1. Penn ESE370 Fall2013 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 19: October 16, 2013 Energy and Power Optimization

2. Previously Three components of power –Static –Short circuit –Capacitive switching P tot = P static + P sc + P dyn Penn ESE370 Fall2013 -- DeHon 2

3. Static Penn ESE370 Fall2013 -- DeHon 33 CMOS circuit in steady-state –Leaks subthreshold current determined by off device –P static = V dd × I static

4. Switching (Charging) Penn ESE370 Fall2013 -- DeHon 44 CMOS circuit switching output from 0  1 –Spends energy CV dd 2 charging load

5. Today Power Sources –Static –Short Circuit –Capacitive Switching Reducing Switching Energy Energy-Delay tradeoffs Penn ESE370 Fall2013 -- DeHon 5

6. Short Circuit Power Penn ESE370 Fall2013 -- DeHon 6

7. Preclass 1 Vin vs. I pwr,gnd ? –0V –140mV –400mV –500mV –600mV –840mV –1V Penn ESE370 Fall2013 -- DeHon 7

8. Short Circuit Power Between V TN and V dd -V TP –Both N and P devices conducting Roughly: Penn ESE370 Fall2013 -- DeHon 8

9. Peak Current Penn ESE370 Fall2013 -- DeHon 9 I peak around V dd /2 –If |V TN |=|V TP | and sized equal rise/fall

10. Short-Circuit Energy Penn ESE370 Fall2013 -- DeHon 10

11. Short-Circuit Energy Penn ESE370 Fall2013 -- DeHon 11

12. Short Circuit Energy Looks like a capacitance –Q=I×t –Q=CV Penn ESE370 Fall2013 -- DeHon 12

13. Short Circuit Energy and Power Every time switch –Also dissipate short-circuit energy: E = CV 2 –Different C = C sc –C cs “fake” capacitance (for accounting) Largely same dependence as charging Penn ESE370 Fall2013 -- DeHon 13

14. Switching Energy Penn ESE370 Fall2013 -- DeHon 14

15. Reminder Output switches 0  1 charge output from Vdd Output switches 1  0 discharge output to ground – no current from Vdd Penn ESE370 Fall2013 -- DeHon 15

16. Capactive Charging Switching Power Every time output switches 0  1 pay: –E = C load V 2 P dyn = (# 0  1 trans) × CV 2 / time # 0  1 trans = ½ # of transitions P dyn = (# trans) × ½CV 2 / time Penn ESE370 Fall2013 -- DeHon 16

17. Data Dependent Activity Consider an 8b counter –How often do each of the following switch? Low bit? High bit? –Average switching across all 8 output bits? Assuming random inputs (no glitching) –Activity at output of nand4? –Activity at output of xor4? Penn ESE370 Fall2013 -- DeHon 17

18. 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 Fall2013 -- DeHon 18

19. Switching Power P dyn = (#trans/clock) ½CV 2 f Let a = activity factor a = average #tran/clock P dyn = a½CV 2 f P sc = aC sc V 2 f Penn ESE370 Fall2013 -- DeHon 19

20. Total Power P tot = P static + P sc + P dyn P dyn + P sc = a(½C load +C sc )V 2 f P tot ≈ a(½C load +C sc )V 2 f+VI ’ s (W/L)e -Vt/(nkT/q) Penn ESE370 Fall2013 -- DeHon 20

21. Dynamic Power Penn ESE370 Fall2013 -- DeHon 21

22. Reduce Dynamic Power? P dyn = a × ½CV 2 f How do we reduce dynamic power? Penn ESE370 Fall2013 -- DeHon 22

23. Slow Down What happens to power contributions as reduce clock frequency? What suggest about V th ? Penn ESE370 Fall2013 -- DeHon 23

24. Reduce V What happens as reduce V? –Delay? –Energy? Static Switching Penn ESE370 Fall2013 -- DeHon 24

25. Penn ESE370 Fall2013 -- DeHon 25 Old Reduce V (no vsat)   gd =Q/I=(CV)/I  I d =(  C OX /2)(W/L)(V gs -V TH ) 2   gd impact?   gd α 1/V

26. Saturation Observe Ignoring leakage Penn ESE370 Fall2013 -- DeHon 26

27. Penn ESE370 Fall2013 -- DeHon 27 Reduce V (velocity saturation)   gd =Q/I=(CV)/I  I ds =( sat C OX )(W)(V gs -V TH -V DSAT /2)  Preclass 4

28. Reduce Short-Circuit Power? P sc = aC sc V 2 f Penn ESE370 Fall2013 -- DeHon 28

29. Energy vs. Power? Which do we care about? –Battery operated devices? –Desktops? –Pay for energy by kW-Hr? Penn ESE370 Fall2013 -- DeHon 29

30. Increase V th ? What is impact of increasing threshold on –Delay? –Leakage? Penn ESE370 Fall2013 -- DeHon 30

31. Penn ESE370 Fall2013 -- DeHon 31 Increase V th   gd =Q/I=(CV)/I  I ds =( sat C OX )(W)(V gs -V TH -V DSAT /2)  Preclass 5

32. Optional Penn ESE370 Fall2013 -- DeHon 32

33. Optional Exercise Vin vs. I pwr,gnd vs. Vin @ Vdd=500mV? –0V –140mV –250mV –360mV –500mV Penn ESE370 Fall2013 -- DeHon 33

34. Optional 2: Glitches Inputs Transition from 0 1 0  1 1 1 –What does output look like? Penn ESE370 Fall2013 -- DeHon 34

35. Idea Short circuit energy looks like more capacitance for switching energy Tradeoff –Speed –Switching energy –Leakage energy Energy-Delay tradeoff: E  2 ? E  Penn ESE370 Fall2013 -- DeHon 35

36. Admin HW6 Due tomorrow Project 1 out –Milestone piece due in one week –Full Report in two weeks –That means you need to be starting on it now…and working on it all next week Read assignment today Lecture Friday Penn ESE370 Fall2013 -- DeHon 36