3.Scattering Parameters and Vector Network Analyze

中華大學通訊系1ScatteringParametersandVectorNetworkAnalyzer中華大學通訊系田慶誠[e-mail]035186030中華大學通訊系2OverviewofSParametersPowerWaveDefinition(Z0=50W):50W22211211SSSS212221121121aaSSSSbba1b1a2b2Port1Port250W中華大學通訊系3ComplexPowerWaves011ZVa022ZVa011ZVb022ZVb211aP222aP211bP222bPIncidentWaveReflectedWaveIncidentPowerReflectedPower中華大學通訊系4CalculationsofSParameters0a11112abS0a12212abS50W50Wa1b1a2=0b2Port1Port2MatchedS11S21=Port1reflectcoefficientwhenPort2ismatched=Port1toPort2transmissioncoefficientwhenport2ismatched(gainorinsertionloss)0a11112abS0a12212abS中華大學通訊系5InterpretationofMatchedPort50W50Wa1b1a2=0b2Port1Port2MatchedS11S21各接面可視為由虛擬50W傳輸線(長度視為0)連接，因此傳輸線內形成入射波a1anda2與反射波b1andb2。當port2接上50W負載(matched)，b2直接從50W傳輸線進入50W負載，因此沒有反射波產生，即a2=0。50W50W中華大學通訊系6CalculationsofSParameters50W50Wa2b2a1=0b1Port2Port1MatchedS22S120a22221abS0a21121abS=Port2reflectcoefficientwhenPort1ismatched=Port2toPort1transmissioncoefficientwhenport1ismatched(reversegainorisolation)0a22221abS0a21121abS中華大學通訊系7CalculationsofSParameters(UsingVoltageWavesDefinitions)50W50WPort1Port2MatchedS11S21+-++--VSV1V250W50WPort1+-+-VSV1=V1+LetV1-=0V1+=V1=VS/2STEP1中華大學通訊系8STEP250W50WPort1Port2MatchedS11S21+-++--VSV1V2V1=V1++V1-=V1-=V1-VS/21VV2VVabSS1111111CalculationsofSParameters(UsingVoltageWavesDefinitions)中華大學通訊系9STEP350W50WPort1Port2MatchedS11S21+-++--VSV1V2S2121221VV2VVabSV2=V2++V2-=V2-=V2同理可求出S12及S22V2+=0CalculationsofSParameters(UsingVoltageWavesDefinitions)中華大學通訊系10MeasurementofSParametersUsingVectorNetworkAnalyzer(VNA)Bias1Bias2VNASamplerDirectionalCoupler中華大學通訊系11SparametersofBJTTransistor50W50WDCBiasCircuitExample:SiemensBFP420中華大學通訊系12S11andS22ofBFP420IC=5mAVCE=4Vf=0.05GHz-7.68GHzCalculatedfromGummel-Poonmodel(Serenade8.0)fLOWfHIGH中華大學通訊系13InputandOutEquivalentCircuitsLookintoBaseLookintoCollector中華大學通訊系14S21andS12ofBFP420fLOWfHIGH中華大學通訊系15TabularFormofSParameters#GHzSMAR50(TouchstoneFormat)中華大學通訊系16PowerGainv.s.FrequencyInsertionPowerGainMaximumStableGainMaximumAvailablePowerGain-6dB/OctaveVDS=2VIDS=25mA中華大學通訊系17IsolationofTransistorIsolation=|S21S12|fS=transducercutofffrequency(|S21|=1)-20dB/decade20dB/decade中華大學通訊系18ImpedancesandReflectionCoefficientsinanAmplifierCircuitTransistorInputMatchingNetworkOutputMatchingNetwork50W50WGaZaGOUTZOUTGINZINGSZSGLZLGbZb再次叮嚀大家：此處所有的反射係數G的定義是由阻抗Z相對於特性阻抗50W所計算出。(Transientreflectioncoefficients)中華大學通訊系19SignalFlowGraphofaRFAmplifierbsa1a2b2b1GSGLS11S21S22S12ZLZSVS+-Transistora1b1b2a21各接面可視為由虛擬50W傳輸線連接，每次進入傳輸線的信號看到50W特性阻抗即產生反射，因此傳輸線內形成無限多入射波組合成ai與無限多反射波組合成bi。