Hambley electrical engineering principles and applications 5th txtbk

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Hambley electrical engineering principles and applications 5th txtbk

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Electrical Engineering Principles and Applications Electrical Engineering Principles and Applications FIFTH EDITION Allan R Hambley Department of Electrical and Computer Engineering Michigan Technological University arhamble@mtu.edu Upper Saddle River Boston Columbus San Francisco New York Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai Madrid Hong Kong Mexico City Munich Paris Amsterdam Cape Town Vice President and Editorial Director, ECS: Marcia J Horton Senior Editor: Andrew Gil llan Associate Editor: Alice Dworkin Editorial Assistant: William Opaluch Vice President, Production: Vince O Brien Senior Managing Editor: Scott Disanno Production Liaison: Jane Bonnell Production Editor: Maheswari PonSaravanan, TexTech International Senior Operations Supervisor: Alan Fischer Senior Marketing Manager: Tim Galligan Marketing Assistant: Mack Patterson Art Director: Kenny Beck Cover Art Director: Kristine Carney Cover Designer: Black Horse Designs Cover Image: Tom Mareschal/Stone/Getty Images, Inc Art Editor: Greg Dulles Media Editor: Daniel Sandin Media Project Manager: Danielle Leone Composition/Full-Service Project Management: TexTech International LabVIEW and NI Multisim are trademarks of National Instruments MATLAB is a registered trademark of The MathWorks Mylar is a registered trademark of DuPont Teijin Films OrCAD and PSpice are registered trademarks of Cadence Design Systems Copyright © 2011, 2008, 2005, 2002, 1997 by Pearson Education, Inc., Upper Saddle River, New Jersey 07458 All rights reserved Manufactured in the United States of America This publication is protected by Copyright and permissions should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise To obtain permission(s) to use materials from this work, please submit a written request to Pearson Higher Education, Permissions Department, Lake Street, Upper Saddle River, NJ 07458 The author and publisher of this book have used their best efforts in preparing this book These efforts include the development, research, and testing of the theories and programs to determine their effectiveness The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs Library of Congress Cataloging-in-Publication Data Hambley, Allan R Electrical engineering : principles and applications / Allan R Hambley 5th ed p cm Includes index ISBN-13: 978-0-13-213006-6 ISBN-10: 0-13-213006-8 Electrical engineering I Title TK146.H22 2011 2009038177 621.3 dc22 10 ISBN-13: 978-0-13-213006-6 ISBN-10: 0-13-213006-8 To Judy, Tony, Pam, and Mason Practical Applications of Electrical Engineering Principles 1.1 Using Resistance to Measure Strain 29 2.1 An Important Engineering Problem: Energy-Storage Systems for Electric Vehicles 3.1 Electronic Photo Flash 145 4.1 Electronics and the Art of Automotive Maintenance 194 5.1 Where Am I? What Time Is It? (An Application of Phase Measurement) 230 6.1 Active Noise Cancellation 295 7.1 Biomedical Engineering Application of Electronics: Cardiac Pacemaker 8.1 Fresh Bread Anyone? 415 9.1 The Virtual First-Down Line 452 11.1 Electronic Stud Finder 557 12.1 Where Did Those Trout Go? 601 13.1 Soup Up Your Automobile by Changing Its Software? 626 14.1 Mechanical Application of Negative Feedback: Power Steering 674 16.1 Magnetic Flowmeters, Faraday, and The Hunt for Red October vi 776 393 100 Contents Practical Applications of Electrical Engineering Principles Preface xi Introduction 1.1 1.2 1.3 1.4 1.5 1.6 1.7 vi 3.4 3.5 3.6 3.7 3.8 Overview of Electrical Engineering Circuits, Currents, and Voltages Power and Energy 13 Kirchhoff s Current Law 16 Kirchhoff s Voltage Law 19 Introduction to Circuit Elements 22 Introduction to Circuits 30 Summary 34 Problems 35 Resistive Circuits 46 2.1 Resistances in Series and Parallel 47 2.2 Network Analysis by Using Series and Parallel Equivalents 51 2.3 Voltage-Divider and Current-Divider Circuits 55 2.4 Node-Voltage Analysis 60 2.5 Mesh-Current Analysis 79 2.6 Thévenin and Norton Equivalent Circuits 88 2.7 Superposition Principle 101 2.8 Wheatstone Bridge 104 Summary 106 Problems 108 Inductance and Capacitance 3.1 Capacitance 125 3.2 3.3 124 Capacitances in Series and Parallel 132 Physical Characteristics of Capacitors 134 Inductance 138 Inductances in Series and Parallel 143 Practical Inductors 144 Mutual Inductance 147 Symbolic Integration and Differentiation Using MATLAB 148 Summary 156 Problems 157 Transients 166 4.1 4.2 4.3 4.4 First-Order RC Circuits 167 DC Steady State 171 RL Circuits 173 RC and RL Circuits with General Sources 177 4.5 Second-Order Circuits 183 4.6 Transient Analysis Using the MATLAB Symbolic Toolbox 196 Summary 203 Problems 204 Steady-State Sinusoidal Analysis 215 5.1 5.2 5.3 5.4 Sinusoidal Currents and Voltages 216 Phasors 222 Complex Impedances 228 Circuit Analysis with Phasors and Complex Impedances 232 5.5 Power in AC Circuits 238 5.6 Thévenin and Norton Equivalent Circuits 251 5.7 Balanced Three-Phase Circuits 256 vii viii Contents 5.8 AC Analysis Using MATLAB 268 Summary 272 Problems 273 Frequency Response, Bode Plots, and Resonance 286 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Fourier Analysis, Filters, and Transfer Functions 287 First-Order Lowpass Filters 295 Decibels, the Cascade Connection, and Logarithmic Frequency Scales 