Lecture2说课讲解.doc

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1、Good is good, but better carries it.精益求精，善益求善。Lecture2-Lecture2Goodmorning,OK.Letsgetstarted.Wehaveonehandouttoday.Thatsyourlecturenotes.Theressomecopiesstilloutsideforthosewhohaventpickedoneup.Ingeneral,whatIdois,inthelecturenotes,Ileaveoutlargeamountsofmaterial.So,thiswillenableyoutokeepyourhandsb

2、usywhileImlecturingandtakedownsomenotesandsoon.So,dontassumethateverythingthatItalkaboutisonhere.Pleasefollowalong.OK,soasismyusualpractice,letmestartwithaquickreviewofwhatwecoveredsofar.Sowhatwedidprimarilywaslookedatthisdisciplinethatwecallthelumpmatterdiscipline,whichwasverysimilar,veryreminiscen

3、tofthepointmasssimplificationinphysics.Andthisdiscipline,thissetofconstraintsweimposedonourselves,allowedustomovefromMaxwellsequationstoavery,verysimpleformofalgebraicequations.Andspecifically,thedisciplinetooktwoforms.Oneis,wesaidthatwewilldealwithelementsforwhomtherateofchangeofmagneticfluxiszeroo

4、utsideoftheelements,andforwhomtherateofchangeofchargeIwanttochargeinsidetheelementwaszero.So,ifItookanyelement,anyelementthatIcalledalumpcircuitelement,likearesistororavoltagesource,andIputablackboxaroundit,thenwhatImsayingisthatthenetchargeinsidethatisgoingtobezero.Andthisisnottrueingeneral.Wewills

5、eeexampleswhere,ifyouchoosesomepieceofanelementforexample,theremightbechargebuildup,butnetinsidethe,ifIputaboxaroundtheentireelement,Iamgoingtoassumethattherateofchangeofchargeisgoingtobezero.So,whatthisdidwasitenabledustocreatethelumpcircuitabstraction,whereIcouldtakeelements,someelementofthesort,t

6、hiscouldbearesistor,avoltagesource,orwhatever,andIcouldnowascribeavoltage,somevoltageacrossanelement,andalsosomecurrent,i,thatwasgoingintotheelement.AndasIgoforward,whenIlabelthevoltagesandcurrentsacrossandthroughelements,Imgoingtobefollowingaconvention.OK,theconventionisthatImgoingtolabel,ifIlabelV

7、inthefollowingmanner,thenImgoingtolabeliforthatelementasacurrentflowingintothepositiveterminal.Itsjustaconvention.Bydoingthis,itturnsoutthatthepowerconsumedbytheelementisviispositive.OK,sobychoosingIgoinginthiswayintothepositiveterminal,thepowerconsumedbytheelementisgoingtobepositive.OK,soingeneralo

8、fevensimplyfollowingthisconvention,whenIlabelvoltagesandcurrents,Illbelabelingthecurrentintoanelemententeringinthroughtheplusterminal.Remember,ofcourse,ifthecurrentisgoingthisway,letshaveoneampofcurrentflowingthisway,thenwhenIcomputethecurrent,iwillcomeouttobenegative.OK,sobymakingtheseassumptions,t

9、heassumptionsofthelumpedmatterdiscipline,IsaidIwasabletosimplifymylifetremendously.And,inparticularwhatitdidwasitallowedmetotakeMaxwellsequations,OK,andsimplifythemintoaverysimplealgebraicform,whichhasbothavoltagelawandacurrentlawthatIcallKirchhoffsvoltagelaw,andKirchhoffscurrentlaw.KVLsimplystatest

10、hatifIhavesomecircuit,andifImeasuredthevoltagesinanyloopinthecircuit,soifIlookatthevoltagesinanyloop,thenthevoltagesintheloopwouldsumtozero.OK,soImeasurevoltagesintheloop,andtheywillsumtozero.Similarly,forthecurrent,ifItakeanodeofacircuit,ifIbuildthecircuit,anodeisapointinthecircuitwheremultipleedge

