Power and Energy Basics

Jan M. Rabaey

Low Power Design Essentials ©2008 Chapter 3

Power and Energy Basics

Low Power Design Essentials ©2008 3.2

Chapter Outline

Metrics Dynamic power Static power Energy-delay trade-off’s


Metrics

Delay (sec):– Performance metric

Energy (Joule)– Efficiency metric: effort to perform a task

Power (Watt)– Energy consumed per unit time

Power*Delay (Joule)– Mostly a technology parameter – measures the efficiency of

performing an operation in a given technology Energy*Delay = Power*Delay2 (Joule-sec)

– Combined performance and energy metric – figure of merit of design style

Other Metrics: Energy-Delayn (Joule-secn)– Increased weight on performance over energy


Where is Power Dissipated in CMOS?

Active (Dynamic) power– (Dis)charging capacitors– Short-circuit power

Both pull-up and pull-down on during transition Static (leakage) power

– Transistors are imperfect switches Static currents

– Biasing currents


Active (or Dynamic) Power

Sources: Charging and discharging capacitors Temporary glitches (dynamic hazards) Short-circuit currents

Key property of active power:

fPdyn with f the switching frequency


Charging Capacitors

210 CVE

2

21 CVER

R

CV

2

21 CVEC

Applying a voltage step

Value of R does not impact energy!


Applied to Complementary CMOS Gate

One half of the power from the supply is consumed in the pull-up network and one half is stored on CL

Charge from CL is dumped during the 10 transition Independent of resistance of charging/discharging network

Vdd

Vout

iL

CL

PMOSNETWORK

NMOS

A1

AN

NETWORK

210 DDLVCE

221

DDLR VCE

221

DDLC VCE


Circuits with Reduced Swing

C

0→V - VTH

V

0→V

€

E0→1 = VC0

∞

∫ dVC

dtdt = CV dVC

0

V −VT

∫ = CV (V −VTH )

Energy consumed is proportional to output swing


Charging Capacitors - Revisited

RC EEE 10

2)( CVT

RCER

R

CI

2

21 CVEC

Driving from a constant current source

22

0

)()( CVT

RCTRIdtRIIE

ICVT

R

Energy dissipated in resistor can be reducedby increasing charging time T (that is, decreasing I)


Charging Capacitors

Using constant voltage or current driver?

Energy dissipated using constant current charging can be made arbitrarily small at the expense of delay:Adiabatic charging

Econstant_current < Econstant_voltage

if

T > 2RC

Note: tp(RC) = 0.69 RC t0→90%(RC) = 2.3 RC


Charging Capacitors

Driving using a sine wave (e.g. from resonant circuit)

Energy dissipated in resistor can be made arbitrarily smallif frequency w << 1/RC (output signal in phase with input sinusoid)

R

Cv(t)

2

21 CVEC


Dynamic Power Consumption

Power = Energy/transition • Transition rate

= CLVDD2 • f01

= CLVDD2 • f • P01

= CswitchedVDD2 • f

Power dissipation is data dependent – depends on the switching probability

Switched capacitance Cswitched = P01CL= a CL(a is called the switching activity)


Impact of Logic Function

A B Out0 0 10 1 01 0 01 1 0

Example: Static 2-input NOR gate

Assume signal probabilities pA=1 = 1/2 pB=1 = 1/2

Then transition probability p01 = pOut=0 x pOut=1

= 3/4 x 1/4 = 3/16

aNOR = 3/16

If inputs switch every cycle

NAND gate yields similar result


Impact of Logic Function

A B Out0 0 00 1 11 0 11 1 0

Example: Static 2-input XOR Gate

Assume signal probabilities pA=1 = 1/2 pB=1 = 1/2

Then transition probability p01 = pOut=0 x pOut=1

= 1/2 x 1/2 = 1/4

P01 = 1/4

If inputs switch in every cycle


Transition Probabilities for Basic Gates

p01

AND (1 - pApB)pApB

OR (1 - pA)(1 - pB)(1 - (1 - pA)(1 - pB))

XOR (1 - (pA +pB – 2pApB))(pA + pB – 2pApB)

Activity for static CMOS gatesa = p0p1

As a function of the input probabilities


Activity as a Function of Topology

aNOR,NAND = (2N-1)/22N aXOR = 1/4

XOR versus NAND/NOR

XOR

NAND/NOR


How about Dynamic Logic?

Energy dissipated when effective output is zero!or P0→1 = P0

VDD

Eval

Precharge

Always larger than P0P1!

Activity in dynamic circuits hence always higher than static.But … capacitance most often smaller.

E.g. P0→1(NAND) = 1/2N ; P0→1(NOR) = (2N-1)/2N


Differential Logic?

VDD

Out Out

Gate

Static: Activity is doubled Dynamic: Transition probability is 1!