300 Bode Plots 304 First-Order Highpass Filters 307 Series Resonance 311 Parallel Resonance 316 Ideal and Second-Order Filters 319 Transfer Functions and Bode Plots with MATLAB 325 Digital Signal Processing 330 Summary 339 Problems 341 Computer-Based Instrumentation Systems 441 9.1 Measurement Concepts and Sensors 442 9.2 Signal Conditioning 447 9.3 Analog-to-Digital Conversion 454 9.4 LabVIEW 457 Summary 470 Problems 471 10 Diodes 475 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 Logic Circuits 355 7.1 7.2 7.3 7.4 7.5 7.6 Basic Logic Circuit Concepts 356 Representation of Numerical Data in Binary Form 359 Combinatorial Logic Circuits 367 Synthesis of Logic Circuits 374 Minimization of Logic Circuits 381 Sequential Logic Circuits 385 Summary 396 Problems 397 Microcomputers 408 8.1 Computer Organization 409 8.2 Memory Types 412 8.3 Digital Process Control 414 8.4 The 68HC11 Microcontroller 417 8.5 The Instruction Set and Addressing Modes for the 68HC11 422 8.6 Assembly-Language Programming 430 Summary 435 Problems 436 Basic Diode Concepts 476 Load-Line Analysis of Diode Circuits 479 Zener-Diode Voltage-Regulator Circuits 482 Ideal-Diode Model 486 Piecewise-Linear Diode Models 488 Recti er Circuits 491 Wave-Shaping Circuits 496 Linear Small-Signal Equivalent Circuits 501 Summary 506 Problems 507 11 Ampli ers: Speci cations and External Characteristics 519 11.1 Basic Ampli er Concepts 520 11.2 Cascaded Ampli ers 525 11.3 Power Supplies and Ef ciency 528 11.4 Additional Ampli er Models 531 11.5 Importance of Ampli er Impedances in Various Applications 534 11.6 Ideal Ampli ers 537 11.7 Frequency Response 538 11.8 Linear Waveform Distortion 543 11.9 Pulse Response 547 11.10 Transfer Characteristic and Nonlinear Distortion 550 11.11 Differential Ampli ers 552 11.12 Offset Voltage, Bias Current, and Offset Current 556 Summary 561 Problems 562 Contents 12 Field-Effect Transistors 12.1 12.2 12.3 12.4 12.5 12.6 12.7 574 NMOS and PMOS Transistors 575 Load-Line Analysis of a Simple NMOS Ampli er 582 Bias Circuits 585 Small-Signal Equivalent Circuits 588 Common-Source Ampli ers 593 Source Followers 596 CMOS Logic Gates 601 Summary 606 Problems 607 13.7 13.8 13.9 14 Current and Voltage Relationships 616 Common-Emitter Characteristics 619 Load-Line Analysis of a Common-Emitter Ampli er 620 pnp Bipolar Junction Transistors 626 Large-Signal DC Circuit Models 628 Large-Signal DC Analysis of BJT Circuits 631 Small-Signal Equivalent Circuits 638 Common-Emitter Ampli ers 641 Emitter Followers 646 Summary 652 Problems 653 Operational Ampli ers 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 Magnetic Circuits and Transformers 716 15.1 15.2 15.3 15.4 15.5 15.6 Magnetic Fields 717 Magnetic Circuits 726 Inductance and Mutual Inductance 731 Magnetic Materials 735 Ideal Transformers 739 Real Transformers 746 Summary 751 Problems 751 DC Machines 762 Bipolar Junction Transistors 615 13.4 13.5 13.6 15 16 13 13.1 13.2 13.3 ix 663 Ideal Operational Ampli ers 664 Inverting Ampli ers 665 Noninverting Ampli ers 672 Design of Simple Ampli ers 675 Op-Amp Imperfections in the Linear Range of Operation 680 Nonlinear Limitations 684 DC Imperfections 689 Differential and Instrumentation Ampli ers 693 Integrators and Differentiators 695 Active Filters 698 Summary 703 Problems 704 16.1 16.2 16.3 16.4 16.5 16.6 16.7 Overview of Motors 763 Principles of DC Machines 772 Rotating DC Machines 777 Shunt-Connected and Separately Excited DC Motors 783 Series-Connected DC Motors 788 Speed Control of DC Motors 792 DC Generators 796 Summary 801 Problems 802 17 AC Machines 811 17.1 Three-Phase Induction Motors 812 17.2 Equivalent-Circuit and Performance Calculations for Induction Motors 820 17.3 Synchronous Machines 829 17.4 Single-Phase Motors 841 17.5 Stepper Motors and Brushless DC Motors 844 Summary 846 Problems 847 APPENDICES A Complex Numbers Summary 860 Problems 860 853 Index 68HC11/12, 417 435 A Abbreviations, pre x 16 Absolute-value assembly program 431 432 Ac circuit: complex impedances 228 232 mesh-current analysis 237 238 node-voltage analysis 236 237 power 238 251 series/parallel analysis 235 236 steady-state analysis 215 285 step-by-step analysis 233 Thévenin/Norton equivalents 251 256 three-phase, balanced 256 268 Ac coupling 540 Ac motors 765, 811 852 single-phase 841 844 three-phase induction 812 829 universal 791 Ac voltage 12, 216 222 Accumulator 418 Accuracy 447 Active: lter 698 703 noise cancellation 295 region, BJT 625, 629 630 Actuators 411 Adding sinusoids 225 Addressing: direct 426, 429 extended 423 426, 429 immediate 427, 429 indexed 427, 429 inherent 427, 429 relative 428, 429 Air gap 727 729 Algebra, Boolean 369 371 Aliasing 454 455 Alpha, BJT 617 Alternating current 10, 216 222 Alternator, automotive 830 ALU 409 AM radio 299 Amortisseur conductors 840 Ampere units Ampère s law 722 725 Ampli cation, distortionless 545 546 Ampli ers 519 573 bandpass 542 basic concepts 520 525 cascaded 525 528 common collector 646 652 common drain 596 600 common emitter 620 625, 641 646 common source 582 585, 593 596 current model 531 532 dc imperfections 556 561 design, op amp 675 680 differential 447, 552 556, 693 695 ef ciency 529 530 emitter follower 646 652 external characteristics 519 573 frequency response 538 543 ideal 537 538 input resistance/impedance 522, 534 535, 594, 644, 648 649 instrumentation 447, 693 695 inverting 520, 665 671 midband frequency range 540 narrowband 542 noninverting 520, 672 673, 675 677 operational (op amp) 663 