1. ELEC 5270/6270 Spring 2015 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
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

2. Examples of Power Saving and Energy Recovery
Power saving by power transmission at high voltage:
1000W transmitted at 100V, current I = 10A
If resistance of transmission circuit is 1Ω, then power loss = I2R = 100W
Transmit at 1000V, current I = 1A, transmission loss = 1W
Energy recovery from automobile braking:
Normal brake converts mechanical energy into heat
Instead, the energy can be stored in a flywheel, or
Converted to electricity to charge a battery
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

3. Reexamine CMOS Gate V2/ Rp V Most energy dissipated here i2Rp
i = Ve–t/RpC/Rp
v(t)
Power
v(t)
V×i = V2e–2t/RpC/ Rp C V
v(t)
3RpC
Time, t
Energy dissipation per transition = Area/2 = C V 2/ 2
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

4. Charging with Constant Current
V(t)
i2Rp
i = constant
it/C V
v(t) = it/C
C2V2Rp/T2
Output voltage, v(t)
Power C
T=CV/i
Time, t
Time (T) to charge capacitor to voltage V
v(T) = V = iT/C, or T = CV/i
Current, i = CV/T
Power = i2Rp = C2V2Rp/T2
Energy dissipation
= Power × T = (RpC/T) CV2
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

5. Or, Charge in Steps 0→V/2→V i2Rp i = Ve–t/RpC/2Rp V2e–2t/RpC/4Rp v(t)
V2/4Rp C V
v(t)
Power
V/2
3RpC
6RpC
Energy = Area = CV2/8
Time, t
Total energy = CV2/8 + CV2/8 = CV2/4
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

6. Energy Dissipation of a Step
Voltage step = V/N T
E = ∫ V2e–2t/RpC/(N2Rp) dt
= [CV2/(2N2)] (1 – e–2T/RpC)
≈ CV2/(2N2) for large T ≥ 3RpC
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

7. Charge 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, 2007
ELEC6270 Spring 15, Lecture 10

8. Reexamine Charging of a Capacitor
v(t)
i(t) C V
Charge on capacitor, q(t) = C v(t)
Current, i(t) = dq(t)/dt = C dv(t)/dt
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

9. ∫ ───── = ∫ ──── 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, 2007
ELEC6270 Spring 15, Lecture 10

10. – t v(t) = V [1 – exp( ── )] RC dv(t) V – t
i(t) = C ─── = ── exp( ── )
dt R RC
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

11. Total Energy Per Charging Transition from Power Supply
∞ ∞ V 2 – t
Etrans = ∫ V i(t) dt = ∫ ── exp( ── ) dt
R RC
= CV2
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

12. Energy Dissipated per Transition in Resistance
∞ V 2 ∞ –2t
R ∫ i 2(t) dt = R ── ∫ exp( ── ) dt
R RC 1
= ─ CV 2 2
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

13. Energy Stored in a Charged Capacitor
∞ ∞ – t V – t
∫ v(t) i(t) dt = ∫ V [1– exp( ── )] ─ exp( ── ) dt
RC R RC 1
= ─ CV 2 2
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

14. Slow Charging of a Capacitor
v(t)
i(t) C
V(t)
Charge on capacitor, q(t) = C v(t)
Current, i(t) = dq(t)/dt = C dv(t)/dt
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

15. ∫ ────── = ∫ ──── 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, 2007
ELEC6270 Spring 15, Lecture 10

16. Effects of Slow Charging
Voltage across R
Voltage
V(t)
v(t) t
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

17. Constant Current Is Optimum
I(t) R
t = [0,T] V C
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

18. Average and Instantaneous Current
Let T be the time to charge C to voltage V T
Average current : (1/T) ∫ I(t) dt = I0
Instantaneous current: I(t) = I0 + i(t)
Where ∫ i(t) dt = 0
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

19. Energy Dissipation E = R ∫ I2(t) dt = R ∫ [I0 + i(t)]2 dt 0 0 T
0 0 T
= R ∫ [I02 + 2I0i(t) + i2(t)] dt
T T
= RI02T RI0 ∫ i(t) dt R ∫ i2(t) dt
= RI02T R ∫ i2(t) dt ≥ RI02T
= RI02T, minimum value, when i(t) ≡ 0, i.e., I(t) = I0
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

