电路基础英文版Chapter-9--Sinusoids-and-Phasors-(new)

Chapter9SinusoidsandPhasors要求深刻理解与熟练掌握的重点内容有：1．正弦量，相量法的基础，有效值和相位差的2．电路定律的相量形式。34．电路的相量图表示法，参考正弦量的概念，会用相量图法分析串联电路、并联电路。难点：相量图表示•9-1Introduction•9-2Sinusoids•9-3Phasors•9-4PhasorRelationshipsforCircuitElements•9-5ImpedanceandAdmittance•9-6Kirchhoff’sLawsintheFrequencyDomain•9-7ImpedanceCombinations•9-10SummaryandReview9.1Introduction1.Terms2.Introductionofthischaptersinusoidalvariation正弦振动ripple波动economicfluctuation经济波动derivative导数1.TermsFourieranalysis傅立叶分析periodicsignal周期信号impedance阻抗admittance导纳trigonometricidentity三角恒等式thehorizontalaxis横轴theverticalaxis纵轴polarcoordinate极坐标vector向量complexplane复平面imaginarypart虚部conjugate共轭velocity速度thetimedomain时域thephasordomain频域reactance电抗susceptance电纳Asinusoidissignalthathastheformofthesineorcosinefunction.2.IntroductionCircuitsdrivenbysinusoidalcurrentorvoltagesourcesarecalledac(alternatingcurrent)circuits.Weareinterestedinsinusoidsforanumberofreasons.First,natureitselfischaracteristicallysinusoidal.Second,asinusoidalsignaliseasytogenerateandtransmit.Third,throughFourieranalysis,anypracticalperiodicsignalcanberepresentedbyasumofsinusoids.Lastly,asinusoidiseasytohandlemathematically.1.CharacteristicsofSinusoids2.TheSineWave9.2Sinusoids3.Sinusoidswithdifferentphases4.Averageandeffectivevalue1、CharacteristicsofSinusoids()sin()ftAttf(t)01、CharacteristicsofSinusoids()sin()ftAttf(t)01、CharacteristicsofSinusoids()sin()ftAttf(t)0Aamplitude1、CharacteristicsofSinusoids()sin()ftAttf(t)0ATperiod1、CharacteristicsofSinusoids()sin()ftAttf(t)0ATwhere：A=theamplitudeofthesinusoid(ormaximumvalue)；振幅，最大值=theangularfrequencyinradians/s；角频率=phase；初相t+=theargumentofthesinusoid；幅角()sin()ftAt2、TheSineWaveT：theperiodofthesinusoidf：frequencyHeinrichRudorfHertz(1857-1894)：赫兹12,2ffTT工频：f=50Hz，=2f=314rad/sWhileisinradianspersecond(rad/s),fisinhertz(Hz)3、Sinusoidswithdifferentphasessin(),sin()mumiuUtiIt()()uiuittLeading,laggingandinphase.Thereference：u=Umsin(t),theni=Imsin(t-)Thereference：i=Imsin(t),thenu=Umsin(t+)ψ=0inphase同相π/2orthogonalintersection正交πinphaseopposition反相u,i0ωtu,i0ωtωtu,i04.AverageandeffectivevalueTheaveragecurrentistheaverageoftheinstantaneouscurrentoveroneperiod.01()dTavIittT01()dTavUuttTa.AverageValue平均值Theeffectivevalueofaperiodiccurrentisthedccurrentthatdeliversthesameaveragepowertoaresistorastheperiodiccurrent.202:d:TacWRitdcWRIT201dTIitTrms：root-mean-square,thesquarerootofthemean(oraverage)b.EffectiveValue有效值方均根220011ddTTWPRititRTTT201dTUutTc.EffectiveValueofSinusoidsin()miIt2022222001d11cos2()sin()dd22TTTmmmIitTIItIItttTT,22mmIUIU2sin()iIt1.ComplexNumber2.PhasorIdea9.3phasors3.PhasorDiagramRectangularform：z=x+jy，x=Re(z)，y=Im(z)1、ComplexNumber复数phasors相量Aphasorisacomplexnumberthatrepresentstheamplitudeandphaseofasinusoid.Acomplexnumberzcanbewritteninrectangularformasz=x+jyWhere1jxistherealpartofz;yistheimaginarypartofz.cossinAAjAmagnitude：phase：22Aab1btgaExponentialform：,cossinjjAAeejPolarform：AAIfA=a+jb，a=Re(A)，b=Im(A)A1±A2=(a1+a2)±j(b1±b2)1211221212()AAAAAAAdditionandsubtraction:Multiplication:A1A2=(a1+jb1)(a2+jb2)=(a1a2－b1b2)+j(a1b2+a2b1)θ1θ2A1A2θ2+θ1Reciprocal:AA11Squareroot:2AAComplexconjugate:jeAAjbaA1111122222()AAAAAADivision:2、PhasorIdeaItisacomplexnumbercontainingtheamplitudeandphaseofthesinusoid.)cos(2tUuUU)cos(2]2Re[)2Re(tUtUeUutjPhasor-domainrepresentationTime-domainrepresentationThedifferencesbetweenu(t)andU1．u(t)istheinstantaneousortime-domainrepresentation,whileisthefrequencyorphasor-domainrepresentation.U2．u(t)istimedependent,whileisnot.U3．u(t)isalwaysrealwhileisgenerallycomplex.URotatingpointinthecomplexplaneReu(t)tatt=t0t00Imatt=0Rotationatrad/sOPjte振幅相量旋转因子tjmtjmtjmmeUeUeUtU)()()(mmUU)cos()cos(2tUtUumThederivativeofi(t)istransformedtothephasordomainIjdtdi)cos(2itIitjtjtjeIjeIdtdeIdtddtdi)(2Re)2(Re)2Re(Theintegralofi(t)istransformedtothepasordomainjIidt)cos(2itIitjtjtjejIdteIdteIidt)(2Re2Re)2Re(3、PhasorDiagramxy+zrzxjyrExample：Findu。Solution：u=u1+u200210309040UUUVjj000001.53500sin300cos3090sin4090cos40u1+u_u2tVuVtu314sin230,)90314sin(240201Vtu)1.53314sin(2500.U153.1.U2.UPhasordiagram:12102sin(230)52sin(230),1002cos(245)itAitAutV，Todrawaphasordiagram.Solution：.I2.U.I1+Example：AI013010AI00000021505305180130501305Vttu)1352sin(2100)452cos(210000VU0135100Usingthephasorapproach,determinethecurrenti(t)inacircuitdescribedbytheintegrodifferentialequation)752cos(503840tdtdiidtiExample：Solution：Weobtainthephasorformofthegivenequationas07550384mmmIjjIIButω=2rad/s,so07550)644(jjImAjIm00002.143642.42.6877.1075501047550ConvertingthistothetimedomainAtti)2.1432cos(642.4)(01.Resistors2.Inductors9.4Phasorrelationshipsforcircuitelements3.Capacitors)cos(2)(tIti1.Resistors(a)Ohm’sLawi+u－ROhm’slawinthe