715 output resistance/impedance 522, 535, 594, 644, 649 source follower 596 600 speci cations 519 573 summing 678 680 transconductance model 532 533 transresistance model 533 534 voltage model 522 523 wideband 542 Amplitude distortion 543 Analog signal 355 356 Analog-to-digital conversion 454 457 Analog-to-digital converter (ADC)(A/D) 330 332, 442 Analogy: uid 8, 126, 139, 146, 167, 616 mechanical 185 for transformer 742 Analysis: ac steady-state 215 285 assumed states 486 488 computer-aided 868 869 dc steady-state 171 173 large-signal (BJT) 631 638 load line 480 482, 483 485, 582 585, 620 625 mesh-current 79 88, 237 Multisim 868 869 network 51 node-voltage 60 77, 236 237 series/parallel 51 54, 235 236 sinusoidal steady-state 215 285 small-signal 593 600, 638 641 SPICE-based 868 869 transient 166 214 AND gate 367 368 Angle: electrical 831 881 882 Index Angle (continued) phase 216 power 242 torque 831 Angular frequency 216 Anode 476 Antialias lter 455, 701 Apparent power 242 Arbitrary references 32 34 Arithmetic: binary 361 complement 365 366 complex 853 861 logic unit (ALU) 409 Armature 765 dc machine 778 780 synchronous machine 829 Assembler 428 430 Assembly language programming 430 435 Assumed states 486 488 Asymptote 304 305 Attenuator, voltage-controlled 503 506 Automobile ignition circuit 194 195 Automotive: alternator 830 applications Auxiliary windings 843 Average power, de ned 217 218 Average-value VI 459 469 B Back emf 781 Balanced: bridge 105 three-phase ac 256 268 Balancing circuits 560 561 Band-reject lter 320, 322 Bandpass: ampli er 542 lter 312 314, 319, 322 Band-reject lter 320, 322 Bandwidth 314, 317 full-power 688 op-amp 681 684 Base, BJT 616 Baseband ampli er 542 Battery 99 100 BCD code 363, 379 380 Beta, BJT 618 Bias: current 556 561, 689 692 error 446 forward 476 line 586 reverse 476 Bias circuit: BJT 631 638 xed-base 632 633 four-resistor 636 638 self- plus xed- 585 588 Biasing: BJTs 631 638 NMOS 582, 585 588 Binary: arithmetic 361 -coded decimal (BCD) 363, 379 380 -to-decimal conversions 359 numbers 359 361 signal 356 Bits 358 BJT (bipolar junction transistor) 615 662 active region 625, 629 630 alpha 617 base 616 beta 618 collector 616 common-emitter characteristics 619 620 current voltage relationships 616 618 cutoff 625 emitter 616 uid- ow analogy 616 large-signal models 628 631 pnp 626 628 saturation region 625 small-signal model 638 641 structure 616 Block diagram 459 Bode plot 304 307, 309 311 Body terminal 575 Boole, George 369 Boolean algebra 369 371 Branch instructions 428 Bread machine 415 416 Break frequency 305, 310 Breakdown: reverse 476 voltage 478 Breakover torque 819 Bridge: diode 495 Wheatstone 104 106 Brushes 765 Brushless dc motors 845 846 Buffer: logic gate 373 tristate 410 411 Buses 410 411 Butterworth function 698 Bypass capacitors 593, 641 Byte 358 C Canonical forms: product-of-sums 375 376 sum-of-products 374 376 Capacitance 125 132 ac power 240 dc steady-state 171 de ned 126 energy storage 129 130 impedance 229 interwinding 145 in parallel 132 in series 134 Capacitor 134 138 bypass 593 coupling 504, 540, 593 electrolytic 136 parallel-plate 134 136 parasitic effects 137 for power factor correction 250, 834 practical 136 smoothing 492 494, 496 start motor 843 synchronous 834 Cardiac pacemaker 393 395 Cascade connection 302 303 Cascaded ampli ers 525 528 Cathode 476 Central processing unit (CPU) 409 Characteristic curves: BJT 619 620 NMOS 579 580 Index Characteristic curves (continued) PMOS 582 torque speed 767 768 Characteristic equation 186 Characteristic impedance 536 Charge 126 Circuit(s) 13 ac steady-state 215 285 balancing 560 561 clamp 497 501 clipper 496 497 combinational 367 374 current divider 56 59 dc, steady-state 171 173 de ned elements 22 30 rst-order 167 171, 173 177 uid- ow analogy 8, 139, 146, 167 grounding 61, 449 450, 494, 521 522 headlight ignition 194 195 introduction 30 34 laws 16 21, 232 linear 103 logic 355 407 magnetic 726 731 Norton 94 96, 252 253 open 22 overview of parallel 20 21 resistive 46 123 second-order 183 196 series 18 series-parallel 51 54, 235 236 short 22 Thévenin 88 96, 251 three-phase 256 268 voltage divider 55 56, 59 wave-shaping 496 501 Clamp circuit 497 501 Clipper circuit 496 497 Clipping 550 551 Clock signal 385 Clocked SR ip- op 388 389 Closed switch Closed-loop bandwidth 682 684 Closed-loop gain 667 CMOS logic gates 601 606 CMRR 448, 554 556 Coaxial cable 451 Code: BCD 363, 379 380 Gray 364 365 machine 428 object 430 operation (op) 428 source 430 Coef cient: coupling 756 damping 184 emission 478 Collector, BJT 616 Color code, resistors 862 863 Combinatorial logic circuits 367 374 Comment statement 431 Common: -collector ampli er 646 652 -drain ampli er 596 600 -emitter ampli er 620 625, 641 646 -emitter characteristics 619 620 -gate ampli er 600 ground 61, 449 450, 494, 521 522 -mode rejection ratio (CMMR) 448, 554 556 -mode signal 448, 553 554, 664 -source ampli er 582 585, 593 596 Communication systems Commutator 765, 778 780 Compiler 430 Complement, one s 365 Complement, two s 365 Complementary solution 179, 185 Complex: conjugate 853 gain 538 539 impedance 228 232 numbers 853 861 plane 853 Computer 3, 408 440 -based instrumentation 441 474 embedded 408 host 430 organization 409 412 systems Computer-Aided Analysis ac circuits 268 272 rst-order circuit 196 197 883 rms values 221 second-order circuit 197 198 SPICE-based 868 869 system of differential equations 199 203 Condition-code register 418 Conductance 26 parallel 50 