1EE141 – Fall 2005Lecture 11Wire ModelsWire ModelsEE141 2Administrative Stuff No Labs, no Hw this week Lab 5 next week Review session today • 6:30-8:30pm (277 Cory) Thursday, October 6• No lecture on Thu• Midterm 1: 6:30-8:00pm (277 Cory)2EE141 3Agenda Last lecture• Introduction to wires: wire capacitance and resistance Today’s lecture• Introduction to wires: inductance, wire modelsInterconnectInterconnectCapacitanceCapacitance3EE141 5Modern InterconnectEE141 6WLtcdidiintε=LLCwireSSSSS1=⋅=Capacitance: The Parallel Plate ModelDielectricLWHElectrical-field linesCurrent flowtdiSubstrate4EE141 7W - H/2H+(a)(b)Fringing CapacitancefringeppEE141 8Fringing vs. Parallel PlateFrom: Bakoglu905EE141 9Interwire CapacitancefringingparallelEE141 10Impact of Interwire CapacitanceFrom: Bakoglu906InterconnectInterconnectResistanceResistanceEE141 12Wire ResistanceWLHR = ρH WLSheet ResistanceR0R1R2=7Interconnect:Interconnect:Modeling the WireModeling the WireEE141 14The Lumped ModelDriverVoutRdriverVinClumpedVoutCwire8EE141 15The Distributed RC Line2)(2LrcVout⋅=τ22xVtVrc∂∂=∂∂The Diffusion EquationEE141 16Step-Response of RC Wire as a Function of Time and Space0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.511.522.5time (nsec)voltage (V)x = L / 10 x = L / 4 x = L / 2 x = L9EE141 17The Elmore Delay: RC Chain∑∑∑∑====⋅=⋅=ijjNiiNijjNiiNRCCR111τEE141 18Wire Model Assume: Wire modeled by N equal-length segments For large values of N:()()NNRCNNNrcLNrcrcrcNLDN212)1(...2222+=+=+++=τ222rcLRCDN==τ10EE141 19RC ModelsEE141 20The Lumped RC-ModelThe Elmore Delay∑==NkikkDiRC1τ11EE141 21Driving an RC-LineVoutVinRS(rw,cw,L)222LcrCRCRCRwwwSwwwSD+=+=τwwwSpCRCRt 38.069.0+=EE141 22Design Rules of Thumb rc delays should only be considered when tpRC>> tpgateof the driving gate: rc delays should only be considered when the rise (fall) time at the line input is smaller than RC, the rise (fall) time of the linetrise< RC• when not met, the change in the signal is slower than the propagation delay of the wirerctLpgatecrit38.0>>M.J. Irwin, PSU, 200012InterconnectInterconnectInductanceInductanceEE141 24Common Wire Cross-Sectionscl = εµc - capacitance/lengthl - inductance/lengthCoaxialCableTri-plateStrip LineMicro StripWire aboveGround Plane12log2rrcπε=12log2 rrlπµ=Whcε=Whlµ=13EE141 25Inductance of Package Pins Make rise and fall times as slow as possibleChipMountingCavityLead FrameBonding WirePinLL’EE141 26VinrlcrlcrlcrlcVoutxg g g gThe Wave EquationThe Transmission Line2222tvlctvrcxv∂∂+∂∂=∂∂14EE141 27Lossless Transmission Line –Parameters Propagation speed: only a function of surrounding mediumrrclcvµεεµ011===lcvtf==1Speed of light in vacuumε: permittivity of insulatorµ: permeability of insulator Characteristic impedance = impedance presented by wireclZ =0100 to 500Ω for typical wiresEE141 28Wave Propagation SpeedDielectric Constants and Wave Propagation Speeds forVarious Materials used in Electronic CircuitsSource: Bakoglu9015EE141 29Wave Reflection for Different Terminations00ZRZRIIVVincreflinclrefl+−===ρReflectionCoefficientEE141 30T-Line Response (RL= ∞)VDestVSource0.01.02.03.04.05.0V0.01.02.03.04.0V0.0 5.0 10.0 15.00.02.04.06.08.0V(a)(b)(c)t (in tflight)RS= 5Z0RS= Z0RS= Z0/516EE141 31V at each end = Vlast+ Vincident+ VreflectedLattice Diagram0.8333 V1.6666 V+ 0.8333+ 0.8333+ 0.5556+ 0.5556+ 0.3704+ 0.2469+ 0.3704+ 0.24692.2222 V3.1482 V3.7655 V...2.7778 V3.5186 V4.0124 VL/νtVSourceVDestEE141 32(1990, Bakoglu)100-200ps todayLcrit ~ 1cmCritical Line Lengths vs. Rise Times17EE141 33Design Rules of Thumb Transmission line effects should be considered when the rise or fall time of the input signal (tr, tf ) is smaller than the time-of-flight of the transmission line (tflight):tr (tf ) < 2.5tflight Transmission line effects should only be considered when the total resistance of the wire is limited:R < 5Z0 The transmission line is considered lossless when the total resistance is substantially smaller than the characteristic impedance: R < Z0/ 2EE141 34Should We be Worried? Transmission line effects cause overshooting and non-monotonic behaviorClock signals in 400 MHz IBM Microprocessor(measured using e-beam probe) [Restle98]18EE141 35Next Lecture CMOS
View Full Document