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Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 11
ELEC 5270/6270 Spring 2013ELEC 5270/6270 Spring 2013Low-Power Design of Electronic CircuitsLow-Power Design of Electronic Circuits
Adiabatic LogicAdiabatic Logic
Vishwani D. AgrawalVishwani D. AgrawalJames J. Danaher ProfessorJames J. Danaher Professor
Dept. of Electrical and Computer EngineeringDept. of Electrical and Computer EngineeringAuburn University, Auburn, AL 36849Auburn University, Auburn, AL 36849
[email protected]://www.eng.auburn.edu/~vagrawal/COURSE/E6270_Spr13/course.html
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 22
Examples of Power Saving and Examples of Power Saving and Energy RecoveryEnergy Recovery
Power saving by power transmission at high Power saving by power transmission at high voltage:voltage: 1000W transmitted at 100V, current I = 10A1000W transmitted at 100V, current I = 10A If resistance of transmission circuit is 1If resistance of transmission circuit is 1ΩΩ, then power loss , then power loss
= I= I22R = 100WR = 100W Transmit at 1000V, current I = 1A, transmission loss = Transmit at 1000V, current I = 1A, transmission loss =
1W1W Energy recovery from automobile braking:Energy recovery from automobile braking:
Normal brake converts mechanical energy into heatNormal brake converts mechanical energy into heat Instead, the energy can be stored in a flywheel, orInstead, the energy can be stored in a flywheel, or Converted to electricity to charge a batteryConverted to electricity to charge a battery
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 33
Reexamine CMOS GateReexamine CMOS Gate
i = Ve–t/RpC/Rp
i2Rp
VV2/ Rp
C
Time, t
Pow
er
Most energy dissipated here
V×i = V2e–2t/RpC/ Rp
0
Energy dissipation per transition = Area/2 = C V 2/ 2
v(t)V
v(t)
v(t)
3RpC
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 44
Charging with Constant CurrentCharging with Constant Current
i = constant i2Rp
V(t)
C
Pow
er0
v(t) = it/C
Time (T) to charge capacitor to voltage V v(T) = V = iT/C, or T = CV/iCurrent, i = CV/T
Out
put v
olta
ge, v
(t)
0
V
Time, t T=CV/i
it/C
Power = i2Rp = C2V2Rp/T2
Energy dissipation = Power × T = (RpC/T) CV2
C2V2Rp/T2
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 55
Or, Charge in StepsOr, Charge in Steps
i = Ve–t/RpC/2Rp
i2Rp
0→V/2→V
V2/4Rp
C
Time, t
Pow
er
V2e–2t/RpC/4Rp
0Energy = Area = CV2/8
v(t)
V v(t)
v(t)
V/2
Total energy = CV2/8 + CV2/8 = CV2/4
3RpC 6RpC
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 66
Energy Dissipation of a StepEnergy Dissipation of a Step
TE = ∫ V2e–2t/RpC/(N2Rp) dt 0
= [CV2/(2N2)] (1 – e–2T/RpC)
≈ CV2/(2N2) for large T ≥ 3RpC
Voltage step = V/N
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 77
Charge in N StepsCharge in N Steps
Supply voltage 0 → V/N → 2V/N → 3V/N → . . . NV/N
Current, i(t) = Ve–t/RpC/NRp
Power, i2(t)Rp = V2e–2t/RpC/N2Rp
Energy = N CV2/2N2 = CV2/2N → 0 for N → ∞
Delay = N × 3RpC → ∞ for N → ∞
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 88
Reexamine Charging of a CapacitorReexamine Charging of a Capacitor
V C
R
i(t) v(t)
Charge on capacitor, q(t) = C v(t)
Current, i(t) = dq(t)/dt = C dv(t)/dt
t = 0
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 99
i(t) = C dv(t)/dt = [V – v(t)] /R dv(t) V – v(t) ─── = ───── dt RC dv(t) dt∫ ───── = ∫ ──── V – v(t) RC
– t ln [V – v(t)] = ── + A
RC
Initial condition, t = 0, v(t) = 0 → A = ln V – t
v(t) = V [1 – exp(───)]
RC
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1010
– t v(t) = V [1 – exp( ── )]
RC
dv(t) V – ti(t) = C ─── = ── exp( ── )
dt R RC
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1111
Total Energy Per Charging Total Energy Per Charging Transition from Power SupplyTransition from Power Supply
∞ ∞ V 2 – tEtrans = ∫ V i(t) dt = ∫ ── exp( ── ) dt
0 0 R RC
= CV2
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1212
Energy Dissipated per Transition in Energy Dissipated per Transition in ResistanceResistance
∞ V 2 ∞ –2tR ∫ i 2(t) dt= R ── ∫ exp( ── ) dt 0 R2 0 RC
1= ─ CV 2
2
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1313
