmS 1155 Chapter 17 analog filter deSign 17.1 17.2 1166 Introduction 1166 Analog Butterworth LPF Design 1167 17.2.1 Backward Transformation 1168 17.2.2 Finding the order of the normalized LPF 1168 17.2.3 Finding the Pole Locations 1171 17.3 17.4 17.5 17.6 17.7 17.8 Analog Butterworth HPF Design 1182 Analog Butterworth Bandpass Filter Design 1191 Analog Butterworth Bandstop Filter Design 1202 Analog Chebyshev Type LPF Design 1214 Analog Chebyshev Type LPF Design 1226 MATLAB 1242 Summary 1245 PrOBLEmS 1245 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 viii ConTEnTS Chapter 19 Chapter 18 fourier SerieS 18.1 18.2 fourier tranSforM 1259 Introduction 1259 Signal Representation Using Orthogonal Functions 1259 18.2.1 orthogonal Functions 1259 18.2.2 Representation of an Arbitrary Signal by orthogonal Functions 1270 18.2.3 Trigonometric Fourier Series 1278 18.2.4 Proof of orthogonality 1279 18.2.5 Exponential Fourier Series 1282 18.2.6 Proof of orthogonality 1283 18.3 Trigonometric Fourier Series 19.1 19.2 18.4 19.3 18.5 18.5.1 Conversion of Fourier Coefficients 1336 18.5.2 Two-Sided Magnitude Spectrum and Two-Sided Phase Spectrum 1337 18.5.3 Triangular Pulse Train 1343 18.5.4 Sawtooth Pulse Train 1348 18.5.5 Rectified Cosine 1350 18.5.6 Rectified Sine 1353 18.5.7 Average Power of Periodic Signals 1356 18.6 Properties of Exponential Fourier Coefficients 1357 18.8 Solving Circuit Problems Using Exponential Fourier Series 1365 PSpice and Simulink 1373 Summary 1377 PrOBLEmS 1384 Properties of Fourier Transform 1408 19.3.7 Modulation Property 1425 19.3.8 Time-Differentiation Property 1428 19.3.9 Frequency-Differentiation Property 1431 19.3.10 Conjugate Property 1432 19.3.11 Integration Property 1433 19.3.12 Convolution Property 1434 19.3.13 Multiplication Property 1437 19.4 Fourier Transform of Periodic Signals 1439 19.4.1 Fourier Series and Fourier Transform of Impulse Train 1440 19.5 19.6 Parseval’s Theorem Simulink 1449 Summary 1452 PrOBLEmS 1452 1443 Chapter 20 two-Port CirCuitS 20.1 20.2 1457 Introduction 1457 Two-Port Circuit 1458 20.2.1 z -Parameters (Impedance Parameters) 1458 20.2.2 y-Parameters (Admittance Parameters) 1464 20.2.3 h-Parameters (Hybrid Parameters) 1470 20.2.4 g-Parameters (Inverse Hybrid Parameters) 1473 20.2.5 ABCD -Parameters (Transmission Parameters, a-Parameters) 1477 20.2.6 Inverse Transmission Parameters (b-Parameters) 1485 18.6.1 DC Level 1357 18.6.2 Linearity Property (Superposition Principle) 1358 18.6.3 Time-Shifting Property 1358 18.6.4 Time Reversal Property 1364 18.6.5 Time Differentiation Property 1365 18.6.6 Convolution Property 1365 18.7 1399 19.3.1 Linearity Property (Superposition Principle) 1411 19.3.2 Time-Shifting Property 1411 19.3.3 Time-Scaling Property 1414 19.3.4 Symmetry Property (Duality Property) 1416 19.3.5 Time-Reversal Property 1420 19.3.6 Frequency-Shifting Property 1422 1283 Solving Circuit Problems Using Trigonometric Fourier Series 1324 Exponential Fourier Series 1333 Introduction 1399 Definition of Fourier Transform 19.2.1 Symmetries 1403 19.2.2 Finding Fourier Transform from Fourier Coefficients 1407 18.3.1 Trigonometric Fourier Series Using Cosines only 1286 18.3.2 one-Sided Magnitude Spectrum and one-Sided Phase Spectrum 1287 18.3.3 DC Level 1296 18.3.4 Time Shifting 1298 18.3.5 Triangular Pulse Train 1302 18.3.6 Sawtooth Pulse Train 1306 18.3.7 Rectified Cosine 1309 18.3.8 Rectified Sine 1313 18.3.9 Average Power of Periodic Signals 1317 18.3.10 Half-Wave Symmetry 1320 1399 20.3 Conversion of Parameters 1489 20.3.1 Conversion of z-Parameters to All the other Parameters 1489 20.3.2 Conversion of z-Parameters to y-Parameters 1489 20.3.3 Conversion of z-Parameters to ABCD Parameters 1490 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 ConTEnTS 20.3.4 Conversion of z-Parameters to b-Parameters 1491 20.3.5 Conversion of z-Parameters to h-Parameters 1491 20.3.6 Conversion of z-Parameters to g-Parameters 1492 20.3.7 Conversion of y-Parameters to All the other Parameters 1493 20.3.8 Conversion of h-Parameters to All the other Parameters 1494 20.3.9 Conversion of g-Parameters to All the other Parameters 1494 20.3.10 Conversion of ABCD Parameters to All the other Parameters 1495 20.3.11 Conversion of b-Parameters to All the other Parameters 1496 20.4 Interconnection of Two-Port Circuits 1500 20.4.1 Cascade Connection 1500 20.4.2 Series Connection 1502 20.4.3 Parallel Connection 1505 20.4.4 Series-Parallel Connection 1507 