電路分析基礎（英文版第2版）PPT完整全套教學課件

Chapter1.FundamentalElements全套PPT課件2Introduction–FundamentalConceptsIntroduction–LinearElectronicDevicesContentsToprovideasoundunderstandingofbasicdevicesandcircuitsinElectronicEngineering.AimofthisCourse31.1Introduction–FundamentalConceptsChargeElectrostaticPotential&VoltageCurrent&ResistanceOhm’sLawPower&EnergyNowwewillreviewsomebasicconcepts4ChargeExperimentallydeterminedtobeoftwotypes;Thedistinctionisdesignated+and–;Theunitofchargeisaquantumunit,+eor–e;Aproton(質子)isdesignatedtohavecharge+e;Anelectronisdesignatedtohavecharge–e;1Coulombofchargehasabout6.242×1018e;5InsideaconductorSomeesinconductorsarenotboundtoparticularatombutarefreetomovefromatomtoatom.Theseconductionesmaybeimaginedasgasparticlesinabox.Inametaltheconductionesmoveagainstacrystallatticebackgroundofatomicsites.Their“collision”witheachotherandthelatticeisthesourceofresistance(tobedescribed)6TheelectrostaticpotentialExternalworkmustbeappliedtomoveachargeagainsttheforceofanelectrostaticfieldthatitexperiences.Electrostaticpotentialisexactlytheexternalworkexertedonaunitchargewhenitisremovedfromtheobservationspottoinfinity.P7Voltageisproportionaltopotentialenergydifferencebetweentwopoints+-qabVolts8Current&CurrentIntensityCurrent:I(A:Ampare)Howmanychargesflowacrosstheconductorwithin1s?CurrentIntensity:(A/m2)Howmanychargesflowacrosspersquarex-sectiontheconductorwithin1s?9Ohm’sLawR=U/IAmacroscopicalview10Resistanceisproportionaltolength

andinverselyproportionaltothecrosssectionalareaResistancedependsonthematerialLongwireshavelargeresistanceThickcrosssectionbarswillhavelowresistanceLsA11Power&EnergyBydefinitionpoweristherateatwhichworkisdone,eitherbyasystem,ortoasystem.

Thepowerdeliveredtoacircuitbyasourceofe.m.fisInversely,theenergydeliveredisthetimeintegralofthepowerapplied12ExamplesofvoltagesourcesDCtimevoltageACPulsedRamp13Foranidealvoltagesource,voltageisindependentofcurrent.VIReferencecurrentconventionofavoltagesourceisarbitraryv(t)+_14Inanidealcurrentsource,currentisindependentofvoltage.VIi(t)15AboutDependentSourceItprovidesacurrentorvoltagewhosevalueisdependentonthecurrentorvoltageelsewhere.Itiscontrolledbytheparametersoftheotherelements.Itisgiveadiamondsymbolwithacontrollingsignal,suchas+-Vs=0.4ixIs=Aiy16Example117Example2181.2Introduction–LinearElectronicDevicesResistorsCapacitorsInductors19ResistorsResistorsarecommonlyavailableinarangefrom1to10Mandpowerratingsfrom1/8WatttoseveralWattsEarlyresistorsconsistedofacarboncompositioninaninsulatingtubeModernresistorsconsistofametaloxidedepositedonaceramicrod.TheoxidemayhaveaspiralgroovecutinittoincreaseitsresistanceSomehighpowerresistorsuseNichrome(stainlesssteel)wirewoundroundaceramiccoreandcoveredwithvitreousenamel(glass)20Resistorsarenotperfect:Theyarenottotallyindependentoftemperature,perhapsincreasingbyafew%at-50Cand+150C.Theywillhavesomecapacitancebetweenthetwoends.Thenwilltheyhavesomeinductance?Thenhowandwhere?Theywillhavesomeinductance,particularlythewirewoundversions.Howevertheseeffectsarenegligibleinnearlyallcasesandresistorscanberegardedas“perfect”formostpurposes.21ExerciseAwire50minlengthand2mm2incrosssectionhasaresistanceof0.56W..A100mlengthofwireofthesamematerialhasaresistanceof2Watthesametemperature.Findthediameterofthiswire.22Capacitors10mF100kVDangerHighVoltage1mF440pFElectrolyticcapacitorAcapacitorconsistsoftwoconductorsseparatedbyaninsulator.MadeofpaperCeramiccapacitorGenerally3types23Thecapacitancedependsonitssizeandmaterial,independentofwhetheritischargedornot.Theunitofcapacitanceisfarad(F).C=Q/VForalltypicalcapacitors24Capacitancecanbereadilycalculatedforgeometricfigureswithconstantcross-section.e

