Pecht,M.,Lall,P.,Ballou,G.,Sankaran,C.,Angelopoulos,N.“PassiveComponents”TheElectricalEngineeringHandbookEd.RichardC.DorfBocaRaton:CRCPressLLC,2000www.power-bbs.comwww.dianyuanbbs.com://www.dianyuanbbs.com©2000byCRCPressLLC1PassiveComponents1.1ResistorsResistorCharacteristics•ResistorTypes1.2CapacitorsandInductorsCapacitors•TypesofCapacitors•Inductors1.3TransformersTypesofTransformers•PrincipleofTransformation•ElectromagneticEquation•TransformerCore•TransformerLosses•TransformerConnections•TransformerImpedance1.4ElectricalFusesRatings•FusePerformance•SelectiveCoordination•Standards•Products•Standard—ClassH•HRC•Trends1.1ResistorsMichaelPechtandPradeepLallTheresistorisanelectricaldevicewhoseprimaryfunctionistointroduceresistancetotheflowofelectriccurrent.Themagnitudeofoppositiontotheflowofcurrentiscalledtheresistanceoftheresistor.Alargerresistancevalueindicatesagreateroppositiontocurrentflow.Theresistanceismeasuredinohms.Anohmistheresistancethatariseswhenacurrentofoneampereispassedthrougharesistorsubjectedtoonevoltacrossitsterminals.Thevarioususesofresistorsincludesettingbiases,controllinggain,fixingtimeconstants,matchingandloadingcircuits,voltagedivision,andheatgeneration.Thefollowingsectionsdiscussresistorcharacteristicsandvariousresistortypes.ResistorCharacteristicsVoltageandCurrentCharacteristicsofResistorsTheresistanceofaresistorisdirectlyproportionaltotheresistivityofthematerialandthelengthoftheresistorandinverselyproportionaltothecross-sectionalareaperpendiculartothedirectionofcurrentflow.TheresistanceRofaresistorisgivenby(1.1)whereristheresistivityoftheresistormaterial(W·cm),listhelengthoftheresistoralongdirectionofcurrentflow(cm),andAisthecross-sectionalareaperpendiculartocurrentflow(cm2)(Fig.1.1).Resistivityisaninherentpropertyofmaterials.Goodresistormaterialstypicallyhaveresistivitiesbetween2´10–6and200´10–6W·cm.RlA=rMichaelPechtUniversityofMarylandPradeepLallMotorolaGlenBallouBallouAssociatesC.SankaranElectro-TestNickAngelopoulosGouldShawmutCompanywww.power-bbs.comwww.dianyuanbbs.com://www.dianyuanbbs.com©2000byCRCPressLLCTheresistancecanalsobedefinedintermsofsheetresistivity.Ifthesheetresistivityisused,astandardsheetthicknessisassumedandfactoredintoresistivity.Typically,resistorsarerectangularinshape;thereforethelengthldividedbythewidthwgivesthenumberofsquareswithintheresistor(Fig.1.2).Thenumberofsquaresmultipliedbytheresistivityistheresistance.(1.2)wherersheetisthesheetresistivity(W/square),listhelengthofresistor(cm),wisthewidthoftheresistor(cm),andRsheetisthesheetresistance(W).TheresistanceofaresistorcanbedefinedintermsofthevoltagedropacrosstheresistorandcurrentthroughtheresistorrelatedbyOhm’slaw,(1.3)whereRistheresistance(W),Visthevoltageacrosstheresistor(V),andIisthecurrentthroughtheresistor(A).Wheneveracurrentispassedthrougharesistor,avoltageisdroppedacrosstheendsoftheresistor.Figure1.3depictsthesymboloftheresistorwiththeOhm’slawrelation.Allresistorsdissipatepowerwhenavoltageisapplied.Thepowerdissipatedbytheresistorisrepresentedby(1.4)wherePisthepowerdissipated(W),Visthevoltageacrosstheresistor(V),andRistheresistance(W).Anidealresistordissipateselectricenergywithoutstoringelectricormagneticenergy.ResistorNetworksResistorsmaybejoinedtoformnetworks.Ifresistorsarejoinedinseries,theeffectiveresistance(RT)isthesumoftheindividualresistances(Fig.1.4).(1.5)FIGURE1.1Resistanceofarectangularcross-sectionresistorwithcross-sectionalareaAandlengthL.Rlwsheetsheet=rRVI=PVR=2RRTiin==å1FIGURE1.2Numberofsquaresinarectangularresistor.FIGURE1.3AresistorwithresistanceRhavingacurrentIflowingthroughitwillhaveavoltagedropofIRacrossit.www.power-bbs.comwww.dianyuanbbs.com://www.dianyuanbbs.com©2000byCRCPressLLCIfresistorsarejoinedinparallel,theeffectiveresistance(RT)isthereciprocalofthesumofthereciprocalsofindividualresistances(Fig.1.5).(1.6)TemperatureCoefficientofElectricalResistanceTheresistanceformostresistorschangeswithtemperature.Thetem-peraturecoefficientofelectricalresistanceisthechangeinelectricalresistanceofaresistorperunitchangeintemperature.Thetempera-turecoefficientofresistanceismeasuredinW/°C.Thetemperaturecoefficientofresistorsmaybeeitherpositiveornegative.Apositivetemperaturecoefficientdenotesariseinresistancewithariseintem-perature;anegativetemperaturecoefficientofresistancedenotesadecreaseinresistancewithariseintemperature.Puremetalstypicallyhaveapositivetemperaturecoefficientofresistance,whilesomemetalalloyssuchasconstantinandmanganinhaveazerotemperaturecoef-ficientofresistance.Carbonandgraphitemixedwithbindersusuallyexhibitnegativetemperaturecoefficients,althoughcertainchoicesofbindersandprocessvariationsmayyieldpositivetemperaturecoeffi-cients.ThetemperaturecoefficientofresistanceisgivenbyR(T2)=R(T1)[1+aT1(T2–T1)](1.7)whereaT1isthetemperaturecoefficientofelectricalresistanceatreferencetemperatureT1,R(T2)istheresistanceattemperatureT2(W),andR(T1)istheresistanceattemperatureT1(W).Thereferencetemperatureisusuallytakentobe20°C.Becausetheva