20.4.5 Parallel-Series Connection 1508 20.4.6 Cascade Connection for b-Parameters 1508 20.5 PSpice and Simulink Summary 1512 PrOBLEmS 1513 1509 Answers to Odd-Numbered Questions Index 1548 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1517 ix www.downloadslide.net Index general second-order circuits, 580–599 Gibbs phenomenon, 1291, 1341 g-parameters, 1457, 1473–1477 coefficient, 1473–1474 conversion to ABCD parameters, 1495 to all other parameters, 1494–1495 to b-parameters, 1495 to h-parameters, 1495 to y-parameters, 1495 to z-parameters, 1495 equation, 1473 matrix notation, 1473 parallel-series connection, 1508 variables, 1473 ground node, 31, 118 H Haar wavelets, 1266 half-wave symmetry trigonometric Fourier series, 1320–1324 even symmetry and, 1320 odd symmetry and, 1320–1321 high-pass filter (HPF), 692, 693, 1074 Butterworth design, 1182–1191 See also Butterworth HPF first-order, 1081–1084 cutoff frequency, 1083 frequency response, 1081 frequency scaling, 1083, 1084 half-power frequency, 1083 magnitude response, 1082 magnitude scaling, 1083, 1084 phase response, 1082 transfer function of, 1081, 1084 second-order, 1100–1112 corner frequency, 1101 damping coefficient, 1101 equal R, equal C method, 1108–1109 frequency response, 1101 magnitude response, 1101–1102 normalization, 1111–1112 normalized filter, 1109–1110 parallel RLC, 1104–1105 phase response, 1102 quality factor, 1101 Sallen-Key circuit, 1105–1108 series RLC, 1102–1103 transfer function of, 1100 unity gain method, 1110–1111 homogeneous differential equation, 506 h-parameters, 1457, 1470–1473 coefficient, 1471 conversion to ABCD parameters, 1494 to all other parameters, 1494 to b-parameters, 1494 to g-parameters, 1494 to y-parameters, 1494 to z-parameters, 1494 equation, 1471 matrix notation, 1470 series-parallel connection, 1507–1508 variables, 1470 hybrid parameters See h-parameters I ideal transformer, 865–879 autotransformer, 874–879 immittance parameters, 1465 impedance parameters See z-parameters impedances, 638–644 See also wire impedance capacitor, 640–642 delta-wye (∆-Y) transformation, 656–660 inductor, 642–644 Ohm’s law, 638 parallel connection, 653–656 reactance, 639 resistor, 639–640 series connection, 652–653 wye-delta (Y-∆) transformation, 656–660 impulse response, LTI system, 1038–1039 transfer function, 998 impulse train, Fourier transform of, 1440–1443 induced voltage, 835–848 inductors, 379, 397–413 admittance, 643, 644 impedance, 642–644 parallel connection, 409–412 series connection, 408–409, 412–413 sinusoidal input, 407–408 initial value, step response RC circuit, 438 RL circuit, 462 initial value problem, 506 initial value theorem Laplace transform, 910–912 inner product, 1259–1260 instantaneous frequency, 624–625 instantaneous phase, 624 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1555 www.downloadslide.net 1556 Index instantaneous power, 9, 733, 734, 736 on capacitors, 383–384 time-varying part of, 737 phasor representation of, 737 instrumentation amplifier, 346–347 Wheatstone bridge circuit connected to, 365 integral property, Laplace transform, 902–904 integration property, of Fourier transform, 1433–1434 integrator, operational amplifier (op amp), 395–396 interconnections, two-port circuits, 1457, 1500–1509 cascade ABCD-parameters, 1500–1502 b-parameters, 1508–1509 parallel, 1505–1507 parallel-series, 1508 series, 1502–1504 series-parallel, 1507–1508 International System of Units (SI), 1–4 inverse hybrid parameters See g-parameters inverse Laplace transform, 887, 914–923 complex poles, 928–934 partial fraction expansion, 923–925 repeated poles, 934–942 simple real poles, 925–928 inverse transmission parameters See b-parameters inverting op amp configuration analysis of, 351–357 input resistance, 354 output resistance, 354–357 PSpice model for, 363–364 Simulink model for, 366–368 summing amplifier, 333–336 K KCL See Kirchhoff’s current law (KCL) kelvin, kilogram, Kirchhoff’s current law (KCL), 38–46 nodal analysis, 117, 118–141 phasors, 649–652 Kirchhoff’s voltage law (KVL), 46–52 mesh analysis, 117, 153–175 phasors, 649–652 KVL See Kirchhoff’s voltage law (KVL) L lagging, 407, 644 power factor, 742 Laplace transform, 886–950 abscissa of absolute convergence, 888 final value theorem, 912–914 Fourier transform, 1402–1403 initial value theorem, 910–912 inverse, 887, 914–923 complex poles, 928–934 partial fraction expansion, 923–925 repeated poles, 934–942 simple real poles, 