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ESE370: Circuit-Level Previously Modeling, Design, and Optimization for Digital Systems • Where capacitance arises • What drives delay – How to optimize • Power as a limiting constraint Day 17: October 15, 2012 Energy and Power Basics – Energy, Power Density 1 Penn ESE370 Fall2012 -- DeHon 2 Penn ESE370 Fall2012 -- DeHon Today Power • P=I×V Power Sources • Static • Capacitive Switching • Short Circuit (Day 18) • Where should we look at I? 3 Penn ESE370 Fall2012 -- DeHon 4 Penn ESE370 Fall2012 -- DeHon Power Observe • P=IV • What’s V? • What is I? • I changes over time • Data dependent • At least two components – Steady-State (input fixed)? – When input switches – Istatic – no switch – Iswitch – when switch • 01 • 10 Penn ESE370 Fall2012 -- DeHon 5 Penn ESE370 Fall2012 -- DeHon 6 1 Data Dependent? Static Power • How does value of input impact Istatic? • Where does Istatic come from? – Subthreshold leakage – Gate-Drain leakage IDS ⎛ VGS −VT ⎞ ⎟ nkT / q ⎠ ⎛ W ⎞ ⎜ = ISʹ′⎜ ⎟e⎝ ⎝ L ⎠ ⎛ VDS ⎞ ⎞ ⎛ ⎟ −⎜ ⎜1 − e ⎝ kT / q ⎠ ⎟(1+ λVDS ) ⎝ ⎠ 7 Penn ESE370 Fall2012 -- DeHon Penn ESE370 Fall2012 -- DeHon 8 € Data Dependent? Billion Transistor Leakage • How does value of input impact Istatic? • • • • 9 Penn ESE370 Fall2012 -- DeHon ITRS 2009 45nm 100nA/µm Isd,sat 1200 µA/µm Cg,total 1fF/µm Vth 285mV Penn ESE370 Fall2012 -- DeHon 10 Leakage Power High Performance Isd,leak 4 Billion transistors Say 1 Billion gates Each with one W=2 transistor leaking How much leakage current? • 4 Billion Transistor chip doing nothing • Total Leakage? • Leakage Power? Ileak0 = 0.045µm × Isd,leak Penn ESE370 Fall2012 -- DeHon 11 Penn ESE370 Fall2012 -- DeHon 12 2 Reduce Leakage? ITRS 2009 45nm Low Power Isd,leak High Performance 100nA/µm Isd,sat Cg,total 1200 µA/µm 1fF/µm 560µA/µm 0.91fF/µm Vth 285mV 585mV • P=VI IDS ⎛ VGS −VT ⎞ ⎟ nkT / q ⎠ ⎛ W ⎞ ⎜ = ISʹ′⎜ ⎟e⎝ ⎝ L ⎠ ⎛ VDS ⎞ ⎞ ⎛ ⎟ −⎜ ⎜1 − e ⎝ kT / q ⎠ ⎟(1+ λVDS ) ⎝ ⎠ • How do we reduce leakage? Ileak0 = 0.045µm × Isd,leak € 13 Penn ESE370 Fall2012 -- DeHon 50pA/µm 14 Penn ESE370 Fall2012 -- DeHon Low Power Process • 4 Billion Transistor chip doing nothing • Total Leakage? • Leakage Power? Switching 15 Penn ESE370 Fall2012 -- DeHon Switching Penn ESE370 Fall2012 -- DeHon 16 Switching Currents • Where does current go during switching? • Charge (discharge) output • If both transistor on: – Current path from Vdd to Gnd Penn ESE370 Fall2012 -- DeHon 17 Penn ESE370 Fall2012 -- DeHon 18 3 Switching Currents Charging • Iswitch(t) = Isc(t) + Idyn(t) • Idyn(t) – why changing? – Ids = f(Vds,Vgs) – and Vgs, Vds changing • I(t) = Istatic(t)+Iswitch(t) ⎛ ⎞ V IDS ≈ ν sat COX W ⎜VGS − VT − DSAT ⎟ ⎝ 2 ⎠ ⎛ W ⎞⎡ V 2 ⎤ IDS = µn COX ⎜ ⎟⎢(VGS − VT )VDS − DS ⎥ ⎝ L ⎠⎣ 2 ⎦ 