Transcript ppt
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 6: September 17, 2012 Restoration 1 Penn ESE370 Fall2012 -- DeHon Today • How do we make sure logic is robust – Can assemble into any (feed forward) graph – Can tolerate voltage drops and noise – ….while maintaining digital abstraction 2 Penn ESE370 Fall2012 -- DeHon Outline • • • • • • Two problems Cascade failure Restoration Transfer Curves Noise Margins Non-linear 3 Penn ESE370 Fall2012 -- DeHon Two Problems 1. Output not go to rail – Stops short of Vdd or Gnd 2. Signals may be perturbed by noise Vx = Videal ± Vnoise 4 Penn ESE370 Fall2012 -- DeHon Output not go to Rail • CMOS, capacitive load – Mostly doesn’t have problem • CMOS, resistive load? 5 Penn ESE370 Fall2012 -- DeHon Output not go to Rail • Consider: – Vdd=1V – Vin=Gnd (both inputs) – Ron (PMOS) = 500Ω – Rload = 10KΩ Ron=500 Ω Ron=500 Ω Rload=10K Ω • What is Vout? – How close to rail do I need to get? 6 Penn ESE370 Fall2012 -- DeHon Wire Resistance Last Wednesday: Rwire=10Ω Penn ESE370 Fall2012 -- DeHon R L A 7 Wire Resistance • 1000 mm long wire? • 1 cm long wire? • Length of die side? 8 Penn ESE370 Fall2012 -- DeHon Die Sizes Processor Die Size Transistor Count Process Core 2 Extreme X6800 143 mm² 291 Mio. 65 nm Core 2 Duo E6700 143 mm² 291 Mio. 65 nm Core 2 Duo E6600 143 mm² 291 Mio. 65 nm Core 2 Duo E6400 111 mm² 167 Mio. 65 nm Core 2 Duo E6300 111 mm² 167 Mio. 65 nm Pentium D 900 280 mm² 376 Mio. 65 nm Athlon 64 FX-62 230 mm² 227 Mio. 90 nm Athlon 64 5000+ 183 mm² 154 Mio. 90 nm http://www.tomshardware.com/reviews/core2-duo-knocks-athlon-64,1282-4.html 9 Penn ESE370 Fall2012 -- DeHon Implications • What does the circuit really look like for an inverter in the middle of the chip? 10 Penn ESE370 Fall2012 -- DeHon Implications • What does the circuit really look like for an inverter in the middle of the chip? Rwire Rwire Rrest_of_chip 11 Penn ESE370 Fall2012 -- DeHon IR-Drop Rrest_of_chip • Since interconnect is resistive and gates pull current off the supply interconnect – The Vdd seen by a gate is lower than the supply Voltage by • Vdrop=Isupply x Rdistribute – Two gates in different locations • See different Rdistribute • Therefore, see different Vdrop 12 Penn ESE370 Fall2012 -- DeHon Output not go to Rail • CMOS, capacitive load no problem • CMOS, resistive load voltage divider • Due to IR drop, “rails” for two communicating gates may not match 13 Penn ESE370 Fall2012 -- DeHon Two Problems 1. Output not go to rail – Is this tolerable? 2. Signals may be perturbed by noise – Voltage seen at input to a gate may not lower/higher than input voltage 14 Penn ESE370 Fall2012 -- DeHon Noise Sources? • What did we see in lab when zoomed in on signal transition? • Signal coupling – Crosstalk • Leakage • Ionizing particles • IR-drop in signal wiring 15 Penn ESE370 Fall2012 -- DeHon Signals will be degraded 1. Output not go to rail – Is this tolerable? 2. Signals may be perturbed by noise – Voltage seen at input to a gate may not lower/higher than input voltage • What happens to degraded signals? 16 Penn ESE370 Fall2012 -- DeHon Preclass • All 1’s logical output? 17 Penn ESE370 Fall2012 -- DeHon Preclass • 1.0 inputs, gate: o=1-AB output voltage? 18 Penn ESE370 Fall2012 -- DeHon Preclass • 0.95 inputs, gate: o=1-AB output voltage? 