AdvancedImpedance MatchingMicrowave EngineeringEE 172Dr. Ray KwokAdvanced Impedance Matching - Dr. Ray KwokAdvanced Impedance MatchingSo far….• 2-elements tuning• Lumped Elements (L,C)• Transmission Lines• Stubs (single & double)• 1-port network• single frequencyNow:• are all tuning the same?• wideband matching – multiple sections• multi-ports (simultaneously tuned)Advanced Impedance Matching - Dr. Ray KwokLet’s compare our 2-element tuning examples over frequency…• Lumped Elements (L,C)• Transmission Lines• Stubs (Single and Double)• Quarter-Wave transformerAdvanced Impedance Matching - Dr. Ray KwokLumpedElementsR=1G=1If ZLis inside the G=1 circle,first element cannot be shuntZL(0.4, 1)YL(0.34, -0.87)Z (0.4, 0.48)Y (1, -1.24)=0.4+j1ZLjB = +j1.24 = jZoωCjX = -j0.52 = -j/ωCZoZ (0.4, -0.48)Y (1, 1.24)=0.4+j1ZLjB = -j1.24 = -jZo/ωLjX = -j1.48 = -j/ωCZoZ (1, 1.4)Y (0.34, -0.48)jB = +j0.39 = jZoωC=0.4+j1ZLjX = -j1.4 = -j/ωCZoZ (1, -1.4)Y (0.34, 0.48)jB = +j1.35 = jZoωC=0.4+j1ZLjX = j1.4 = jωL/ZoIf ZLis inside the R=1 circle,first element cannot be in seriesAdvanced Impedance Matching - Dr. Ray KwokReturn Loss0.01 0.11 0.21 0.31 0.41 0.5Frequency (GHz)Lump-50-40-30-20-100DB(|S[1,1]|)Lump1DB(|S[1,1]|)Lump2DB(|S[1,1]|)Lump3DB(|S[1,1]|)Lump4Advanced Impedance Matching - Dr. Ray KwokUsing StubsZL(0.4, 1)YL(0.34, -0.87)Z (0.4, -0.48)Y (1, 1.24)=0.4+j1ZLshort shunt stubjB = -j1.24 = -jcotβlopen series stubjX = -j1.48 = -jcotβlZ (1, 1.4)Y (0.34, -0.48)open shunt stubjB = +j0.39 = jtanβl=0.4+j1ZLopen series stubjX = -j1.4 = -jcotβlllllβ=β−=β−=β=tanjYYcotjYYcotjZZtanjZZooposhooposhOne way, simply replace lumped elements with stubsZocan be anything hereprevious exampleAdvanced Impedance Matching - Dr. Ray KwokOpen – Short Stubs0.01 0.11 0.21 0.31 0.41 0.5Frequency (GHz)Stubs-50-40-30-20-100DB(|S[1,1]|)Stub1DB(|S[1,1]|)Stub2Advanced Impedance Matching - Dr. Ray KwokZL(0.4, 1)YL(0.34, -0.87)=0.4+j1ZLTransmission Line Matchingusually requires 1 more elementprevious example0.130λλλλ0.185λλλλ0.055λ50 ΩjX = -j1.85 = -j/ωCZo=0.4+j1ZL0.435λλλλ0.305λ50 ΩY (1, 1.9)short shunt stubjB = -j1.9 = -jcotβlZ (1, 1.85)Advanced Impedance Matching - Dr. Ray KwokSingle Stub Tuningrefers to sliding a stub (any kind)along a transmission line. previous example0.130λλλλ0.064λλλλ=0.4+j1ZL0.435λλλλ0.305λ50 ΩY (1, 1.9)short shunt stubjB = -j1.9 = -jcotβlIn practice, usually shunt stubs, short stub for waveguides,open stub for microstrip.=0.4+j1ZL0.434λ50 Ωopen shunt stubjB = j1.9 = jtanβlZL(0.4, 1)YL(0.34, -0.87)Y (1, -1.9)Advanced Impedance Matching - Dr. Ray KwokAny Stubtanβl can be “+” or “-” previous example0.130λλλλ0.064λλλλ=0.4+j1ZL0.435λλλλ0.305λ50 ΩY (1, 1.9)open shunt stubjB = - j1.9 = jtanβlβl = -1.086 + π = 2.055length = 0.327λ > λ/4can use any type depends on realization.e.g. use shunt open stub only…=0.4+j1ZL0.434λ50 Ωopen shunt stubjB = j1.9 = jtanβlβl = 1.086length = 0.173λZL(0.4, 1)YL(0.34, -0.87)Y (1, -1.9)Advanced Impedance Matching - Dr. Ray KwokTransmission Line + Stub0.01 0.11 0.21 0.31 0.41 0.5Frequency (GHz)xline_stub-50-40-30-20-100DB(|S[1,1]|)single_stub1DB(|S[1,1]|)single_stub2DB(|S[1,1]|)single_stub3DB(|S[1,1]|)single_stub4DB(|S[1,1]|)single_stub5Advanced Impedance Matching - Dr. Ray KwokDouble Stub Tuninge.g. 2 shunt short stubs (50Ω)separated by a 50Ω line of 0.2λ0.3λλλλ0.5λλλλ– 0.2λλλλ• rotate the 1-circle by line length• adjust d1along constant-G circle • stop at the rotated blue-circle• xline will bring it to the green circle• adjust d2along the green circle to Zo• not for all ZL!! Forbidden zone.d1d2ZL0.2λ50 Ω=0.4+j1ZL(0.4,1)YL(0.34,-0.87)Y (0.34,-0.2)Y (1,1.22)-cotβd1 = +0.67βd1= -0.98 +π = 2.16d1= 0.344λ-cotβd2 = −1.22βd2= 0.687d2= 0.109λ50 Ω50 ΩAdvanced Impedance Matching - Dr. Ray Kwoke.g. Quarter-Wavee.g. shunt stub (100Ω) then λ/4ZL= 20 + j 50 Ω• move Z to the real axis• normalized Zc= √Z = √3.1; Zc= 1.76• Zc= 50(1.76) = 88 ΩZL(0.4,1)YL(0.34, -0.87)Z (3.1,0)Y(0.34,0)(1/100) tanβd= (0.87)(1/50)βd = 1.05d = 0.167λdZLλ/4Zc=0.4+j150 Ω100ΩAdvanced Impedance Matching - Dr. Ray KwokDouble Stub / Quarter-wave0.01 0.11 0.21 0.31 0.41 0.5Frequency (GHz)double_n_quarter-30-20-100DB(|S[1,1]|)do uble_s tubDB(|S[1,1]|)qu arter_waveAdvanced Impedance Matching - Dr. Ray KwokMixed matching samples0.01 0.11 0.21 0.31 0.41 0.5Frequency (G Hz)Mixed-40-30-20-100DB(|S[1,1]|)double_s tubDB(|S[1,1]|)Lump1DB(|S[1,1]|)quarter_waveDB(|S[1,1]|)single_stub2DB(|S[1,1]|)Stub 1Advanced Impedance Matching - Dr. Ray Kwok2-port tuning2 – portnetworkMatchingNetwork ?Especially useful for active component design : amplifier (transistor)or inserting devices into a system (such as SAW filter…)for matched load11inS=ΓAdvanced Impedance Matching - Dr. Ray KwokUnmatched load (from previous lecture)2 – portnetworkb1b2a1a2= ΓLb2ZLThis is what we measure.How does that affect our matching process?L2221L1211in11L22121L121111L2212122L2212122212122L121112121111212221121121S1SSSabS1aSSaSbS1aSbbSaSaSaSbbSaSaSaSbaaSSSSbbΓ−Γ+=Γ≡Γ−Γ+=Γ−=⇒Γ+=+=Γ+=+==Advanced Impedance Matching - Dr. Ray KwokTo what we match? (from previous lecture)( ) ( )( )22g2g2g2gg2gininlossLoadgg2XR4RV21X2R2RV21RI21PP+=+===−( )2g2goo2go2totalgoLineLoadXRZZV21ZZV21ZI21PP2++====Case 1: match ZL= Zo= real → ΓL= 0, VSWR = 1 on the lineZinlZoZLZg=Rg+ jXgVgZinZgVgCase 2: match Zin= Zg→ Γin= 0, VSWR > 1g2g2gg2gLoadRV81R4RV21P ===Case 3: match Zin= Z*g→ Xin= -Xg= max power availableconjugate matchingIdeally, match all Zo= Zg= ZL= real, then all 3 PLoadare the same = Pmax.Advanced Impedance Matching - Dr. Ray KwokConjugate Match ZoOutputmatchingInputmatchingDeviceto be matchedZoΓinΓoutΓLΓSL2221L1211inS1SSSΓ−Γ+=ΓS1121S1222outS1SSSΓ−Γ+=Γ*inSΓ=Γwant*outLΓ=ΓandAdvanced Impedance Matching - Dr. Ray KwokSimultaneous Conjugate Match G. Gonzales: Microwave Transistor Amplifiers21122211*11222*221112211222222222111222222L121211SSSSSSSSCSSCSS1BSS1BC2C4BBC2C4BB−==∆∆−=∆−=∆−−+=∆−−+=−±=Γ−±=ΓAdvanced Impedance Matching - Dr. Ray KwokExample 01.01.0-1. 010.010.0-10.05.05.0-5.02.02.0-2.03.03.0-3.04.04.0-4.00.20.2-0.20.40.4-0.40.60.6-0.60.80.8-0.8S_ParametersSwp Max6GHzSwp Min6GHzS[1,1]ex1_raw_sparaS[2,2]ex1_raw_sparaMatch this FET