EE2411UC Berkeley EE241 B. NikolicEE241 - Spring 2002Advanced Digital Integrated CircuitsLecture 25Driving InterconnectUC Berkeley EE241 B. NikolicReadingl Chapter 17, Techniques for Driving Interconnect, by S.V. Mortonl Chapter 18, I/O and ESD Circuit Design, by S.C. Thiearuf and W.R. Andersonl Digital Systems Engineering, by W.J. Dally and J.W. Poulton, Cambridge’98l High-Speed Digital System Design, by S.H. Hall, G.W. Hall, J.A. McCall, Wiley 2000.EE2412UC Berkeley EE241 B. NikolicCommon Wire Cross-SectionsCoaxialCableTriplateStrip LineMicroStrip Wire aboveGround PlaneCL = εµUC Berkeley EE241 B. NikolicWire ExamplesType W R C LOn chip 0.6µm 150kΩ/m 200pf/m 600nH/mPC Board 150µm 5Ω/m 100pf/m 300nH/m24AWG pair 511µm 0.08Ω/m 40pf/m 400nH/m[Dally]EE2413UC Berkeley EE241 B. NikolicTransmission LinesVinrlcrlcrlcrlcVoutxg g g gReturn pathWith g = 0:UC Berkeley EE241 B. NikolicTransmission LinesRdxLdxCdx GdxdxtILRIxV∂∂+=∂∂Drop across R and LCurrent into C and GtVCGVxI∂∂+=∂∂2222tVLCtVLG)(RCRGVxV∂∂+∂∂++=∂∂[Dally]EE2414UC Berkeley EE241 B. NikolicThe Lossless Transmission LineUC Berkeley EE241 B. NikolicTraveling WavesRdx LdxCdx GdxZ0V(s,x)V(s,x+dx)+–+–I(s,x)( )( )( )[ ]( )( )[ ]21210)exp()0,(),()()()()()(LsRCsGAAxsVxsVsVLsRCsGZsVLsRsILsRxsV++=−=++−=+−=+−=∂∂EE2415UC Berkeley EE241 B. NikolicTraveling Waves( )( )( )21021maxmax2222,,,0,==−−=−=∂∂=∂∂−CLZLCvvxxtxVtxVvxtVtxVtVLCxVrfResponse equals sum of incident and reflected wavesLossless LC,wave equationUC Berkeley EE241 B. NikolicWave Reflection for Different TerminationsEE2416UC Berkeley EE241 B. NikolicTransmission Line Response (RL= ∞)0.01.02.03.04.05.0V0.01.02.03.04.0V0.0 5.0 10.0 15.0t (in tlightf)0.02.04.06.08.0VRS = 5Z0RS = Z0RS = Z0/5(a)(b)(c)VDestVSourceUC Berkeley EE241 B. NikolicLossy LRC Transmission Lines(1) Resistive LossIf (R > Lω)Line acts as RC lineIf (R < Lω)Incident and reflected waves are attenuated:combination of travelling wave and diffusive behaviorV(x)/V(0) = exp(-Rx/2Z0) = exp(-Ax)Wave propagationDiffusion anddispersionCut-off frequency:fo= R/(2ΠL)EE2417UC Berkeley EE241 B. NikolicWaveforms in lossy transmission lineUC Berkeley EE241 B. NikolicWaveforms inlossytransmission lineIf R l >> 2 Z0RC like behaviorif R l = Z0/278% of step reachesend of lineHence transmission linebehavior if Rl < Z0/2On-chip wires(Al, 0.35 micron):R = 74 Ω/mm(minimum width)Z0 = ~ 50 Ω(assume c = 160 fF/mmand l = 0.27 nH/mm)or:l < 1/3 mm forminimum width wireEE2418UC Berkeley EE241 B. NikolicInductance versus ResistanceUC Berkeley EE241 B. NikolicCopper MetalizationIBM 7S processLeff = 0.12 micron6 copper layersEE2419UC Berkeley EE241 B. NikolicSkin EffectFor f > fsUC Berkeley EE241 B. NikolicImpact of Skin EffectResistance andAttenuation for5 mil strip guideand 24 AWG twisted
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