1. Penn ESE370 Fall2010 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 37: December 8, 2010 Adiabatic Amplification

2. Today It is possible to switch without dissipating energy? –Dissipate less than CV 2 driving load C to voltage V? Energy dissipation can be proportional to speed –Slower switching reduces energy –even without reducing V Penn ESE370 Fall2010 -- DeHon 2

3. Adiabatic Adiabatic – a thermodynamic process without heat transfer Penn ESE370 Fall2010 -- DeHon 3

4. Look at Energy Penn ESE370 Fall2010 -- DeHon 4 Day 16

5. Capacitor Charging Energy Penn ESE370 Fall2010 -- DeHon 5 Day 16

6. Energy Dissipation When we switch node to zero –Dump charge to ground Every 0  1  0 transition burns CV 2 Penn ESE370 Fall2010 -- DeHon 6

7. Energy Recycling? Can we avoid discarding the charge? –Can we recycle the energy rather than throwing it away? –Slogan: “Cycling” rather than “Dumping” Two sub-problems: 1.Pool of reusable charge 2.Moving to/from pool without loss Penn ESE370 Fall2010 -- DeHon 7

8. Energy Dissipation Where does the dissipated energy go? Dissipated across transistor charging resistance Penn ESE370 Fall2010 -- DeHon 8

9. Dissipation in R Penn ESE370 Fall2010 -- DeHon 9

10. Conventional CMOS Spend CV 2 in 0  1  0 cycle –0.5CV 2 dissipated in pullup transistor charging –0.5CV 2 dissipated in pulldown transistor discharging Penn ESE370 Fall2010 -- DeHon 10

11. Challenge 2: Reduce Dissipation Can we charge capacitor without dissipation? –With less dissipation? Two sub-problems: 1.Pool of reusable charge 2.Moving to/from pool without loss Penn ESE370 Fall2010 -- DeHon 11

12. Adiabatic Switching Described Two Ways (same idea) First Way Penn ESE370 Fall2010 -- DeHon 12

13. Constant Current Charging E r = P×T =I 2 RT Charge over time T –Want this T to be a control variable I=(CV dd )/T Penn ESE370 Fall2010 -- DeHon 13

14. Slow Switching (chilling out?) If can charge with constant current –Energy dissipated is inversely proportional to charging time –Slower we charge, the less energy we dissipate Penn ESE370 Fall2010 -- DeHon 14

15. How Make Constant? Why normally constant not current? –Input changing (V gs )  changing I ds –I(t) = [V dd -V out (t)]/R V out changing How make I(t) constant? –Input settle with no voltage across supply/output –Make  V constant –Ramp V supply with V out Penn ESE370 Fall2010 -- DeHon 15

16. Adiabatic Switching Second Way Penn ESE370 Fall2010 -- DeHon 16

17. Charging with Small  V Energy cost is due to large  V drop over R –P=I  V Adiabatic discipline: –Never turn on a device with a large voltage drop across it Spend 0.5C(  V) 2 to charge  V –Charge in many small steps N=V/  V Penn ESE370 Fall2010 -- DeHon 17

18. Charging with Small  V Spend 0.5C(  V) 2 to charge  V Charge in many small steps N=V/  V E total = N 0.5C(  V) 2 E total = (V/  V) 0.5C(  V) 2 = 0.5CV×  V E total = 0.5CV 2  Time ~ RC per step –Same ratio as before Penn ESE370 Fall2010 -- DeHon 18

19. Visually Charge from V dd –N+N-1+N-2+….2+1=N 2 /2 Charge from Ramp –1+1+1+….+1 = N Penn ESE370 Fall2010 -- DeHon 19

20. Adiabatic Amplifier Penn ESE370 Fall2010 -- DeHon 20

21. Adiabatic Amplifier Discipline: –Set input X before switching V supply Y=/Y=V supply –Ramp V supply slowly to charge Y or /Y –Return V supply to zero before change X Adiabatically –Move charge to Y, /Y Penn ESE370 Fall2010 -- DeHon 21

22. Power Supply Want power supply looks like slow ramp Not clear how to produce without energy cost Penn ESE370 Fall2010 -- DeHon 22

23. “Ramped” Supply Can produce sine waves with LC circuit –LC circuit moves charge without loss Penn ESE370 Fall2010 -- DeHon 23

24. Challenge 1: Reusable Charge Can we borrow and return charge? Two sub-problems: 1.Pool of reusable charge 2.Moving to/from pool without loss Penn ESE370 Fall2010 -- DeHon 24

25. Pulsed Supply Pulse enable FET to allow charge to slosh into circuit (or back) Penn ESE370 Fall2010 -- DeHon 25

26. Pulsed Supply and Load Penn ESE370 Fall2010 -- DeHon 26

27. Resonant Supply Charge moves back and forth between circuit and supply like RLC circuit –Some loss based on circuit R –Small if LC slow (adiabatic switching) –Only that loss that needs to be replaced Costs energy Penn ESE370 Fall2010 -- DeHon 27

28. Energy Adiabatic Amplifier Penn ESE370 Fall2010 -- DeHon 28  shape factor since sine instead of ramp  for sine wave (~1.2)

29. V dd Selection Minimize with V dd =4V th Penn ESE370 Fall2010 -- DeHon 29

30. Leakage and V th Concern with this solution –Runs slow, high leakage –Possibly compensate with large V th Need to run even slower Traditional voltage scaling –Limited V scaling Variation and leakage –Preventing us from scaling V down Sets a lower bound on Energy/Operation Saves energy without scaling down V dd Penn ESE370 Fall2010 -- DeHon 30

31. Critical Questions Can we make the supplies efficient enough? –Avoid just moving E loss to supplies Can make sufficiently efficient resonator? Can we get sufficiently good inductors? Can contain leakage sufficiently? Penn ESE370 Fall2010 -- DeHon 31

32. Next Time Asymptotically Zero Energy Computation? –Thermodynamically possible? –Connection between information and energy –Reversibility Penn ESE370 Fall2010 -- DeHon 32

33. Admin Proj3b Friday Review for final: Monday – Andrew Penn ESE370 Fall2010 -- DeHon 33

34. Idea Asymptotically Zero Energy Switching –Energy proportional T -1 –Slower we switch, the more we save Alternate to reducing V dd Two sub-problems: 1.Pool of reusable charge 2.Moving to/from pool without loss Penn ESE370 Fall2010 -- DeHon 34