中華大學通訊系20RulesforaSignalFlowGraph(1)Nodes:powerwaveai,bj(常為無限多次反射或入射的組合)(2)Branch:EachS-parameter,SijReflectioncoefficients,GSGL(3)Nodes+Branch:a2b1S12212221121121aaSSSSbba1b1GS中華大學通訊系21RulesforaSignalFlowGraph(4)Calculationofnodalpowerwavesa1b2S21S22b2=S21*a1+S22*a2a2Anodalpowerwaveisequaltothesumofthebranchesenteringit.中華大學通訊系22SignalFlowGraphofaTwo-portNetwork(Transistor)212221121121aaSSSSbba1a2b2b1S11S21S22S12中華大學通訊系23SignalFlowGraphofRFSourcebs:powerwavedeliveredfromsourceto50Wreferencedstandardload.ZSVS+-a1b1=050WbSPS=|bs|2=sourcepowerdeliveredto50Wreferencedstandardload中華大學通訊系24SignalFlowGraphofRFSourceZSVS+-a1b1bSTransistorGSa1=bS+b1GSa1b1GSbS11SSSba50Z50ZG1GS中華大學通訊系25SignalFlowGraphofLoadZLTransistorb2a2a2=b2GL22LLLba50Z50ZGa2b2GLGL中華大學通訊系26InputReflectionCoefficientGINZL50WVS+-Transistora1b1b2a2GINa2b1GLS11S22S12a1b211INabGS21GS=0中華大學通訊系27CalculateGINbySignalFlowGrapha2b1GLS11S22S12a1b211INabGb1=a1S11+a1S21GLS12+a1S21GL(S22GL)S12+a1S21GL(S22GL)2S12+a1S21GL(S22GL)3S12+………………..S21S11,S22andGLaretransientreflectioncoefficients.中華大學通訊系28CalculateGINbySignalFlowGraph1SifS1SSSabL22L2212L211111INGGGGImportantphysicalmeanings：(1)InputreflectioncoefficientGINisfunctionofGL，代表電晶體前端看入的反射係數或輸入阻抗會隨負載而變。(2)若輸出接上50W負載，即GL=0GIN=S11(3)若S120，電晶體形成雙向(Bilateral)元件(4)若S12=0，電晶體則為單向(Unilateral)元件(5)若S12=0GIN=S11中華大學通訊系29OutputReflectionCoefficientGOUTZSTransistora1b1b2a250WGOUTa1a2b2b1GSGL=0S11S21S22S1222OUTabG中華大學通訊系30CalculateGOUTbySignalFlowGrapha1a2b2b1GSS11S21S22S1222OUTabGb2=a2S22+a2S12GSS21+a2S12GS(S11GS)S21+a2S12GS(S11GS)2S21+a2S12GS(S11GS)3S21+………………..S11,S22andGSaretransientreflectioncoefficients.中華大學通訊系31CalculateGOUTbySignalFlowGraph1SifS1SSSabS11S1121S122222OUTGGGGImportantphysicalmeanings：(1)OutputreflectioncoefficientGOUTisfunctionofGS，代表電晶體後端看入的反射係數或輸出阻抗會隨Sourceimpedance而變。(2)若輸入接上50Wsource，即GS=0GOUT=S22(3)若S120，電晶體形成雙向(Bilateral)元件，當inputmatching做好後，outputmatching已被改變。再度修正outputmatching時，inputmatching又被改變了……….中華大學通訊系32DiscussionCase(1)S11=0butGL0Amplifier設計時若inputmatching只匹配至S11真的讓電晶體的前端不造成反射了嗎？答案是包含輸入匹配電路的新電晶體電路的S11=0(S11定義上後級應接上50Wload)，但是後級若不再接上50Wload(GL0)，電路的輸入端就不再匹配了(GIN0)。0S1SSL2212L21INGGG中華大學通訊系33DiscussionCase(2)S11=0andS12=0Amplifier設計時若inputmatching只匹配至S11真的讓電晶體的前端不造成反射了嗎？答案是包含輸入匹配電路的新電晶體電路的S11=0(S11定義上後級應接上50Wload)。電晶體若接近unilateraldevice(S120)，即使後級不再接上50Wload(GL0)，電路的輸入端永遠保持匹配(GIN=0)。0S10SL22L21INGGG中