正弦交流電路的基本概念課件講解

BasicConceptsofSinusoidalAlternatingCircuit正弦交流電路的基本概念正弦交流信號在工程中應(yīng)用非常廣泛。SinusoidalACsignalsfindwidespreadapplicationsinengineering.圖中所示是幾種產(chǎn)生正弦交流信號的方法。ThefollowingdiagramillustratesseveralmethodsforgeneratingsinusoidalACsignals.Fig.1正弦交流電的產(chǎn)生Generationofsinusoidalalternatingcurrent1.什么是正弦交流電WhatisSinusoidalAlternatingCurrent(AC)?其中，圖(a)為交流發(fā)電機；(b)為風(fēng)力發(fā)電機；(c)為太陽能發(fā)電裝置；(d)為函數(shù)發(fā)生器，它可以產(chǎn)生多種頻率的正弦信號。Amongthem,(a)depictsanACgenerator;(b)representsawindturbinegenerator;(c)showsasolarpowergenerationdevice;and(d)displaysafunctiongeneratorcapableofproducingsinusoidalsignalsatvariousfrequencies.大小和方向隨時間按正弦函數(shù)規(guī)律變化的電流或電壓稱為正弦交流電流或正弦交流電壓，統(tǒng)稱正弦交流電。Acurrentorvoltagethatvarieswithtimeaccordingtothesinusoidalfunctionintermsofmagnitudeanddirectionisreferredtoassinusoidalalternatingcurrent(AC)orsinusoidalalternatingvoltage,collectivelyknownassinusoidalAC.正弦交流電流波形圖ThesinusoidalACcurrentwaveform1.什么是正弦交流電WhatisSinusoidalAlternatingCurrent(AC)?如圖所示的正弦交流電流為ThesinusoidalACcurrentwaveformshownintheleftdiagramisi＝Imsin(ωt+φi)1.瞬時值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue確定一個正弦量必須具備三個要素：最大值Im、角頻率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).(1)瞬時值Instantaneousvalue正弦交流電流不同的時刻有不同的大小，任一時刻t所對應(yīng)的電流值叫瞬時值，用i表示。Thesinusoidalalternatingcurrenthasdifferentmagnitudesatdifferentmoments,andthevalueofthesinusoidalACcurrentatanygivenmomenttiscalledtheinstantaneousvalue,denotedasi.正弦交流電流波形圖ThesinusoidalACcurrentwaveform2.正弦量的三要素ThreeElementsofSinusoidalQuantity1.瞬時值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue確定一個正弦量必須具備三個要素：最大值Im、角頻率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).(2)最大值PeakValue最大的瞬時值稱最大值，也稱振幅或峰值，用Im表示。最大值反映了正弦量變化的范圍。Thelargestinstantaneousvalueiscalledthepeakvalue,amplitude,orpeakvalue,representedbyIm.Thepeakvaluereflectstherangeofvariationofthesinusoidalquantity.正弦交流電流波形圖ThesinusoidalACcurrentwaveform2.正弦量的三要素ThreeElementsofSinusoidalQuantity1.瞬時值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue確定一個正弦量必須具備三個要素：最大值Im、角頻率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).(3)有效值EffectiveValue交流電有效值是根據(jù)電流的熱效應(yīng)來定義的。如果交流電流i通過電阻R在一個周期T內(nèi)所消耗的電能，與直流電流I通過同一電阻在同一周期內(nèi)所消耗的電能相等，則這個直流電流I的數(shù)值稱為交流電流的有效值，用I表示。TheeffectivevalueofanACcurrentisdefinedbasedonitsthermaleffects.IftheelectricalenergyconsumedbyACcurrentipassingthrougharesistorRinoneperiodTisequaltotheelectricalenergyconsumedbyaDCcurrentIpassingthroughthesameresistorinthesameperiod,thenthenumericalvalueofthisDCcurrentIiscalledtheeffectivevalueoftheACcurrent,denotedasI.正弦交流電流波形圖ThesinusoidalACcurrentwaveform2.正弦量的三要素ThreeElementsofSinusoidalQuantity1.瞬時值、最大值和有效值InstantaneousValue,PeakValue,andEffectiveValue確定一個正弦量必須具備三個要素：最大值Im、角頻率ω和初相位φ。Todetermineasinusoidalquantity,threeelementsmustbeconsidered:thepeakvalue(Im),angularfrequency(ω),andinitialphaseangle(φ).理論與實驗都可證明，有效值與最大值的關(guān)系為Therelationshipbetweeneffectivevalueandpeakvalueistheoreticallyandexperimentallyproventobe2.正弦量的三要素ThreeElementsofSinusoidalQuantityI=—=0.707Im