11、sconnect.IfItakeanode,thenthecurrentcomingintothatnode,thenetcurrentcomingintoanodeisgoingtobezero.OK,soifItakeanynodeofthecircuitandsumupallthecurrentsgoingintothatnode,theywillallnetsumtozero.So,noticewhatIvedoneisbythisdiscipline,bythisconstraintIimposedonmyself,Iwasabletomakethisincredibleleapfr

12、omMaxwellsequationstothesereally,reallysimplealgebraicequations,KVLandKCL.AndIpromiseyou,goingforwardtotherestof6.002,ifthisisallyouknow,youcanprettymuchsolveanycircuitusingthesetwoverysimplerelations.Itsactuallyreally,reallysimple.Itsallverysimplealgebra,OK?So,justtoshowyouanexample,letmedoalittled

13、emonstration.Letmebuildletmebuildasmallcircuitandmeasuresomevoltagesforyou,andshowyouthatthevoltages,indeed,adduptozero.So,heresmylittlecircuit.So,Imgoingtoshowyouasimplecircuitthatlookslikethis,andletsgoaheadandmeasuresomevoltagesandcurrents.Intermsofterminologytoremember,thisiscalledaloop.SoifIsta

14、rtfromthepointCandItravelthroughthevoltagesource,cometothenodeAdownthroughR1andallthewaydownthroughR2backtoC,thatsaloop.Similarly,thispointAisanodewhereresistorR1thevoltagesourceV0,andR4areconnected.OK,justmakesureyourterminologyiscorrect.So,whatIlldoisIllmakesomequickmeasurementsforyou,andshowyouth

15、attheseKVLandKCLareindeedtrue.So,thecircuitsupthere,couldIhaveavolunteer?Anyvolunteer?Allyouhavetodoiswritethingsontheboard.Comeonover.OK,soletmetakesomemeasurements,andwhydontyouwritedownwhatImeasureontheboard?WhatIlldois,letmeborrowanotherpieceofchalkhere.WhatIlldoisfocusonthisloophere,andfocusont

16、hisnodeandmakesomemeasurements.Allright,soyouseethecircuitupthere.OK,soIget3voltsforthevoltagefromCtoA.sowhydontyouwritedown3volts?OK,sothenextoneis-1.6.Andsothatwillbe,ImdoingAB,V_AB.OK,andthenletmedothelastone.Itis-1.37.Themeasurements,Iguess,havebeenthisway.So,whatswrittenisV_AC.ButitsOKfornow.Do

17、ntworryaboutit.So,well,thankyou.Iappreciateyourhelphere.OK,sowithinthebondsofexperimentalerror,noticedthatifIaddupthesethreevoltages,theynicelysumuptozero.OK,nextletmefocusonthisnodehere.Andatthisnode,letmegoaheadandmeasuresomecurrents.WhatIlldonowischangetoanACvoltagesothatIcangoaheadandmeasurethec

18、urrentwithoutbreakingmycircuit.OK,thistimearound,youllgettoseethemeasurementsthatImtakingaswell.So,whatIhavehere,Iguessyoucanseeitthisway.WhatIhavehereisthreewiresthatIhavepulledoutfromD.AndthisisthenodeD,OK?So,IhavethreewirescomingintothenodeDjusttomakeitalittlebiteasierformetomeasurestuff.OK,soeve

19、rybodykeepyourfingerscrossedsoIdontlooklikeafoolhere.Ihopethisworksout.So,youroughlyget,whatsthat,10mV.OK,soitsabout10mVpeaktopeakoutthere,andletssaythatifthewaveformraisesontheleft-handside,itspositive.So,itspositive10mV.Andanotherpositive10mV,sothats20mV.Andthistime,itsanegative,roughly20,Iguess,-