925–928 one-sided, 887 overview, 886 pair, 887 pole-zero diagram, 889 properties of, 891 convolution, 1021 frequency differentiation, 904–907 frequency integration, 907–908 frequency translation, 895–898 integral, 902–904 linearity, 893 multiplication, 898–900 time differentiation, 900–902 time-scaling, 908–909 time-shifting, 894–895 PSpice, 947–948 region of convergence (ROC), 888 table, 891–892 Simulink, 948–950 solving differential equations, 942–947 two-sided, 887 Laplace-transformed circuits current divider rule, 961–964 elements, 955 capacitor, 956 inductor, 957 resistor, 955–956 mesh analysis, 971–980 nodal analysis, 964–971 voltage divider rule, 958–961 leading, 389, 642 power factor, 742 LED See light-emitting diode (LED) light-emitting diode (LED), 351 linear, time-invariant (LTI) system, 1325–1326 s-domain, 1037–1040 concept of, 1037–1038 impulse response of, 1038–1039 output of, 1038 step response of, 1039–1040 linearity property exponential Fourier coefficients, 1358 Fourier transform, 1411 Laplace transform, 893 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Index linear system, 1037 linear transformer, 855–865 line voltages, 780 magnitude of, 780 loop of circuit, 31, 153 low-pass filter (LPF), 692, 693, 1074 Butterworth design, 1167–1182 See also Butterworth LPF first-order, 1079–1081 cutoff frequency, 1079 frequency response, 1079 frequency scaling, 1080, 1081 half-power frequency, 1079 magnitude response, 1079, 1080 magnitude scaling, 1081 normalized, 1080 phase response, 1079, 1080 transfer function, 1079, 1081 voltage divider rule, 1081 second-order, 1084–1100 corner frequency, 1084 damping coefficient, 1084, 1085 equal R, equal C method, 1092–1093 frequency response, 1085 magnitude response, 1085–1086 normalized filter, 1093–1094 parallel RLC, 1088–1090 phase response, 1086–1088 pole-zero diagram, 1085 quality factor, 1084–1085 Sallen-Key circuit, 1090–1092 transfer function of, 1084 unity gain method, 1098–1100 M Maclaurin series, 626 magnetically coupled circuits, 829–881 combined mutual and self-induction voltage, 838–848 dot convention, 835–848 energy of coupled coils, 853–855 equivalent circuits, 848–853 induced voltage, 835–848 mutual inductance, 829–835 Ampere’s law, 830 Coulomb’s law, 829 Faraday’s law, 830–833 second coil wrapped around a solenoid, 833–835 self-induction voltage, 838–848 transformer autotransformer, 874–879 defined, 829 1557 ideal, 865–879 linear, 855–865 step-down, 829 step-up, 829 magnitude of line voltage, 780 of phase voltage, 778–779 magnitude response, 999 Chebyshev type LPF, 1214 Chebyshev type LPF, 1227 first-order analog filters HPF, 1082 LPF, 1079, 1080 second-order analog filter BPF, 1113–1115 BSF, 1130–1131 HPF, 1101–1102 LPF, 1085–1086 magnitude scaling, 1075–1076 first-order analog filters HPF, 1083, 1084 LPF, 1081 frequency scaling and, 1078–1079 MATLAB, 118, 122–123, 1242–1245 analog filter design, 1242 Bode diagram, 1043-1044, 1051 conversion of parameters, 1497–1500 D2Y.m, 97–98 first-order differential equation, 432, 442, 446, 456, 473, 481, 484, 487 Fourier series, 1293, 1301, 1329, 1341, 1361, 1371 inverse Laplace transform, 927–928, 930, 934 Laplace transform, 890 maximum power transfer, 294 mesh analysis, 156, 159, 166, 170, 189, 978 nodal analysis, 122, 134, 138, 146, 152, 966 Norton's theorem, 283 P.m, 63 P2Rd.m, 633 P2Rr.m, 633 Parseval's theorem, 1448 phasor transformed circuit, 671, 675, 678, 680 power factor correction, 763, 766 resistive circuits, 69, 79, 89 second-order differential equation, 517, 524, 529, 535, 544, 562, 565, 579, 582, 585, 599 Thévenin's theorem, 251, 256 three-phase systems, 790, 810, 812 transfer function, 1015 Y2D.m, 94 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net 1558 Index matrix notation ABCD parameters, 1477 b-parameters, 1486 g-parameters, 1473 h-parameters, 1470 y-parameters, 1464 z-parameters, 1458 maximum power transfer, 284–295 ac power, 752–756 Norton equivalent circuit, 756 Thévenin equivalent circuit, 752–755 mean square value of a signal, 1318 mesh, 31, 117, 153 circuit with, 153 labeling, 117 supermesh, 175–190 mesh analysis, 117, 153–175 Laplace-transformed circuits, 971–980 phasor-transformed circuits, 678–681 mesh currents, 117–118 labeling, 117 meter, meter-kilogram-second (MKS) system, microfarad, 380 MKS See meter-kilogram-second (MKS) system modulation property, of Fourier transform, 1425–1428 mole, multiplication, phasor, 636 multiplication