第一章电磁兼容的基础知识

第一章电磁兼容的基础知识Chapter1BasicConceptsforEMC徐征重庆大学重庆大学[e-mail]2010年9月gq电磁兼容的基础知识电磁兼容的基础知识§1.1电尺寸与波1.1ElectricalDimensionsandWaves§1.2分贝与常用的EMC单位1.2DecibelsandCommonUnits§1.3周期信号的频谱§1.4数字信号的频谱分析1.3Thespectrumofperiodicsignals§1.4数字信号的频谱分析1.4Spectrumanalysisfordigitalsignals§1.5电网络理论1.5CircuitNetworkTheory§1.1电尺寸与波§1.1电尺寸与波ElectricalDimensions电尺寸：zl=ElectricalDimensions电尺寸：被观测物的物理尺寸相对于所研究频率电磁波的波长的比值。lλ=cfλ=真空或空气中电磁波波长与其频率的关系：f506000fHzkmλ==例：3G手机天线的电尺寸实际尺寸10左右f3001fMHzmλ==实际尺寸：10cm左右电尺寸：0.7倍波长2.114fGHzcmλ==激励源在天线两端的相位差为：0.7*360°=252°激励源在天线两端的相位差为：0.7360252为什么引入电尺寸？事物是相对的为什么引入电尺寸？事物是相对的在分析辐射结构辐射电磁能量的能力时其物理尺寸不重要重要的是电尺寸！在分析辐射结构辐射电磁能量的能力时，其物理尺寸不重要，重要的是电尺寸！Electricallysmall/lλElectricallylarge/lλ电小尺寸：/10lλ电大尺寸：/10lλ电小尺寸系统分析方电大尺寸系统分析方法:电路的方法，采用元件的集总参数模型法:电磁场的方法，采用Maxwell方程组进行分件的集总参数模型方程进行分析EASYCOMPLEX分析具体问题的电尺寸大小，确定不同的分析方法!电尺寸习题电尺寸习题§1.2分贝与常用的EMC单位§1.2分贝与常用的EMC单位分贝是一种相对的单位DECIBELSisaunitusedtoexpressrelativedifferenceinpoweroritit分贝具有数据压缩的作用:intensity810100000000160dB=⇒其他分贝单位其他分贝单位dBVμdBVμDecibelsaretheratiooftwoquantities.Voltagesarecommonlyexpressedrelativeto1uVasdBuV:Voltagesarecommonlyexpressedrelativeto1uVasdBuV:Example:其他分贝单位：习题其他分贝单位：习题§1.3周期信号的频谱Analysisforperiodicsignal§周期信号的频谱ypgSpectrumanalysisSpectrumanalysisdeterministicsignal•Periodicsignal周期信号•Sin/cos•Complexdeterministicsignal确定性信号周期信号•Aperiodicsignal非周期信号•TransientsignalComplex•Quasicperiodic非周期信号•Quasic-periodicstochasticsignal随机信号•stationaryrandomprocess•nonstationaryrandomprocess随机信号•nonstationaryrandomprocessTimedomainandFrequencydomainFourierTransformFourierTransform周期信号的复指数展开形式ThliliffidiilThecomplex-exponentialexpansionformofperiodicsignal周期信号的傅里叶级数展开的复数形式：周期信号的傅里叶级数展开的复数形式：0()jntxtceω∞=∑Positive-valuedharmonicfrequencies00002221012()nnjtjtjtjtxtcecececceceωωωω=−∞−−−−=++++++∑qNegative-valuedharmonicfrequenciesgq1011()tTjntntcxtedtTω+−=∫1101()tTtcxtdtT+=∫复级数的展开系数ExpansioncoefficientofcomplexFourierSeries101()tTjntcxtedtω+−∫101()tTjntcxtedtcω+∗∫01()jntcxtedtT=∫01()jnntcxtedtcT−==∫candcarecomplexnumbersandtheyaretheconjugatesofc-nandcnarecomplexnumbers,andtheyaretheconjugatesofeachother.jc∠∠jc∠∗njcnnnncccce∠=∠=njcnnnccce−∠∗−==00()jntjntxtcceceωω∞−∞=++∑∑011()nnnnxtccece==−=++∑∑000()jntjntxtcceceωω∞∞−∗=++∑∑011()nnnnxtccece==++∑∑00()()0()nnjntcjntcxtcceceωω∞∞+∠−+∠=++∑∑011()nnnnxtccece==++∑∑复级数与三角函数级数的关系Relationshipbetweencomplexseriesandtrigonometricseries()()jtjt∞∞+∠+∠∑∑00()()011()nnjntcjntcnnnnxtcceceωω+∠−+∠===++∑∑()()jtjt∞+∠+∠∑θθ00()()01()nnjntcjntcnncceeωω+∠−+∠==++∑∞∑cos2jjeeθθθ−+=0012cos()nnnccntcω==++∠∑sin2jjeejθθθ−−=000()jntjntnnxtcceceωω∞−∞=++∑∑()2()tt∞∠∑011()nnnn==−∑∑001()2cos()nnnxtccntcω==++∠∑复级数与三角函数级数的关系RelationshipbetweencomplexseriesandtrigonometricseriesAperiodic“squarewave”pulsetrainTwo-sidedmagnitudespectrumOne-sidedmagnitudespectrum傅里叶级数的重要特性ImportantcharacteristicsofFourierSeries1线性特性Linearity1.