isthedielectricconstant,

e=ereoer

=relativedielectricconstanteo

=edS25Acapacitorconsistsoftwoconductorsseparatedbyaninsulator.Toconstructalargecapacitance,thedifficultiesare:Gettingtheareaoftheconductors,S,aslargeaspossibleinaconfinedspace.Gettingtheinsulatorthickness,d,asthinaspossible.Iftoothinitwillbreakdownunderthevoltageapplied.26CapacitorValuesCapacitorsareavailablefromafewpF(10-12)upto1000sofμF(rarelycalledmilliFarads).Capacitorsneedtobespecifiedfortheirvoltagecapability.Theymayalsoberestrictedintheircurrentcarryingcapacity.Capacitorsrarelylooklikeperfectcapacitance.Theyhavelossesintheinsulatorwhichlookslikeseriesresistanceandleakage(electrolytics)whichlookslikeparallelresistance.Thewoundcapacitorsalsohavesignificantinductance!27Effective(ornet)capacitanceofparallel(a)&series(b)capacitorcombinationsC1C2C3V(a)C1C2C3V(b)28InductorsDirectionofthecurrentandtheinductivemagneticfield.Useyourrighthand.29Fluxlinkagealsoequalscurrenttimesinductance.i(t)+_v(t)LUnitofinductanceisHenryFluxLinkageInductance30Inductancecanbereadilycalculatedforalongsolenoid.NomagneticcoredAPermeability磁導通率31Inaninductor,voltageisproportionaltothederivativeofcurrentNotereferencedirectionsi(t)+_v(t)L32NetInductanceofSeriesInductorsL3L2L1+-vsi+-+-+-v1v2v333NetInductanceofParallelInductorsL1L2L3+-isv34SummaryofterminalrelationsforpassiveelementsResistorCapacitordtdv

C

=iInductor

vdtd

L

i=Memorize!!dtdq

R

=vChapter2.SomeCircuitSimplificationTechniques36Contents2.1SuperpositionTheorem2.2SourceTransformationGoal:Usethesetwotheoremstosimplifycircuits372.1SuperpositionTheorem38SuperpositionTheoremIfalinearcircuitisexcitedbymorethanoneindependentsource,thetotalresponseisthealgebraicsumofalltheindividualresponses.Theindividualresponseistheresultofanindependentsourceactingalone.39ExcitationandResponseExcitationResponse40CommentsonSuperpositionActalone:

Considereachindependentsourceoneatatime;Otherindependentsourcesare“killed”,or“turnedoff”,or“zeroedout”.41CommentsonSuperpositionIfavoltagesourceiszeroedout,itistreatedasashortcircuit;Ifacurrentsourceiszeroedout,itistreatedasanopencircuit;Superpositiontheoremdoesnotapplytopowercalculation.42Example1Findtheunknownbranchcurrenti.43SolutionSetthecurrentsourcetobezero:44Setthevoltagesourcetobezero:45Bysuperposition,wehave:46Example2Usesuperpositiontheoremtofindthevoltageuabinthecircuit.47SolutionFirst,turnoffthecurrentsource,48Second,turnoffthevoltagesourceThelaststep,adduab1

