Continuous-Time Hybrid Computation with Programmable ...yipenghuang.com/wp-content/uploads/2016/07/ESSCIRC...Continuous-Time Hybrid Computation with Programmable Nonlinearities Columbia

Continuous-TimeHybridComputationwithProgrammable

Nonlinearities

ColumbiaUniversityNewYork,NYUSA

NingGuo,Yipeng Huang,TaoMai,Sharvil Patil,ChiCao,Mingoo Seok,Simha Sethumadhavan,andYannis Tsividis

ESSCIRC201541thEuropeanSolid-StateCircuitsConference

SessionB5L:Continuous-TimeHybridComputationwithProgrammableNonlinearities 1



CTHYBRIDCOMPUTER

t

t0 0

111

Both analoganddigitalsignalsarefunctionsofcontinuous-time

Thistalkpresentsanewprinciple:Continuous-timehybridcomputation

DIGITALCOMPUTER

INTERFAC

ESynergywithadigitalcomputerthroughacommoninterface

Timeintervals:Importantinfo,unlike thecaseinasync digital.

Outline1. Backgroundandmotivation

2. Mathoperations

3. Systemarchitecture

4. Circuitdesign

5. Measurementresults

6. Conclusions

3ESSCIRC201541thEuropeanSolid-StateCircuitsConference

SessionB5L:Continuous-TimeHybridComputationwithProgrammableNonlinearities

Backgroundandmotivation

• Analogcomputersweredominantinthe1960s;theyhelpedsendMantothemoon!• Solvingordinary/partial differential equations• Parallelcomputation• Noconvergence issues



https://en.wikipedia.org/wiki/Analog_computer


• Analogcomputerswereabandonedinthe1960sand1970s,whiletheywerestillusingthetechnologyyousawonthepreviousslide.



[1]G.Cowanetal.,ISSCC2005

• TheirpotentialinmodernVLSItechnologywasnotconsidereduntilrecently[1].

• ItwasshownthatVLSIanalogcomputersaresuitablefor:• Low-power, self-contained approximatecomputation• Speed-up ofdigitalcomputation throughco-processing.

�̈� = −0.2�̇� − 0.5𝑥 + 1;

Mathequation:

Initialconditions:𝑥 0 = 9;�̇� 0 = −7



BackgroundandmotivationAnalogcomputationexample

𝑥

Physicalsystem

Mass

Spring∫ ∫

Force

Mass

Spring∫ ∫

Force

Physicalsystem



BackgroundandmotivationAnalogcomputationexample

�̇��̈� 𝑥

-0.2

-0.5

1

�̈� = −0.2�̇� − 0.5𝑥 + 1;

Mathequation:

Initialconditions:𝑥 0 = 9;�̇� 0 = −7

𝑥

Electricalsystem

-10

-5

0

5

10

20 40 60

𝑥 (µA)

𝑡 (ms)


• Wepresentanewprinciple:continuous-timehybridcomputation• Continuous-time analogcomputation• Continuous-time digitalcomputation

• Comparedtothefullyanalogapproach,thenewapproachresultsin:• Betteraccuracy• Higherprogrammabilityandgenerality



NOCLOCK

Basicarithmeticoperations:

∫

Addition𝑧 𝑡 = 𝑥 𝑡 + 𝑦(𝑡)

Subtraction𝑧 𝑡 = 𝑥 𝑡 − 𝑦(𝑡)

Multiplication𝑧 𝑡 = 𝑥 𝑡 𝑦(𝑡)

Integration𝑦 𝑡 = ∫ 𝑥 𝜏 𝑑𝜏C

D

Nonlinearfunction𝑦 𝑡 = 𝐹(𝑥 𝑡 )

Mathoperations



F( )

Problemvariable

Machinevariable

Amplitude scaling:

Mathoperations



Problemvariable- 10cm + 10cm

0

- 2µA + 2µA0

Machinevariable

Example:

Problemtime

Machinetime

Timescaling:

Problemtime

Machinetime

0 1s

0 1µs

Example:

4 AN

ALO

G O

UTPU

TS

8 FANOUT BLOCKS 4 INTEGRATORS 8 MULTIPLIER/VGAs

8 8 8 8

8 8 8 8SPI CONTROLLER

SRAM SRAM

∫

∫

∫

∫

CT

AD

C

CT

DA

C

8 8DIGITAL OUTPUT

DIG

ITAL

INPU

T

4SPI

4 ANALOG INPUTS

CT

AD

C

CT

DA

C

Accuracy: 8-bit

Signalrepresentation:Differential current

Analogblockinterface:DCcoupled,Class-AB

Offsets:<1LSBaftercalibration

Analogsignalbandwidth:DC- 20KHz

Systemarchitecture



Inputstage Integrationstage Outputstage

Circuitdesign:Integratorblock



+

-

Gm

8

DACDigital code

Input current mirrors

Output transconductor

C

Initial condition setting block

Common mode feedback block

+

-

Gm

IC+

IC-

IIN-

IIN+

IDAC+

IDAC-

10RF ,RF

10RF ,RF

VC+

VC-

VREF

10R, R10R, R

VCM

IOUT-

IOUT+

Multiplierblock(principle)

Analogsignalrouting

MG,MI,MJ,MK inweakinversion𝑉MNG + 𝑉MNJ = 𝑉MNI + 𝑉MNK ⇒ 𝐼G 𝐼J = 𝐼I𝐼K

Fanoutblock

CircuitdesignCircuittechniquesusedinotherblocks:

∫ ONON



M1

VA VA

I1 I2 I3 I4

M2 M3 M4

VA

VB

VC

VD

IIN+ IOUT1-

VA

VD

IOUT2-IOUT3-

AVDD

4 AN

ALO

G O

UTPU

TS

8 FANOUT BLOCKS 4 INTEGRATORS 8 MULTIPLIER/VGAs

8 8 8 8

8 8 8 8SPI CONTROLLER

SRAM SRAM

∫

∫

∫

∫

CT

AD

C

CT

DA

C

8 8DIGITAL OUTPUT

DIG

ITAL

INPU

T

4SPI

4 ANALOG INPUTS

CT

AD

C

CT

DA

C

Systemarchitecture



Nonlinearfunction𝑦 𝑡 = 𝐹(𝑥 𝑡 )

F( ) 𝑦 𝑡x 𝑡

CT DAC

8

TRIGGER

DATA8

TRIGGER

DATAANALOG

INPUTANALOG OUTPUT

NONLINEAR FUNCTION F( )

CT ADC

SRAM

x F(x)

Ourapproach:Acontinuous-time programmablelookuptable

Advantagesoverdiscrete-timecounterpart:

• Activity-dependent powerdissipation• Fasterresponse toinputchanges• Noaliasing

Circuitdesign:Nonlinearfunctionblock



[2]B.Schelletal.,ISSCC2008

NOCLOCK

Implementation:




NOCLOCK[2]B.Schelletal.,ISSCC2008

[2]

CT DAC

8

TRIGGER

DATA8

TRIGGER

DATAANALOG

INPUTANALOG OUTPUT

CT ADC

SRAM

TRIGGER

Voltage mode

CT ADC DATA

8

I-V CONVERTERDELAY

x F(x)


i-

i+

RF ,10RF

RF ,10RFVREF

t0 0

1118t

AnalogInput ADC’soutput

Implementation:





[2]

CT DAC

8

TRIGGER

DATA8

TRIGGER

DATAANALOG

INPUTANALOG OUTPUT

CT ADC

SRAM

TRIGGER

DFF

s

DFF

s8 COLUMNSX 32 WORDS

X 8BIT

88D

ECO

DER

SRAM IN READ MODE

DATA

Voltage mode

CT ADC DATA

8

I-V CONVERTER

8

DELAYDELAY DELAY

x F(x)


i-

i+

RF ,10RF

RF ,10RFVREF

t0 0

1118 t0 0

1118t

AnalogInput ADC’soutput SRAM’soutput

NOCLOCK

Implementation:





[2]

CT DAC

8

TRIGGER

DATA8

TRIGGER

DATAANALOG

INPUTANALOG OUTPUT

CT ADC

SRAM

TRIGGER

DFF

s

DFF

s8 COLUMNSX 32 WORDS

X 8BIT

88D

ECO

DER

SRAM IN READ MODE

DATA

Voltage mode

CT ADC DATA

8

I-V CONVERTER

1/8

3 MSBs

DFF

s

1/8

... +

1/161/8 1/32 1/256

...

