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Berkeley ELENG 290C - Channels : Physical Components & Channel Modeling

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1EE290C - Spring 2004Advanced Topics in Circuit DesignHigh-Speed Electrical InterfacesLecture #2Channels : Physical Components & Channel ModelingJared Zerbe1/22/042AgendaComponentsBasic wiresReal wires & metricsDesign and modeling Channel model verification23Signaling componentsLarge span of different types of interconnectChip to chip on a PCBShort, well controlled, often busses are cheapPackaging usually limits speedCables connecting chips on two different PCBsCables are lossy, but relatively clean if coaxConnector transitions usually the bad partHigh-speed board-to-board connectorsDaughtercard (mezzanine-type)Backplane connectors4Caveat EmptorThere’s a lot of old junk out thereThere’s even new junk out therePeople are always looking for a way to run fast without spending $$ on expensive components35Different Components You’ll FindSMA connectorsGood SIcan be a pain (threaded)SMB connectorsNot as good SIsnap on/offSSMB connectorssomewhere in-betweensnap on/off; gimbledmore expensiveBackplane, connector, linecardCat4k router6AgendaComponentsBasic wiresReal wires & metricsDesign and modeling Channel model verification47Resistance of WiresMost real wires have resistanceDepends on material (resistivity)lengthcross sectionCauses delaylossLARLA=ρMaterialρ (nΩ-m)Ag 16Cu 17Au 22Al 27becomesFigure © 2001 Bill Dally8Capacitance of WiresReal wires have capacitanceline chargeparallel platefringingTo computeassume Qcompute E fieldintegrate to get VCrroi=2πεlogCQV=EQr=2πCsr=2πεlog()Cwdsr=+επε22log()22πεlogsrFigure © 2001 Bill Dally59Inductance of WiresReal wires have inductanceIn a homogenous mediumCL =εµLI=ΛFigure © 2001 Bill Dally10Some Example WiresType W R C LOn chip 0.6µm 150kΩ/m 200pf/m 600nH/mPC Board 150µm5Ω/m 100pf/m 300nH/m24AWG pair 511µm0.08Ω/m 40pf/m 400nH/mScale model of a line has different R, but same L and C per unit lengthFigure © 2001 Bill Dally611RLGC Wire ModelModel an infinitesimal length of wire, dx, with lumped componentsL, R, C, and G(as per unit length parameters)Lossless line Rdx, Gdx ~ 0When not 0DC lossAttenuationRdxLdxCdx GdxdxFigure © 2001 Bill Dally12Transmission Line EquationsRdxLdxCdx GdxdxtILRIxV∂∂+=∂∂Drop across R and LCurrent into C and GtVCGVxI∂∂+=∂∂2222tVLCtVLG)(RCRGVxV∂∂+∂∂++=∂∂Differentiating the first (∂/∂x) and substituting into the secondFrom KVL and KCLFigure © 2001 Bill Dally713ImpedanceAn infinite length of LRCG transmission line has an impedance Z0Driving a line terminated into Z0is the same as driving Z0In general Z0is complex and frequency dependentFor LC lines its real and independent of frequencyRdxLdxCdx GdxZ0=Z0210++=CsGLsRZAt high frequency (LC lines)210=CLZFigure © 2001 Bill Dally14Propagation ConstantUsing impedance, we can solve for V(s,x)Propagation is governed by a constant, Areal part is attenuationimaginary part is phase shiftvelocity-1Rdx LdxCdx GdxZ0V(s,x)V(s,x+dx)+–+–I(s,x)()()()[]()()[]21210)exp()0,(),()()()()()(LsRCsGAAxsVxsVsVLsRCsGZsVLsRsILsRxsV++=−=++−=+−=+−=∂∂Figure © 2001 Bill Dally815Skin EffectAs signal goes up in frequency, current crowds along the surface of the conductorSkin depth proportional to f -½Model as if skin is δ thickEffect does not occur until frequency, fs, at which skin depth equals conductor radiusFigure © 2001 Bill Dally16100100MHz 500MHz MHz 500MHz 1GHz1GHzW=210um、t=28umδ=6.6 um δ=2.08 umδ=2.95 umSkin depthSkin Effect – Current Crowding f(freq)917Frequency-Dependent LossHigh frequency signals jiggle molecules in the insulatorInsulator actually absorbs energyEffect is approximately linear with frequencyModeled as conductance term in transmission line equationsDielectric loss often specified in terms of loss tangentTransfer fcn = e^(-alpha *unit-L)Figure © 2001 Bill Dally18What’s an S21?An S21 (or S12) is simply a plot of output magnitude normalized to input magnitude as a function of frequency (plotted in –db or linear)Very helpful in forming understanding of channel characteristicsBreakdown of a 26" FR4 channel with 270 mil stubs0.00.10.20.30.40.50.60.70.80.91.00.0E+00 5.0E+08 1.0E+09 1.5E+09 2.0E+09 2.5E+09 3.0E+09 3.5E+09 4.0E+09Frequency, HzTransfer functionPCB trac esPCB traces & connectorsPCB trac es, connectors & viasEnt ire chan nel1019Conductor and Dielectric LossesPCB Loss: DC, skin & dielectric lossSkin Loss ∝√fDielectric loss ∝ f : a bigger issue at higher fFrequency8 mil wide and 1 m long 50 Ohm strip line-40.0-30.0-20.0-10.00.01.E+06 1.E+07 1.E+08 1.E+09 1.E+10Frequency, HzAttenuationFR4Roger 435020AgendaComponentsBasic wiresReal wires & metricsDesign and modeling Channel model verification1121The Real Backplane EnvironmentConnectorLine card trace PackageChipBackplane trace Backplane viaPackage-to-board viaLine card via22Practical PCB Differential WiresDifferential signaling has nice propertiesMany sources of noise can be made common-modeDifferential impedance raised as f(mutuals) between wiresStrong mutual L, C can improve immunitytttWS-HH+SWεrttH+-µ -StripStrip-line1223Differential Wires – O/E ImpedanceAs space increases between wires they become essentially single-endedRaise impedance of single-trace to make 100Ohm diff0102030405060700123456S/Wimpedance (Ω)ZoddZevenZevenZodd= 2 * common-mode impedance= ½ differential impedance24Hspice Differential W-element ModelFreq dependent loss termsMutual termsRdxLdxCdx GdxDiagonal terms ofMatrix; only one sideCompute RLGC at anyFrequency and you can computeRs, Gd1325ReflectionsSources of Reflections : Z - DiscontinuitiesPCB ZsConnector ZsVias (through) ZsPackage Zs Termination ZsTDR impedance profile 70758085909510010511011500.511.52Time, nsImpedance, OhmsLCPackageLC viaBP viaConnectorZ1Z2Z2 - Z1Z1 + Z2______26Example of Reflections400–+50Ω, 5ns1KΩSR1VFigure © 2001 Bill Dally1427Example of Reflections400–+50Ω, 5ns1KΩSRkrS=−+=400 50400 500778.1VVV Vi=+=150400 500111.krR=−+=1000 501000 500905.Figure © 2001 Bill Dally28Example of Reflections400–+50Ω, 5ns1KΩSRkrS=−+=400 50400 500778.1VVV Vi=+=150400 500111.krR=−+=1000 501000 500905.Vwave Vline tVi1 0.111 0.111 0Vr1 0.101 0.212 5Vi2 0.078 0.290 10Vr2 0.071 0.361 15Vi3 0.055 0.416 20Vr3 0.050 0.465 25Vi4 0.039 0.504 30Vr4 0.035 0.539 35Vi5 0.027 0.566 40Figure © 2001 Bill


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