and

uab2

together492.2SourceTransformation50SourceTransformationababEquivalent51Whatisequivalent?WhatevertheloadRx=?IftheseequationsalwayssatisfiedWesaythesetwoBlackBoxesareequivalentFortwo2-terminalBlackBoxes,52SourceTransformationababEquivalent=53SourceTransformation=54Example1NOTEthereferencedirectionofvoltageandcurrentsources.55Example2Findthecurrentinthe5kresistorbysourcetransformations.ANS:i0=3mA56SpecialCasesofSourceTransformation57Example3Usesourcetransformationtofindv0.58Solution:ANS:v0=400VChapter3.TechniquesofCircuitAnalysis60Contents3.1Basicconcepts3.22b-methodforCircuitAnalysis3.3Node-VoltageAnalysisMethod3.4Mesh-CurrentAnalysisMethod3.5ThéveninandNortonTheorem3.6MaximumPowerTransferTheorem613.1Basicconcepts62BeforethestudyofDCcircuitanalysis,let’sgettoknowsometermsforplanarcircuits.AplanarcircuitAnon-planarcircuit63Importanttermsforelectriccircuittopology(1)Elementsconnectedinseriescarrythesamecurrent(2)Elementsareconnectedinparallelifthesamevoltageisacrossthem(3)Node:apointwhere2ormoreelementsjoinEssentialNode:apointwhere>2elementsjoinTrivialNode:apointwhere2elementsjoinListedinTable3.1inP56textbook64Anodeisapointwhere>2elementsareconnectedtogether.Trivialnode-onlytwoelementsareconnectedtogetherEssentialnode-morethantwoelementsareconnectedtogetherTakenfrom/class/enee204-2.S2000/chapters.htm65Herearesomemoreexamplesofnodes.TrivialnodeThisisallonenode23451Takenfrom/class/enee204-2.S2000/chapters.htm66(4)Branch:apathwithoutpassingthroughanessentialnode;inotherwords,apathcarryingsamecurrentEssentialBranch:apathconnecting2essentialnodesandwithoutpassingthroughanessentialnodeTrivialBranch:apathconnecting1ormoretrivialnodesandwithoutpassingthroughanessentialnodeWhenwerefertothenodesandthebranchesthereafter,weusuallymeantheessentialsindefault.67Abranchisatwo-terminalelement.Branch1istrivial.Branch2istrivial.branch1branch2branch3Branch3isessential.Branch:apathwithoutpassingthroughanessentialnode;inotherwords,apathcarryingsamecurrent68(5)Loop:anysimpleclosedpathinacircuit.‘simple’meanspassingnoelementmorethanonce.(6)Mesh:aloopnotenclosinganyelements;orinotherwords,aloopdoesnotencloseanyotherloopEssentialMesh:meshpassingthrough≥3essentialnodesTrivialMesh:meshpassingthrough<3essentialnodes69Aloop

isasetofbranchesthatformaclosedpath.Eachnodeisencounteredonlyonceastheloopistraced.Takenfrom/class/enee204-2.S2000/chapters.htm70Ameshisthesimplesttypeofloop.*Meshesdonotencloseanybranches*ForaplanarcircuitsonlyTakenfrom/class/enee204-2.S2000/chapters.htm71ExampleHowmanybranches,nodes,loops&meshes?426372Howmanymeshes?Branches?Essentialandtrivialnodes?Takenfrom/class/enee204-2.S2000/chapters.htm73Takenfrom/class/enee204-2.S2000/chapters.htm6essentialnodes3trivialnodes6meshesTheansweris:11branches743.22b-methodforCircuitAnalysisWhatistheQuestion?Twotheorems2b-method75WhatistheQuestion?First,whatshouldwedoforcircuitanalysis?Buildequationsforagivencircuit;Solveequationstodeterminecurrentsandvoltagesforall(orrequired)circuitelements.Then,howmanyindependentequationsshouldwehavetosolveforagivencircuit?76Therearetwounknowns(voltage¤t)

