Transcript ppt
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 16: October 7, 2013 Inverter Performance 1 Penn ESE370 Fall2013 -- DeHon Previously • Delay as RC-charging • Transistor – Capacitance – Drive Current – As a function of geometry (W/L) 2 Penn ESE370 Fall2013 -- DeHon Today t-model • Sizing • Large Fanout • Capacitance Revisited – Miller Effect – Parallel Gate Capacitance 3 Penn ESE370 Fall2013 -- DeHon Transistor Sizing • What happens to Ids as a function of W? VDSAT IDS satCOX W VGS VT 2 • What happens to Cg as a function of W? CG CoxWL • Conclude: faster transistors present more load on their inputs Penn ESE370 Fall2013 -- DeHon 4 First Order Delay • R0 = Resistance of minimum size NMOS device • C0 = gate capacitance of minimum size NMOS device • Rdrive = R0/W • Cg = WC0 5 Penn ESE370 Fall2013 -- DeHon First Order Delay (alt view) • I0 = Ids of minimum size NMOS device • C0 = gate capacitance of minimum size NMOS device • Idrive = WI0 • Cg = WC0 IDS VDSAT satCOX W VGS VT 2 6 Penn ESE370 Fall2013 -- DeHon t model • All delays are RC delays (CV/I delays) • Always have an R0C0 term (C/I term) t= R0C0 (equivalently C0/I0) • Express all delays in t units • Like l units for measurement – Separate delay into • Technology dependent term t= R0C0 • Technology independent term 7 Penn ESE370 Fall2013 -- DeHon Inverter Sizing • What is the impact of the delay on the middle inverter if double size of all the transistors? 8 Penn ESE370 Fall2013 -- DeHon How Size • How size to equalize Rise and Fall? mn=500cm2/Vs, mp=200cm2/Vs – When velocity saturated – Rdrive=R0/2 (Idrive=2I0) IDS VDSAT satCOX W VGS VT 2 9 Penn ESE370 Fall2013 -- DeHon SPICE Simulation 10 Penn ESE370 Fall2013 -- DeHon SPICE Simulation 22nm 11 Penn ESE370 Fall2013 -- DeHon Worst Case Delay • Largest R • Rdrive = max(Rpullup,Rpulldown) • If equalize Rpullup and Rpulldown – Rdrive = Rpullup=Rpulldown 12 Penn ESE370 Fall2013 -- DeHon Equalizing Delay • For simplicity, for today – Assume Wp=Wn equalizes Ids 13 Penn ESE370 Fall2013 -- DeHon Large Fanout • What is delay if must drive fanout=100? 14 Penn ESE370 Fall2013 -- DeHon What Delay? • What is delay here? 15 Penn ESE370 Fall2013 -- DeHon How Size • How size transistors to minimize delay? 16 Penn ESE370 Fall2013 -- DeHon Optimizing • • • • • Delay = 2Wmid/1 + 200/Wmid How minimize? D(Delay)/D(Wmid) = 0 2 – 200/(Wmid)2=0 Wmid=sqrt(100) = 10 17 Penn ESE370 Fall2013 -- DeHon Delay? • Delay at optimal Wmid? 18 Penn ESE370 Fall2013 -- DeHon Try again • What is the delay here? 19 Penn ESE370 Fall2013 -- DeHon …and Again • Delay here? 20 Penn ESE370 Fall2013 -- DeHon Lesson • • • • Don’t drive large fanout with a single stage Must scale up over a number of stages …but not too many Exact number will be technology dependent 21 Penn ESE370 Fall2013 -- DeHon Charge on Capacitors 22 Penn ESE370 Fall2013 -- DeHon Questions • What is DQ when switched? • Equivalent Capacitance? • Contribution from each transistor? 23 Penn ESE370 Fall2013 -- DeHon Gate-Drain Capacitance • What is the voltage across Vin—V2 – When Vin=Vdd – When Vin=Gnd • What is DV across Vin—V2 when Vin switches from Vdd to Gnd? 24 Penn ESE370 Fall2013 -- DeHon Miller Effect • For an inverting gate • Capacitance between input and output must swing 2 Vhigh • Or…acts as doublesized capacitor 25 Penn ESE370 Fall2013 -- DeHon If Time Permits (back to scaling) 26 Penn ESE370 Fall2013 -- DeHon Improving Gate Delay tgd=Q/I=(CV)/I V S×V How might we accelerate? Id=(mCOX/2)(W/L)(Vgs-VTH)2 Id S×Id C S×C tgd S×tgd Penn ESE370 Fall2013 -- DeHon Lower C. Don’t scale V. Don’t scale V: VV II/S tgd S2×tgd 27 …But Power Dissipation (Dynamic) • Capacitive (Dis)charging P=(1/2)CV2f V V C S×C • Increase Frequency? f f/S2 ? P P/S If not scale V, power dissipation not scale down. 28 Penn ESE370 Fall2013 -- DeHon …And Power Density • P P/S (increase frequency) • But… A S2×A • What happens to power density? • P/A (1/S3)P • Power Density Increases …this is where some companies have gotten into trouble… 29 Penn ESE370 Fall2013 -- DeHon Historical Voltage Scaling http://software.intel.com/en-us/articles/gigascale-integration-challenges-and-opportunities/ • Frequency impact? • Power Density impact? Penn ESE370 Fall2013 -- DeHon 30 Scale V separately from S tgd=Q/I=(CV)/I V Id=(mCOX/2)(W/L)(Vgs-VTH)2 Id V2/S×Id C S×C tgd (SV/(V2/S))×tgd tgd (S2/V)×tgd Penn ESE370 Fall2013 -- DeHon Ideal scale: S=1/100 V=1/100 t=1/100 Fideal=100 Cheating: S=1/100 V=1/10 t=1/1000 Fcheat=1000 fcheat/fideal=10 31 Power Density Impact • P=1/2CV2 f • P~= S V2 (V/S2) = V3/S • P/A = (V3/S) / S2 = V3/S3 • V=1/10 S=1/100 • P/A 1000 (P/A) 32 Penn ESE370 Fall2013 -- DeHon uProc Clock Frequency MHz The Future of Computing Performance: Game Over or Next Level? National Academy Press, 2011 33 Penn ESE370 Fall2013 -- DeHon http://www.nap.edu/catalog.php?record_id=12980 uP Power Density Watts The Future of Computing Performance: Game Over or Next Level? National Academy Press, 2011 34 Penn ESE370 Fall2013 -- DeHon http://www.nap.edu/catalog.php?record_id=12980 Ideas • First order delay reason in t=R0C0 units – Equivalently (C0/I0) units • Scaling everything up doesn’t help • Drive large capacitive loads in stages 35 Penn ESE370 Fall2013 -- DeHon Admin • HW5 due Tuesday • Midterm solutions posted 36 Penn ESE370 Fall2013 -- DeHon