1. Penn ESE370 Fall2011 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 17: October 19, 2011 Energy and Power Basics

2. Previously Where capacitance arises What drives delay –How to optimize Power as a limiting constraint –Energy, Power Density Penn ESE370 Fall2011 -- DeHon 2

3. Today Power Sources Static Capacitive Switching Short Circuit (Day 18) Penn ESE370 Fall2011 -- DeHon 3

4. Power P=I×V Where should we look at I? Penn ESE370 Fall2011 -- DeHon 4

5. Power P=IV What’s V? What is I? –Steady-State (input fixed)? –When input switches 0  1 1  0 Penn ESE370 Fall2011 -- DeHon 5

6. Observe I changes over time Data dependent At least two components –I static – no switch –I switch – when switch Penn ESE370 Fall2011 -- DeHon 6

7. Static Power Where does I static come from? –Subthreshold leakage –Gate-Drain leakage Penn ESE370 Fall2011 -- DeHon 7

8. Data Dependent? How does value of input impact I static ? Penn ESE370 Fall2011 -- DeHon 8

9. Data Dependent? How does value of input impact I static ? Penn ESE370 Fall2011 -- DeHon 9

10. Billion Transistor Leakage 4 Billion transistors Say 1 Billion gates Each with one W=2 transistor leaking How much leakage current? Penn ESE370 Fall2011 -- DeHon 10

11. ITRS 2009 45nm Penn ESE370 Fall2010 -- DeHon 11 High Performance I sd,leak 100nA/  m I sd,sat 1200  A/  m C g,total 1fF/  m V th 285mV I leak0 = 0.045  m × I sd,leak

12. Leakage Power 4 Billion Transistor chip doing nothing Total Leakage? Leakage Power? Penn ESE370 Fall2011 -- DeHon 12

13. Reduce Leakage? P=VI How do we reduce leakage? Penn ESE370 Fall2011 -- DeHon 13

14. ITRS 2009 45nm Penn ESE370 Fall2010 -- DeHon 14 High Performance Low Power I sd,leak 100nA/  m50pA/  m I sd,sat 1200  A/  m560  A/  m C g,total 1fF/  m0.91fF/  m V th 285mV585mV I leak0 = 0.045  m × I sd,leak

15. Low Power Process 4 Billion Transistor chip doing nothing Total Leakage? Leakage Power? Penn ESE370 Fall2011 -- DeHon 15

16. Switching Penn ESE370 Fall2011 -- DeHon 16

17. Switching Where does current go during switching? Penn ESE370 Fall2011 -- DeHon 17

18. Switching Currents Charge (discharge) output If both transistor on: –Current path from V dd to Gnd Penn ESE370 Fall2011 -- DeHon 18

19. Switching Currents I switch (t) = I sc (t) + I dyn (t) I(t) = I static (t)+I switch (t) Penn ESE370 Fall2011 -- DeHon 19

20. Charging I dyn (t) – why changing? –I ds = f(V ds,V gs ) –and V gs, V ds changing Penn ESE370 Fall2011 -- DeHon 20

21. Look at Energy Penn ESE370 Fall2011 -- DeHon 21

22. Energy to Switch Penn ESE370 Fall2011 -- DeHon 22

23. Integrating Do we know what this is? Penn ESE370 Fall2011 -- DeHon 23

24. Capacitor Charge Do we know what this is? What is Q? Penn ESE370 Fall2011 -- DeHon 24

25. Capacitor Charge Penn ESE370 Fall2011 -- DeHon 25

26. Capacitor Charging Energy Penn ESE370 Fall2011 -- DeHon 26

27. Switching Power Every time switch 0  1 pay: –E = CV 2 P dyn = (# 0  1 trans) × CV 2 / time # 0  1 trans = ½ # of transitions P dyn = (# trans) × ½CV 2 / time Penn ESE370 Fall2011 -- DeHon 27

28. Charging Power P dyn = (# trans) × ½CV 2 / time Often like to think about switching frequency Useful to consider per clock cycle –Frequency f = 1/clock-period P dyn = (#trans/clock) ½CV 2 f Penn ESE370 Fall2011 -- DeHon 28

29. Charging Power P dyn = (#trans/clock) ½CV 2 f Let a = activity factor a = average #tran/clock P dyn = a½CV 2 f Penn ESE370 Fall2011 -- DeHon 29

30. ITRS 2009 45nm Penn ESE370 Fall2010 -- DeHon 30 High Performance Low Power I sd,leak 100nA/  m50pA/  m I sd,sat 1200  A/  m560  A/  m C g,total 1fF/  m0.91fF/  m V th 285mV585mV C 0 = 0.045  m × C g,total C 0 = 0.045 × 10 -15 F

31. Switching Power 4 Billion Transistors –Organized into 1 billion gates (e.g. nand2) C load = 22C 0 a=0.2 f=1GHz Power? Penn ESE370 Fall2011 -- DeHon 31

32. Switching Power V=1V C load =22C 0 ≈ 1 fF = 10 -15 F P=a(0.5×10 -15 )(N gate )f a=0.2 P=10 -16 (N gate )f Penn ESE370 Fall2010 -- DeHon 32

33. Dynamic vs. Static Power At what speed (f) does leakage power dominate switching power? Penn ESE370 Fall2011 -- DeHon 33

34. Compare W N = 2  I leak = 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 Fall2010 -- DeHon 34

35. Charging Power P switch = a(½C)V 2 f What values can a take on? o a>1? o a<1? Penn ESE370 Fall2011 -- DeHon 35

36. 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 Fall2011 -- DeHon 36

37. Glitches Inputs Transition from 0 1 0  1 1 1 –What does output look like? Penn ESE370 Fall2011 -- DeHon 37

38. Admin HW5 due Friday Penn ESE370 Fall2011 -- DeHon 38

39. Ideas Three components of power –Static –Short-circuit –Charging P tot = P static + P sc + P dyn Penn ESE370 Fall2011 -- DeHon 39