tobedeterminedforeveryelement;Generally,foracircuitwithbbranches,wehave2bunknownvariables:2b=b(voltages)+b(currents)Therefore,wehavetosolve2bindependentequationsforacircuitwithbbranches!77Howcanwegetthenecessary2bequations?Canacircuitbesolvedbyequationslessthan2b?Ifyes,howmanyatleast,andhowcanwegetthem?WhatistheQuestionnow?78Theorem1Foracircuitwithnnodes,KCLyields(n-1)independentequationsforany(n-1)nodes.79ForExample:ApplyKCLtoallnodes:Only3equationsareindependent.80Theorem2Foracircuitwithnnodesandbbranches:Thecircuitmusthavem=b-(n-1)meshes;KVLyieldsm=b-(n-1)independentequationsforthem=b-(n-1)meshes.81n=4,b=5m=b-(n-1)=2ⅠⅡApplyKVLtomeshⅠandⅡ:ForExample:822b-MethodHowtogettherequired2bindependentequations?(n-1)KCLequationsby(n-1)nodesb-(n-1)KVLequationsbyb-(n-1)meshesbVCRequationsbybbranchesbyelementconstraints,eg.Ohm’sLaw832b-MethodTotalnumberofequations:(n-1)nodes(KCL)m=b-(n-1)meshes(KVL)b

branches(elementconstraint)84ExampleDeterminethevoltageandcurrentforeverybranch.85Analysis:Thecircuithas5branches;5voltagesand5currentstobedetermined;Therefore,10independentequationstobesolved;Howcanweobtainthe10independentequations?86ApplyKCLtonode1,2,3:Solution:m=b-(n-1)=5-(4-1)=2ApplyKVLtomeshⅠandⅡ:87Foreverybranch,wehave:88Thenwegettherequired10independenteq:89ConsideringIndependentSourcesAssumingthenumberofindependentsourcesiss:Unknownvariables:s+2(b-s)=(2b-s)sunknownsforsindependentsources2(b-s)unknownsfor(b-s)branches90ConsideringIndependentSourcesTotalnumberofequations:(n-1)nodes(KCL)m=b-(n-1)meshes(KVL)b-sbranches(elementconstraint)91Howcanwegetthenecessary2bequations?Canacircuitbesolvedbyequationslessthan2b?Ifyes,howmanyatleast,andhowtogetthem?WhatistheQuestionnow?92OfcourseYes.Node-VoltageAnalysisMethodMesh-CurrentAnalysisMethod933.3Node-VoltageAnalysisWhatisnodevoltage?Whyisnodevoltageused?Howisnodevoltageanalysismethodimplemented?94Nodevoltageisdefinedasthevoltagerisefromthereferencenode;Voltagesacrossallbranchescanberepresentedbynodevoltages.WhatisNodeVoltage?95NodevoltageReferencenodeWhatisNodeVoltage?96WhyNodeVoltageAnalysis?Thenumberofnodeinacircuitisn:n-1<b<2bUsenode-voltageasunknownstosolveagivencircuitcangreatlyreducethenumberofequationstobesolved.97HOWisnodevoltageanalysismethodimplemented?98ExampleFindv1,v2,andi1.99Solution:Step1:Selectreferencenodeanddefinenodevoltages:Referencenodeu1u2100Step2:BuildKCLequationsfornodesexceptthereferencenode101Step3:Solveequationstogetnodevoltages:102Step4:Determinerequiredunknownvoltagesandcurrentsbysolvednodevoltages:103Further,ifnecessary,otherunknownvoltages,currents,orpowerscanalsobedetermined,andthecircuitiscompletelysolved;Ifnecessary,answerscanbecheckedbypowerbalance.104StepsofNode-VoltageMethodSelectoneofthenodesasthereferencenode,anddefinenodevoltagesforothernodes;BuildKCLequationsfornodesexceptthereferencenode;Solveequationsforthenodevoltages;Determinerequiredvoltages,currentsorpowersbynodevoltages.105ExampleFindthepowerdissipatedbyallresistorsinthecircuit.106Solution:Selectthereferencenodeanddefinenodevoltages:v1v2v3v4107BuildKCLequationsfornodesexceptthereferencenode:108109SolveequationsfornodevoltagesbyCramer’srule:Then,calculatepowerdissipatedbyallresistors…110v1v2v3v4Usenode-voltagemethodtofindthevalueofv3andv4.ExamplewithDependentSource111v1v2v3v4ConceptofSuperNode1123.4Mesh-CurrentAnalysisMethodWhatismeshcurrent?Whyismeshcurrentused?Howismeshcurrentanalysismethodimplemented?113WhatisMeshCurrent?Meshcurrentisintroducedjustasanimaginaryquantity;Meshcurrentflowsaroundamesh;AllbranchcurrentsdonotchangeforintroducingmeshcurrentsAllbranchcurrentscanberepresentedbymeshcurrents.114iaibicic=ia-ibBranchcurrents:im1im2ic=im1–im2Meshcurrents:ia=im1ib=im2WhatisMeshCurrent?115WhyMeshCurrentanalysis?Thenumberofmeshinacircuit:m=b-(n-1)<b<2bUsemesh-currentasunknownstosolveacircuitcangreatlyreducethenumberofequationstobesolved.116HOWismeshcurrentanalysismethodimplemented?117Example:Determinethecurrentsofeverybranch.118Solution:Step1:Selectmeshcurrentiaandibiaib119Step2:BuildKVLequationsforallmeshes120Step3:Solveequationstogetmeshcurrentiaandib121Step4:Determinerequiredcurrentsbymeshcurrentiaandib.122Further,ifnecessary,otherunknownvoltagesandcurrentscanalsobedetermined,andthecircuitiscompletelysolved;Ifnecessary,answerscanbecheckedbypowerbalance.123StepsofMesh-CurrentMethodAssumemeshcurrentanditsreferencedirection(clockwise)foreverymesh;BuildKVLequationsforeverymesh;Solveequationsformeshcurrents;Determinerequiredunknowncurrentsandvoltagesbymeshcurrents.124ExamplewithDependentSourceUsemesh-currentmethodtofindthetotalpowerdevelopedinthecircuit.125ExampleofSuper-MeshUsemesh-currentmethodtofindthetotalpowerdissipatedinthecircuit.126ConceptofSuper-Meshiaib127NodalmethodVSMeshmethodMeshanalysisonlyappliestoplanarcircuits;Node-voltagemethodresultsindirectcalculationofvoltage;whereasmesh-currentanalysisprovidescurrents;Meshanalysisresultsinm=b-(n-1)equations;andnodalanalysisresultsin(n-1)equations.1283.5ThéveninandNortonEquivalentsThéveninEquivalentCircuitNortonEquivalentCircuit129abAttimes,weonlyhaveinterestinthebehavioratthetwoterminals;ThéveninandNortonEquivalentsarecircuitsimplificationtechniquesthatfocusonterminalbehavior.ThéveninandNortonEquivalents130ThéveninEquivalentCircuitAnetworkwithtwoterminalscanbeequivalenttoanindependentvoltagesourcevTH