series 50 Conductors 7, 8, 22, 27 amortisseur 840 damper 840 Connection, Wye wye 258 259 Conservation of energy 20 Constant: Boltzmann s 478 dielectric 135 machine 781 sensitivity 442 time 168 169, 174 Control, speed: dc motors 792 796 wound-rotor induction motor 828 Control systems Control unit 409 Controlled sources 23, 25, 74 76, 87 88 Converters: (ADC) (A/D) 330 332, 442 current-to-voltage 444 (DAC) (D/A) 330 332 Copper loss 784 Core loss 145, 737, 746, 747 Corner frequency 305 Correction, power-factor 249 250 Counter: circuits 393 program 418 Coupling: ac 540 capacitors 504, 540, 593 coef cient 756 direct (dc) 540 CPU 409 Critically damped response 186 Cubes 382 385 Current: ac 10, 216 222 ampli er, ideal 537 ampli er model 531 532 884 Index Current (continued) bias 556 561, 689 692 controlled sources 24, 25 dc 10 de ned divider 56 59 eddy 145, 737 738 gain 523, 644 law, Kirchhoff s 16 18 line 258 mesh analysis 79 88, 237 offset 556 561, 689 692 ratio, transformer 741 saturation 478 sinusoidal 216 222 source 24 25 -to-voltage converter 444 Cutoff region: BJT 625, 630 NMOS 576 Cylindrical rotor 830 D D ip- op 389 390 Damper conductors 840 Damping ratio 186 Data bus 410 Data-acquisition (DAQ) board 442 Data- ow concepts 459 Dc (direct current) brushless motors 845 846 coupling 540 imperfections, op amp 689 693 linear machines 772 776 machines 762 810 motors 765 796 motor equivalent circuit 781 permanent magnet motor 788 rotating machines 777 801 separately excited motors 787 788 series motors 788 791 shunt motors 783 787 speed control 792 796 steady-state 171 173 voltage 12 De Morgan s laws 372 373 Debounce circuit 386 388 Decade 303 Decibel (dB) 300 302 Decimal-to-binary conversion 359 361 Decoders 379 Delay ip- op 389 390 Delta-connected load 264 Delta delta connection 265 268 Delta wye transformation 264 Dependent sources 23 25, 74 77, 87 88, 102 Design: active lter 701 703 ampli ers (op-amp) 675 680 close-tolerance 678 lter 323 325, 701 703 logic-circuit 377 379 noninverting ampli er 675 677 summing ampli er 678 680 Developed power 781, 822 823 Dielectric 125 Dielectric constant 135 Difference equation 333 Differential: ampli er 447, 552 556, 693 695 equation 167, 184 185 gain 553, 693 695 signal 553 Differentiator, op amp 697 698 Digital: circuits 355 407 process control 414 417 signal processing 330 339 signals 356 word 358 Digital-to-analog converter (DAC)(D/A) 330 332 Diode 475 518 dynamic resistance 502 equation 478 479 ideal 486 488 light-emitting 509, 536 physics 477 piecewise linear model 488 491 pn junction 477 reverse biased 478 small-signal 477 Zener 479 Diode circuits: battery charging 491 492 clamp 497 501 clipper 496 497 full-wave recti ers 494 496 half-wave recti ers 491 494 load-line analysis 479 482 wave-shaping 496 501 Diode models: ideal 486 488 piecewise linear 488 491 small-signal 501 506 Direct: addressing 426, 429 -coupled (dc) ampli er 540 current 10 Disk, hard 414 Display, seven-segment 380 Distortion: amplitude 543 harmonic 550 552 linear 543 547 nonlinear 550 552, 624 625 phase 544 Distortionless ampli cation 545 547 Divider: current 56 59 voltage 55 56, 59 Domains, magnetic 736 Don t cares 377 Doped semiconductor 477, 616 Dot convention 733 Double-subscript notation 10 11, 12 13 Drain 575 Drain resistance 590 592 Drift 446 DSP 330 339 DVD 878 879 Dynamic memory 412 Dynamic resistance 502 E Eddy currents 145, 737 738 Edge-triggered ip- op 389 390 Effective value 218 Ef ciency: ampli er 529 530 motor 767 transformer 748 750 Electric vehicles 100 101 Electrical angles 831 Electrocardiogram 540 541 Electrolytic capacitors 136 Index Electromagnetics Electronic photo ash 145 146 Electronics 4, 475 715 Elements: circuit 22 30 energy-storage 124 parallel 20 21 parasitic 137, 145 passive 124 series 18 Embedded computer 408 Emission coef cient 478 Emitter, BJT 616 Emitter follower 646 652 Encoders 379 End directive 431 Energy 13 16 conservation of 20 magnetic eld 738 missing 137 138 storage 124, 129 132, 140 143 Engine knock Engineering: computer control power Enhancement MOSFET 575 Equalizer, graphic 291 Equation: characteristic 186 differential 167, 184 185 homogeneous 179 KCL 62 63 mesh current 80 82 Shockley 478 solving 67 69 Equivalence gate 374 Equivalent: capacitance 132 134 inductance 143 144 resistance 47 54 Equivalent circuits: BJT, large signal 628 631 BJT, small signal 638 641 dc motor 781 diode, piecewise linear 488 491 diode, small-signal 501 506 induction motor 820 828 NMOS, small signal 588 592 Norton 94 96, 252 253 sensor 443 444 synchronous motor 831 833 Thévenin 88 96, 251 256 transformer 746 748 Erasable PROM 413 Errors, measurement 445 447 Euler s identity 857 Examination, FE 5, 46, 864 867 Excitation source 442 Exciter, synchronous machine 829 Exclusive-OR gate 373 Exponential form 858 859 Extended addressing 423 426, 429 F Factor: power 242 quality 312, 317 Farad 126 Faraday s law 720 721 FE Examination 5, 46, 864 867 Feedback: mechanical 674 negative 665 positive 671 672 Femto- 16 Ferrite 145 FETs (Field-effect transistors) 574 614 Field: around a long straight conductor 723 724 dc machine 777 778 magnetic 717 725 synchronous machine 829 toriodal coil 724 725 windings 764 765 Filter 289 active 698 703 antialias 455, 701 band-reject 320, 322 bandpass 312 314, 319, 322 Butterworth 698 703 design 323 325, 701 703 digital 332 339 highpass 307 311, 319, 322 ideal 319 321 lowpass 295 300, 319, 321, 333 334 notch 301, 320, 322, 335 336 885 Sallen-key 699 second-order 