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Lessons In Electric Circuits, Volume II -- AC PDF

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SixthEdition,lastupdateJuly25,2007 2 Lessons In Electric Circuits, Volume II – AC By Tony R. Kuphaldt Sixth Edition, last update July 25, 2007 i (cid:13)c2000-2011,TonyR.Kuphaldt ThisbookispublishedunderthetermsandconditionsoftheDesignScienceLicense. These termsandconditionsallowforfreecopying,distribution,and/ormodificationofthisdocument bythegeneralpublic. ThefullDesignScienceLicensetextisincludedinthelastchapter. As an open and collaboratively developed text, this book is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITYorFITNESSFORAPARTICULARPURPOSE.SeetheDesignScience Licenseformoredetails. AvailableinitsentiretyaspartoftheOpenBookProjectcollectionat: openbookproject.net/electricCircuits PRINTINGHISTORY • First Edition: Printed in June of 2000. Plain-ASCII illustrations for universal computer readability. • SecondEdition: PrintedinSeptemberof2000. Illustrationsreworkedinstandardgraphic (epsandjpeg)format. SourcefilestranslatedtoTexinfoformatforeasyonlineandprinted publication. • ThirdEdition: Equationsandtablesreworkedasgraphicimagesratherthanplain-ASCII text. • Fourth Edition: Printed in November 2001. Source files translated to SubML format. SubML is a simple markup language designed to easily convert to other markups like LATEX,HTML,orDocBookusingnothingbutsearch-and-replacesubstitutions. • Fifth Edition: Printed in November 2002. New sections added, and error corrections made,sincethefourthedition. • SixthEdition: PrintedinJune2006. AddedCH13,sectionsadded,anderrorcorrections made,figurenumberingandcaptionsadded,sincethefifthedition. ii Contents 1 BASICACTHEORY 1 1.1 Whatisalternatingcurrent(AC)? . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 ACwaveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 MeasurementsofACmagnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 SimpleACcircuitcalculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 ACphase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6 Principlesofradio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 COMPLEXNUMBERS 27 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 VectorsandACwaveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3 Simplevectoraddition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 Complexvectoraddition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5 Polarandrectangularnotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Complexnumberarithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.7 MoreonAC”polarity” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.8 SomeexampleswithACcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3 REACTANCEANDIMPEDANCE–INDUCTIVE 57 3.1 ACresistorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2 ACinductorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Seriesresistor-inductorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Parallelresistor-inductorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5 Inductorquirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.6 Moreonthe“skineffect” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4 REACTANCEANDIMPEDANCE–CAPACITIVE 81 4.1 ACresistorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 ACcapacitorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3 Seriesresistor-capacitorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 Parallelresistor-capacitorcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 iii iv CONTENTS 4.5 Capacitorquirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5 REACTANCEANDIMPEDANCE–R,L,ANDC 99 5.1 ReviewofR,X,andZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 SeriesR,L,andC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.3 ParallelR,L,andC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4 Series-parallelR,L,andC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.5 SusceptanceandAdmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6 RESONANCE 121 6.1 Anelectricpendulum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.2 Simpleparallel(tankcircuit)resonance . . . . . . . . . . . . . . . . . . . . . . . . 126 6.3 Simpleseriesresonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.4 Applicationsofresonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.5 Resonanceinseries-parallelcircuits . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6.6 Qandbandwidthofaresonantcircuit . . . . . . . . . . . . . . . . . . . . . . . . 145 6.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7 MIXED-FREQUENCYACSIGNALS 153 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.2 Squarewavesignals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.3 Otherwaveshapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.4 Moreonspectrumanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.5 Circuiteffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 7.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 8 FILTERS 189 8.1 Whatisafilter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 8.2 Low-passfilters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.3 High-passfilters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.4 Band-passfilters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 8.5 Band-stopfilters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 8.6 Resonantfilters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 8.8 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 9 TRANSFORMERS 217 9.1 Mutualinductanceandbasicoperation . . . . . . . . . . . . . . . . . . . . . . . . 218 9.2 Step-upandstep-downtransformers . . . . . . . . . . . . . . . . . . . . . . . . . 