inserieswitharesistorRTH;vTHistheopen-circuitvoltagewhenthetwoterminalsaredisconnected;RTHistheequivalentresistanceofthetwo-terminalnetworkwhenallindependentsourcesinitarezeroedout(killed).131ThéveninEquivalentCircuitabab132ExampleFindtheThéveninequivalentofthecircuitbetweenterminalsaandb.133Solution:Findtheopencircuitvoltagebetweentwoterminalsaandb:voc134Bynode-voltageanalysismethod,wehave:135FindtheThéveninequivalentresistancebetweentwoterminalsaandb:136Then,theThéveninequivalentofthecircuitbetweenterminalsaandbis:137ThéveninEquivalentCircuitabOpen-CircuitVoltageShort-CircuitCurrent138ThéveninEquivalentCircuitabab139ExampleFindtheThéveninequivalentofthecircuitbetweenterminalsaandb.140Solution:Findtheopencircuitvoltagebetweenaandb:voc141Findtheshortcircuitcurrentfromatob:v142Bynode-voltagemethod,wehave:143Then,wehave:144ExampleFindtheThéveninequivalentwithrespecttotheterminalsofaandb.145Solution:Findtheopencircuitvoltage:146Bynode-voltagemethod,wehave:147Findshortcircuitcurrentfromatob:148Bynode-voltagemethod,wehave:149150ExampleFindtheThéveninequivalentwithrespecttotheterminalsa,b.151Solution:Sincethecircuitcontainsnoindependentsources,152Applyatestvoltagesourcetoterminalaandb:v153Bynodevoltagemethod,wehave:154155NortonEquivalentCircuitAnetworkwithtwoterminalscanbeequivalenttoanindependentcurrentsourceisc