321 325 First-order circuit: RC 167 171 RL 173 176 First-order lters 295 300, 307 311, 322, 334 Fixed base bias circuit 632 633 Fixed- plus self-bias circuit 585 588 Flip- op 386 391 clocked SR 388 389 D (edge-triggered) 389 390 JK 390 391 SR 386 388 toggle 390 391 Floating sensor 449 450 Flowmeter, magnetic 776 777 Fluid- ow analogy 8, 126, 139, 146, 167, 616 Flux: density 717 lines 717 linkage 720 721 Follower: emitter 646 652 source 596 600 voltage 673 Force, magnetic eld: charge moving 718 719 on wire 720 Force, magnetomotive 726 Forced response 170, 178, 185 Forcing function 178, 184 Forward bias 476, 617 Four cube 382 Fourier series 287 289 Four-resistor bias circuit 636 638 Frequency 216 angular 216 break 305 corner 305 domain 287 289 half-power 297, 542 ranges, selected signals 288 resonant 184, 311, 316 response, ampli er 538 543 sampling 331 scale, logarithmic 303 304 slip 817 undamped resonant 184 Fringing, magnetic eld 728 886 Index Front panel 459, 461 Full-power bandwidth 688 Full-wave recti er 494 496 Fundamentals of Engineering (FE) Examination 5, 46, 864 867 G Gain: bandwidth 683 closed-loop 667, 683 684 common mode 554 556, 694 current 523 differential 553, 693 695 open-loop 665 power 523 transconductance 532 transresistance 533 534 voltage 520, 522 523, 594, 597 598, 643, 648 Gate, NMOS 575 Gates, logic 367 374, 601 606 Gauge, strain 29 Giga- 16 GPS 230 Graphic equalizer 291 Gray code 364 365 Ground 494, 521 522 loop 449 450 symbol 61, 494 H Half-power: bandwidth 542 frequency 297, 542 Half-wave recti er 491 494 Hard disk 414 Harmonic distortion 550 552 Harmonics 550 Henry 139 Hertz 216 Hexadecimal numbers 361 363 High-frequency asymptote 305 High-frequency response, ampli er 541 543 High-logic value 357 Highpass lter 307 311, 319, 322 Holes and electrons 477 Homogeneous equation 179 Host computer 430 Hybrid stepper motors 845 Hysteresis: error 446 magnetic 736 I Ideal: ampli ers 537 538 diode 486 488 lters 319 321 op amp 664 665 transformer 739 746 Ignition circuit 194 195 Imaginary number 853 Immediate addressing 427, 429 Impedance: complex 228 232 input, ampli er 522, 534 535, 594, 644, 648 649 output, ampli er 522, 535, 594, 644, 649 re ected 744 746 Thévenin 251 transformer 739 746 Independent sources 22, 24 Index register 418 Indexed addressing 427, 429 Induced voltage 720 722 Inductance 138 148 ac power 239 240 dc steady-state 171 energy storage 140 141 impedance 228 229 leakage 746 747 magnetizing 747 in parallel/series 143 144 related to elds 731 735 rotor 817 818 self and mutual 147 Induction motor: circuit model 820 822 performance calculations 822 828 selection 828 829 single-phase 841 844 squirrel cage 816 817 starting current 826 827 stator eld 812 816 wound rotor 828 Inductors 138 139 Inherent addressing 427, 429 Input: bias current 556 561, 689 692 characteristic, BJT 619 offset voltage 556 561, 689 692 resistance 522, 594 resistance/impedance 522, 534 535, 594, 644, 648 649 Input/output (I/O) 411 412 Instruction set 422 430 Instrumentation: ampli er 694 695 computer-based 441 474 Insulator 27 Integrator, op amp 695 697 Interpreter 430 Interrupts 417 Interwinding capacitance 145 Inverter, logic 368, 601 604 Inverting: ampli er 520 input terminal 552 I/O, computer 411 412 J JK ip- op 390 Junction, pn, 477, 616 617 K Karnaugh maps 382 385 KCL equations 62 63 Kilo- 16 Kirchhoff s laws: current law 16 18, 232 233 voltage law 19, 232 Knock, engine L LabVIEW 457 469, 878 Lagging: phase 227 power factor 242 Laminations 138 Large-signal: analysis BJT 631 638 model BJT 628 631 Last-in rst-out memory (LIFO) 419 Index Laws: Ampère s 722 725 De Morgan s 372 373 Faraday s 720 721 Kirchhoff s current 16 18, 232 233 Kirchhoff s voltage 19, 232 Lenz s 721 Ohm s 25 26 Leading: edge 389 phase 226 227 power factor 242 Leakage inductance 746 747 Lenz s law 721 LIFO 419 Light-emitting diodes 509, 536 Line: current 258 -to-line voltage 261 of magnetic ux 717 -to-neutral voltage 258, 261 voltage 261 Linear: circuit 103 dc machine 772 776 distortion 543 547 equation 103 variable differential transformer 147 148 Linearity 103 Linearization, piecewise 488 491 Linkages, magnetic ux 720 721 Load cell 442 Load resistance 520 Load-line analysis: common emitter 620 625 complex circuits 483 diode 479 482 NMOS ampli er 582 585 Zener regulator 483 485 Loading effects 444, 525 Logarithmic frequency scale 303 304 Logic: addition 368 CMOS 601 606 multiplication 367 negative 357 positive 357 values 356 variables 357 Logic circuits 355 407 combinatorial 367 374 design 377 379 minimization 381 385 sequential 385 393 synthesis 374 380 Logic gates: AND gate 367 buffer 373 CMOS 601 606 equivalence 374 inverter 368 NAND 373 374, 604 NOR 373 374, 604 606 OR 368 369 XOR 373 Loop 19 (mesh) analysis 79 88, 237 ground 449 450 LORAN 230 Low logic value 357 Low-frequency asymptote 305 Low-frequency response, ampli er 540 541 Lowpass lter 295 300, 319, 321, 333 334 M Machine code 428 Machine constant 781 Machines: ac 765, 811 852 dc 762 810 linear 772 776 Magnetic: circuits 726 731 domains 736 eld intensity 722 elds 717 725 owmeter 776, 777 ux density 717 ux lines 717 forces induced by 718 720 fringing 728 lines 717 materials 735 739 permeability 722 723 reluctance 726 887 saturation 735 736 voltage induced by 720 722 Magnetization curve, dc machine 782 Magnetizing inductance 747 Magnetomotive force (mmf) 726 Magnitude: complex number 855 plots, Bode 304 306, 309 310 Map, Karnaugh 382 385 Mask-programmable ROM 413 Mass storage 