20、20.So,Imgetting,intermsofcurrents,Ihavea-10,-10,Imsorry,positive10,positive10,anda-20thataddsuptozero.Butmoreinterestingly,Icanshowyouthesamethingbyholdingthiscurrentmeasuringprobedirectlyacrossthenode.And,noticethatthenetcurrentthatisenteringintothisnodehereiszero.OK,sothatshouldjustshowyouthatKCLd

21、oesindeedholdinpractice,anditisnotjustafigmentofourimaginations.So,beforeIgoon,Iwantedtopointoneotherthingout.NoticethatIvewrittendowntwoassumptionsofthelumpedmatterdiscipline,OK?Thereisatotalassumptionofthelumpmatterdiscipline,andthatassumptionis,inspirit,atleast,sharedbythepointmasssimplificationi

22、nphysicsaswell.Cansomeonetellmewhatthatassumptionis?Atotalassumption,whichIdidnotmention,whichyoucanreadinyournotesinsection8.2intheappendix,whatsatotalassumptionthatissharedinspiritwiththepointmasssimplification?Anybody?Atotalassumptiontobemadehereisthatinallthesignalsthatwewillstudyinthiscourse,we

23、vemadetheassumptionthatthesignalspeedsofinterest,transitionspeeds,andsoon,aremuchslowerthanthespeedoflight.OK,thatmysignaltransitionspeedsofinterestaremuchslowerthanthespeedoflight.Remember,thelawsofmotion,thediscretelawsofmotionbreakdownifyourobjectsbeginmovingatthespeedoflight.OK,thesametokenhere,

24、ourlumpcircuitabstractionbreaksdownifweapproachthespeedoflight.Andtherearefollowoncoursesthattalkaboutwaveguidesandotherdistributedanalysistechniquesthatdealwithsignalsthattravelclosetospeedsoflight.OK,sowiththat,letmegoontotalkingaboutmethodoneofcircuitanalysis.ThisiscalledthebasicKVLKCLmethod.Soju

25、stbasedonthosetwosimplealgebraicrelations,Icananalyzeveryinterestingandcomplicatedcircuits.Themethodgoesasfollows.So,letssayourgoalis,givenacircuitlikethis,ourgoalistosolveit.OK,inthiscourse,wewilldotwokindsofthings:analysisandsynthesis.Analysissays,givenacircuit,OK,whatcanyoutellmeaboutthecircuit?O

26、K,sowellsolveexistingcircuitsforallthevoltagesandcurrents,voltagesacrosselements,andcurrentsthroughthoseelements.Synthesissays,givenafunction,Imayaskyoutogoandbuildcircuits.OK,soforanalysishere,wecanapplythismethodthatIwanttoshowyou.Andtheideahereisthat,givenacircuitlikethis,letusfigureoutallthevolt

27、agesandcurrentsthatareafunctionofthewaytheseelementsareconnected.So,thebasicKVLandKCLmethodhasthefollowingsteps.ThefirststepistowritedowntheelementVIrelationships.OK,rightdowntheelementVIrelationshipsforalltheelements.ThesecondstepiswriteKCLforallthenodes,andthethirdstepistowriteKVLforalltheloopsint

28、hecircuit.Thatsit.Justgoaheadandwritedownelementrules,KVL,andKCL,andthengoaheadandsolvethecircuit.So,whatwelldo,welldoanexample,ofcourse.But,justasarefresher,wevelookedatabunchofelementssofar,andfortheresistor,theelementrelationsaysthatVispiR,whereRistheresistanceoftheelementhere.Foravoltagesource,V

29、isequaltoVnought.Thatstheelementrelationship.Andforacurrentsource,theelementistherelationis,iissimplythecurrentflowingthroughtheelement.OK,sothesearesomeofthesimpleelementrulesforthedevicesthatthecurrentsource,voltagesource,andtheresistor.Soletsgoaheadandsolvethissimplecircuit.AndwhatIlldoisgoaheada

