Differential Impedance Finally Made Simple

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Slide -1Training for Signal Integrity and Interconnect DesignMYTHSDifferential Impedance finally made simpleEric BogatinPresidentBogatin ric@bogent.com Eric Bogatin 2000www.BogatinEnterprises.comSlide -2Training for Signal Integrity and Interconnect DesignMYTHS OverviewWhat’s impedanceDifferential Impedance: a simple perspectiveCoupled Transmission line formalismMeasuring differential impedanceEmulating effects of a split in return pathCalculating differential impedance Eric Bogatin 2000www.BogatinEnterprises.com

Slide -3Training for Signal Integrity and Interconnect DesignFirst Order Model of a Transmission Line(Loss Less Model)MYTHS xLCLCLCLCLCLCC CL x capacitanceL LL x inductance(loop)(unbalanced transmission line)The circuit analysis result:Z0 LLCLTD LtotalC total Eric Bogatin 2000υ 1LLC Lwww.BogatinEnterprises.comSlide -4Training for Signal Integrity and Interconnect Design“ be the signal”MYTHScourtesy ICE Eric Bogatin 2000www.BogatinEnterprises.com

Slide -5Training for Signal Integrity and Interconnect DesignMYTHS0th Order Model of TransmissionLine xVinCCCL Capacitance per length [pF/in]CCCCCCCC C L x Q CV, xevery t vI, V definition ofTransmission Line:I Qt vCL x V vCLV xWhat’s the impedance? Eric Bogatin 2000www.BogatinEnterprises.comSlide -6Training for Signal Integrity and Interconnect DesignMYTHSInstantaneous Impedance of aTransmission LineI v C LVV 1Z V vCvCLILV1Z0 vCLFeatures of the impedance: looks like a resistor dependant on intrinsic properties only is an intrinsic property independent of length defined as the "characteristic impedance" Z0 also called the “surge impedance” or “wave impedance” Eric Bogatin 2000www.BogatinEnterprises.com

Slide -7Training for Signal Integrity and Interconnect DesignMYTHSCharacteristic Impedance andCapacitance per LengthWhat happens to thecapacitance per length? Thecharacteristic impedance?increase hw 10 milsh 5 mils50 Ohm PCB cross sectionincrease wZ0 What happens to thecapacitance per length? Thecharacteristic impedance?1CL Eric Bogatin 2000www.BogatinEnterprises.comSlide -8Training for Signal Integrity and Interconnect DesignMYTHSWhat Does it Mean to Have a 50 Ohm Line?coax50 OhmggggglonVerrrryΩWhat will Ohm-meter read?For the first second? After 3 seconds? After 10 sec? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -9Training for Signal Integrity and Interconnect DesignMYTHSAn important Distinction THE impedance of the transmission line (may be timedependent) The instantaneous impedance of the transmission line The Characteristic impedance of the transmission lineJust referring to “ the impedance” may be a bit ambiguous Eric Bogatin 2000www.BogatinEnterprises.comSlide -10Training for Signal Integrity and Interconnect DesignMYTHSReturn Path in T LinesCurrent into signal lineTD 1 secWhere is the return path?For DC currents:For RF currents? When does current come out return path? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -11Training for Signal Integrity and Interconnect DesignCurrent Flow in theTransmission LineMYTHSsignalLCLLCCLCLCLCIt’s a propagating wave.What happens initially if the end is open?, shorted?, terminated?To control impedance, manage the returnpath as carefully as the signal path Eric Bogatin 2000www.BogatinEnterprises.comSlide -12Training for Signal Integrity and Interconnect DesignMYTHSThe Growing Importance ofDifferential Pair UseEarly Applications for Differential PairsMECL IMECL IIMECL IIIMECL 10kMECL 10kH19621966196819791981ANSI/TIA/EIA-644-1995 is the generic physical layer standard for LVDS. Itwas approved in November of 1995, and first published in March of 1996.Example: high speed serial transmissionà IEEE1394à IEEE488à Gigabit EthernetTI 1.8 Gbps LVDS TRX Eric Bogatin 2000www.BogatinEnterprises.com