ImU=—=0.707Um

Um

工程上所說的交流電壓、交流電流的大小，均是指有效值。如電燈電壓220V，交流用電設(shè)備銘牌上所標(biāo)的電壓和電流，儀表測量的交流電壓和交流電流都是指有效值。Inengineering,ACvoltageandcurrentmagnitudesrefertoeffectivevalues.Forexample,thevoltageofalightbulbis220V,andthevoltageandcurrentmarkedonthenameplateofAC-powereddevices,aswellasthosemeasuredbyinstruments,allrefertoeffectivevalues.2.周期、頻率和角頻率Period,Frequency,andAngularFrequency(1)周期正弦量變化一個循環(huán)所需的時間稱為周期，用T表示，單位為s（秒）。Period:Thetimerequiredforonecycleofvariationofasinusoidalquantityiscalledtheperiod,denotedasT,withtheunitofseconds(s).f＝—1T2.正弦量的三要素ThreeElementsofSinusoidalQuantity(2)頻率正弦量每秒時間內(nèi)完成循環(huán)變化的次數(shù)稱為頻率，用f表示，單位為Hz（赫[茲]）。Frequency:Thenumberofcyclescompletedbyasinusoidalquantityinonesecondiscalledthefrequency,denotedasf,withtheunitofhertz(Hz).周期與頻率的關(guān)系為Therelationshipbetweenperiodandfrequencyisgivenby2.周期、頻率和角頻率Period,Frequency,andAngularFrequency2.正弦量的三要素ThreeElementsofSinusoidalQuantity(3)角頻率正弦量變化一周經(jīng)歷了2π弧度,如果正弦量每秒內(nèi)變化f周,則經(jīng)歷了2πf弧度。正弦量在每秒內(nèi)經(jīng)歷的弧度數(shù)稱為角頻率，用ω表示，單位為rad/s（每秒弧度）。AngularFrequency:Asinusoidalquantityundergoesacompletecyclecovering2πradians.Ifthesinusoidalquantityundergoesfcyclespersecond,itcovers2πfradianspersecond.Theradianscoveredbyasinusoidalquantitypersecondistermedangularfrequency,denotedasω,withtheunitofradianspersecond(rad/s).角頻率、頻率與周期的關(guān)系為Therelationshipbetweenangularfrequency,frequency,andperiodisgivenbyω=2πf=——2πT(1)相位Phase只有當(dāng)（ωt+φi）這個角度一定時，才給出正弦量在某一瞬間的狀態(tài)，這個角度稱為正弦量的相位角，簡稱相位，單位為rad（弧度），有時也用角度。Thestateofasinusoidalquantityataspecificinstantisonlydefinedwhentheangle(ωt+φi)iscertain.Thisangleiscalledthephaseangle,simplyreferredtoasphase,withtheunitofradiansandsometimesdegrees.相位不僅確定正弦量瞬時值的大小、方向，而且反映出正弦量變化的進程。Thephasenotonlydeterminesthemagnitudeanddirectionoftheinstantaneousvalueofthesinusoidalquantitybutalsoreflectstheprogressionofitsvariation.正弦交流電流SinusoidalACcurrentisexpressedasi＝Imsin(ωt+φi)3.相位、初相與相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantity(2)初相InitialPhase在計時起點t＝0時，相位ωt+φ=φ，即φ是正弦量的起始相位，稱為初相位，簡稱初相。Atthestartingtimet=0,thephaseωt+φ=φ,whereφistheinitialphaseofthesinusoidalquantityandistermedtheinitialphase,simplyreferredtoastheinitialphase.初相確定了正弦量在t＝0時的初始值。Theinitialphasedeterminestheinitialvalueofthesinusoidalquantityatt＝0.正弦交流電流SinusoidalACcurrentisexpressedasi＝Imsin(ωt+φi)3.相位、初相與相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantity(3)相位差PhaseDifference在同一個正弦交流電路中，電壓u與電流i的頻率是相同的，但初相不一定相同。InthesamesinusoidalACcircuit,thevoltageuandthecurrentisharethesamefrequencybutmaynothavethesameinitialphase.正弦交流電流SinusoidalACcurrentisexpressedasi＝Imsin(ωt+φi)3.相位、初相與相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantity設(shè)電壓u和電流i分別為Letthevoltageuandcurrentibe3.相位、初相與相位差Phase,InitialPhase,andPhaseDifference2.正弦量的三要素ThreeElementsofSinusoidalQuantityφui=(ωt+φu)–(ωt