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ECTE170–Lecture10/111ECTE170–Lecture10/111Chapter16–BoylestadSeries-ParallelACNetworksAnalysisSeries-ParallelACNetworks2Chapter16–BoylestadSeries-16.1–Introduction

Ingeneral,whenworkingwithseries-parallelACnetworks,considerthefollowingapproach:Redrawthenetworkemployingblockimpedancestocombineobviousseriesandparallelelements,whichwillreducethenetworktoonethatclearlyrevealsthefundamentalstructureofthesystem.316.1–IntroductionIngeneraIntroductionStudytheproblemandmakeabriefsketchoftheoverallapproachyouplantouse.Doingthismayresultintime-andenergy-savingshortcuts.Insomecasesalengthy,drawn-outanalysismaynotbenecessary.Asingleapplicationofafundamentallawofcircuitanalysismayresultinthedesiredsolution.4IntroductionStudytheproblemIntroductionAftertheoverallapproachhasbeendetermined,considereachbranchinvolvedinyourmethodindependentlybeforetyingthemtogetherinseries-parallelcombinations.Inmostcases,workbackfromtheobviousseriesandparallelcombinationstothesourcetodeterminethetotalimpedanceofthenetwork.Thesourcecurrentcanthenbedetermined,andthepathbacktospecificunknownscanbedefined5IntroductionAftertheoverallIntroductionWhenyouhavearrivedatasolutionchecktoseethatitisreasonablebyconsideringthemagnitudesoftheenergysourceandtheelementsinthecircuit.Ifnot,eithersolvethenetworkusinganotherapproach,orcheckoveryourworkverycarefully.Atthispointacomputersolutioncanbeaninvaluableassetinthevalidationprocess.6IntroductionWhenyouhavearri16.2–IllustrativeExamplesExample16.1CalculateZT.DetermineIS.CalculateVRandVc.FindIC.Computerthepowerdelivered.FindFpofthenetwork.716.2–IllustrativeExamplesExExamplesolution8Examplesolution8Examplecontinued9Examplecontinued9ExampleContinued10ExampleContinued10IllustrativeExamplesExample16.2SolutionRedrawthecircuitUsethecurrentdividerrule,determineI,I1andI211IllustrativeExamplesExample1Example16.2solution12Example16.2solution12IllustrativeExamplesExample16.4SolutionRedrawthecircuitUsethecurrentdividerrule,determineI1andI2andVab13IllustrativeExamplesExample1Solutiontoexample16.414Solutiontoexample16.414IllustrativeExamplesTofindVab,Kirchhoff’svoltagelawmustbeappliedaroundtheloop.15IllustrativeExamplesToSolutionto16.4continued16Solutionto16.4continued1616.3–LadderNetworksHerewewillcalculatethetotalresistanceandresultingsourcecurrent,andthenworkbackthroughtheladderuntilthedesiredcurrent,I6,(orvoltage)isobtained.1716.3–LadderNetworksHereweLadderNetworksImpedanceZT,ZT'andZT''andthecurrentsI1andI3aredefined:18LadderNetworksImpedanceZT1919Series-ParallelCircuitsBoylestad,p719Fig16.14ComputeIFindI1,I2andI3VerifyKirchhoff’scurrentlawbyshowingthatI=I1+I2+I320Series-ParallelCircuitsBoylesSolutionto16.1421Solutionto16.1421Solutioncontinued22Solutioncontinued22AwordaboutnodalandmeshanalysisSameasDC,butneedtodoitwillallthephasesinAC,otherwisethesameLetsdoaNodalanalysisexample23Awordaboutnodalandmeshan2424Solutioncontinued25Solutioncontinued25Solutioncontinued26Solutioncontinued2616.5–ApplicationsGFCI(GroundFaultCircuitInterrupter)GFCIoutletsaretobeusedinareaswherewateranddampnesscouldresultinseriousinjury,suchasbathrooms,kitchens,pools,outdoorreceptacles.Aprotectioncircuitseparatesthepowersourcefromtheoutlet.Theprotectioncircuitmustbeconnectedtothecentralground.2716.5–ApplicationsGFCI(GrounApplicationsThenetworksensesbothcurrententering(Ii)andcurrentleaving(Io),andprovidesadirectconnectiontotheoutletwhentheyareequal.Ifafaultdevelops,theprotectioncircuitwillsensethedifference,betweenfeedandreturncurrents,andcutoffpowertotheoutlet.28ApplicationsThenetworksensesApplicationsThetestbuttonwillplacealarge-valueresistorbetweenthelineandgroundto“unbalance”thelineandcauseafaultcondition.Whenthetestbuttonisreleased,itwillremovetheresistorfromtheline,removingthefaultcondition.Theresetbuttonisusedtoreconnecttheoutlettothesupplyafterafault(fromanexternaldeviceorthe“testbutton”)hasbeenremoved.29ApplicationsThetestbuttonwi

