Day 17: October 15, 2012 Energy and Power Basics ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 17: October 15, 2012 Energy and Power Basics Penn ESE370 Fall2012 -- DeHon

Previously Where capacitance arises What drives delay How to optimize Power as a limiting constraint Energy, Power Density Penn ESE370 Fall2012 -- DeHon

Today Power Sources Static Capacitive Switching Short Circuit (Day 18) Penn ESE370 Fall2012 -- DeHon

Power P=I×V Where should we look at I? Penn ESE370 Fall2012 -- DeHon

Power P=IV What’s V? What is I? Steady-State (input fixed)? When input switches 01 10 Penn ESE370 Fall2012 -- DeHon

Observe I changes over time Data dependent At least two components Istatic – no switch Iswitch – when switch Penn ESE370 Fall2012 -- DeHon

Static Power Where does Istatic come from? Subthreshold leakage Gate-Drain leakage Penn ESE370 Fall2012 -- DeHon

Data Dependent? How does value of input impact Istatic? Penn ESE370 Fall2012 -- DeHon

Data Dependent? How does value of input impact Istatic? Penn ESE370 Fall2012 -- DeHon

Billion Transistor Leakage 4 Billion transistors Say 1 Billion gates Each with one W=2 transistor leaking How much leakage current? Penn ESE370 Fall2012 -- DeHon

ITRS 2009 45nm Ileak0 = 0.045mm × Isd,leak High Performance Isd,leak 100nA/mm Isd,sat 1200 mA/mm Cg,total 1fF/mm Vth 285mV Ileak0 = 0.045mm × Isd,leak Penn ESE370 Fall2012 -- DeHon

Leakage Power 4 Billion Transistor chip doing nothing Total Leakage? Penn ESE370 Fall2012 -- DeHon

Reduce Leakage? P=VI How do we reduce leakage? Penn ESE370 Fall2012 -- DeHon

ITRS 2009 45nm Ileak0 = 0.045mm × Isd,leak High Performance Low Power 100nA/mm 50pA/mm Isd,sat 1200 mA/mm 560mA/mm Cg,total 1fF/mm 0.91fF/mm Vth 285mV 585mV Ileak0 = 0.045mm × Isd,leak Penn ESE370 Fall2012 -- DeHon

Low Power Process 4 Billion Transistor chip doing nothing Total Leakage? Leakage Power? Penn ESE370 Fall2012 -- DeHon

Switching Penn ESE370 Fall2012 -- DeHon

Switching Where does current go during switching? Penn ESE370 Fall2012 -- DeHon

Switching Currents Charge (discharge) output If both transistor on: Current path from Vdd to Gnd Penn ESE370 Fall2012 -- DeHon

Switching Currents Iswitch(t) = Isc(t) + Idyn(t) I(t) = Istatic(t)+Iswitch(t) Penn ESE370 Fall2012 -- DeHon

Charging Idyn(t) – why changing? Ids = f(Vds,Vgs) and Vgs, Vds changing Penn ESE370 Fall2012 -- DeHon

Look at Energy Penn ESE370 Fall2012 -- DeHon

Energy to Switch Penn ESE370 Fall2012 -- DeHon

Integrating Do we know what this is? Penn ESE370 Fall2012 -- DeHon

Capacitor Charge Do we know what this is? What is Q? Penn ESE370 Fall2012 -- DeHon

Capacitor Charge Penn ESE370 Fall2012 -- DeHon

Capacitor Charging Energy Penn ESE370 Fall2012 -- DeHon

Switching Power Every time switch 01 pay: E = CV2 Pdyn = (# 01 trans) × CV2 / time # 01 trans = ½ # of transitions Pdyn = (# trans) × ½CV2 / time Penn ESE370 Fall2012 -- DeHon

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 Penn ESE370 Fall2012 -- DeHon

Charging Power Pdyn = (#trans/clock) ½CV2 f Let a = activity factor a = average #tran/clock Pdyn = a½CV2 f Penn ESE370 Fall2012 -- DeHon

ITRS 2009 45nm C0 = 0.045mm × Cg,total C0 = 0.045 × 10-15 F High Performance Low Power Isd,leak 100nA/mm 50pA/mm Isd,sat 1200 mA/mm 560mA/mm Cg,total 1fF/mm 0.91fF/mm Vth 285mV 585mV C0 = 0.045mm × Cg,total C0 = 0.045 × 10-15 F Penn ESE370 Fall2012 -- DeHon

Switching Power 4 Billion Transistors Cload = 22C0 a=0.2 f=1GHz Power? Organized into 1 billion gates (e.g. nand2) Cload = 22C0 a=0.2 f=1GHz Power? Penn ESE370 Fall2012 -- DeHon

Switching Power V=1V Cload=22C0 ≈ 1 fF = 10-15F P=a(0.5×10-15)(Ngate)f P=10-16(Ngate)f Penn ESE370 Fall2012 -- DeHon

Dynamic vs. Static Power At what speed (f) does leakage power dominate switching power? Penn ESE370 Fall2012 -- 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? Penn ESE370 Fall2012 -- DeHon

Charging Power Pswitch = a(½C)V2f What values can a take on? a>1? Penn ESE370 Fall2012 -- 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? Penn ESE370 Fall2012 -- DeHon

Glitches Inputs Transition from 0 1 0  1 1 1 What does output look like? Penn ESE370 Fall2012 -- DeHon

Admin Andre out on Tuesday Back on Wednesday HW5 due Thursday No office hours Back on Wednesday HW5 due Thursday Penn ESE370 Fall2012 -- DeHon

Ideas Three components of power Ptot = Pstatic + Psc + Pdyn Static Short-circuit Charging Ptot = Pstatic + Psc + Pdyn Penn ESE370 Fall2012 -- DeHon