property Fourier transform, 1437–1438 Laplace transform, 898–900 mutual inductance, 829–835 Ampere’s law, 830 Coulomb’s law, 829 Faraday’s law, 830–833 second coil wrapped around a solenoid, 833–835 nodal analysis, 117, 118–141 essential nodes, 118 labeling circuit for, 118 Laplace-transformed circuits, 964–971 phasor-transformed circuits, 676–678 node currents leaving through resistors, 117 defined, 31 ground, 31 labeling, 117 reference, 31, 117 simple, 31 node voltage, 31 node-voltage equations, 117 node voltages, 117 noninverting op amp configuration analysis of, 358–363 input resistance, 360 output resistance, 360–363 model of, 318 PSpice model for, 365–366 simplified model for, 318 Simulink model for, 366, 368–370 summing amplifiers, 336–341 alternative, 341–343 normalized filter, 1074 BPF, 1123–1125 BSF HPF, 1109–1110 LPF, 1093–1094 Norton equivalent circuits, 263–284 ac power maximum power transfer, 756 in s-domain, 990–997 Norton equivalent current, 208–209 Norton equivalent resistance, 209 Norton’s theorem, 208–209, 263–284 N O nanofarad, 380 natural response defined, 424 RC circuit, 424–434 time constant, 428–430 RL circuit, 448–459 time constant, 450–452 transient response, 450 negative resistance circuit current amplifier, 349–350 neper frequency, 507 neutrons, odd symmetry exponential Fourier series, 1335–1336 Fourier transform, 1403 trigonometric Fourier series, 1285 Ohm’s law, 35–38 complex power, 739 impedances, 638 one-sided Laplace transform, 887 one-sided magnitude spectrum, trigonometric Fourier series, 1287–1296 one-sided phase spectrum, trigonometric Fourier series, 1288–1296 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Index operational amplifier (op amp), 314–370 circuit symbol for, 314 concept, 314 difference amplifier, 343–345 differentiator, 397 ideal, 315–333 integrator, 395–396 inverting configuration See inverting op amp configuration noninverting configuration See noninverting op amp configuration overview, 314 pin configuration, 314, 314 PSpice, 363–366 Simulink, 366–370 summing amplifier, 333–343 voltage follower, 322–333 orthogonal functions, 1259–1283 arbitrary signal representation by, 1270–1278 exponential Fourier series, 1282–1283 inner product, 1259–1260 trigonometric Fourier series, 1278–1282 orthonormal function, 1260 overdamped response parallel RLC circuit step response, 567–569 zero input response, 532 second-order differential equations constant unit, 546–547 constant input, 546–547 zero input response, 507–509 series RLC circuit step response, 550–552 zero input response, 513 P P.m, 63 P2Rd.m, 633 P2Rr.m, 633 pair Laplace transform, 887 parallel connection of capacitors, 392–395 impedances, 653–656 of inductors, 409–412 of resistor, 58–73 two-port circuits, 1505–1507 y-parameters, 1505–1507 parallel RLC circuit phasor-transformed circuits transfer function, 707–713 second-order analog filter BPF, 1118–1119 BSF, 1134–1135 HPF, 1104–1105 LPF, 1088–1090 step response of, 566–580 critically damped, 569–570 overdamped, 567–569 underdamped, 570–571 zero input response, 530–544 critically damped, 532 overdamped, 532 underdamped, 532 parallel-series connection two-port circuits, 1508 parameters, two-port circuits, 1457 ABCD, 1457, 1477–1485 cascade connection, 1500–1502 coefficient, 1477–1478 conversion, 1495–1496 equation, 1477 matrix notation, 1477 variables, 1477 b-parameters, 1457, 1485–1489 cascade connection, 1508–1509 coefficient, 1486 conversion, 1496 equation, 1486 matrix notation, 1486 variables, 1485–1486 g-parameters, 1457, 1473–1477 coefficient, 1473–1474 conversion, 1494–1495 equation, 1473 matrix notation, 1473 parallel-series connection, 1508 variables, 1473 h-parameters, 1457, 1470–1473 coefficient, 1471 conversion, 1494 equation, 1471 matrix notation, 1470 series-parallel connection, 1507–1508 variables, 1470 y-parameters, 1457, 1464–1470 coefficient, 1465 conversion, 1493 equation, 1465 equivalent circuit, 1465 matrix notation, 1464 parallel connection, 1505–1507 variables, 1464 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1559 www.downloadslide.net 1560 Index z-parameters, 1457, 1458–1464 See impedance parameters coefficient, 1458–1459 conversion, 1490–1491, 1492, 1493 equation, 1458 equivalent circuit, 1459–1460 matrix notation, 1458 series connection, 1502–1504 variables, 1458 Parseval’s theorem See also Fourier series Fourier transform, 1443–1449 trigonometric Fourier series, 1318 partial fraction