19 Penn ESE370 Fall2012 -- DeHon Degradation • Cannot have signal degrade across gates • Want to be able to cascade arbitrary set of gates 20 Penn ESE370 Fall2012 -- DeHon Gate Creed • Gates should leave the signal “better” than they found it – “better” closer to the rails 21 Penn ESE370 Fall2012 -- DeHon Restoration Discipline • Define legal inputs – Gate works if Vin “close enough” to the rail • Restoration – Gate produces Vout “closer to rail” • This tolerates some drop between one gate and text (between out and in) • Call this our “Noise Margin” 22 Penn ESE370 Fall2012 -- DeHon Noise Margin • Voh – output high • Vol – output low • Vih – input high • Vil – input low • NMh = Voh-Vih • NMl = Vil-Vol Penn ESE370 Fall2012 -- DeHon One mechanism, addresses numerous noise sources. 23 Restoration Discipline (getting precise) • Define legal inputs – Gate works if Vin “close enough” to the rail – Vin > Vih or Vin < Vil • Restoration – Gate produces Vout “closer to rail” • Vout < Vol or Vout > Voh Note: don’t just say Vin>Vih Vout>Voh Penn ESE370 Fall2012 -- DeHon 24 Transfer Function What gate is this? 25 Penn ESE370 Fall2012 -- DeHon Restoring Transfer Function 26 Penn ESE370 Fall2012 -- DeHon Decomposing • Where is there gain? • What is gain? |DVout/Dvin| > 1 • Where is there not gain? • Dividing point? 27 Penn ESE370 Fall2012 -- DeHon Restoring Transfer Function Vil, Vih = slope -1 points Voh =f(Vil) Vol=f(Vih) 28 Penn ESE370 Fall2012 -- DeHon Restoring Transfer Function Vil, Vih = slope -1 points Voh =f(Vil) • Closer to rail Vol=f(Vih) than Vil, Vih • Not make much difference on Vout • Making Vil lower would reduce NM = Vil-Vol 29 Penn ESE370 Fall2012 -- DeHon Restoring Transfer Function For multi-input functions, should be worst case. i.e. hold non-controlling inputs at Vil, Vih respectively. (relate preclass exercise) 30 Penn ESE370 Fall2012 -- DeHon Ideal Transfer Function 31 Penn ESE370 Fall2012 -- DeHon Class Ended Here 32 Penn ESE370 Fall2012 -- DeHon Linear Transfer Function? • O=Vdd-A Noise Margin? 33 Penn ESE370 Fall2012 -- DeHon Linear Transfer Function? • Consider two in a row (buffer) • O1=Vdd-A • What is transfer function to buffer output O2? • O2=(Vdd-O1) = Vdd-(Vdd-A)=A 34 Penn ESE370 Fall2012 -- DeHon Linear Transfer Function? • For buffer: O2=A • Consider chain of buffers • What happens if A drops a bit between each buffer? Ai+1 = Ai-Δ Conclude: Linear transfer functions do not provide restoration. 35 Penn ESE370 Fall2012 -- DeHon Non-linearity • Need non-linearity in transfer function • Could not have built restoring gates with – R, L, C circuit – Linear elements 36 Penn ESE370 Fall2012 -- DeHon Transistor Non-Linearity 37 Penn ESE370 Fall2012 -- DeHon All Gates • If we hope to assemble design from collection of gates, – Voltage levels must be consistent and supported across all gates – Must adhere to a Vil, Vih, Vol, Voh that is valid across entire gate set Vol MAX g.Vol Vil MIN g.Vil Voh MIN g.Voh Vih MAX g.Vih gG gG Penn ESE370 Fall2012 -- DeHon gG gG 38 Admin • Wednesday in Ketterer – Lab combo – Read through HW2 – Transfer library/schematics to eniac – Be ready to run electric and spice on linux • CETS machines • <or> own laptop that you bring with you • Friday back here 39 Penn ESE370 Fall2012 -- DeHon Big Idea • Need robust logic – Can assemble into any (feed forward) graph – Can tolerate loss and noise – ….while maintaining digital abstraction • Restoration and noise margins – Every gate makes signal “better” – Design level of noise tolerance 40 Penn ESE370 Fall2012 -- DeHon