inparallelwitharesistorRN;iscistheshort-circuitcurrentwhenthetwoterminalsaredirectlyconnected;RNistheequivalentresistanceofthetwo-terminalnetworkwhenallindependentsourcesinitarezeroedout(killed).156abNortonEquivalentCircuitab157NortonequivalentcanbederivedfromThéveninequivalentbysourcetransformation;andviceversa.NortonEquivalentCircuitabab158ThéveninandNortonEquivalentsBothThéveninandNortoncircuitsprovideanequivalentfora2-terminalnetwork,andthe“l(fā)oad”network(RL)wouldnot“know”ifitwas“seeing”theequivalent;ThéveninequivalentcanbederivedfromNortonequivalentbysourcetransformation;andviceversa.1593.6MaximumPowerTransferabProblem:TodeterminethevalueoftheloadRLthatpermitsmaximumpowerdeliveredtoRL.160ababPowerdeliveredtoRL:161ThederivativeofpowerpwithrespecttoRL:Let,weget:Maximumpowertransferoccurs162ThemaximumpowerdeliveredtoRLis:Conditionofmaximumpowertransfer:MaximumPowerTransfer163KeyNotesofChapter3Node-voltageanalysismethodMesh-currentanalysismethodThéveninandNortonEquivalentMaximumpowertransferChapter4OperationalAmplifier165ContentsStructuresandCharacteristicsInvertingConfigurationNon-InvertingConfigurationSuperpositioninCircuitswithOp-Amp.IntegratorDifferentiatorFilterswithOp-AmpImpedancesinCircuitswithOp-Amp166-+v1v20+Vout-A1.StructuresandCharacteristics167-+v1v20+vout=A(v2-v1)-InfiniteinputimpedanceZerooutputimpedanceVeryhigh(infinite)gainCharacteristicsofPerfectOp-AmpTypicalA=104~107AAlmostnocurrentRLIndependentofRLZi1Zi2168VirtualShort&VirtualOpenduetoinfinitegain-+v1v20+vout=A(v2-v1)-0?A￥?VirtualshortIntermsofvoltageiduetoinfiniteinputimpedanceIntermsofcurrentZ￥?i=0VirtualopenAlmostnocurrent169R2-+v1v2+vout-R1+-vs2.InvertingConfigurationi1i2i1=VS/R1

i2=－

Vout/R2v1=v2=0virtualshortIntermsofvoltageFindthecurrents.“inverting”means…170R2-+v1v2+vout-R1+-vsi1i2i1=VS/R1

i1=

i2Vout=-VSR2/R1InfiniteinputimpedanceVirtualOpeni2=－

Vout/R2171R2-+v1v2+vout-R1+-vsi1i2ASummaryforInvertingConfiguration172-+10

kW+-vs1MW+Vout=?-50W100WSincevirtualshortisinparallelwiththeresistorTheresistorbetweentheinputterminalshasnoeffectonthegainofidealoperationalamplifierExample1-100VSv1=v2=0virtualshortv1v21731.Findthepotentialsatthe+or-inputterminals2.Usingvirtualshortequatethepotentialsat+&-terminals3.Usingvirtualopenfindthecurrentflowingintothefeedbackresistor4.CalculatetheoutputvoltageStepsofAnalysis174R-+v1v2+Vout-Rvsi1i2Vout=-VSExample2---Inverter175Vout=8v4+4v3+2v2+v1Example3-+1kW1KW-++vout-10kW10kWv3v1v20.5kW0.25kWv40.125kWPleasefindVout176-+v1v2+Vout-R1R2+-vsi1i2i1=-VS/R1i1=i2i2=(VS－Vout)/R2Virtualshortv1=v2=VS3.Non-invertingConfigurationFindv1&v2Findi1&i2177-+v1v2+Vout-R1R2+-vsi1i2ASummaryforNon-invertingConfiguration178Signaladditioncanalsobedonewithnon-invertingconfiguration.Example---Adder-++Vout=?