expansion, inverse Laplace transform, 923–942 passive sign convention, path, circuit, 31 periodic signals average power exponential Fourier series, 1356–1357 trigonometric Fourier series, 1317–1320 Fourier transform of, 1439–1443 impulse train, 1440–1443 mean square value of, 1318 root mean square (rms) value, 1318 permittivity of free space, phase current, 793 phase response first-order analog filters HPF, 1082 LPF, 1079, 1080 second-order analog filter BPF, 1116 BSF, 1132 HPF, 1102 LPF, 1086–1088 phase voltages, 779 magnitude of, 778–779 phasors, 624–638 arithmetic, 635–637 addition, 635 division, 636 multiplication, 636 subtraction, 635–636 sum of sinusoids, 636–637 Cartesian coordinate system, 629–633 Euler’s rule, 626 instantaneous frequency, 624–625 instantaneous phase, 624 Maclaurin series, 626 polar coordinate system, 633–635 phasor-transformed circuits, 644–649 analysis, 668–721 current divider rule, 672–675 KCL, 649–651 KVL, 651–652 mesh analysis, 678–681 nodal analysis, 676–678 Norton equivalent circuit, 689–692 PSpice, 718–719 Simulink, 720–721 source transformation, 683–686 superposition principle, 681–683 Thévenin equivalent circuit, 686–689 transfer function, 692–718 parallel RLC circuit, 707–713 series RLC circuit, 701–707 voltage divider rule, 669–672 picofarad, 380 planar, 153 Plancherel theorem, 1444–1445 pol2cart, 633 polar coordinate system, 633–635 poles and zeros Butterworth design BPF, 1191, 1194 BSF, 1202–1203, 1205 HPF, 1182, 1184 LPF, 1174, 1175 Chebyshev type LPF, 1218–1219 Chebyshev type LPF, 1230–1231 s-domain Bode diagram, 1059–1062 transfer function, 999–1020 pole-zero diagram, 999 Laplace transform, 889 low-pass filter (LPF), 1085 power, 9–10 See also ac power conservation of, defined, instantaneous, power factor, 733 lagging, 742 leading, 742 power factor correction (PFC), 756–766 power spectral density (PSD), 1318 power transfer, maximum ac power, 752–756 Norton equivalent circuit, 756 Thévenin equivalent circuit, 752–755 circuit theorems, 284–295 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Index power triangle, 733, 742–743 Pythagorean theorem to, 742–743 properties Fourier transform, 1408–1438 conjugate, 1432–1433 convolution, 1434–1437 frequency-differentiation, 1431–1432 frequency-shifting, 1422–1425 integration, 1433–1434 linearity property, 1411 modulation, 1425–1428 multiplication, 1437–1438 symmetry, 1416–1420 time-differentiation, 1428–1431 time-reversal, 1420–1422 time-scaling, 1414–1416 time-shifting, 1411–1413 Laplace transform, 891 frequency differentiation, 904–907 frequency integration, 907–908 frequency translation, 895–898 integral, 902–904 linearity, 893 multiplication, 898–900 time differentiation, 900–902 time-scaling, 908–909 time-shifting, 894–895 protons, PSpice, 100–103 ac power, 767–769 capacitors, 413–414 circuits with dependent sources, 190–193 first-order circuits, 488–494 Fourier series, 1373–1376 Laplace transform, 947–948 magnetically coupled circuits, 879–880 operational amplifier (op amp), 363–366 phasor and impedance, 661–664 phasor-transformed circuits, 718–719, 718–721 solving differential equations using, 601–603 Thévenin equivalent resistance, 296–299 Thévenin equivalent voltage, 296–299 three-phase systems, 821–824 two-port parameters, 1509–1510 Pythagorean theorem, to power triangle, 742–743 R R2P.m, 630 ramp function, 21 ramp response, s-domain, transfer function, 998 RC circuit 1561 natural response, 424–434 time constant, 428–430 step response, 435–448 final value, 438 general first-order differential equation with a constant coefficient and constant input, 440–441 initial value, 438 time constant, 438–440 reactive power, 733, 736 apparent power, 738 reciprocal two-port circuits, 1460 rectangular pulse, 24–25 rectified cosine waveform exponential Fourier series, 1350–1353 full-wave, 1352 half-wave, 1350 trigonometric Fourier series, 1309–1313 full-wave, 1311 half-wave, 1309 rectified sine waveform exponential Fourier series, 1353–1356 full-wave, 1355 half-wave, 1353 trigonometric Fourier series, 1313–1317 full-wave, 1315 half-wave, 1313 reference node, 31 region of convergence (ROC), 888 relative permittivity, 380 repeated poles, inverse Laplace transform, 934–942 resistor, 33–34 impedance, 639–640 parallel connection of, 58–73 series connection of, 53–58 resistors impedance, 639 admittance, 640 resonant frequency, 507 RLC circuits, 505–603 See also second-order differential equations parallel step