232 9.3 Electricalisolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 9.4 Phasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 9.5 Windingconfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 9.6 Voltageregulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 CONTENTS v 9.7 Specialtransformersandapplications . . . . . . . . . . . . . . . . . . . . . . . . . 251 9.8 Practicalconsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 9.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 10 POLYPHASEACCIRCUITS 283 10.1 Single-phasepowersystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 10.2 Three-phasepowersystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 10.3 Phaserotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 10.4 Polyphasemotordesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 10.5 Three-phaseYandDeltaconfigurations. . . . . . . . . . . . . . . . . . . . . . . . 306 10.6 Three-phasetransformercircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 10.7 Harmonicsinpolyphasepowersystems . . . . . . . . . . . . . . . . . . . . . . . . 318 10.8 Harmonicphasesequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 10.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 11 POWERFACTOR 347 11.1 PowerinresistiveandreactiveACcircuits . . . . . . . . . . . . . . . . . . . . . . 347 11.2 True,Reactive,andApparentpower . . . . . . . . . . . . . . . . . . . . . . . . . . 352 11.3 Calculatingpowerfactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 11.4 Practicalpowerfactorcorrection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 11.5 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 12 ACMETERINGCIRCUITS 367 12.1 ACvoltmetersandammeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 12.2 Frequencyandphasemeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . 374 12.3 Powermeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 12.4 Powerqualitymeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 12.5 ACbridgecircuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 12.6 ACinstrumentationtransducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 12.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 13 ACMOTORS 407 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 13.2 SynchronousMotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 13.3 Synchronouscondenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 13.4 Reluctancemotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 13.5 Steppermotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 13.6 BrushlessDCmotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 13.7 Teslapolyphaseinductionmotors . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 13.8 Woundrotorinductionmotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 13.9 Single-phaseinductionmotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 13.10 Otherspecializedmotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 13.11 Selsyn(synchro)motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 13.12 ACcommutatormotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 vi CONTENTS Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 14 TRANSMISSIONLINES 483 14.1 A50-ohmcable? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 14.2 Circuitsandthespeedoflight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 14.3 Characteristicimpedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 14.4 Finite-lengthtransmissionlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 14.5 “Long”and“short”transmissionlines . . . . . . . . . . . . . . . . . . . . . . . . . 499 14.6 Standingwavesandresonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 14.7 Impedancetransformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 14.8 Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 A-1 ABOUTTHISBOOK 537 A-2 CONTRIBUTORLIST 541 A-3 DESIGNSCIENCELICENSE 549 INDEX 552 Chapter 1 BASIC AC THEORY Contents 1.1 Whatisalternatingcurrent(AC)? . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 ACwaveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 MeasurementsofACmagnitude . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 SimpleACcircuitcalculations . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 ACphase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6 Principlesofradio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.1 What is alternating current (AC)? Moststudentsofelectricitybegintheirstudywithwhatisknownasdirectcurrent(DC),which iselectricityflowinginaconstantdirection,and/orpossessingavoltagewithconstantpolarity. DCisthekindofelectricitymadebyabattery(withdefinitepositiveandnegativeterminals), orthekindofchargegeneratedbyrubbingcertaintypesofmaterialsagainsteachother. As useful and as easy to understand as DC is, it is not the only “kind” of electricity in use. Certain sources of electricity (most notably, rotary electro-mechanical generators) naturally produce voltages alternating in polarity, reversing positive and negative over time. Either as a voltage switching polarity or as a current switching direction back and forth, this “kind” of electricityisknownasAlternatingCurrent(AC):Figure1.1 WhereasthefamiliarbatterysymbolisusedasagenericsymbolforanyDCvoltagesource, thecirclewiththewavylineinsideisthegenericsymbolforanyACvoltagesource. One might wonder why anyone would bother with such a thing as AC. It is true that in somecasesACholdsnopracticaladvantageoverDC.Inapplicationswhereelectricityisused to dissipate energy in the form of heat, the polarity or direction of current is irrelevant, so long as there is enough voltage and current to the load to produce the desired heat (power dissipation). However, with AC it is possible to build electric generators, motors and power 1

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Lessons In Electric Circuits, Volume II – AC. By Tony . 3 REACTANCE AND IMPEDANCE – INDUCTIVE. 57 3.4 Parallel resistor-inductor circuits .
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