414 Materials, magnetic 735 739 MathScript 469 470, 878 ac circuits 268 272 adding new function 269 DSP demo 336 339 mesh-current analysis 83 solving network equations 68 69 MATLAB 68 ac circuits 268 272 adding new functions 269 Bode plots 325 330 DSP demo 336 339 mesh-current analysis 83 node voltage analysis 69 70 piecewise functions 151 156 solving network equations 67 68 symbolic integration and differentiation 148 156 symbolic solutions 77 79 transient analysis 196 203 Maximum power transfer 99 101, 253 256 Maxterm 376 Measurand 442 Measurement error 445 447 Mechanical analog 185, 742 Mechatronics Meg- or mega- 16 Memory 410, 412 414 dynamic 412 LIFO 419 logic circuit 385 -mapped I/O 412 RAM 412 ROM 413 selection of 414 static 412 volatile 412 888 Index Mesh: analysis 79 88, 237 super 86 Micro- 16 Microcomputer 408 440 Microcontroller 409 68HC11/12, 417 435 Midband region 540 Milli- 16 Minimization of logic circuits 381 385 Minterm 375 Mmf 726 Models: BJT 628 631, 638 641 current-ampli er 531 532 dc motor 781 diode, small-signal 501 506 ideal diode 486 488 induction motor 820 822 NMOS, small signal 588 592 piecewise linear 488 491 synchronous motor 831 833 transconductance-ampli er 532 533 transformer 746 747 transresistance-ampli er 533 534 voltage-ampli er 522 523 Modulo-two addition 373 Motor: ac 765, 811 852 basic construction 763 764 brushless dc 845 846 characteristics, compared 764 dc 765 766, 772 810 induction 769 770, 812 829, 841 844 overview of 763 772 performance 771 772 permanent-magnet 788, 845 series-connected 770, 788 791 shunt-connected 770, 783 787 single-phase 791, 841 844 speed control 792 796, 828 stepper 844 845 synchronous 769, 829 841 universal 791 Multiplexer 442 Multisim 868 869, 878 879 Mutual inductance 147 148, 733 735 N NAND gate 373 374, 604 Nano- 16 Natural response 179 NCEES 864 Negative: feedback 665 logic 357 phase sequence 257 Network: analysis 51 computer-aided analysis 868 869 nonplanar 79 planar 79 two-port 289, 302 303 Neutral wire 258 Nibble 358 NMOS transistors 575 580 characteristics 579 580 cutoff region 576 load-line analysis 582 585 saturation region 578 579 saturation triode boundary 579 580 threshold voltage 576 triode region 576 578 Node 16 Node-voltage analysis 60 79, 236 237 Noise 356 357, 450 452 cancellation 295 margins 357 358 quantization 455 456 Nominal values, resistors 863 Noninverting: ampli er 520, 672 673, 675 677 input terminal 552, 664 Nonlinear: distortion 550 552, 624 625 error 446 limitations, op amp 684 689 Nonplanar network 79 NOR gate 373 374, 604 605 Norton equivalent circuit 94 96 Norton equivalent circuit, ac 252 256 NOT gate 368 Notation: double-subscript 10, 12 13 electronic circuit 503 504, 588 589, 638 639 Notch lter 301, 320, 322, 335 336 npn transistor 616 n-type material 477 Number system: BCD 363, 379 380 binary 359 361 hexadecimal 361 363 octal 361 363 two s complement 365 366 Numbers, complex 853 861 O Object code 430 Octal numbers 361 363 Octave 303 Offset: current 556 561, 689 693 errors 446 voltage 556 561, 689 693 Ohm s law 25 26 One s complement 365 Op code 428 Open circuit 22 transresistance gain 533 voltage 89 voltage gain 523 Open switch Open-loop: bandwidth 681 gain 665, 681 Operating point 501, 583, 622 Operation code 428 Operational ampli er (op amp) 663 715 active lter 698 703 bandwidth 681 684 bandwidth, full-power 688 bias current 689 693 current limits 686 current-to-voltage converter 445, 707 differentiator 697 698 ideal 664 665 imperfections, linear range 680 684 input impedance 680 681 Index Operational ampli er (continued) input offset voltage 689 instrumentation ampli er 694 695 integrator 695 697 inverting ampli er 665 671 noninverting ampli er 672 673 nonlinear limitations 684 688 offset current 689 offset voltage 689 output impedance 680 681 power-supply connections 665 slew rate 687 summing circuit 670 summing-point constraint 665 voltage follower 673 voltage limits 684 685 OR gate 368 369 OrCAD Capture 869, 879 Output: characteristics, BJT 619 current limits, op amp 686 resistance/impedance 522, 535, 594, 644, 649 voltage swing, op amp 684 685 Overdamped response 186 Overexcited synchronous machine 834 Over ow 366 Overshoot 192, 548 P Pacemaker, cardiac 393 395 Parallel: capacitances 132 134 circuits 20 21 inductances 143 145 LC circuits 193 196 -plate capacitor 134 136 resistances 48 49 resonance 316 319 -in shift register 391 transmission 358 Parasitic elements 137, 145 Particular solution 178, 185 Passive circuit elements 124 Passive reference guration 13, 25 p-channel MOSFETs 580 582 PE license 5, 864 Peak inverse voltage 494 Peak recti er 492 494 Peak value, sinusoid 216 Period, sinusoid 216 Permanent-magnet motors: dc 788 stepper 845 846 Permeability, magnetic 722 Phase: angle 216 capacitance 229 231 distortion 544 545 inductance 229 plots 307, 310 relationships 226 228 resistance 231 232 sequence 257 Phasor 222 228 Phasor diagram: synchronous machine 835 three-phase 257, 262 Photo ash 145 146 Photonics Pico- 16 Piecewise-linear model 488 491 Pinouts (68HC11A8) 419 PIV 494 Planar network 79 Plot, Bode 304 307, 309 311 PMOS transistors 580 582 pn junction 477, 616 617 pnp transistor 626 628 Polar form, complex number 855 Polar-to-rectangular conversion 855 Polarities, reference 12 Polling 417 POS 376 Position transducer 59 Positive: feedback 671 672 logic 357 phase sequence 257 Power 13 16 ac circuits 238 251 angle 242 apparent 242 243 average 217 218 capacitance 240 control 54 de ned 13 889 