-R1+-vs2R2+-vs1R3R4v1v2Wewillanalyzethiscircuitlater.179-++vout-R1R2+-vs1+-vs

24.SuperpositioninCircuitswithOp-Amp.WithoutvS2WithoutvS1180R2-+v1v2+vout-R1+-vsforInvertingConfigurationSummary-+v1v2+Vout-R1R2+-vsforNon-invertingConfiguration181ConvertingthistocircuitlanguageWecannowbuildacircuitdiagramExercise:ImplementingLinearAlgebra182183184ContentsIntegratorDifferentiatorFilterswithOp-AmpImpedancesinCircuitswithOp-Amp185-++vout-RC+-vsi1i2Vout=-VCAssumeVS=0andVC=0fort<0Integrator+VC－186Differentiator-++vout-RC+-vsi1i2i2=-Vout/R+VS－187ASummaryIntegratorDifferentiator188Solution:Thesimplestcase:Initialcondition:v(0)=V0-++v(t)-R1+-f(t)-+R2R2t=0V0+-C=1/R1Thecircuit:Applications---Solvingdifferentialequations189-v(t)-++v(t)-R1+-f(t)-+R2R2t=0V0+-C=1/R1IntegratorIdentifyeachstageofthecircuitInverter??190-v(t)-++v(t)-R1+-f(t)-+R2R2t=0V0+-C=1/R1IntegratorIdentifytheinitialconditionInverterv(0)=V0191Solution:v(0)=V0Identifytheequation-v(t)-++v(t)-R1+-f(t)-+R2R2t=0V0+-C=1/R1IntegratorInverter192SecondorderequationDifferentialequation:v(0)=V0,v’(0)=0-++v(t)-C=1/R1-+R2aR2t=0V0-+R1-a

v(t)-+R1C=1/R1t=0dt2d2vdtdv193-+v1v20+vout=A(v2-v1)-Infiniteinputimpedance-->virtualopenZerooutputimpedance-->forgetabouttheloadInfinitegain-->virtualshortAnalysisofacircuitwithanidealoperationalamplifierisdrasticallysimplified194FilterswithOp-Amp195Lowpassfilters196LPFHPF197BPFBSFLPF&HPFinseriesLPF&HPFinparallel198BPFBSF199HomeworkProblems4.17,4.24,4.27,4.29,4.32Chapter5.TheNaturalandStepResponseofRLandRCCircuits(1)ContentsCapacitorandCapacitanceInductorandInductanceDynamicElementandCircuitRCandRLCircuitsSwitchingTheoremGoalsKnowandusetheVCRofcapacitorsKnowandusetheVCRofinductorsCalculatetheenergyforcapacitorandinductorCapacitorsandinductorsinseriesandparallelAbilitytodeterminetheinitialvaluesofcircuitsContentsCapacitorandCapacitanceInductorandInductanceDynamicElementandCircuitRCandRLCircuitsSwitchingTheoremCapacitorisachargestoringdevice;CVRofidealcapacitor:

ReferencevoltageandcurrentdefinedwithpassivesignconventionCapacitorandCapacitancePowerandEnergyPower:Energy:ContentsCapacitorandCapacitanceInductorandInductanceDynamicElementandCircuitRCandRLCircuitsSwitchingTheoremInductorisaenergystoringdevice;WCRofidealInductor:

InductorandInductanceReferencevoltageandcurrentdefinedwithpassivesignconventionPowerandEnergyPower:Energy:InductorsinSeriesInductorsinParallelContentsCapacitorandCapacitanceInductorandInductanceDynamicElementandCircuitRCandRLCircuitsSwitchingTheoremDynamicElementResistor:VCRofterminalsisalinearalgebraicequation;VCRis“instantaneous”or“memoryless”;Staticelement.DynamicElementCapacitorandInductor:VCRisadifferentialorintegralequation;VCRis“historical”or“memorial”;Dynamicelements.ContentsCapacitorandCapacitanceInductorandInductanceDynamicElementandCircuitRCandRLCircuitsSwitchingTheoremNaturalResponseThecapacitor/inductorisabruptlydisconnectedfromitssource;Energystoredinthecapacitor/inductorisreleasedtoaresistivenetwork.ContentsCapacitorandCapacitanceInductorandInductanceDynamicElementandCircuitRCandRLCircuitsSwitchingTheoremInitialValuesSwitchingTimeSwitchingTheoremMethodforInitialValuesSwitchingThe