Slide -13Training for Signal Integrity and Interconnect DesignMYTHSWhat’s a Differential PairTransmission Line? Eric Bogatin 2000www.BogatinEnterprises.comSlide -14Training for Signal Integrity and Interconnect DesignMYTHSWhat’s a Differential PairTransmission Line?Answer: .any two, coupled transmission lines (with their return paths).12A special case: a symmetric pairWhat’s differential impedance? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -15Training for Signal Integrity and Interconnect DesignDifferentially Driving aDifferential PairMYTHS1Difference signalV 0àà1vV 1vàà0v212What is the difference signal? Eric Bogatin 2000www.BogatinEnterprises.comSlide -16Training for Signal Integrity and Interconnect DesignThe Difference SignalMYTHSDifference signalV 0àà1vV 1vàà0v12 1Difference voltage 2v : -1v à 1v-1What is the impedance the difference signal sees? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -17Training for Signal Integrity and Interconnect DesignDifferential ImpedanceMYTHSDifferential Impedance: the impedance the difference signal seesZ (diff ) V (diff ) 2V 2(Z0 small )IoneI oneDifferential impedance decreases as coupling increasesC12 1vIone-1vItwoxC11C22How will the capacitance matrix elements be affected by spacing? Eric Bogatin 2000www.BogatinEnterprises.comSlide -18Training for Signal Integrity and Interconnect DesignMYTHSCapacitance Matrix ElementsC12C11 1vC22S 1vCapacitance per Length (pF/in)4C11321C2100123456789 10 11 12 13 14 15 16 17 18 19 20Edge to Edge Separation (mils)What happens to the differentialimpedance as S gets smaller? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -19Training for Signal Integrity and Interconnect DesignHow to Terminate theDifference Signal?MYTHSDifference signalV 0àà1vV 1vàà0vZ (diff ) V (diff ) 2V 2(Z0 small )IoneI oneIf there is no coupling, and each line is 50ΩΩ,what resistor terminates the differential pair? Eric Bogatin 2000www.BogatinEnterprises.comSlide -20Training for Signal Integrity and Interconnect DesignMYTHSTerminate with aresistor to matchimpedance of thedifference signalFormalism:Mode Pattern for Identical TracesHyperlynx simulation 1vIodd 1v-1v 1vIevenxxMode: odd, or 1, or aMode: even, or 2, or bCorresponds to differential drivenCorresponds to common drivenWhat is Iodd compared to Ieven?How do they vary with spacing? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -21Training for Signal Integrity and Interconnect DesignOdd and Even Mode ImpedanceMYTHSZodd 1vIoddVZeven IoddVIeven 1v-1vHyperlynx simulation 1vIevenxxMode: odd, or 1, or aMode: even, or 2, or bOdd mode current increases astraces are brought togetherEven mode current decreasesas traces are brought togetherOdd mode impedancedecreasesEven mode impedanceincreases Eric Bogatin 2000www.BogatinEnterprises.comSlide -22Training for Signal Integrity and Interconnect DesignMYTHSDifferential Impedance andOdd Mode ImpedanceDifference signalV 1vàà0vV 0àà1vZ (diff ) V (diff ) 2V 2 x ZoddIoneIone Eric Bogatin 2000www.BogatinEnterprises.com

Slide -23Training for Signal Integrity and Interconnect DesignThe Characteristic Impedance MatrixMYTHSI1xI2xV1V2Define a Characteristic Impedance MatrixV1 Z11I1 Z12I 2How is Z12 influenced by coupling?Is Z12 large or small?V2 Z 22I 2 Z 21I1Characteristic Impedance Matrix [ohms]:121 49.6 6.426.449.6Hyperlynx simulation Eric Bogatin 2000www.BogatinEnterprises.comSlide -24Training for Signal Integrity and Interconnect DesignMYTHSDefinition of Odd and Even ModeImpedance(Special case: symmetric)I1xI2xV11(V1 V2 )2Zodd 1Veven (V1 V2 )2Zeven Vodd Define:V2VoddI1 Veven 0VevenI1 Vodd 0What is the voltage when Veven 0? When Vodd 0? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -25Training for Signal Integrity and Interconnect DesignOdd and Even ModeImpedanceMYTHSV1 Z11I1 Z12I 2V2 Z 22I 2 Z21I1Odd Mode:I1 I 2Vodd Zodd1(V V ) (Z11 Z12 )I12 1 2 (Z11 Z12 )Odd mode impedance is reduced with couplingEven Mode:1(V V2 ) (Z11 Z12 )I12 1Zeven Z11 Z12I1 I 2Veven Even mode impedance is increased with coupling Eric Bogatin 2000www.BogatinEnterprises.comSlide -26Training for Signal Integrity and Interconnect DesignMYTHSMode ImpedancesOdd mode impedance is the impedance of one linewhen the pair is driven differentiallyDifferential impedance:Z (diff ) V (diff ) 2V 2(Zodd ) 2(Z11 Z12 )IIEven mode impedance is the impedance ofone line when the pair is driven commonlyCommon impedance:Zodd (Z11 Z12 )Zeven Z11 Z12Zcommon Zeven Z11 Z12 Eric Bogatin 2000www.BogatinEnterprises.com