Hence: power always increases.


Evaluating Power Dissipation of Complex Logic

Simple idea: start from inputs and propagate signal probabilities to outputs

But:– Reconvergent fanout– Feedback and temporal/spatial correlations

0.10.50.9

0.1

0.1

0.5

0.5

0.045

0.25

0.99 0.989

P1


Reconvergent Fanout (Spatial Correlation)

A

B

XZ

PZ = 1- PA . P(X|A) = 1

Becomes complex and intractable real fast

Inputs to gate can be interdependent (correlated)

no reconvergencePZ = 1-(1-PA)PB

A XZ

reconvergentPZ = 1-(1-PA)PA ?

NO!PZ = 1

reconvergence

Must use conditional probabilities

PZ: probability that Z=1

probability that X=1 given that A=1


Temporal Correlations

Activity estimation the hardest part of power analysis Typically done through simulation with actual input

vectors (see later)

R LogicX

Feedback

X is a function of itself→ correlated in time

Temporal correlation ininput streams

01010101010101…00000001111111…

Both streams have same P = 1 but different switching statistics


Glitching in Static CMOS

ABC 101 000

X

Z

Gate Delay

The result is correct,but extra power is dissipated

A

BX

ZC

Glitch

Analysis so far did not include timing effects

Also known as dynamic hazards:“A single input change causing multiple changes in the output”


Example: Chain of NAND Gates

1Out1 Out2 Out3 Out4 Out5

0 200 400 6000.0

1.0

2.0

3.0

Time (ps)

Out8

Out6

Out2

Out6

Out1

Out3

Out7

Out5

Volta

ge (V

)


What Causes Glitches?A

B

C

D

Y

Z

X

A,B

C,D

X

Y

Z

A

B

D

C

X

ZY

A,B

C,D

X

Y

Z

Uneven arrival times of input signals of gate due tounbalanced delay pathsSolution: balancing delay paths!


Short-Circuit Currents

(also called crowbar currents)

Vin Vout

CL

VDD

Isc

vin

VDD -VT

ishort

VTt

t

Ipeak

PMOS and NMOS simultaneously on during transition

Psc ~ f


Short-Circuit Currents

Equalizing rise/fall times of input and output signals limits Psc to 10-15% of the dynamic dissipation

Large load Small load

VinVout

CL

VDD

Isc~ 0

VinVout

CL

VDD

Isc IMAX

time (s)0 20

-0.5

0

0.5

1

1.5

2

2.5

40 60

I sc (A

)x 10-4

CL = 20 fF

CL = 100 fF

CL = 500 fF

[Ref: H. Veendrick, JSSC’84]


Modeling Short-Circuit Power

Can be modeled as capacitor

)( bakCout

inSC

a, b: technology parametersk: function of supply and threshold voltages, and transistor sizes

2DDSCSC VCE

Easily included in timing and power models


Transistors Leak

Drain leakage– Diffusion currents– Drain-induced barrier lowering (DIBL)

Junction leakages– Gate-induced drain leakage (GIDL)

Gate leakage– Tunneling currents through thin oxide


Sub-threshold Leakage

Off-current increases exponentially when reducing VTH

SV

leak

TH

WWII

-

100

0 Pleak = VDD.Ileak


Sub-Threshold Leakage

Leakage current increases with drain voltage(mostly due to DIBL)

SVV

leak

DSdTH

WWII

-

100

0 (for VDS > 3 kT/q)

Hence

)10)(10(0

0SV

DDS

V

leak

DDdTH

VWWIP

-

Leakage Power strong function of supply voltage


Stack Effect

NAND gate:

Assume that body effect in shortchannel transistor is small

SVV

Mleak

MdTH

II-

1002,

SVVVV

Mleak

MDDdTHM

II)(

01, 10---

DDd

dM VV

21

)21

1(

10 d

dDDd

SV

inv

stack

II

-

(instead of theexpected factor of 2)

VDD


Stack Effect

factor 9

Leakage Reduction2 NMOS 9

3 NMOS 17

4 NMOS 24

2 PMOS 8

3 PMOS 12

4 PMOS 16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3x 10

-9

VM (V)

I lea

k (A

) IM1 IM2

90 nm NMOS


Gate Tunneling

IGD~ e-ToxeVGD, IGS~ e-ToxeVGS

Independent of the sub-threshold leakage V DD 0V

V DD

I SUB

I GD

IGS

ILeak

Exponential function of supply voltage

Modeled in BSIM4Also in BSIM3v3 (but not always included in foundry models)NMOS gate leakage usually worse than PMOS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

x 10-10

VDD (V)

I gate

(A)