线性特性Linearity12()()()xtxtxt=+011()jntnxtceω∞=∑n=−∞022()jntnxtceω∞=∑n=−∞00()jntjntxtceceωω∞∞=+∑∑0012()()nnnnjntjntxtcececceceωω=−∞=−∞∞∞=++∑∑∑∑0012()jjnnnnnccece=−∞=−∞=+=∑∑ImportantcharacteristicsofFourierSeriesImportantcharacteristicsofFourierSeries2时移特性Timeshifting2.时移特性Time-shifting()jtjjt∞∞∑∑000()()jntjnjntnnnnxtceeceωτωτωτ−−=−∞=−∞−==∑∑∞0()jntnnxtceω∞=−∞=∑Multiplytheexpansioncoefficientsofx(t)by,wecanbtithiffiitf0jneωτ−()tobtaintheexpansioncoefficientsof()xtτ−ImportantcharacteristicsofFourierSeriesImportantcharacteristicsofFourierSeries3单位冲击函数3.单位冲击函数UnitImpulseFunction(UIF)周期性时延冲击函数的展开周期性时延冲击函数的展开ExpansionofPeriodictime-delayUIF傅里叶级数的重要特性傅里叶级数的重要特性4微分特性Derivatives4.微分特性Derivatives0()jnttω∞∑0()jntnnxtceω=−∞=∑()kjkdxt∞∑00()()(0)jntknkndxtjncendtωω=−∞∞=≠∑0()jntknnceω=−∞=∑()01()knnkccjnω=TwoQuestionsTwoQuestionsWHYweexpressaperiodicWHYweexpressaperiodicfunctionintheformofFourierseries?HOWcanweanalyzeacomplexperiodicfunction?复杂波形的傅里叶展开复杂波形的傅里叶展开例一：例ThditifUitStFtiiUitIlFtiThederivativeofthewaveformisshownasfollow:ThederivativeofUnitStepFunctionisUnitImpulseFunctionExample1：Expansionofasquarewavepulsetrainppqp()1kccDerivativecharacteristic:()0()nnkccjnω=ijjeeθθθ−−sin2eejθ=Example1：Expansionofasquarewavepulsetrainppqp0()jnttω∞∑0()jntnnxtceω=−∞=∑SincFunctionWaveplotofSincFunctionMagnitudespectrumMagnitudespectrumExample1：ExpansionofasquarewavepulsetrainppqpIllustrationofthedecompositionofasquarewaveintoitsfrequencycomponentsIllustrationofthedecompositionofasquarewaveintoitsfrequencycomponents复杂波形的傅里叶展开复杂波形的傅里叶展开例二：例二：§1.4数字信号的频谱分析§1.4数字信号的频谱分析SPECTRAOFDIGITALWAVEFORMSRisetimerτDefinetheriseandfalltimeasFalltimefτDefinetherise-andfalltimeasbeingfromthe10%to90%points.Pulsewidthτ(50%pointsofthewaveformamplitude)§1.4数字信号的频谱分析§1.4数字信号的频谱分析§1.4数字信号的频谱分析§1.4数字信号的频谱分析§1.4数字信号的频谱分析§1.4数字信号的频谱分析Thehigh-frequencyisdueThehighfrequencyisdueprimarilytotherise/falltime.Pulseshavingsmallrise/falltimesillhlhihfwillhavelargerhigh-frequencyspectralcontentthanpulseshavinglargerrise/falltimes.ggInordertoreducethehigh-ftddfrequencyspectrum,andreducetheemissionsofaproduct,weshouldincreasetherise/falltimesBoundsontheone-sidedmagnitudespectrumofatrapezoidalpul