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ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 17: October 19, 2011 Energy and Power Basics 1 Penn ESE370 Fall2011 -- DeHon Previously • Where capacitance arises • What drives delay – How to optimize • Power as a limiting constraint – Energy, Power Density 2 Penn ESE370 Fall2011 -- DeHon Today Power Sources • Static • Capacitive Switching • Short Circuit (Day 18) 3 Penn ESE370 Fall2011 -- DeHon Power • P=I×V • Where should we look at I? 4 Penn ESE370 Fall2011 -- DeHon Power • P=IV • What’s V? • What is I? – Steady-State (input fixed)? – When input switches • 01 • 10 5 Penn ESE370 Fall2011 -- DeHon Observe • I changes over time • Data dependent • At least two components – Istatic – no switch – Iswitch – when switch 6 Penn ESE370 Fall2011 -- DeHon Static Power • Where does Istatic come from? – Subthreshold leakage – Gate-Drain leakage IDS W IS e L VGS VT nkT / q VDS kT / q 1 e 1 VDS 7 Penn ESE370 Fall2011 -- DeHon Data Dependent? • How does value of input impact Istatic? 8 Penn ESE370 Fall2011 -- DeHon Data Dependent? • How does value of input impact Istatic? 9 Penn ESE370 Fall2011 -- DeHon Billion Transistor Leakage • • • • 4 Billion transistors Say 1 Billion gates Each with one W=2 transistor leaking How much leakage current? 10 Penn ESE370 Fall2011 -- DeHon ITRS 2009 45nm High Performance Isd,leak 100nA/mm Isd,sat 1200 mA/mm Cg,total 1fF/mm Vth 285mV Ileak0 = 0.045mm × Isd,leak 11 Penn ESE370 Fall2010 -- DeHon Leakage Power • 4 Billion Transistor chip doing nothing • Total Leakage? • Leakage Power? 12 Penn ESE370 Fall2011 -- DeHon Reduce Leakage? • P=VI IDS W IS e L VGS VT nkT / q VDS kT / q 1 e 1 VDS • How do we reduce leakage? 13 Penn ESE370 Fall2011 -- DeHon ITRS 2009 45nm Low Power Isd,leak Isd,sat High Performance 100nA/mm 1200 mA/mm Cg,total Vth 1fF/mm 285mV 0.91fF/mm 585mV 50pA/mm 560mA/mm Ileak0 = 0.045mm × Isd,leak 14 Penn ESE370 Fall2010 -- DeHon Low Power Process • 4 Billion Transistor chip doing nothing • Total Leakage? • Leakage Power? 15 Penn ESE370 Fall2011 -- DeHon Switching 16 Penn ESE370 Fall2011 -- DeHon Switching • Where does current go during switching? 17 Penn ESE370 Fall2011 -- DeHon Switching Currents • Charge (discharge) output • If both transistor on: – Current path from Vdd to Gnd 18 Penn ESE370 Fall2011 -- DeHon Switching Currents • Iswitch(t) = Isc(t) + Idyn(t) • I(t) = Istatic(t)+Iswitch(t) 19 Penn ESE370 Fall2011 -- DeHon Charging • Idyn(t) – why changing? – Ids = f(Vds,Vgs) – and Vgs, Vds changing IDS IDS VDSAT satCOX W VGS VT 2 2 W VDS mnCOX VGS VT VDS L 2 Penn ESE370 Fall2011 -- DeHon 20 Look at Energy E P(t)dt P E dyn /t switch E I(t)V dt dd 21 Penn ESE370 Fall2011 -- DeHon Energy to Switch E I(t)V E Vdd dt dd I(t)dt 22 Penn ESE370 Fall2011 -- DeHon Integrating • Do we know what this is? I(t)dt 23 Penn ESE370 Fall2011 -- DeHon Capacitor Charge • Do we know what this is? Q I(t)dt • What is Q? 24 Penn ESE370 Fall2011 -- DeHon Capacitor Charge Q CV I(t)dt 25 Penn ESE370 Fall2011 -- DeHon Capacitor Charging Energy E Vdd I(t)dt Q CV I(t)dt 2 E CVdd 26 Penn ESE370 Fall2011 -- DeHon Switching Power • Every time switch 01 pay: – E = CV2 • Pdyn = (# 01 trans) × CV2 / time • # 01 trans = ½ # of transitions • Pdyn = (# trans) × ½CV2 / time Penn ESE370 Fall2011 -- DeHon 27 Charging Power • Pdyn = (# trans) × ½CV2 / time • Often like to think about switching frequency • Useful to consider per clock cycle – Frequency f = 1/clock-period • Pdyn = (#trans/clock) ½CV2 f 28 Penn ESE370 Fall2011 -- DeHon Charging Power • Pdyn = (#trans/clock) ½CV2 f • Let a = activity factor a = average #tran/clock • Pdyn = a½CV2 f 29 Penn ESE370 Fall2011 -- DeHon ITRS 2009 45nm Low Power Isd,leak Isd,sat High Performance 100nA/mm 1200 mA/mm Cg,total Vth 1fF/mm 285mV 0.91fF/mm 585mV 50pA/mm 560mA/mm C0 = 0.045mm × Cg,total C0 = 0.045 × 10-15 F Penn ESE370 Fall2010 -- DeHon 30 Switching Power • 4 Billion Transistors – Organized into 1 billion gates (e.g. nand2) • • • • Cload = 22C0 a=0.2 f=1GHz Power? 31 Penn ESE370 Fall2011 -- DeHon Switching Power • V=1V • Cload=22C0 ≈ 1 fF = 10-15F • P=a(0.5×10-15)(Ngate)f • a=0.2 • P=10-16(Ngate)f 32 Penn ESE370 Fall2010 -- DeHon Dynamic vs. Static Power • At what speed (f) does leakage power dominate switching power? 33 Penn ESE370 Fall2011 -- DeHon Compare • • • • • 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? 34 Penn ESE370 Fall2010 -- DeHon Charging Power • Pswitch = a(½C)V2f • What values can a take on? o a>1? o a<1? 35 Penn ESE370 Fall2011 -- DeHon Data Dependent Activity • Consider an 8b counter – What is activity, a, for: • Low bit? • High bit? • Average across all 8 output bits? • Assuming random inputs (no glitching) – Activity at output of nand4? – Activity at output of xor4? 36 Penn ESE370 Fall2011 -- DeHon Glitches • Inputs Transition from 0 1 0 1 1 1 – What does output look like? 37 Penn ESE370 Fall2011 -- DeHon Admin • HW5 due Friday 38 Penn ESE370 Fall2011 -- DeHon Ideas • Three components of power – Static – Short-circuit – Charging • Ptot = Pstatic + Psc + Pdyn 39 Penn ESE370 Fall2011 -- DeHon