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EE141EE141-- Spring 2005Spring 2005Digital Integrated Digital Integrated CircuitsCircuits

Lecture 20Lecture 20PowerPowerSequential CircuitsSequential Circuits

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Administrative StuffAdministrative Stuff

Hw 7 has been posteddue Fr. 5pm

Midterm 2: April 12th by popular demand!Material:

– Wires– Complex logic– Arithmetic

HW Lab this weekProject 1 has been gradedReview session on Th 6:30-8pm

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Project 1 ResultsProject 1 Results

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Class MaterialClass Material

Last lectureMultipliersShifters

Today’s lecturePowerIntro Sequential Circuits

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PowerPower

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The Power ChallengeThe Power Challenge400 million computers in the world

0.16 PW (PetaWatt = 1015 W) of power dissipationEquivalent to 26 nuclear plants!

Data centers represent the absolute challenge

1 single server rack is between 5 and 20 kW100’s of those racks in a single room!

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PowerPower--andand--Energy ChallengesEnergy ChallengesCourtesy of IBM

Power and energy management and minimizationhave emerged as some of the most dominant roadblocks. The best opportunity lies in a very aggressive scaling and adaptation of supply and threshold values in concert with a careful orchestration of the system activity.

138 W/cm2

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Portability:Portability:Battery storage the limiting factorBattery storage the limiting factor

Little change in basic technologystore energy using a chemical reaction

Battery capacity doubles every 10 yearsEnergy density/size, safe handling are limiting factor

Energy densityof material

KWH/kg

Gasoline 14

Lead-Acid 0.04

Li polymer 0.15

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Battery ProgressBattery Progress

020406080

100120140160

1940 1950 1960 1970 1980 1990 2000 2010

First Commercial Use

Energy Density(Wh/kg) Trend Line

NiCd SLA NiMH Li-Ion ReusableAlkaline

Li-Polymer

Facture 4 over the last 10 years!

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Power Dissipation in CMOSPower Dissipation in CMOSDynamic power

Charging capacitancesDominant today

Leakage powerLeaky transistorsConcern in low-activity, portable devices

Short circuit powerStatic power

E.g. pseudo-NMOS

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Dynamic Power ConsumptionDynamic Power Consumption

( ) ( ) ∫∫ ∫ ====→

DDV

DDLoutLDD

T T

DDDDDD VCdvCVdttiVdttPE0

2

0 010

( ) ( ) ∫∫ ∫ ====DDV

DDLoutoutL

T T

LoutCC VCdvvCdttivdttPE0

2

0 0 21

Vdd

Vout

iL

CL

PMOSNETWORK

NMOS

A1

AN

NETWORK

210 DDLVCE =→

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Dynamic Power ConsumptionDynamic Power Consumption

One half of the power from the supply is consumed in the pull-up network and one half is stored on CLCharge from CL is dumped during the 1→0 transition

Vdd

Vout

iL

CL

PMOSNETWORK

NMOS

A1

AN

NETWORK

210 DDLVCE =→

221

DDLR VCE =

221

DDLC VCE =

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Dynamic Power ConsumptionDynamic Power ConsumptionPower = Energy/transition • Transition rate

= CLVDD2 • f0→1

= CLVDD2 • f • P0→1

= CswitchedVDD2 • f

Power dissipation is data dependent – depends on the switching probabilitySwitched capacitance Cswitched = CL • P0→1

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Transition Activity and PowerTransition Activity and PowerEnergy consumed in N cycles, EN:

EN = CL • VDD2 • n0→1

n0→1 – number of 0→1 transitions in N cycles

fVCN

nfNEP DDLN

NNavg ⋅⋅⋅

=⋅= →

∞→∞→

210limlim

fN

nN

⋅= →

∞→→10

10 limα

fVCP DDLavg ⋅⋅⋅= →2

10α

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“Dynamic” or timing dependent component

Type of Logic Function (NOR vs. XOR)“Static” component (does not account for timing)

Circuit Topology

Type of Logic Style (Static vs. Dynamic)

Signal StatisticsInter-signal Correlations

Signal Statistics and Correlations

Factors Affecting Transition ActivityFactors Affecting Transition Activity

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Type of Logic Function: NOR vs. XORType of Logic Function: NOR vs. XOR

011001010100

OutBA

Example: Static 2-input NOR Gate

Assume signal probabilitiespA=1 = 1/2pB=1 = 1/2

Then transition probabilityp0→1 = pOut=0 x pOut=1

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

α0→1 = 3/16

If inputs switch every cycle

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Type of Logic Function: NOR vs. XORType of Logic Function: NOR vs. XOR

011101110000

OutBA

Example: Static 2-input XOR Gate

Assume signal probabilitiespA=1 = 1/2pB=1 = 1/2

Then transition probabilityp0→1 = pOut=0 x pOut=1

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

α0→1 = 1/4

If inputs switch in every cycle

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Power Consumption of Dynamic GatesPower Consumption of Dynamic Gates

In1

In2 PDNIn3

Me

Mp

CLK

CLKOut

CL

Power only dissipated when previous Out = 0

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Dynamic Power Consumption is Dynamic Power Consumption is Data DependentData Dependent

011001010100

OutBA

Dynamic 2-input NOR Gate

Assume signal probabilitiesPA=1 = 1/2PB=1 = 1/2

Then transition probabilityP0→1 = Pout=0 x Pout=1

= 3/4 x 1 = 3/4

Switching activity always higher in dynamic gates!P0→1 = Pout=0

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Vdd

I

I

Vdd

IN

INB

OUTB OUT

Guaranteed transition for every operation!

