Transcript ppt - SEAS
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 6: September 10, 2014 Restoration 1 Penn ESE370 Fall2014 -- 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 Fall2014 -- DeHon Outline • • • • • • Two problems Cascade failure Restoration Transfer Curves Noise Margins Non-linear 3 Penn ESE370 Fall2014 -- 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 Fall2014 -- DeHon Wire Resistance Monday: Rwire=10Ω Penn ESE370 Fall2014 -- DeHon R L A 5 Wire Resistance • 1000 mm long wire? • 1 cm long wire? • Length of integrated circuit chip side? – (we often call an IC chip a “die”) 6 Penn ESE370 Fall2014 -- DeHon Die Sizes Trans. Year Maker feature mm2 Bulldozer 1.2B 2012 AMD 32nm 315 Core i7 1.4B 2012 Intel 22nm 160 GK10 Kepler 7B 2012 NVIDIA 28nm 561 Chip source: http://en.wikipedia.org/wiki/Transistor_count 7 Penn ESE370 Fall2014 -- DeHon Implications • What does the circuit really look like for an inverter in the middle of the chip? 8 Penn ESE370 Fall2014 -- DeHon Implications • What does the circuit really look like for an inverter in the middle of the chip? Rwire Rwire Rrest_of_chip 9 Penn ESE370 Fall2014 -- 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 10 Penn ESE370 Fall2014 -- DeHon Output not go to Rail • Due to IR drop, “rails” for two communicating gates may not match Rrest_of_chip 11 Penn ESE370 Fall2014 -- 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 12 Penn ESE370 Fall2014 -- DeHon Noise Sources? • What did we see in lab when zoomed in on signal transition? • Signal coupling – Crosstalk • Leakage • Ionizing particles 13 Penn ESE370 Fall2014 -- 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? 14 Penn ESE370 Fall2014 -- DeHon Preclass • All 1’s logical output? 15 Penn ESE370 Fall2014 -- DeHon Preclass • 1.0 inputs, gate: o=1-AB output voltage? 16 Penn ESE370 Fall2014 -- DeHon Preclass • 0.95 inputs, gate: o=1-AB output voltage? 17 Penn ESE370 Fall2014 -- DeHon Degradation • Cannot have signal degrade across gates • Want to be able to cascade arbitrary set of gates 18 Penn ESE370 Fall2014 -- DeHon Gate Creed • Gates should leave the signal “better” than they found it – “better” closer to the rails 19 Penn ESE370 Fall2014 -- 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 next (between out and in) • Call this our “Noise Margin” 20 Penn ESE370 Fall2014 -- DeHon Noise Margin • Voh – output high • Vol – output low • Vih – input high • Vil – input low • NMh = Voh-Vih • NMl = Vil-Vol Penn ESE370 Fall2014 -- DeHon One mechanism, addresses numerous noise sources. 21 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 Fall2014 -- DeHon 22 Transfer Function What gate is this? 23 Penn ESE370 Fall2014 -- DeHon Restoring Transfer Function 24 Penn ESE370 Fall2014 -- DeHon Decomposing • What is gain? |DVout/DVin| > 1 • Where is there gain? • Where is there not gain? • Dividing point? 25 Penn ESE370 Fall2014 -- DeHon Restoring Transfer Function Vil, Vih = slope -1 points Voh =f(Vil) Vol=f(Vih) 26 Penn ESE370 Fall2014 -- 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 27 Penn ESE370 Fall2014 -- DeHon Controlling Value • Consider a nor2 gate – If want one input to control the output – What value should the other input be? • We call this input the non-controlling input since it does not determine the output • What should the non-controlling input value be for a nand2 gate? 28 Penn ESE370 Fall2014 -- 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) 29 Penn ESE370 Fall2014 -- DeHon Ideal Transfer Function 30 Penn ESE370 Fall2014 -- DeHon Linear Transfer Function? • O=Vdd-A Noise Margin? 31 Penn ESE370 Fall2014 -- 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 32 Penn ESE370 Fall2014 -- 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. 33 Penn ESE370 Fall2014 -- DeHon Non-linearity • Need non-linearity in transfer function • Could not have built restoring gates with – R, L, C circuit – Linear elements 34 Penn ESE370 Fall2014 -- DeHon Transistor Non-Linearity 35 Penn ESE370 Fall2014 -- 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 Fall2014 -- DeHon gG gG 36 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 37 Penn ESE370 Fall2014 -- DeHon Admin • HW2 due Thursday (tomorrow) – Noise margin problem • Friday in Ketterer (note combo) – Read through HW3 – Transfer library/schematics to eniac – Be ready to run electric and spice on linux • CETS machines • <or> own laptop that you bring with you • Monday back here 38 Penn ESE370 Fall2014 -- DeHon