正弦交流电路的基本概念课件讲解

BasicConceptsofSinusoidalAlternatingCircuit正弦交流电路的基本概念正弦交流信号在工程中应用非常广泛。SinusoidalACsignalsfindwidespreadapplicationsinengineering.图中所示是几种产生正弦交流信号的方法。ThefollowingdiagramillustratesseveralmethodsforgeneratingsinusoidalACsignals.Fig.1正弦交流电的产生Generationofsinusoidalalternatingcurrent1.什么是正弦交流电WhatisSinusoidalAlternatingCurrent(AC)?其中，图(a)为交流发电机；(b)为风力发电机；(c)为太阳能发电装置；(d)为函数发生器，它可以产生多种频率的正弦信号。Amongthem,(a)depictsanACgenerator;(b)representsawindturbinegenerator;(c)showsasolarpowergenerationdevice;and(d)displaysafunctiongeneratorcapableofproducingsinusoidalsignalsatvariousfrequencies.大小和方向随时间按正弦函数规律变化的电流或电压称为正弦交流电流或正弦交流电压，统称正弦交流电。Acurrentorvoltagethatvarieswithtimeaccordingtothesinusoidalfunctionintermsofmagnitudeanddirectionisreferredtoassinusoidalalternatingcurrent(AC)orsinusoidalalternatingvoltage,collectivelyknownassinusoidalAC.正弦交流电流波形图ThesinusoidalACcurrentwaveform1.什么是正弦交流电WhatisSinusoidalAlternatingCurrent(AC)?如图所示的正弦交流电流为ThesinusoidalACcurrentwaveformshownintheleftdiagramisi＝Imsin(ωt+φi)1.瞬时值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue确定一个正弦量必须具备三个要素：最大值Im、角频率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).(1)瞬时值Instantaneousvalue正弦交流电流不同的时刻有不同的大小，任一时刻t所对应的电流值叫瞬时值，用i表示。Thesinusoidalalternatingcurrenthasdifferentmagnitudesatdifferentmoments,andthevalueofthesinusoidalACcurrentatanygivenmomenttiscalledtheinstantaneousvalue,denotedasi.正弦交流电流波形图ThesinusoidalACcurrentwaveform2.正弦量的三要素ThreeElementsofSinusoidalQuantity1.瞬时值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue确定一个正弦量必须具备三个要素：最大值Im、角频率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).(2)最大值PeakValue最大的瞬时值称最大值，也称振幅或峰值，用Im表示。最大值反映了正弦量变化的范围。Thelargestinstantaneousvalueiscalledthepeakvalue,amplitude,orpeakvalue,representedbyIm.Thepeakvaluereflectstherangeofvariationofthesinusoidalquantity.正弦交流电流波形图ThesinusoidalACcurrentwaveform2.正弦量的三要素ThreeElementsofSinusoidalQuantity1.瞬时值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue确定一个正弦量必须具备三个要素：最大值Im、角频率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).(3)有效值EffectiveValue交流电有效值是根据电流的热效应来定义的。如果交流电流i通过电阻R在一个周期T内所消耗的电能，与直流电流I通过同一电阻在同一周期内所消耗的电能相等，则这个直流电流I的数值称为交流电流的有效值，用I表示。TheeffectivevalueofanACcurrentisdefinedbasedonitsthermaleffects.IftheelectricalenergyconsumedbyACcurrentipassingthrougharesistorRinoneperiodTisequaltotheelectricalenergyconsumedbyaDCcurrentIpassingthroughthesameresistorinthesameperiod,thenthenumericalvalueofthisDCcurrentIiscalledtheeffectivevalueoftheACcurrent,denotedasI.正弦交流电流波形图ThesinusoidalACcurrentwaveform2.正弦量的三要素ThreeElementsofSinusoidalQuantity1.瞬时值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue确定一个正弦量必须具备三个要素：最大值Im、角频率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).理论与实验都可证明，有效值与最大值的关系为Therelationshipbetweeneffectivevalueandpeakvalueistheoreticallyandexperimentallyproventobe2.正弦量的三要素ThreeElementsofSinusoidalQuantityI=—=0.707Im