Energy Stored in a Charged Energy Stored in a Charged Capacitor Capacitor
∞ ∞ – t V – t∫ v(t) i(t) dt = ∫ V [1– exp( ── )] ─ exp( ── ) dt0 0 RC R RC
1 = ─ CV 2
2
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1414
Slow Charging of a CapacitorSlow Charging of a Capacitor
V(t) C
R
i(t) v(t)
Charge on capacitor, q(t) = C v(t)
Current, i(t) = dq(t)/dt = C dv(t)/dt
t = 0
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1515
i(t) = C dv(t)/dt = [V(t) – v(t)] /R
dv(t) V(t) – v(t) ─── = ───── dt RC dv(t) dt∫ ────── = ∫ ──── V(t) – v(t) RC
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1616
Effects of Slow ChargingEffects of Slow Charging
V(t) v(t)
t
Voltage across R
Vol
tage
Constant Current Is OptimumConstant Current Is Optimum
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1717
R t = [0,T]I(t)
C
V
Average and Instantaneous Average and Instantaneous CurrentCurrent
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1818
Let T be the time to charge C to voltage V
TAverage current: (1/T) ∫ I(t) dt = I0
0
Instantaneous current: I(t) = I0 + i(t)
TWhere ∫ i(t) dt = 0
0
Energy DissipationEnergy Dissipation
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 1919
T TE = R ∫ I2(t) dt= R ∫ [I0 + i(t)]2 dt
0 0T
= R ∫ [I02 + 2I0i(t) + i2(t)] dt
0 T T
= RI02T + 2RI0 ∫ i(t) dt + R ∫ i2(t) dt
0 0 T
= RI02T + 0 + R ∫ i2(t) dt ≥ RI0
2T 0
= RI02T, minimum value, when i(t) = 0, i.e., I(t) = I0
Minimum EnergyMinimum Energy
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2020
For a constant current I0,
Charging time, T = CV/I0
Emin = RCVI0
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2121
ReferencesReferences C. L. Seitz, A. H. Frey, S. Mattisson, S. D. C. L. Seitz, A. H. Frey, S. Mattisson, S. D.
Rabin, D. A. Speck and J. L. A. van de Rabin, D. A. Speck and J. L. A. van de Snepscheut, “Hot-Clock nMOS,” Snepscheut, “Hot-Clock nMOS,” Proc. Chapel Proc. Chapel Hill Conf. VLSIHill Conf. VLSI, 1985, pp. 1-17., 1985, pp. 1-17.
W. C. Athas, L. J. Swensson, J. D. Koller, N. W. C. Athas, L. J. Swensson, J. D. Koller, N. Tzartzanis and E. Y.-C. Chou, “Low-Power Tzartzanis and E. Y.-C. Chou, “Low-Power Digital Systems Based on Adiabatic-Switching Digital Systems Based on Adiabatic-Switching Principles,” Principles,” IEEE Trans. VLSI SystemsIEEE Trans. VLSI Systems, vol. 2, , vol. 2, no. 4, pp. 398-407, Dec. 1994.no. 4, pp. 398-407, Dec. 1994.
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2222
A Conventional Dynamic CMOS A Conventional Dynamic CMOS InverterInverter
V
C
v(t)
CK
vin
CK
vin
v(t)
P E P E P E
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2323
Adiabatic Dynamic CMOS InverterAdiabatic Dynamic CMOS Inverter
C
v(t)
CK
vin
A. G. Dickinson and J. S. Denker, “Adiabatic Dynamic Logic,” IEEE J. Solid-State Circuits, vol. 30, pp. 311-315, March 1995.
CK
vin
v(t)
V
0
V-Vf
0
Vf+
P E P E P E P E
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2424
Cascaded Adiabatic InvertersCascaded Adiabatic Inverters
CK1 CK2 CK1’ CK2’
vin
CK1
CK2
CK1’
CK2’
precharge
input
evaluatehold
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2525
Complex ADL GateComplex ADL Gate
CK
B
A. G. Dickinson and J. S. Denker, “Adiabatic Dynamic Logic,” IEEE J. Solid-State Circuits, vol. 30, pp. 311-315, March 1995.
AC
AB + C
Vf < Vth
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2626
ClocksClocks
EVAL. HOLD EVAL. HOLD
0
0
VDD
VDD
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2727
Possible Cases:• The circuit output node X is LOW
and the pMOS tree is turned ON: X follows as it swings to HIGH (EVALUATE phase)
• The circuit node X is LOW and the nMOS tree is ON. X remains LOW and no transition occurs (HOLD phase)
• The circuit node X is HIGH and the pMOS tree is ON. X remains HIGH and no transition occurs (HOLD phase)
• The circuit node X is HIGH and the nMOS tree is ON. X follows down to LOW.
Quasi-Adiabatic Logic DesignQuasi-Adiabatic Logic Design
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2828
A Case StudyA Case Study
K. Parameswaran, “Low Power Design of a 32-bit Quasi-Adiabatic ARM Based Microprocessor,” Master’s Thesis,Dept. of ECE, Rutgers University, New Brunswick, NJ, 2004.