developed 781, 822 823 dissipation 529 factor 242 factor correction 249 250, 833 834, 837 839 gain 523, 644 inductance 239 240 losses, motors 766 767 rating, motors 767 reactive 242, 261 resistance 27 28, 239 steering 674 supply 528 530, 665 three-phase 259 260 transfer, maximum 99 101, 253 256 transformer 748 750 triangle 243, 247 249 units 13, 243 Power systems engineering Precision 447 Pre xes 16 Primary winding 739 740 Principle: current-division 57 superposition 101 104 voltage-division 55 56 Process control 414 417 Processing unit, central 409 Product-of-sums 375 376 Professional Engineer (PE) 5, 864 Program: computer 410 counter (PC) 418 Programmable ROM (PROM) 413 Programming, assembly-language 430 435 PSpice 869, 879 p-type material 477 Pull-out torque 839 Pulse response 547 550 Q Q point 501, 583, 622 Quality factor 312, 317 318 Quantization: error 331 332 noise 455 456 Quiescent bias point 501, 583, 622 890 Index R Radian frequency 216 217 RAM (Read-and-write memory) 412 Random errors 446 Ratings, motors 766 767 Ratio, damping 186 RC circuits 167 171 Reactance 229 Reactance, synchronous 832 Reactive power 241 242, 261 Read-and-write memory 412 Read-only memory, (ROM) 413 Real number 853 Rectangular form, complex number 853 Rectangular-to-polar conversion 856 857 Recti er 491 496 full-wave 494 496 half-wave 491 494 three-phase 792 793 Reference: arbitrary 32 33 direction node 61 passive guration 13, 25 polarities 12 Register 391 Regulation: speed 768 voltage 748 Regulator, voltage 482 485 Relative addressing 428, 429 Relative dielectric constant 135 Reluctance 726 Resistance 25 26 ac power 239 calculation 28 combining 49 51 dynamic 502 input 522, 594, 598 output 522, 535, 594, 598, 599, 644, 649 related to physical parameters 27 28 Resistive circuits 46 123 Resistivity 27 28 Resistor(s) 25 30 color code 862 863 nominal values 863 parallel 48 49 practical values 676 677 series 47 48 versus resistance 29 30 Resolution 447 Resonance: parallel 316 319 series 311 316 Resonant frequency 184, 311, 316 Response: critically damped 186 forced 170, 178, 185 frequency, ampli er 538 543 natural 179, 182 overdamped 186 pulse 547 550 steady-state 170, 171 173 step 191 192 transient 170 underdamped 186 187 Reverse: bias 476, 616 breakdown 476 Right-hand rule 717 718 Ringing 192, 548 Ripple: counter 393 voltage 493 Rise time 547 RL circuits 173 176 Rms value 217 219, 459 469 ROM 413 Root-mean-square value 217 219, 459 469 Roots of characteristic equation 186 187 Rotating: dc machine 777 810 eld 812 816 vectors 226 Rotor 763, 777 778, 816, 830 Rotor inductance 817 818 S Salient poles 830 Sallen Key circuits 699 Sample and hold (S/H) 442 Sampling 330 332, 454 455 Sampling rate 331, 454 Saturation: current, BJT 617 current, diode 478 magnetic 736 region, BJT 625, 630 Scale: current, BJT 617 error 446 Second-order: circuits 183 196 lters 321 325 Secondary winding 739 740 Self- plus xed biasing circuit 585 588 Semiconductor 27, 476 477, 575, 616 Sensitivity constant 442 Sensor 442 445 equivalent circuit 443 444 oating 449 450 LVDT 147 148 magnetic owmeter 776 777 position 59 strain 29 variable-resistance 445 Separately excited dc motor 787 788 Sequence, phase 257 Sequential logic circuits 385 393 Serial transmission 358 Serial-in shift register 391 Series: capacitances 134 circuit 18 inductances 143 144 motor, dc 788 791 resistances 47 48 resonance 311 316 Series/parallel: analysis 51 54 impedances 235 236 Seven-segment display 380 Shaded-pole motors 843 844 Shift registers 391 393 Shockley equation 478 Short circuit 22 current 89 current gain 531 transconductance gain 532 virtual 667 668 Shunt dc motor 783 787 Index Sign convention, passive 13, 25 Signal conditioner 442 Signal conditioning 447 452 Signal processing 4, 287, 330 339 Signals: analog vs digital 355 clock 385 common-mode 553 554, 664 differential 553, 664 digital 356 frequency-ranges 288 Silicon 477, 575, 616 617 n-type 477, 575, 616 617 p-type 477, 575, 616 617 Single-phase motors: capacitor start 843 induction 841 843 shaded pole 843 844 split-phase 843 universal 791 Sinusoidal sources 216 222 Sinusoidal steady-state analysis 215 285 rst-order RC 180 183 Slew rate 687 688 Slip 817 Slip rings 829 Small-signal equivalent circuits: BJT 638 641 diode 501 506 NMOS 588 592 Smoothing capacitor 492 494, 496 SOP 375 Source: code 430 delta-connected 264 dependent 23 25, 74 76, 87 88, 93 94 excitation 442 follower 596 600 independent 22, 24 NMOS terminal 575 sinusoidal 216 222 three-phase 256 257 transformation 97 98 voltage 22 24 wye-connected 256 257 Speed, synchronous 769, 815 816 Speed control: dc motors 792 796 wound-rotor induction motor 828 Speed regulation 768 SPICE-based network analysis 868 869 Split-phase motors 843 Square-wave 288 289 Squirrel-cage motor 816 817 SR ip- op 386 388 Stack 419 422 Stack pointer register 419 Stall torque 819 Standard nominal values, resistors 863 Starting torque 819 Static memory 412 Stator 763, 777 778 rotating eld 812 814 three-phase induction 812 816 Steady-state: analysis, sinusoidal 215 285 dc 171 173 response 170 Steering, power 674 Step: function 191 192 response 191 192, 334 Step-by-step solution: ac steady-state 233 adding sinusoids 225 rst-order transient 173, 179 180 mesh current 88 node voltage 76 77 series/parallel 52 Thévenin/Norton 95 Stepper motors 844 845 Stored energy: capacitance 129 131 inductance 140 141 Strain gauges 29 Stud nder 557 Subroutines 433 435 Substrate, NMOS 575 Suf ciency, logic gates 374 Sum-of-products 