response, 566–580 zero input response, 530–544 series step response of, 549–565 zero input response, 511–530 RL circuit natural response, 448–459 time constant, 450–452 transient response, 450 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net 1562 Index RL circuit (continued) step response, 459–475 final value, 462 general first-order differential equation with a constant coefficient and constant input, 464 initial value, 462 time constant, 462–464 RMS value, 620–624 mean square value, 621 root mean square (rms) value, 622 root mean square (rms) value of signal, 1318 S Sallen-Key circuit BPF, 1120–1122 BSF, 1136–1147 HPF, 1105–1108 LPF, 1090–1092 sawtooth pulse train exponential Fourier series, 1348–1350 trigonometric Fourier series, 1306–1309 s-domain Bode diagram, 1040–1062 complex poles and zeros, 1059–1062 linear scale, 1040–1041 LTI system, 1037–1040 concept of, 1037–1038 impulse response of, 1038–1039 output of, 1038 step response of, 1039–1040 Norton equivalent circuit in, 990–997 Simulink, 1062–1063 Thévenin equivalent circuit in, 980–989 transfer function, 997–1020 impulse response, 998 poles and zeros, 999–1020 ramp response, 998 sinusoidal input, 998–999 step response, 998 second, second harmonic frequency, 1286 second-order analog filter BPF, 1113–1129 damping coefficient, 1113 Deliyannis-Friend circuit, 1125–1126 equal R, equal C method, 1122–1123 frequency response, 1113 magnitude response, 1113–1115 normalization, 1126–1129 normalized filter, 1123–1125 parallel RLC, 1118–1119 phase response, 1116 quality factor, 1113 Sallen-Key circuit, 1120–1122 series RLC, 1116–1118 transfer function of, 1113 BSF, 1129–1147 corner frequency, 1129 damping coefficient, 1129 frequency response, 1130 magnitude response, 1130–1131 null frequency, 1129 parallel RLC, 1134–1135 phase response, 1132 quality factor, 1129 Sallen-Key circuit, 1136–1147 series RLC, 1132–1134 transfer function of, 1129 HPF, 1100–1112 corner frequency, 1101 damping coefficient, 1101 equal R, equal C method, 1108–1109 frequency response, 1101 magnitude response, 1101–1102 normalization, 1111–1112 normalized filter, 1109–1110 parallel RLC, 1104–1105 phase response, 1102 quality factor, 1101 Sallen-Key circuit, 1105–1108 series RLC, 1102–1103 transfer function of, 1100 unity gain method, 1110–1111 LPF, 1084–1100 corner frequency, 1084 damping coefficient, 1084, 1085 equal R, equal C method, 1092–1093 frequency response, 1085 magnitude response, 1085–1086 normalized filter, 1093–1094 parallel RLC, 1088–1090 phase response, 1086–1088 pole-zero diagram, 1085 quality factor, 1084–1085 Sallen-Key circuit, 1090–1092 transfer function of, 1084 unity gain method, 1098–1100 second-order circuits, 580–599 second-order differential equations constant input, 545–549 critically damped, 547–548 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Index overdamped, 546–547 particular solution, 545–546 underdamped, 548–549 zero input response, 505–511 critically damped, 509 overdamped, 507–509 underdamped, 510–511 self-inductance, 830 self-induction voltage, 838–848 series connection of capacitors, 390–392 impedances, 652–653 of inductors, 408–409, 412–413 of resistor, 53–58 two-port circuits, 1502–1504 series-parallel connection two-port circuits, 1507–1508 series RLC circuit BPF, 1116–1118 BSF, 1132–1134 HPF, 1102–1103 LPF, 1087–1088 step response of, 549–565 critically damped, 552–553 overdamped, 550–552 underdamped, 553–554 zero input response, 511–530 critically damped, 513 overdamped, 513 underdamped, 513 SI See International System of Units (SI) siemens, 639 See also admittance sifting property of delta function, 19 simple node, 31 simple real poles, inverse Laplace transform, 925–928 Simulink, 104 analog filters, 1147–1148 capacitors and inductors, 414–415 circuit with VCCS, 193 first-order circuits, 488–494 Fourier series, 1373–1376 Fourier transform, 1449–1452 magnetically coupled circuits, 880–881 operational amplifier (op amp), 366–370 phasor and impedance, 661–664 phasor-transformed circuits, 718–721 s-domain circuit analysis, 1062–1063 solving differential equations using, 600–601 Thévenin resistance measurement, 299, 300 Thévenin voltage measurement, 299 two-port parameters, 1510–1512 sine wave, 618–619 sinusoidal input to capacitors, 389–390 to inductors, 407–408 s-domain, transfer function, 998–999 sinusoidal signals, 615–620 cosine wave, 615–618 sine wave, 618–619 sinusoids in phasor representation, 