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 2929
Quasi-Adiabatic 32-bit ARM Based Quasi-Adiabatic 32-bit ARM Based Microprocessor Design SpecificationsMicroprocessor Design Specifications
Operating voltage: 2.5 VOperating voltage: 2.5 V Operating temperature: 25Operating temperature: 25ooCC Operating frequency: 10 MHz to 100 MHzOperating frequency: 10 MHz to 100 MHz Leakage current: 0.5 Leakage current: 0.5 fAmpsfAmps Load capacitance: 6X10Load capacitance: 6X10-18 -18 FF (15% activity) (15% activity) Transistor Count:Transistor Count:
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 3030
Technology DistributionTechnology Distribution Microprocessor has a mix of static CMOS Microprocessor has a mix of static CMOS
and Quasi-adiabatic componentsand Quasi-adiabatic components
ALUALU• Adder-subtractor unit• Barrel shifter unit• Booth-multiplier unit
Control UnitsControl Units• ARM controller unit• Bus control unit
Pipeline UnitsPipeline Units• ID unit• IF unit• WB unit• MEM unit
Quasi-Adiabatic Static CMOS
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 3131
Power AnalysisPower AnalysisDatapathDatapath
ComponentComponent
Power Consumption (mW)Power Consumption (mW)Frequency 25 MHzFrequency 25 MHz
Power Consumption (mW)Power Consumption (mW)Frequency 100 MHzFrequency 100 MHz
Quasi-Quasi-adiabaticadiabatic
Static Static CMOSCMOS
Power Power SavedSaved
Quasi-Quasi-adiabaticadiabatic
Static Static CMOSCMOS
Power Power SavedSaved
32-bit Adder 32-bit Adder SubtracterSubtracter
1.011.01 1.551.55 44%44% 1.291.29 1.621.62 20%20%
32-bit Barrel 32-bit Barrel ShifterShifter
0.90.9 1.6811.681 46%46% 1.3681.368 1.81.8 24%24%
32-bit Booth 32-bit Booth MultiplierMultiplier
3.43.4 5.85.8 40%40% 5.155.15 6.26.2 17%17%
Power Consumption (mW)Power Consumption (mW)Frequency 25 MHzFrequency 25 MHz
Quasi-Quasi-adiabaticadiabatic
Static Static CMOSCMOS
Power Power SavedSaved
60 60 mWmW 85 85 mWmW 40%40%
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 3232
Power Analysis (Cont’d.)Power Analysis (Cont’d.)
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 3333
Area AnalysisArea AnalysisDatapathDatapath
ComponentComponent
Area (mmArea (mm22))
Quasi-Quasi-adiabaticadiabatic
Static CMOSStatic CMOS Area Area IncreaseIncrease
32-bit Adder Subtracter32-bit Adder Subtracter 0.050.05 0.030.03 66%66%
32-bit Barrel Shifter32-bit Barrel Shifter 0.250.25 0.110.11 120%120%
32-bit Booth Multiplier32-bit Booth Multiplier 1.21.2 0.50.5 140%140%
Chip Area (mmChip Area (mm22))
Quasi-Quasi-adiabaticadiabatic
Static Static CMOSCMOS
Area Area IncreaseIncrease
1.551.55 1.011.01 44%44%
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 13, Lecture 10ELEC6270 Spring 13, Lecture 10 3434
SummarySummary In principle, two types of adiabatic logic designs In principle, two types of adiabatic logic designs
have been proposed:have been proposed: Fully-adiabaticFully-adiabatic
Adiabatic chargingAdiabatic charging Charge recovery: charge from a discharging capacitor is Charge recovery: charge from a discharging capacitor is
used to charge the capacitance from the next stage.used to charge the capacitance from the next stage. W. C. Athas, L. J. Swensson, J. D. Koller, N. Tzartzanis and W. C. Athas, L. J. Swensson, J. D. Koller, N. Tzartzanis and
E. Y.-C. Chou, “Low-Power Digital Systems Based on E. Y.-C. Chou, “Low-Power Digital Systems Based on Adiabatic-Switching Principles,” Adiabatic-Switching Principles,” IEEE Trans. VLSI SystemsIEEE Trans. VLSI Systems, , vol. 2, no. 4, pp. 398-407, Dec. 1994.vol. 2, no. 4, pp. 398-407, Dec. 1994.
Quasi-adiabaticQuasi-adiabatic Adiabatic charging and dischargingAdiabatic charging and discharging Y. Ye and K. Roy, “QSERL: Quasi-Static Energy Recovery Y. Ye and K. Roy, “QSERL: Quasi-Static Energy Recovery
Logic,” Logic,” IEEE J. Solid-State CircuitsIEEE J. Solid-State Circuits, vol. 36, pp. 239-248, , vol. 36, pp. 239-248, Feb. 2001.Feb. 2001.