30、ndsolvethecircuitforyou.OK,ifyouturntopagefiveofyournotes,Imgoingtogoaheadandeditthecircuithere.Youcanscribblethevaluesonyournotesonpagefive.OK,soasafirststepofmyKVLKCLmethod,IneedtowritedownallmyelementVIrelationships.So,beforeIdothat,letmegoaheadandlabelallthevoltagesandcurrentsthatareunknownsinth

31、ecircuit.So,letmelabelthevoltagesandcurrentsassociatedwiththevoltagesourceashere.Notice,IcontinuetofollowthisconventionwherewheneverIlabelvoltagesandcurrentsforanelement,Iwillshowthecurrentgoingintothepositiveterminaloftheelementvariable,OK,afterelementvariablevoltage.Sohere,IhaveVnoughtandInought.L

32、etmepausehereforfivesecondsandshowyouapointofconfusionthathappenssometimes.Oftentimes,peopleconfusebetweenwhatiscalledthevariablethatisassociatedwiththeelementversustheelementvalue.OK,noticethathere,capitalVnoughtisthevoltagethatthisvoltagesourceprovides,whilethisnamehere,vnought,issimplyavariableth

33、atweveusedtolabelthevoltageacrossthatelement.So,similarly,Icanlabelv1asthevoltageacrosstheresistor,andi1isthecurrentflowingthroughtheresistor.Sothismethodoflabeling,whereIfollowtheconvention,thatthecurrentflowsintothepositiveterminaliscalledtheassociatedvariablesdiscipline.Iwastryingtousetheworddisc

34、iplineinsituationswhereyouhaveachoice,OK,andofavarietyofpossiblechoices,youpickoneastheconvention.OK,sohere,asaconvention,weusetheassociatedvariablesdiscipline,andusethatmethodtoconsistentlylabeltheunknownvoltagesandcurrentsinourcircuits.OK,soletmecontinuethelabelinghere,v4,i4,i3,v3here,andv2andi2,v

35、5,andi5.Ithinkthatsit.So,Ivegoneaheadandlabeledallmyunknowns.Soeachofthesevoltagesandcurrentsarethevoltagesandcurrentsassociatedwitheachoftheelements.Andmygoalistosolveforthese.OK,sointermsofoursolutionhere,letsfollowthemethodthatIoutlinedforyou.So,asthefirststepIamsimplygoingtogoaheadandwritedownal

36、ltheelementVIrelationships.OK,soasafirststep,ImgoingtogoaheadandwritedownalltheVIrelationships.So,cansomeoneyelloutformetheVIrelationshipforthevoltagesource?OK,good.So,v0iscapitalVnought,thatisthatthevariableVnoughtissimplyequaltothevoltage,v0.Similarly,Icanwritetheothers.v1isi1,R1.v2isi2,R2,andsoon

37、.OK,andIhaveone,two,three,four,five,sixelements.So,Iwillgetsixsuchequations.Steptwo,ImgoingtogoaheadandwriteKCLforthenodesinmysystem.So,letmestartwithnodeA.So,fornodeA,letmetakeaspositivethecurrentsgoingoutofthenode.So,Igetinoughtflowingout,plusi1flowingout,plusi4flowingout,andtheymustsumtozeroforno

38、deA.Then,Icangoaheadanddotheothernodes,letssay,forexample,IdonodeB.FornodeB,Ihavei2goingout.Thatspositive,i3,andi1iscomingin,soIget-i1equalszero.OK,soIhaveone,two,three,four,Ihavefournodes.OK,soIwouldgetfourequations.Itturnsoutthatthefourthequationisnotindependent.Youcanderiveitfromtheothers.So,Iget

39、threeindependentequationsoutofthis.IcanthenwriteKVL.AndforKVL,Ijustgodownmyloopshere.Andletmegothroughthisfirstloophereinthismanner.OK,andasimpletrickthatIuse,youhavetobeincrediblycarefulwhenyougothroughthisinkeepingyourminusesandplusescorrect.Otherwiseyoucangethopelesslymuddled.Onceyoulabelit,youne