19 Penn ESE370 Fall2012 -- DeHon € Penn ESE370 Fall2012 -- DeHon 20 € Look at Energy E= Energy to Switch ∫ P(t)dt ∫ I(t)V dt E = V ∫ I(t)dt E= P ≈ E dyn /t switch E= €€ ∫ I(t)V dd Penn ESE370 Fall2012 -- DeHon dt dd dd 21 22 Penn ESE370 Fall2012 -- DeHon € € Integrating € • Do we know what this is? Capacitor Charge • Do we know what this is? ∫ I(t)dt Q= ∫ I(t)dt • What is Q? Penn ESE370 Fall2012 -- DeHon € 23 Penn ESE370 Fall2012 -- DeHon 24 € 4 Capacitor Charge Q = CV = Capacitor Charging Energy E = Vdd ∫ I(t)dt Q = CV = ∫ I(t)dt E = CVdd2 ∫ I(t)dt 25 Penn ESE370 Fall2012 -- DeHon Penn ESE370 Fall2012 -- DeHon 26 € € € Switching Power • Every time switch 01 pay: – E = • Pdyn = (# trans) × ½CV2 / time • Often like to think about switching frequency • Useful to consider per clock cycle CV2 • Pdyn = (# 01 trans) × CV2 / time – Frequency f = 1/clock-period • # 01 trans = ½ # of transitions • Pdyn = (# trans) × ½CV2 / time Penn ESE370 Fall2012 -- DeHon Charging Power • Pdyn = (#trans/clock) ½CV2 f 27 Charging Power ITRS 2009 45nm • Pdyn = (#trans/clock) ½CV2 f • Let a = activity factor a = average #tran/clock • Pdyn = a½CV2 28 Penn ESE370 Fall2012 -- DeHon f Low Power Isd,leak Isd,sat High Performance 100nA/µm 1200 µA/µm Cg,total Vth 1fF/µm 285mV 0.91fF/µm 585mV 50pA/µm 560µA/µm C0 = 0.045µm × Cg,total Penn ESE370 Fall2012 -- DeHon 29 C0 = 0.045 × 10-15 F Penn ESE370 Fall2012 -- DeHon 30 5 Switching Power Switching Power • 4 Billion Transistors – Organized into 1 billion gates (e.g. nand2) • • • • Cload = 22C0 a=0.2 f=1GHz Power? Penn ESE370 Fall2012 -- DeHon • V=1V • Cload=22C0 ≈ 1 fF = 10-15F • P=a(0.5×10-15)(Ngate)f • a=0.2 • P=10-16(Ngate)f 31 Dynamic vs. Static Power Compare • At what speed (f) does leakage power dominate switching power? Penn ESE370 Fall2012 -- DeHon 32 Penn ESE370 Fall2012 -- DeHon • • • • • 33 Charging Power WN = 2 Ileak = 9×10-9 A P=a(0.5×10-15) f + 9×10-9 W a=0.2 P=10-16×f + 9×10-9 W For what freqs does leakage power dominate switching power? Penn ESE370 Fall2012 -- DeHon 34 Data Dependent Activity • Pswitch = a(½C)V2f • Consider an 8b counter – What is activity, a, for: • Low bit? • High bit? • Average across all 8 output bits? • What values can a take on? o a>1? o a<1? • Assuming random inputs (no glitching) – Activity at output of nand4? – Activity at output of xor4? Penn ESE370 Fall2012 -- DeHon 35 Penn ESE370 Fall2012 -- DeHon 36 6 Glitches Admin • Inputs Transition from 0 1 0 1 1 1 • Andre out on Tuesday – What does output look like? – No office hours • Back on Wednesday • HW5 due Thursday 37 Penn ESE370 Fall2012 -- DeHon Penn ESE370 Fall2012 -- DeHon 38 Ideas • Three components of power – Static – Short-circuit – Charging • Ptot = Pstatic + Psc + Pdyn Penn ESE370 Fall2012 -- DeHon 39 7
