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ESE370:
Circuit-Level
Modeling, Design, and Optimization
for Digital Systems
Day 37: December 8, 2010
Adiabatic Amplification
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Penn ESE370 Fall2010 -- DeHon
Today
• It is possible to switch without
dissipating energy?
– Dissipate less than CV2 driving
load C to voltage V?
• Energy dissipation can be proportional
to speed
– Slower switching reduces energy
– even without reducing V
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Penn ESE370 Fall2010 -- DeHon
Adiabatic
• Adiabatic – a thermodynamic process
without heat transfer
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Penn ESE370 Fall2010 -- DeHon
Day 16
Look at Energy
E
E
 P(t)dt
 I(t)V
dt
dd
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Penn ESE370 Fall2010 -- DeHon
Day 16
Capacitor Charging Energy
E  Vdd  I(t)dt
Q  CV   I(t)dt
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E  CVdd
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Penn ESE370 Fall2010 -- DeHon
Energy Dissipation
• When we switch node to zero
– Dump charge to ground
• Every 010 transition
burns CV2
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Penn ESE370 Fall2010 -- DeHon
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
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Penn ESE370 Fall2010 -- DeHon
Energy Dissipation
• Where does the dissipated energy go?
Dissipated across transistor charging resistance
E
 [V
dd
 Vout ]I(t)dt
 dVout 

I(t)  C
dt 

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Penn ESE370 Fall2010 -- DeHon
Dissipation in R
 dVout 
dt
E   [Vdd Vout ]C
dt 

dVout 
dVout 
dt  C  Vout 
dt
E  Vdd C  
dt 
dt 


2
2
1
C
E  Vdd  C  Vdd  C  Vdd 
2
2
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Penn ESE370 Fall2010 -- DeHon
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Conventional CMOS
• Spend CV2 in 010 cycle
– 0.5CV2 dissipated in pullup transistor
charging
– 0.5CV2 dissipated in pulldown transistor
discharging
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Penn ESE370 Fall2010 -- DeHon
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
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Penn ESE370 Fall2010 -- DeHon
Adiabatic Switching
Described Two Ways
(same idea)
First Way
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Penn ESE370 Fall2010 -- DeHon
Constant Current Charging
• Er = P×T =I2RT
• Charge over time T
– Want this T to be a control variable
• I=(CVdd)/T

Penn ESE370 Fall2010 -- DeHon
CVdd 
E r  
 RT
 T 
2
RC 
2
E r    CVdd 
 T 
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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
RC 
2
E r    CVdd 
 T 
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Penn ESE370 Fall2010 -- DeHon
How Make Constant?
• Why normally constant not current?
– Input changing (Vgs) changing Ids
– I(t) = [Vdd-Vout(t)]/R
• Vout changing
• How make I(t) constant?
– Input settle with no voltage across
supply/output
– Make DV constant
– Ramp Vsupply with Vout
Penn ESE370 Fall2010 -- DeHon
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Adiabatic Switching
Second Way
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Penn ESE370 Fall2010 -- DeHon
Charging with Small DV
• Energy cost is due to large DV drop over R
– P=IDV
• Adiabatic discipline:
– Never turn on a device with a large voltage
drop across it
• Spend 0.5C(DV)2 to charge DV
– Charge in many small steps N=V/DV
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Penn ESE370 Fall2010 -- DeHon
Charging with Small DV
•
•
•
•
•
•
Spend 0.5C(DV)2 to charge DV
Charge in many small steps N=V/DV
Etotal = N 0.5C(DV)2
Etotal = (V/DV) 0.5C(DV)2 = 0.5CV×DV
Etotal = 0.5CV2/N
Time ~ RC per step
RC 
– Same ratio as before
E r    CVdd 
 T 
2
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Penn ESE370 Fall2010 -- DeHon
Visually
• Charge from Vdd
– N+N-1+N-2+….2+1=N2/2
• Charge from Ramp
– 1+1+1+….+1 = N
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Penn ESE370 Fall2010 -- DeHon
Adiabatic Amplifier
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Penn ESE370 Fall2010 -- DeHon
Adiabatic Amplifier
• Discipline:
– Set input X before switching Vsupply
• Y=/Y=Vsupply
– Ramp Vsupply slowly to charge Y or /Y
– Return Vsupply to zero before change X
• Adiabatically
– Move charge to Y, /Y
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Penn ESE370 Fall2010 -- DeHon
Power Supply
• Want power supply looks like slow ramp
• Not clear how to produce without
energy cost
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Penn ESE370 Fall2010 -- DeHon
“Ramped” Supply
• Can produce sine waves with LC circuit
– LC circuit moves charge without loss
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Penn ESE370 Fall2010 -- DeHon
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
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Penn ESE370 Fall2010 -- DeHon
Pulsed Supply
• Pulse enable FET to allow charge to
slosh into circuit (or back)
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Penn ESE370 Fall2010 -- DeHon
Pulsed Supply and Load
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Penn ESE370 Fall2010 -- DeHon
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
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Penn ESE370 Fall2010 -- DeHon
Energy Adiabatic Amplifier
E load

2 
2
Kn
2

  
C Vdd 


 T Cn Vdd  2Vth 
 shape factor since sine instead of ramp
>1for sine wave (~1.2)
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Penn ESE370 Fall2010 -- DeHon
Vdd Selection
E load

2 
2
Kn
2

  
C Vdd 


 T Cn Vdd  2Vth 
• Minimize with Vdd=4Vth
E load
2

  16K n C Vth 
  

T  Cn

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Penn ESE370 Fall2010 -- DeHon
Leakage and Vth
• Concern with this solution
– Runs slow, high leakage
– Possibly compensate with large Vth
• 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 Vdd 30
Penn ESE370 Fall2010 -- DeHon
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?
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Penn ESE370 Fall2010 -- DeHon
Next Time
• Asymptotically Zero Energy Computation?
– Thermodynamically possible?
– Connection between information and energy
– Reversibility
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Penn ESE370 Fall2010 -- DeHon
Admin
• Proj3b Friday
• Review for final: Monday – Andrew
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Penn ESE370 Fall2010 -- DeHon
Idea
• Asymptotically Zero Energy Switching
– Energy proportional T-1
– Slower we switch, the more we save
• Alternate to reducing Vdd
• Two sub-problems:
1.Pool of reusable charge
2.Moving to/from pool without loss
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Penn ESE370 Fall2010 -- DeHon