40、edtobesurethatyougetallyourminusesandplusescorrect.So,forKVL,whatIdliketodois,letssayIstartatC,andfromCImgoingtogotoA.ForAIgotoB,andfromBImgoingtocomebacktoC.OK,thatshowItraversemyloop.And,thetrickthatImgoingtofollowis,asmyfingerwalksthroughthatloop,ImgoingtolabelthevoltageasthefirstsignthatIseefort

41、hatvoltage.OK,soImgoingtostartwithC,andIgoup.Istartbypunchingintothevoltagesourceelement,andthenpunchintoit,IhittheminussignfortheVnought.OK,soImjustgoingtowritedownminusVnought,plusthenIgothroughandasIcomeuptoAandgodowntoB,IpunchtotheplussignoftheV1.So,thatsplusV1.AndthenIpunchintotheplussignoftheV

42、2,andsoIgetplusV2,andthatiszero.OK,good.So,thatmatcheswhatyouhaveinyournotesaswell.So,thisisthefirstequation.Similarly,Icangothroughmyotherloopsandwritedownequationsforeachoftheloops.OK,andtheconventionthatIliketofollowisasIgothroughtheloop,IwritedownasasignforthevoltagethefirstsignthatIcounterforth

43、atelement.OK,youcandotheexactopposite,ifyouwant,justtobedifferent.But,aslongasyoustayconsistent,youllbeOK.Allright,sointhesamemannerhere,therearefourloopsthatIcanhave,sofourequations.Again,oneofthemturnsouttobedependentontheothers.SoIendupgettingthreeindependentequations.So,Igetatotalof12equations.I

44、get12equations.Therearesixelements,OK,voltagesource,andfiveresistors.So,therearesixunknownvoltages,andsixunknowncurrents.So,Ihave12equations,and12unknowns.OK,Icantakealloftheequationsandputthemthroughabigcrank,andsitthereandgrind.AndifIwasreallycruel,Idgivethisasahomeworkproblem,andhaveyougrind,andg

45、rind,andgrinduntilyougetyoursixvoltagesandsixcurrents.OK,itworks.OK,soyouget12equations,andthismethodjustworks.However,noticethatthisisquiteagrubbymethod.Itsquitegrungy.Iget12equations,anditsquiteapainevenforasimplecircuitlikethis.However,sufficeittosaythatthisfundamentalmethodisonestepawayfromMaxwe

46、llsequations,simplyworks.OK?Sowhatyoulldoistherestofthislecture,Illintroduceyoutoacouplemoremethods.Oneisanintuitivemethod,andanotheronecalledthenodemethodisalittlebitmoreformal,butismuchmore,Iguess,terseThantheKVLKCLmethod.Method2.Sotherelevantsectiontoreadinthecoursenotesissection2.4.Oneofthething

47、sthatIwillbestressingthissemesterisintuition.WhatyoullfindisthatasyoubecomeEECSmajors,andsoon,andgoon,orifyoutalktoyourTAsoryourprofessorsandsoon,youwillfindthatveryrarelydotheyactuallygoaheadandapplytheformalmethodsofanalysis.OK,byandlarge,engineersareabletolookatacircuitandsimplybyobservationwrite

48、downananswer.Andusuallyinthepast,whatwehavetriedtodoiskindofignorethatprocessandtoldourstudents,look,weteachyoualltheformalmethods,andyouwilldevelopyourownintuitionandbeabletodoit.Whatwelltrytodothistermistrytostresstheintuitivemethods,andtrytoshowyouhowtheintuitiveprocessgoes,soyoucanveryquicklysol

49、vemanyofthesecircuitssimplybyinspection.OK,sothismethodthatImgoingtoshowyouhereisonesuchanintuitivemethod.AndIllcallitelementcombinationtools.OK,formanysimplecircuits,youcansolvethemveryquicklybyapplyingthismethod.Thecomponentsofthismethodarethese.Ilearnedabouthowtocomposeabunchofelements.So,letssay,forexample,Ihaveasetofresistors,R1throughRN,inseries.OK,youcanuseKVLan