Copyright Agrawal, 2007 Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8 ELEC6270 Spring 11, Lecture 8 1 ELEC 5270/6270 Spring 2011 ELEC 5270/6270 Spring 2011 Low-Power Design of Electronic Low-Power Design of Electronic Circuits Circuits Adiabatic Logic Adiabatic Logic Vishwani D. Agrawal Vishwani D. Agrawal James J. Danaher Professor James J. Danaher Professor Dept. of Electrical and Computer Engineering Dept. of Electrical and Computer Engineering Auburn University, Auburn, AL 36849 Auburn University, Auburn, AL 36849 [email protected]http://www.eng.auburn.edu/~vagrawal/COURSE/E6270_Spr11/c ourse.html
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ELEC 5270/6270 Spring 2011 Low-Power Design of Electronic Circuits Adiabatic Logic
ELEC 5270/6270 Spring 2011 Low-Power Design of Electronic Circuits Adiabatic Logic. Vishwani D. Agrawal James J. Danaher Professor Dept. of Electrical and Computer Engineering Auburn University, Auburn, AL 36849 [email protected] - PowerPoint PPT Presentation
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Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 11
ELEC 5270/6270 Spring 2011ELEC 5270/6270 Spring 2011Low-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
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 33
Reexamine CMOS GateReexamine CMOS Gate
i = Ve–t/RpC/Rp
i2Rp
VV2/ Rp
C
Time, t
Po
we
r
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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 44
Charging with Constant CurrentCharging with Constant Current
i = constant i2Rp
V(t)
C
Po
we
r0
v(t) = it/C
Time (T) to charge capacitor to voltage V v(T) = V = iT/C, or T = CV/iCurrent, i = CV/T
Ou
tpu
t vo
ltag
e, 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 55
Or, Charge in StepsOr, Charge in Steps
i = Ve–t/RpC/2Rp
i2Rp
0→V/2→V
V2/4Rp
C
Time, t
Po
we
r
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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 1313
Energy Stored in Charged Energy Stored in 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 1616
Effects of Slow ChargingEffects of Slow Charging
V(t) v(t)
t
Voltage across R
Vo
ltage
Constant Current Is OptimumConstant Current Is Optimum
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 1717
R t = [0,T]I(t)
C
V
Average and Instantaneous Average and Instantaneous CurrentCurrent
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 1919
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 2020
For a constant current I0,
Charging time, T = CV/I0
Emin = RCVI0
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 2323
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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 11, Lecture 8ELEC6270 Spring 11, Lecture 8 2929
Quasi-Adiabatic 32-bit ARM Based Quasi-Adiabatic 32-bit ARM Based Microprocessor Design SpecificationsMicroprocessor Design Specifications
Copyright Agrawal, 2007Copyright Agrawal, 2007 ELEC6270 Spring 11, Lecture 8ELEC6270 Spring 11, Lecture 8 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.