ImU=—=0.707Um

Um

工程上所说的交流电压、交流电流的大小，均是指有效值。如电灯电压220V，交流用电设备铭牌上所标的电压和电流，仪表测量的交流电压和交流电流都是指有效值。Inengineering,ACvoltageandcurrentmagnitudesrefertoeffectivevalues.Forexample,thevoltageofalightbulbis220V,andthevoltageandcurrentmarkedonthenameplateofAC-powereddevices,aswellasthosemeasuredbyinstruments,allrefertoeffectivevalues.2.周期、频率和角频率Period,Frequency,andAngularFrequency(1)周期正弦量变化一个循环所需的时间称为周期，用T表示，单位为s（秒）。Period:Thetimerequiredforonecycleofvariationofasinusoidalquantityiscalledtheperiod,denotedasT,withtheunitofseconds(s).f＝—1T2.正弦量的三要素ThreeElementsofSinusoidalQuantity(2)频率正弦量每秒时间内完成循环变化的次数称为频率，用f表示，单位为Hz（赫[兹]）。Frequency:Thenumberofcyclescompletedbyasinusoidalquantityinonesecondiscalledthefrequency,denotedasf,withtheunitofhertz(Hz).周期与频率的关系为Therelationshipbetweenperiodandfrequencyisgivenby2.周期、频率和角频率Period,Frequency,andAngularFrequency2.正弦量的三要素ThreeElementsofSinusoidalQuantity(3)角频率正弦量变化一周经历了2π弧度,如果正弦量每秒内变化f周,则经历了2πf弧度。正弦量在每秒内经历的弧度数称为角频率，用ω表示，单位为rad/s（每秒弧度）。AngularFrequency:Asinusoidalquantityundergoesacompletecyclecovering2πradians.Ifthesinusoidalquantityundergoesfcyclespersecond,itcovers2πfradianspersecond.Theradianscoveredbyasinusoidalquantitypersecondistermedangularfrequency,denotedasω,withtheunitofradianspersecond(rad/s).角频率、频率与周期的关系为Therelationshipbetweenangularfrequency,frequency,andperiodisgivenbyω=2πf=——2πT(1)相位Phase只有当（ωt+φi）这个角度一定时，才给出正弦量在某一瞬间的状态，这个角度称为正弦量的相位角，简称相位，单位为rad（弧度），有时也用角度。Thestateofasinusoidalquantityataspecificinstantisonlydefinedwhentheangle(ωt+φi)iscertain.Thisangleiscalledthephaseangle,simplyreferredtoasphase,withtheunitofradiansandsometimesdegrees.相位不仅确定正弦量瞬时值的大小、方向，而且反映出正弦量变化的进程。Thephasenotonlydeterminesthemagnitudeanddirectionoftheinstantaneousvalueofthesinusoidalquantitybutalsoreflectstheprogressionofitsvariation.正弦交流电流SinusoidalACcurrentisexpressedasi＝Imsin(ωt+φi)3.相位、初相与相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantity(2)初相InitialPhase在计时起点t＝0时，相位ωt+φ=φ，即φ是正弦量的起始相位，称为初相位，简称初相。Atthestartingtimet=0,thephaseωt+φ=φ,whereφistheinitialphaseofthesinusoidalquantityandistermedtheinitialphase,simplyreferredtoastheinitialphase.初相确定了正弦量在t＝0时的初始值。Theinitialphasedeterminestheinitialvalueofthesinusoidalquantityatt＝0.正弦交流电流SinusoidalACcurrentisexpressedasi＝Imsin(ωt+φi)3.相位、初相与相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantity(3)相位差PhaseDifference在同一个正弦交流电路中，电压u与电流i的频率是相同的，但初相不一定相同。InthesamesinusoidalACcircuit,thevoltageuandthecurrentisharethesamefrequencybutmaynothavethesameinitialphase.正弦交流电流SinusoidalACcurrentisexpressedasi＝Imsin(ωt+φi)3.相位、初相与相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantity设电压u和电流i分别为Letthevoltageuandcurrentibe3.相位、初相与相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantityφui=(ωt+φu)–(ωt