Slide -27Training for Signal Integrity and Interconnect DesignSummary So FarMYTHS A differential pair is any two transmission lines Special case: symmetric lines Differential driving has symmetric, opposite signal on each line Differential impedance is the impedance the difference signal sees With no coupling, current into one line depends on capacitance per length ofthe line With coupling, current into one line depends on how the other line is driven The impedance of one line will depend on how the other line is drivenThe differential impedance will be twice the impedance ofone line when the pair is driven differentially Eric Bogatin 2000Training for Signal Integrity and Interconnect Designwww.BogatinEnterprises.comSlide -28MYTHSHow can differential impedance bemeasured? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -29Training for Signal Integrity and Interconnect DesignTDR EquipmentMYTHSTDR:TDT:DTDR:DTDT:HP 83480ADigital Communications Analyzer(mainframe)Time Domain ReflectionTime Domain TransmissionDifferential Time Domain ReflectionDifferential Time Domain TransmissionHP 83484A2 Channel 50 GHz ModuleTwo independent voltage channelsHP 54754ADifferential TDR ModuleTwo independent TDR channels- simultaneous TDR/TDT- simultaneous differential TDR Eric Bogatin 2000www.BogatinEnterprises.comSlide -30Training for Signal Integrity and Interconnect DesignConventional Single Channel TDRMYTHSTDR: 400 mV output, unloaded50ΩΩ output impedanceVmeasuredTDR response--400mV(DUT)DeviceUnderTest--300mVw h50ΩΩcablew 2hw 8h3 different line width microstrips,each 9 inches long50 mV/div500 psec/div Eric Bogatin 2000--200mV--100mV--0mvwww.BogatinEnterprises.com

Slide -31Training for Signal Integrity and Interconnect DesignMYTHSConverting Reflected Voltageinto ImpedanceVoltage scaleρ VreflectedVincidentZDUT 50Ω1 ρ1 ρImpedance scale70ΩΩ 60ΩΩ 50ΩΩ Plotting40ΩΩ impedance 30ΩΩ directly20ΩΩ 10ΩΩ/div500 psec/div Eric Bogatin 2000www.BogatinEnterprises.comSlide -32Training for Signal Integrity and Interconnect DesignMYTHSTwo Channel Differential TDR:Differential or Common DrivenDriving differential signal400mV-200mV--open0mV--200mV--openChannel 1Channel 2-400mV-200 psec/divDriving common signal400mV-200mV--open0mV--Channel 1Channel 2-200mV--open-400mV-200 psec/div Eric Bogatin 2000www.BogatinEnterprises.com

Slide -33Training for Signal Integrity and Interconnect DesignMYTHSMeasuring Odd and Even Impedance ofTightly Coupled LinesMeasured Impedance of one trace,trace as the other is driven:Odd mode impedance: differentially driven pairEven mode impedance: commonly driven pairFor identical lines:500 psec/divZ11 ½ (Zeven Zodd)ΩZ12 ½ (Zeven – Zodd) ic40ΩΩimpedance matrixReplace this with a good oneZevenCommon drivenZoddNot drivenDifferentially driven48.5 3.53.5 48.5 Eric Bogatin 2000www.BogatinEnterprises.comSlide -34Training for Signal Integrity and Interconnect DesignMYTHSDirect Measurement ofDifferential ImpedanceZdiff Zodd1 ��45ΩΩ40ΩΩ95ΩΩLine 1 Zodd90ΩΩLine 2 Zodd Eric Bogatin 2000www.BogatinEnterprises.com

Slide -35Training for Signal Integrity and Interconnect DesignMeasuring Differential Impedanceof Low Impedance TracesMYTHS-100ΩΩ- 80ΩΩDifferentialimpedance- 60ΩΩ- 40ΩΩ50ΩΩ 40ΩΩ 30ΩΩ Zodd20ΩΩ Eric Bogatin 2000www.BogatinEnterprises.comSlide -36Training for Signal Integrity and Interconnect DesignMYTHSFull Characterization of a DifferentiallyDriven, Differential MA50mV/divTDR250ΩΩ cableTDR1 Eric Bogatin 2000www.BogatinEnterprises.com

Slide -37Training for Signal Integrity and Interconnect DesignMYTHSFull Characterization of a Single EndDriven, Differential PairTDR1V1FEXTNEXTOdd mode hasshorter TD thaneven NEXT50ΩΩ cableTDR1 Eric Bogatin 2000www.BogatinEnterprises.comSlide -38Training for Signal Integrity and Interconnect DesignMYTHSDifferential Pair Over Split inthe Return Path1 inchWhat will be the behavior when:à single end drivenà differentially driven? Eric Bogatin 2000www.BogatinEnterprises.com

Slide -39Training for Signal Integrity and Interconnect DesignFull Characterization of a Single EndDriven, Differential PairOver a Split in the Return V/div50ΩΩ cableNEXTTDR1return current Eric Bogatin 2000www.BogatinEnterprises.comSlide -40Training for Signal Integrity and Interconnect DesignMYTHSFull Characterization of a DifferentiallyDriven, Differential PairOver a Split in the Return R250ΩΩ cableTDR1 Eric Bogatin 2000www.BogatinEnterprises.com