627–628 sum of, 636–637 source transformations, 208, 221–234 step-down transformer, 829 step function, 19–21 step response defined, 424 parallel RLC circuit, 566–580 critically damped, 569–570 overdamped, 567–569 underdamped, 570–571 RC circuit, 435–448 final value, 438 general first-order differential equation with a constant coefficient and constant input, 440–441 initial value, 438 time constant, 438–440 RL circuit, 459–475 final value, 462 general first-order differential equation with a constant coefficient and constant input, 464 initial value, 462 time constant, 462–464 s-domain LTI system, 1039–1040 transfer function, 998 series RLC circuit, 549–565 critically damped, 552–553 overdamped, 550–552 underdamped, 553–554 step-up transformer, 829 stopband ripple parameter, 1216 subtraction, phasor, 635–636 summing amplifier inverting configuration, 333–336 noninverting configuration, 336–341 alternative, 341–343 Simulink model for, 370 sum of sinusoids, 636–637 supermesh, 175–190 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1563 www.downloadslide.net 1564 Index supernode, 117, 142–152 circuit with, 142 node equation for, 142 superposition principle, 208, 209–221 See also linearity property phasor-transformed circuits, 681–683 symmetrical two-port circuit, 1460 symmetries Fourier series exponential even, 1335 odd, 1335 trigonometric even, 1285 odd, 1285 Fourier transform even, 1403 odd, 1403 symmetry property, 1416–1420 T Table active filter, 1152 Fourier series, 1377 Fourier transform pairs, 1409 Fourier transform properties, 1409 Laplace transform pairs, 892 Laplace transform properties, 891 passive filters, 1149 theorem(s), 208–300 maximum power transfer, 284–295 Norton’s theorem, 263–284 overview, 208–209 Parseval’s, 1318, 1443–1449 Plancherel, 1444–1445 PSpice, 296–299 Pythagorean, 742–743 source transformations, 221–234 superposition principle, 208, 209–221 Thévenin’s theorem, 234–263 Simulink, 299–300 Thévenin equivalent circuit, 234, 235–263 ac power maximum power transfer, 752–755 phasor-transformed circuits, 686–689 in s-domain, 980–989 Thévenin equivalent resistance, 208, 209, 234 Thévenin equivalent voltage, 208, 209 Thévenin’s theorem, 208, 234–263 three-phase systems, 778–824 balanced ∆-∆ circuit, 801–813 with wire impedance, 805–813 balanced ∆-Y circuit, 813–821 with wire impedance, 816–821 balanced Y-∆ circuit, 792–805 with wire impedance, 796–805 balanced Y-Y circuit, 782–792 with wire impedance, 786–792 negative phase sequence, 781–782 overview, 778 PSpice, 821–824 Simulink, 824 sources, 778–782 time constant, 425 RC circuit natural response, 428–430, 428–434 step response, 438–440 RL circuit natural response, 450–452, 450–459 step response, 462–464 time-differentiation property exponential Fourier coefficients, 1365 Fourier transform, 1428–1431 time differentiation property, Laplace transform, 900–902 time-invariant system, 1038 time-reversal property exponential Fourier coefficients, 1364 Fourier transform, 1420–1422 time-scaling property Fourier transform, 1414–1416 Laplace transform, 908–909 time shifting trigonometric Fourier series, 1298–1302 time-shifting property convolution, 1021 exponential Fourier coefficients, 1358–1364 Fourier transform, 1411–1413 Laplace transform, 894–895 transconductance amplifier See voltage-to-current converter transfer function Bode diagram, 1045–1058 Butterworth design BPF, 1192, 1195 BSF, 1205, 1206 HPF, 1182, 1184–1185 LPF, 1174–1175 Chebyshev type LPF, 1219 Chebyshev type LPF, 1231 first-order analog filters HPF, 1081, 1084 LPF, 1079, 1081 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Index phasor-transformed circuits, 692–718 parallel RLC circuit, 707–713 series RLC circuit, 701–707 s-domain, 997–1020 impulse response, 998 poles and zeros, 999–1020 ramp response, 998 sinusoidal input, 998–999 step response, 998 second-order analog filter BPF, 1113 BSF, 1129 HPF, 1100 LPF, 1084 transformer autotransformer, 874–879 defined, 829 ideal, 865–879 linear, 855–865 step-down, 829 step-up, 829 transmission parameters See ABCD parameters transresistance amplifier See current-to-voltage converter triangular pulse, 25–26 triangular pulse train exponential Fourier series, 1343–1348 trigonometric Fourier series, 1302–1306 trigonometric Fourier coefficients, 1284 trigonometric Fourier series, 1278–1282 average power of periodic signals, 1317–1320 dc level, 1296–1297 fundamental frequency, 1278 half-wave symmetry, 1320–1324 