Chapter 10 Sinusoidal steady-state analysis

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1、Chapter10SinusoidalSteady-stateAnalysis要求深刻理解与熟练掌握的重点内容有：正弦稳态电路的分析。难点：相量图表示、提高功率因数、功率分析•10-1Introduction•10-2NodalAnalysis•10-3MeshAnalysis•10-4SuperpositionTheorem•10-5SourceTransformation•10-6TheveninandNortonEquivalentCircuits•10-7OpAmpACCircuits•10-10Summa

2、ryandReview10.1IntroductionStepstoAnalyzeacCircuits:Transformthecircuittothephasororfrequencydomain.Solvetheproblemusingcircuittechniques(nodalanalysis,meshanalysis,superposition,etc.).Transformtheresultingphasortothetimedomain.oscillator振荡器transistor晶体管Capacitan

3、cemultiplier电容倍增器10.2NodalAnalysisThebasisofnodalanalysisisKirchhoff’scurrentlaw.SinceKCLisvalidforphasors,asdemonstratedinSection9.6,wecananalyzeaccircuitsbynodalanalysis.DCCircuitACCircuitExample：Findthetime-domainnodevoltagesv1(t)andv2(t)inthecircuitshowninFig

4、.a.Afrequency-domaincircuitforwhichnodevoltagesV1andV2areidentified.Fig.a....Solution：leftnode:rightnode:Combiningterms,wehave:................Solving,wefindthatV1=2.24-63.4oV,V2=47.47116.6oVConvertingtothetimedomain:v1(t)=2.24*1.414cos(ωt–63.4o)Vv2(t)=47.7*1.4

5、14cos(ωt+116.6o)V..Notethatthevalueofωwouldhavetobeknowninordertocomputetheimpedancevaluesgivenonthecircuitdiagram.Also,bothsourcesmustbeoperatingatthesamefrequency.20cos4tV10Ωix0.1F1H2ix0.5HExample：FindixinthecircuitofFig.10.1usingnodalanalysis.Wefirstconvertthe

6、circuittothefrequencydomain:20cos4t1H0.5H0.1FSolution：10ΩNode1,Node2,TheequationscanbeputinmatrixformasTransformingthistothetimedomain,10.3MeshanalysisKirchhoff’svoltagelaw(KVL)formsthebasisofmeshanalysis.ThevalidityofKVLforaccircuitswasshowninsection9.6andisillu

7、stratedinthefollowingexamples.Mesh-CurrentDCCircuitACCircuitExample:UsephasorsandmeshanalysisonthecircuitofFig.10.63tofind.Solution:Example:Usephasoranalysistodeterminethethreemeshcurrentsi1(t),i2(t),andi3(t)inthecircuitofFig.10.70Solution:Wedefineanadditionalclo

8、ckwisemeshcurrenti4(t)flowingintheupperright-handmesh.i4Theinductorisreplacedbyaj0.004Wimpedance:The750mFcapacitorisreplacedbya–j/0.0015WimpedanceThe1000mFcapa