20. Minimum Energy For a constant current I0, Charging time, T = CV/I0
Or I0 = CV/T
Emin = RI02T = RC2V2/T
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

21. References
C. L. Seitz, A. H. Frey, S. Mattisson, S. D. Rabin, D. A. Speck and J. L. A. van de Snepscheut, “Hot-Clock nMOS,” Proc. Chapel Hill Conf. VLSI, 1985, pp
W. C. Athas, L. J. Swensson, J. D. Koller, N. Tzartzanis and E. Y.-C. Chou, “Low-Power Digital Systems Based on Adiabatic-Switching Principles,” IEEE Trans. VLSI Systems, vol. 2, no. 4, pp , Dec
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

22. A Conventional Dynamic CMOS InverterCK
vin
v(t)
P E P E P E CK
v(t)
vin C
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

23. Adiabatic Dynamic CMOS Inverter
P E P E P E P E V CK
vin
v(t)
v(t)
vin C Vf +
V-Vf CK
A. G. Dickinson and J. S. Denker, “Adiabatic Dynamic Logic,” IEEE J. Solid-State Circuits, vol. 30, pp , March 1995.
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

24. Complex ADL Gate AB + C A C Vf < Vth B CK
A. G. Dickinson and J. S. Denker, “Adiabatic Dynamic Logic,” IEEE J. Solid-State Circuits, vol. 30, pp , March 1995.
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

25. A 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, 2007
ELEC6270 Spring 15, Lecture 10

26. Quasi-Adiabatic 32-bit ARM Based Microprocessor Design Specifications
Operating voltage: 2.5 V
Operating temperature: 25oC
Operating frequency: 10 MHz to 100 MHz
Leakage current: 0.5 fAmps
Load capacitance: 6X10-18 F (15% activity)
Transistor Count:
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

27. Technology Distribution
Microprocessor has a mix of static CMOS and Quasi-adiabatic components
Quasi-Adiabatic
Static CMOS
ALU
Adder-subtractor
unit
Barrel shifter unit
Booth-multiplier
Control Units
ARM controller unit
Bus control unit
Pipeline Units
ID unit
IF unit
WB unit
MEM unit
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

28. Power Consumption (mW)
Power Analysis
Datapath
Component
Power Consumption (mW)
Frequency 25 MHz
Frequency 100 MHz
Quasi-adiabatic
Static CMOS
Power Saved
32-bit Adder Subtracter
1.01
1.55
44%
1.29
1.62
20%
32-bit Barrel Shifter
0.9
1.681
46%
1.368
1.8
24%
32-bit Booth Multiplier
3.4
5.8
40%
5.15
6.2
17%
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

29. Power Analysis (Cont’d.)
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

30. Area Analysis Datapath Component Area (mm2) Quasi-adiabatic
Static CMOS
Area Increase
32-bit Adder Subtracter
0.05
0.03
66%
32-bit Barrel Shifter
0.25
0.11
120%
32-bit Booth Multiplier
1.2
0.5
140%
Chip Area (mm2)
Quasi-adiabatic
Static CMOS
Area Increase
1.55
1.01
44%
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10

31. Summary
In principle, two types of adiabatic logic designs have been proposed:
Fully-adiabatic
Adiabatic charging
Charge recovery: charge from a discharging capacitor is used to charge the capacitance from the next stage.
W. C. Athas, L. J. Swensson, J. D. Koller, N. Tzartzanis and E. Y.-C. Chou, “Low-Power Digital Systems Based on Adiabatic-Switching Principles,” IEEE Trans. VLSI Systems, vol. 2, no. 4, pp , Dec
Quasi-adiabatic
Adiabatic charging and discharging
Y. Ye and K. Roy, “QSERL: Quasi-Static Energy Recovery Logic,” IEEE J. Solid-State Circuits, vol. 36, pp , Feb
Copyright Agrawal, 2007
ELEC6270 Spring 15, Lecture 10