374 375 Summing ampli er 678 680 Summing-point constraint 665 Supermesh 86 Supernode 72 Superposition principle 101 104 Switch 891 Switch, debounce circuit 386 388 Symbolic Toolbox Bode plots 327 330 rst-order circuit 196 197 integration and differentiation 148 156 node voltage analysis 77 79 piecewise functions 151 156 second-order circuit 197 198 system of differential equations 199 203 transfer functions 327 330 transient analysis 196 203 Synchronous capacitors 834 Synchronous logic circuit 385 Synchronous machine 769, 829 841 equivalent circuit 831 833 overexcited 834 performance calculations 835 837 power-factor correction 833 834, 837 839 reactance 832 speed 769, 815 816 starting 840 841 underexcited 834 V curves 837 838 Synthesis, logic circuits 374 380 System: communication computer control energy-storage 100 101 power target 430 Systematic error 446 T T ip- op 390 391 Target system 430 Thermal voltage 478 Thévenin equivalent circuit 88 96 Thévenin equivalent circuit, ac 251 256 Three-phase: circuits 256 268 delta-connected loads 264 delta-connected source 264 delta delta connection 265 268 phase sequence 257 258 892 Index Three-phase (continued) power 259 260 recti er 792 793 wye-connected loads 264 wye-connected source 257 wye wye connection 258 259 Threshold voltage 576 Tilt 549 550 Time: constant 168 169, 174 frequency analyzer 457 458 rise 547 Toroidal: coil 727 core, magnetic eld 724 725 inductor 139 Torque: angle 831 pull-out 839 Torque speed characteristics 767 768, 785 788, 791 speed control 794 796 synchronous motor 840 three-phase induction motor 818 819 wound-rotor induction motor 829 Total harmonic distortion 552 Trailing edge 389 Transconductance: ampli er, ideal 537 ampli er model 532 533 NMOS 589 592 Transducer: LVDT 147 148 position 59 strain 29 Transfer characteristic, ampli er 550 551 Transfer function 290 294 Butterworth 698 rst-order 295 300, 307 311, 322, 334 Transformation of sources 97 98 Transformer 739 750 current relations 741 full-wave recti er 494 496 ideal 739 746 mechanical analogy 742 power 741 742 primary winding 739 real 746 750 re ected impedance 744 746 secondary winding 739 voltage relations 739 741 Transient circuit analysis 166 214 with Symbolic Toolbox 196 203 Transient response: critically damped 186, 189 190 rst-order 167 171, 173 176 overdamped 186, 188 189 underdamped 187, 190 191 Translators 379 Transmission: serial/parallel 358 Transresistance-ampli er model 533 534 Triangle, power 243, 247 249 Triode region 576 578 Tristate buffer 411 Truth table 367 370 Turns ratio 740 741 Twisted-pair cable 451 Two-cube 382 383 Two-port networks 289 290, 302 303 Two s complement 365 366 U Undamped resonant frequency 184 Underdamped response 186 187, 190 191 Underexcited synchronous machine 834 Under ow 366 Unity-gain bandwidth 683 Universal motor 791 V V curves 837 838 VAR 242 Variable-reluctance stepper motor 844 Variable-resistance sensor 445 Vehicles, electric 100 101 Vibration analyzer 457, 458 Virtual: instrument (VI) 457 470 short circuit 667 668 Virtual rst down 452 453 Volatile memory 412 Voltage: ac 12 ampli er, ideal 537 ampli er model 522 523 breakdown 478 -controlled attenuator 503 506 -controlled sources 23 24, 25 dc 12 de ned 11 divider 55 56, 59 follower 673 gain 520, 523, 594, 597 598, 643, 648 induced 720 722 input offset 556 561, 689 692 law, Kirchhoff s 19, 232 line 261 line-to-line 261 line-to-neutral 258, 261 node-, analysis 60 79, 236 237 offset 556 561, 689 693 peak inverse 494 phase 258 polarity 11 12 ratio, transformer 739 740 regulation 748 regulator 482 485 sinusoidal 216 222 source 22 24 thermal 478 threshold 576 W Ward Leonard system 792 Wave-shaping circuits 496 501 Weber (Wb) 717 Wheatstone bridge 104 106 Wideband ampli er 542 Windings: auxiliary 842 843 main 841 primary 739 secondary 739 Index Windowpanes, soaping 80 Wires Word, digital 358 Wound rotor 816, 828 Wye delta transformation 264 Wye wye connection 258 259, 262 264 X XOR gate 373 Z Zener diode 479 Zener-diode voltage regulator 482 485 Zeroing sources 91 92 893 .. .Electrical Engineering Principles and Applications Electrical Engineering Principles and Applications FIFTH EDITION Allan R Hambley Department of Electrical and Computer Engineering. .. Cataloging-in-Publication Data Hambley, Allan R Electrical engineering : principles and applications / Allan R Hambley 5th ed p cm Includes index ISBN-13: 978-0-13-213006-6 ISBN-10: 0-13-213006-8 Electrical engineering. .. between electrical engineering and other elds of science and engineering State and apply Kirchhoff s current and voltage laws List the major sub elds of electrical engineering Identify and describe

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  • Front Cover

  • Title Page

  • Copyright Page

  • Dedication Page

  • Practical Applications of Electrical Engineering Principles

  • CONTENTS

  • Preface

  • 1 Introduction

    • 1.1 Overview of Electrical Engineering

    • 1.2 Circuits, Currents, and Voltages

    • 1.3 Power and Energy

    • 1.4 Kirchhoff s Current Law

    • 1.5 Kirchhoff s Voltage Law

    • 1.6 Introduction to Circuit Elements

    • 1.7 Introduction to Circuits

    • Summary

    • Problems

    • 2 Resistive Circuits

      • 2.1 Resistances in Series and Parallel

      • 2.2 Network Analysis by Using Series and Parallel Equivalents

      • 2.3 Voltage-Divider and Current-Divider Circuits

      • 2.4 Node-Voltage Analysis

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