Slide -41Training for Signal Integrity and Interconnect DesignMeasured ImpedancesMYTHS140ΩΩ 120ΩΩ Differentialimpedance100ΩΩ 70ΩΩ Zodd50ΩΩ 30ΩΩ Eric Bogatin 2000www.BogatinEnterprises.comSlide -42Training for Signal Integrity and Interconnect DesignImpedance as the DielectricThickness IncreasesMYTHSCharacteristic Impedance (Ohms)Ansoft Maxwell 2D ExtractorZ11200180160Zdiff140Z21 Zdiff 140 Ohms with thebottom plane as the return path,when far away1201008060402000510152025303540Dielectric Thickness (mils)Ansoft Maxwell 2D Extractor4550(when Z21 is a large fraction of Z11,coupling dominates, differentialimpedance approaches singleended impedance) Eric Bogatin 2000www.BogatinEnterprises.com

Slide -43Training for Signal Integrity and Interconnect DesignMYTHSWhat Are the Return CurrentsWhen Driven Differentially? Eric Bogatin 2000www.BogatinEnterprises.comSlide -44Training for Signal Integrity and Interconnect DesignReturn Currents inDifferential PairsMYTHSMost return current is carried by the plane whentrace to plane coupling trace to trace couplingEx: most board level interconnectsMost return current is carried by the other tracewhen trace to plane coupling trace to tracecouplingEx: most connectors, shielded twisted pair, twistedpair Eric Bogatin 2000www.BogatinEnterprises.com

Slide -45Training for Signal Integrity and Interconnect DesignFirst Order Approximations toDifferential Impedance: MicrostripMYTHS s Zdiff 2Z0 1 0.48 exp 0.96 h shNational Semiconductor modelApnote 9051102(Z11-Z21)10090Impedance (Ohms)80Symbols are extracted with field solverLine is National model7060Z1150403020100012345678910 11 12 13 14 15 16 17 18 19 20Z21Edge to Edge Separation (mils) Eric Bogatin 2000www.BogatinEnterprises.comSlide -46Training for Signal Integrity and Interconnect DesignFirst Order Approximations toDifferential Impedance: StriplineMYTHS s Zdiff 2Z0 1 0.347 exp 2.9 b sbNational Semiconductor modelApnote 9051102(Z11-Z21)100Impedance (Ohms)90Symbols are extracted with field solverLine is National model807060Z115040302010001 23 45 67 89 10 11 12 13 14 15 16 17 18 19 20Edge to Edge Separation (mils) Eric Bogatin 2000Z21Note, accurate only for Z0values near 50 Ohms!www.BogatinEnterprises.com

Slide -47Training for Signal Integrity and Interconnect DesignImpact from Width of the LineMYTHSb 15 milss 5 milsSweeping wsb1101009080Impedance 12345678910 11 12 13 14 15 1617 18 19 20Line Wdith (mils) Eric Bogatin 2000www.BogatinEnterprises.comSlide -48Training for Signal Integrity and Interconnect DesignShielded Twin Leads,Changing Shield SizeMYTHSRadius of shield, r3Impedance (Ohms)filled with airr1 10 mils Single ended impedance 120ΩΩr2 25 milsε 4Pitch 50 Z11Z21Zdif0100200300400500600700Radius of Shield (mils)differential impedance approaches singleended impedance when rs 3 x pitch Eric Bogatin 2000Ansoft Maxwell 2D Extractorwww.BogatinEnterprises.com

Slide -49Training for Signal Integrity and Interconnect DesignSummaryMYTHS The impedance of one line in a differential pair depends on how the other isbeing driven:ü Measure odd impedance by driving differentiallyü Measure even impedance by driving in commonü Requires Differential TDR (DTDR) Characteristic impedance matrix elements can be extracted from odd andeven impedances A gap in the return path causes huge increase in cross talk in single endedlines due to high mutual inductance If you must cross a split plane, better to use a diff pairü Some increase in differential impedanceü Very little distortion of differential signalü Very little common voltage created Full characterization of differential pairs is possible with DTDR and dualchannel amplifier module Eric Bogatin 2000www.BogatinEnterprises.comSlide -50Training for Signal Integrity and Interconnect DesignMYTHSFor more information on resourcesand references, visit our web site:www.BogatinEnterprises.com Eric Bogatin 2000www.BogatinEnterprises.com

Differential Impedance Differential Impedance: the impedance the difference signal sees ( ) ( ) 2 2( ) Z 0 small I V I V diff Z diff one one Differential impedance decreases as coupling increases 1v -1v I one x I two How will the capacitance matrix elements be affected by spacing? C 12 C 11 C 22 Eric Bogatin 2000 Slide -18 www .File Size: 1MBPage Count: 25

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