ECTE170–Lecture10/1130ECTE170–Lecture10/111Chapter16–BoylestadSeries-ParallelACNetworksAnalysisSeries-ParallelACNetworks31Chapter16–BoylestadSeries-16.1–Introduction

Ingeneral,whenworkingwithseries-parallelACnetworks,considerthefollowingapproach:Redrawthenetworkemployingblockimpedancestocombineobviousseriesandparallelelements,whichwillreducethenetworktoonethatclearlyrevealsthefundamentalstructureofthesystem.3216.1–IntroductionIngeneraIntroductionStudytheproblemandmakeabriefsketchoftheoverallapproachyouplantouse.Doingthismayresultintime-andenergy-savingshortcuts.Insomecasesalengthy,drawn-outanalysismaynotbenecessary.Asingleapplicationofafundamentallawofcircuitanalysismayresultinthedesiredsolution.33IntroductionStudytheproblemIntroductionAftertheoverallapproachhasbeendetermined,considereachbranchinvolvedinyourmethodindependentlybeforetyingthemtogetherinseries-parallelcombinations.Inmostcases,workbackfromtheobviousseriesandparallelcombinationstothesourcetodeterminethetotalimpedanceofthenetwork.Thesourcecurrentcanthenbedetermined,andthepathbacktospecificunknownscanbedefined34IntroductionAftertheoverallIntroductionWhenyouhavearrivedatasolutionchecktoseethatitisreasonablebyconsideringthemagnitudesoftheenergysourceandtheelementsinthecircuit.Ifnot,eithersolvethenetworkusinganotherapproach,orcheckoveryourworkverycarefully.Atthispointacomputersolutioncanbeaninvaluableassetinthevalidationprocess.35IntroductionWhenyouhavearri16.2–IllustrativeExamplesExample16.1CalculateZT.DetermineIS.CalculateVRandVc.FindIC.Computerthepowerdelivered.FindFpofthenetwork.3616.2–IllustrativeExamplesExExamplesolution37Examplesolution8Examplecontinued38Examplecontinued9ExampleContinued39ExampleContinued10IllustrativeExamplesExample16.2SolutionRedrawthecircuitUsethecurrentdividerrule,determineI,I1andI240IllustrativeExamplesExample1Example16.2solution41Example16.2solution12IllustrativeExamplesExample16.4SolutionRedrawthecircuitUsethecurrentdividerrule,determineI1andI2andVab42IllustrativeExamplesExample1Solutiontoexample16.443Solutiontoexample16.414IllustrativeExamplesTofindVab,Kirchhoff’svoltagelawmustbeappliedaroundtheloop.44IllustrativeExamplesToSolutionto16.4continued45Solutionto16.4continued1616.3–LadderNetworksHerewewillcalculatethetotalresistanceandresultingsourcecurrent,andthenworkbackthroughtheladderuntilthedesiredcurrent,I6,(orvoltage)isobtained.4616.3–LadderNetworksHereweLadderNetworksImpedanceZT,ZT'andZT''andthecurrentsI1andI3aredefined:47LadderNetworksImpedanceZT4819Series-ParallelCircuitsBoylestad,p719Fig16.14ComputeIFindI1,I2andI3VerifyKirchhoff’scurrentlawbyshowingthatI=I1+I2+I349Series-ParallelCircuitsBoylesSolutionto16.1450Solutionto16.1421Solutioncontinued51Solutioncontinued22AwordaboutnodalandmeshanalysisSameasDC,butneedtodoitwillallthephasesinAC,otherwisethesameLetsdoaNodalanalysisexample52Awordaboutnodalandmeshan5324Solutioncontinued54Solutioncontinued25Solutioncontinued55Solutioncontinued2616.5–ApplicationsGFCI(GroundFaultCircuitInterrupter)GFCIoutletsaretobeusedinareaswherewateranddampnesscouldresultinseriousinjury,suchasbathrooms,kitchens,pools,outdoo

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