90 nm CMOS


Other sources of static power dissipation

Diode (drain-substrate) reverse bias currents

n well

n+n+ n+p+p+p+

p substrate

• Electron-hole pair generation in depletion region of reverse-biased diodes

• Diffusion of minority carriers through junction• For sub-50nm technologies with highly-doped pn junctions,

tunneling through narrow depletion region becomes an issue Strong function of temperature

Much smaller than other leakage components in general


Other sources of static power dissipation

Circuit with dc bias currents:

Should be turned off if not used, or standby current should be minimized

sense amplifiers, voltage converters and regulators, sensors, mixed-signal components, etc


Summary of Power Dissipation Sources

a – switching activity CL – load capacitance CCS – short-circuit

capacitance Vswing – voltage swing f – frequency

DDLeakDCDDswingCSL VIIfVVCCP a~

IDC – static current Ileak – leakage current

powerstaticrateoperation

energyP


The Traditional Design Philosophy

Maximum performance is primary goal– Minimum delay at circuit level

Architecture implements the required function with target throughput, latency

Performance achieved through optimum sizing, logic mapping, architectural transformations.

Supplies, thresholds set to achieve maximum performance, subject to reliability constraints


CMOS Performance Optimization

Sizing: Optimal performance with equal fanout per stage

Extendable to general logic cone through ‘logical effort’ Equal effective fanouts (giCi+1/Ci) per stage Example: memory decoder

CL

CL

predecoder

3 15

CW

word driver

addrinput

wordline

[Ref: I. Sutherland, Morgan-Kaufman‘98]


Model not Appropriate Any Longer

Traditional scaling model

CVDDf2 3.1)7.0

1()7.0()14.17.0

1(Power 22

1),

7.0(Freqand,7.0VDDIf

CVDD 8.1)2()7.0()14.17.0

1(fPower,2Freqand,7.0VDDIf

222

CVDD 7.2)2()85.0()14.17.0

1(fPower,2Freqand,85.0VDDIf

222

Maintaining the frequency scaling model

While slowing down voltage scaling


The New Design Philosophy

Maximum performance (in terms of propagation delay) is too power-hungry, and/or not even practically achievable

Many (if not most) applications either can tolerate larger latency, or can live with lower than maximum clock-speeds

Excess performance (as offered by technology) to be used for energy/power reduction

Trading off speed for power


12

34

-0. 400.40.8

00.2

0.40.6

0.8

1x 10

-4

VTH (V)

VDD (V)

Pow

er (W

)

A

B

12

34

-0.400.40.8

01

23

45

x 10-10

Del

ay (s

)VTH (V

)VDD (V)

A B

For a given activity level, power is reduced while delay is unchanged if both VDD and VTH are lowered such as from A to B.

Relationship Between Power and Delay

[Ref: T. Sakurai and T. Kuroda, numerous references]


The Energy-Delay Space

VTH

VD

D

Equal performance curves

Energy minimum

Equal energy curves


Energy-Delay Product as a Metric

delay

energy

energy-delay

90 nm technologyVTH approx 0.35V

Energy-delay exhibits minimum at approximately 2 VTH

(typical unless leakage dominates)

0.6 0.7 0.8 0.9 1 1.1 1.20

0.5

1

1.5

2

2.5

3

3.5

VDD


In energy-constrained world, design is trade-off process♦ Minimize energy for a given performance requirement

♦ Maximize performance for given energy budget

Delay

Unoptimized design

DmaxDmin

Energy

Emin

Emax

Exploring the Energy-Delay Space

Pareto-optimaldesigns

[Ref: D. Markovic, JSSC’04]


Summary

Power and energy are now primary design constraints

Active power still dominating for most applications– Supply voltage, activity and capacitance the key

parameters Leakage becomes major factor in sub-100nm

technology nodes– Mostly impacted by supply and threshold voltages

Design has become energy-delay trade-off exercise!


References

D. Markovic, V. Stojanovic, B. Nikolic, M.A. Horowitz, R.W. Brodersen, “Methods for True Energy-Performance Optimization,” IEEE Journal of Solid-State Circuits, vol. 39, no. 8, pp. 1282-1293, Aug. 2004.

J. Rabaey, A. Chandrakasan, B. Nikolic, “Digital Integrated Circuits: A Design Perspective,” 2nd ed, Prentice Hall 2003.

Takayasu Sakurai, ”Perspectives on power-aware electronics,” Digest of Technical Papers ISSCC, pp. 26-29, Febr. 03.

I. Sutherland, B. Sproull, and D. Harris, “Logical Effort”, Morgan Kaufmann, 1999.

H. Veendrick, “Short-Circuit Dissipation of Static CMOS Circuitry and its Impact on the Design of Buffer Circuits,” IEEE Journal of Solid-State Circuits, Vol. SC-19, no. 4, pp.468–473, 1984.

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Power and Energy Basics