EE 541: Class Notes #04Overview Of LectureInterstage GeneralizationUp Conversion Filter (UCF)UCF ModelUCF Design ExampleUp Converter Filter SimulationComments On Design ExampleUp Converter AnalysisUCF Input ResistanceUCF Input ReactanceDown Conversion Filter (DCF)DCF AnalysisDCF Design ExampleDown Converter SimulationComments On DCF Design ExampleDetailed DCF AnalysisDCF Real Part ResponseDCF Imaginary Part ResponsePi–Section Matching FilterPI Filter AnalysisPI Filter Analysis -- Cont’dPI Filter Center Frequency ModelApproximate PI Filter BandwidthPI Filter Design ExampleDesign Example -- Cont’dSimulated Input ImpedanceComments On Pi Section DesignConstant Resistance InterstagesConstant Resistance TeeConstant Resistance EllsConstant Resistance BridgeFirst Order BridgeSecond Order BridgeSecond Order Bridge RealizationBridge -To- Bridged-Tee ConversionBridged-Tee Conversion Case IBridged-Tee Conversion Case IIThird Order Lowpass BesselLowpass Bessel Design IComments On Design Step 1Lowpass Bessel Design 2Lowpass Bessel Design 3Lowpass Bessel Design 4Bessel Example RealizationBessel Final RealizationSimulated Bessel I/O PlotsSimulated Bessel Delay ResponseSimulated Bessel Pulse ResponseComments On Bessel SimulationsINTERSTAGE MATCHINGINTERSTAGE MATCHINGFILTERSFILTERSProf. John ChomaUniversity of Southern CaliforniaDepartment of Electrical Engineering-ElectrophysicsUniversity Park: MC: 0271Los Angeles, California 90089-0271213-740-4692 (USC )213-740-7581 (FAX )213-740-7874 (USC )[email protected] 2004 SemesterEE 541: Class Notes #04EE 541: Class Notes #04University of Southern CaliforniaEE 541: Choma128Overview Of LectureOverview Of Lecturez Impedance Conversion Up Converter Down Converter Pi-Sectionz Constant Resistance Networks Attributes Minimal Phase Filters Non-Minimal Phase Filters All Pass Networks Design ExampleUniversity of Southern CaliforniaEE 541: Choma129InterstageMatchingFilter+−RsRlVsZ(s)inz System Diagramz Design Issues Desire Zin(jωo) = RsMaximum Power Transfer FromSignal Source To Filter Input PortGenerally Accomplished At OnlyA Tuned Center Frequency, ωoGenerally Accomplished For Only A Reasonably Narrow PassbandFilter Is Usually Lossless Topology In RF Communication Systems Convert RlAt Output Port -To- RsAt Input PortUp Converter Implies Rs> RlDown Converter Implies Rs< Rlz Design Specifications Tuned Center Frequency, ωo 3-dB Bandwidth Or Equivalently, Effective System Q Up/Down Impedance Conversion Factor, KzInterstage GeneralizationInterstage GeneralizationUniversity of Southern CaliforniaEE 541: Choma130z Circuit Topologyz Admittance, Yl(s) Radial Center Frequency Is ωo Load Q Admittance Function Implication Is Shunt RL Circuit At Tuned Center Frequency+−RsRlRcLVsVoZ(s)inY(s)lCollcω LQRR=+()()()lolcl222lc2lclc loω1jQωRR jωL1Y(jω)RR jωLRR ωLωRR1Qω−+−== =++++++Up Conversion Filter (UCF)Up Conversion Filter (UCF)University of Southern CaliforniaEE 541: Choma131z At Center Frequency Effective ShuntInductance, Leff Effective ShuntResistance, Reff Resonance, ωo ImpedanceConversion, Kzz Model @ ωo()lol22lc loω1jQωY(jω)ωRR1Qω−=++()()()2llo22llc o lQ1Y(jω )1Q R R jω 1Q L=+++ +2leff2l1QLLQ+=()()2eff l l cR1QRR=+ +()lo2efflQ1ωLC1Q LC==+()eff2sczlll lRRRK11QRR R== =+ +ReffLeffY(j )l oωCZ(j )in oωUCF ModelUCF ModelUniversity of Southern CaliforniaEE 541: Choma132z Specificationsz Calculations Quality Factor: Inductance: Capacitance:z Result (ohms, pF, nH)Load Resistance, Rl: 20 ohmsSource Resistance, Rs: 75 ohmsTuned Matching Frequency, fo: 2.7 GHzEstimated Inductor Resistance, Rc: 3 ohmsslzlcl clRRKQ111.5041RR 1RR=−=−=++()llcoQLRRω2.04 nH=+ =+−752032.04VsVoZ(s)in1.18()2l22loQC1Q ω1.L18 pF==+UCF Design ExampleUCF Design ExampleUniversity of Southern CaliforniaEE 541: Choma133Up Converter Filter SimulationUp Converter Filter Simulation75 Ohms2.72 GHzUniversity of Southern CaliforniaEE 541: Choma134Comments On Design ExampleComments On Design Examplez Filter Satisfies Design Requirements Imaginary Part Of Input Impedance Is Zero At 2.75 GHz Real Part Of Input Impedance Is 75 Ohms At 2.75 GHzz Observations Imaginary Part Of Input ImpedancePositive Below 2.75 GHz Resonance, Indicating Inductive ImpedanceNegative Above 2.75 GHz, Indicating Capacitive Input Impedance Real Part Of Input ImpedanceValue Is As Expected At ResonancePeak Occurs Beyond Resonance And Is Larger Than Resonant Valuez It Can Be Shown (favorite professorial line) Real Part Peak Occurs AtFrequency ωx Peak Real Part Is A Value, Rx Large Q Means Peaking CoincidesWith Resonance {ωx= ωoAndRx= Re[Zin(jωo)]}xo2l2lxino2l1ωω12QQ1RZ(jω )Q34Re=++=+University of Southern CaliforniaEE 541: Choma135()()()22lin24222lllloo1QRRωω1Q 12Q Q Qωω+=+−+ +z Input Impedancez Real Part Input Impedancez ImaginaryPart InputImpedance+−RsRlRcLVsVoZ(s)inClcRRR+in in in2RjωLZ(jω)RjX1 ω LC jωRC+=+−+()()()()()222ll o oin242o22llllooQ1Q 1 ωω ωωXω Lωω1Q 12Q Q Qωω+−=+−+ +Up Converter AnalysisUp Converter AnalysisUniversity of Southern CaliforniaEE 541: Choma136UCF Input ResistanceUCF Input Resistance0102030400.10 0.16 0.25 0.40 0.63 1.00 1.58 2.51 3.98 6.31 10.00Norm alized Frequency, (ω/ωo)Normalized Real PartQ u a lity F a cto r = 4Q u a lity F a cto r = 6Q u a lity F a cto r = 20102030400.10 0.16 0.25 0.40 0.63 1.00 1.58 2.51 3.98 6.31 10.00Norm alized Frequency, (ω/ωo)Normalized Real PartQ u a lity F a cto r = 4Q u a lity F a cto r = 6Q u a lity F a cto r = 2University of Southern CaliforniaEE 541: Choma137-4-3-2-101230.10 0.16 0.25 0.40 0.63 1.00 1.58 2.51 3.98 6.31 10.00Normalized Frequency, (ω/ωo)Normalized ReactanceQuality Factor = 6Quality Factor = 3Quality Factor = 2-4-3-2-101230.10 0.16 0.25 0.40 0.63 1.00 1.58 2.51 3.98 6.31