α0->1 = 1

Dynamic CVSLDynamic CVSL

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Problem: Problem: ReconvergentReconvergent FanoutFanout

A

B

X

Z

Reconvergence

P(Z = 1) = P(B = 1) . P(X = 1 | B=1)

Becomes complex and intractable fast

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InterInter--Signal CorrelationsSignal Correlations

Logic withoutreconvergent fanout

Logic with reconvergent fanout

A

BZ

CA

Z

C

B

p0→1 = (1 – pApB) pApBP(Z = 1) = p(C=1 | B=1) p(B=1)

p0→1 = 0

Need to use conditional probabilities to model inter-signal correlationsCAD tools required for such analysis

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GlitchingGlitching in Static CMOSin Static CMOSA

B

X

CZ

ABC 101 000

X

Z

Gate DelayAlso known as

dynamic hazards

The result is correct,but there is extra power dissipated

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Example: Chain of NOR GatesExample: Chain of NOR Gates1

Out1 Out2 Out3 Out4 Out5

0 200 400 6000.0

1.0

2.0

3.0

Time (ps)

Volta

ge (V

)

Out8Out6

Out2

Out6

Out1

Out3

Out7

Out5

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Principles for Power ReductionPrinciples for Power ReductionPrime choice: Reduce voltage!

Recent years have seen an acceleration in supply voltage reductionDesign at very low voltages still open question (0.6 … 0.9 V by 2010!)Reducing thresholds to improve performance increases leakage

Reduce switching activityReduce physical capacitance

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Sequential Logic

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Sequential LogicSequential Logic

2 storage mechanisms• positive feedback• charge-based

COMBINATIONALLOGIC

Registers

Outputs

Next state

CLK

Q D

Current State

Inputs

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Latch versus RegisterLatch versus RegisterLatchstores data when clock is low

D

Clk

Q D

Clk

Q

Registerstores data when clock rises

Clk Clk

D D

Q Q

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Naming ConventionNaming Convention

In our book, latch is level sensitive, register is edge-triggeredThere are many different naming conventionsMany books call edge-triggered elements flip-flops

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LatchesLatches

In

clk

In

Out

Positive Latch

CLK

DG

Q

Out

Outstable

Outfollows In

In

clk

In

Out

Negative Latch

CLK

DG

Q

Out

Outstable

Outfollows In

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NLatch Logic

Logic

PLatch

φ

LatchLatch--Based DesignBased Design• N latch is transparentwhen φ = 0

• P latch is transparent when φ = 1

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Timing DefinitionsTiming Definitions

t

CLK

t

D

tc →q

tholdtsu

t

Q DATASTABLE

DATASTABLE

Register

CLK

D Q

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Characterizing TimingCharacterizing Timing

Register Latch

Clk

D Q

tC →Q

Clk

D Q

tC →Q

tD →Q

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Maximum Clock FrequencyMaximum Clock Frequency

FF’s

LOGIC

tp,comb

φ

Also:tcdreg + tcdlogic > thold

tcd: contamination delay = minimum delay

tclk-Q + tp,comb + tsetup = T

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Positive Feedback: BiPositive Feedback: Bi--StabilityStabilityVi1 Vo2

Vo2 = Vi1

Vo1 = Vi2

V

o

1

Vi1

A

C

B

V

i

2

5

V

o

1

Vo2

V

i

2

5

V

o

1

Vi1 = Vo2

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MetaMeta--StabilityStability

Gain should be larger than 1 in the transition region

A

C

d

B

Vi2

5V

o1

Vi1 5 Vo2

A

C

d

B

Vi2

5V

o1

Vi1 5 Vo2

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Writing into a Static LatchWriting into a Static Latch

CLK

CLK

CLK

D

Q D

CLK

CLK

D

Converting into a MUXForcing the state(can implement as NMOS-only)

Use the clock as a decoupling signal, that distinguishes between the transparent and opaque states

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PseudoPseudo--Static LatchStatic Latch

D

CLK

CLK

D

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MuxMux--Based LatchesBased LatchesNegative latch(transparent when CLK= 0)

Positive latch(transparent when CLK= 1)

CLK

1

0D

Q 0

CLK

1D

Q

InClkQClkQ ⋅+⋅= InClkQClkQ ⋅+⋅=

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MuxMux--Based LatchBased Latch

CLK

CLK

CLK

D

Q

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MuxMux--Based LatchBased Latch

CLK

CLK

CLK

CLK

QM

QM

NMOS only Non-overlapping clocks

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Storage MechanismsStorage Mechanisms

D

CLK

CLK

Q

Dynamic

CLK

CLK

CLK

D

Q

Static

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Sequential logic (cntd)