one-sided magnitude spectrum, 1287–1296 one-sided phase spectrum, 1288–1296 orthogonality, 1278–1282 rectified cosine waveform, 1309–1313 rectified sine waveform, 1313–1317 sawtooth pulse train, 1306–1309 solving circuit problems, 1324–1333 symmetries, 1284–1285 even, 1285 odd, 1285 time shifting, 1298–1302 triangular pulse train, 1302–1306 using cosines only, 1286–1287 two-port circuits, 1457–1512 interconnections, 1457, 1500–1509 cascade, 1500–1502, 1508–1509 1565 parallel connection, 1505–1507 parallel-series, 1508 series connection, 1502–1504 series-parallel, 1507–1508 overview, 1457 parameters See parameters, two-port circuits reciprocal, 1460 representations, 1457 symmetrical, 1460 two-sided Laplace transform, 887 two-sided magnitude spectrum, exponential Fourier series, 1337–1343 two-sided phase spectrum, exponential Fourier series, 1338–1343 U undamped natural frequency, 507 underdamped response parallel RLC circuit step response of, 570–571 zero input response, 532 second-order differential equations constant input, 548–549 zero input response, 510–511 series RLC circuit step response, 553–554 zero input response, 513 unit ramp function See ramp function unit step function See step function unity gain method HPF, 1110–1111 LPF, 1098–1100 V variables ABCD parameters, 1477 b-parameters, 1485–1486 g-parameters, 1473 h-parameters, 1470 y-parameters, 1464 z-parameters, 1458 VCCS See voltage-controlled current source (VCCS) virtual short, 319, 319 volt (V), voltage, 5–6 voltage-controlled current source (VCCS), 16 voltage-controlled voltage source (VCVS), 16 operational amplifier (op amp) See operational amplifier (op amp) voltage divider rule, 74–80 Laplace-transformed circuits, 958–961 phasor-transformed circuits, 669–672 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net 1566 Index voltage follower, 322–333 voltage source, 11 circuit with, 209 deactivating, 208, 209 with series resistor, 208 Thévenin’s theorem See Thévenin’s theorem voltage-to-current converter, 350–351 W Wheatstone bridge, 80–82 connected to instrumentation amplifier, 365 wire impedance balanced ∆-∆ circuit with, 805–813 balanced ∆-Y circuit with, 816–821 balanced Y-∆ circuit with, 796–805 balanced Y-Y circuit with, 786–792 wye-delta (Y-∆) transformation, 91–99 impedances, 656–660 Y Y2D.m, 94 y-parameters, 1457, 1464–1470 coefficient, 1465 conversion to ABCD parameters, 1493 to all other parameters, 1493 to b-parameters, 1493 to g-parameters, 1493 to h-parameters, 1493 to z-parameters, 1493 equation, 1465 equivalent circuit, 1465 matrix notation, 1464 parallel connection, 1505–1507 variables, 1464 Z overdamped, 532 underdamped, 532 second-order differential equations, 505–511 critically damped, 509 overdamped, 507–509 underdamped, 510–511 series RLC circuit, 511–530 critically damped, 513 overdamped, 513 underdamped, 513 zeros (poles and) Butterworth design BPF, 1191, 1194 BSF, 1202–1203, 1205 HPF, 1182, 1184 LPF, 1174, 1175 Chebyshev type LPF, 1218–1219 Chebyshev type LPF, 1230–1231 s-domain Bode diagram, 1059–1062 transfer function, 999–1020 z-parameters, 1457, 1458–1464 See impedance parameters coefficient, 1458–1459 conversion to ABCD parameters, 1490–1491, 1492 to all other parameters, 1489, 1492 to b-parameters, 1491, 1492 to g-parameters, 1492, 1493 to h-parameters, 1491–1492, 1493 to y-parameters, 1489–1490 equation, 1458 equivalent circuit, 1459–1460 matrix notation, 1458 series connection, 1502–1504 variables, 1458 zero input response parallel RLC circuit, 530–544 critically damped, 532 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 www.downloadslide.net This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Important Notice: Media content referenced within the product description or the product text may not be available in the eBook version Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 ... quantity of heat Power, radiant flux Electric charge, quantity of electricity Electric potential difference, electromotive force Capacitance Electric resistance Electric conductance Magnetic flux... sequence or a three-quarters sequence on electric circuits Suggested Course Outlines The following is a list of topics covered in a typical Electric Circuits courses, with suggested course outlines... by A # vAB vA vB E ? d/ (1.8) B The negative sign implies that moving against the electric field increases the potential For a positive point charge Q at origin with an electric field given by