5 LSBs

THERMO WEIGHTED

BINARY WEIGHTED

THER

MO

D

ECO

DER

8

DELAYDELAY DELAY

x F(x)


i-

i+

RF ,10RF

RF ,10RFVREF

t0 0

1118 t0 0

1118 tt

AnalogInput ADC’soutput SRAM’soutput DAC’soutput

NOCLOCK

Diephoto Keyperformancesummary*Supply voltage 1.2VTechnology TSMC65nmLP

Diearea/active area 3.8 mm²/2.0mm²Integratornonlinearity 0.44%Fanoutnonlinearity 0.13%Multiplier/VGAnonlinearity 0.15%

ADC+DACSNDR@20KHz 53dBDACDNL/INL 0.73LSB /0.67LSB

*MeasurementconditionslistedinDigestpaper

Measurementresults



4× INTEGRATOR

8× FANOUT

8× MULTIPLIER

/ VGA

2×CT ADC 2×CT DAC

SPI CONTROLLER

2×SRAM

Nonlineardifferentialequation

RMSerror(uncalibrated)

RMSerror(calibrated)

VanderPoloscillator 17.7% 1.9%

Largeanglemotionofpendulum

7.3% 1.5%

Mass-springdamperswith

Coulombfriction18.0% 1.5%

Calibrationhelpsimproveaccuracy

*Measurement conditions listedinDigestpaper

Measurementresults



0 20 40 60 80

Fanout

Integrator

Multiplier

VGA

CTADC

CTDAC

SRAM

Powerdissipation*(μW)

Nonlinearfunctiongeneration: Activity-dependentpowerdissipation:

Measurementresults



50556065707580859095

0 2 4 6 8 10 12 14 16 18 20LookupRate(kHz)

F(X)=sin(X)lookup

PowerDissipation(μW)

-1-0.5

00.5

1

X(rad)

F(X)=sin(X)

-2%

-1%0%

1%

2%

-π +π

X(rad)-π

+π

Y

F(Y)=sigmoid(Y)

-6 +6

Y-6 +6

0

0.5

1

-2%-1%0%1%2%

RelativeErrorRelativeError

x

y

Atwo-wheeldriverobotwithmodelpredictivecontrol

Currentstate

Possible futuresstates in0.1s

cossin

x

y =

!!!

Continuous-timesystemdynamics

ω:angularvelocity

ν:linearvelocity

Applicationdemonstration



ω

ν

θ(t)

x(t)

y(t)

CT DAC

CT ADC

SRAM8

DATA

TRIGGER SIGNAL

CT DAC

SRAM

COS( )

SIN( )

θ(t)

8DATA

TRIGGER SIGNAL

8DATA

TRIGGER SIGNAL

8DATA

TRIGGER SIGNAL

∫ ∫

∫

Atwo-wheeldriverobotwithmodelpredictivecontrol

Applicationdemonstration



T=0.84μs,Energy=0.48nJRMSerror=0.6%

x

y

Currentstate

Possible futuresstates in0.1s

cossin

x

y =

!!!

Continuous-timesystemdynamics

ω:angularvelocity

ν:linearvelocity

Onemacroin[1] Our chipSupplyvoltage 2.5V 1.2VTechnology 250nmCMOS 65nmCMOS

Active area(estimate) 6.3mm² 2.0mm²Numberoffunctionblocks 25 26Powerwithallblockson

(estimate) 18.8mW 1.2mW

Calibration Integratorsonly AllblocksComputation types CTanalogonly CTanalog/CThybrid

Nonlinearities availableforcomputation

Specifictypes:exp(),log(), absolute,saturation,etc.

Arbitrary

On-chip ADC,SRAM,DAC N/A Available

Comparisontopriorart

[1]G.Cowanetal.,ISSCC2005ESSCIRC201541thEuropeanSolid-StateCircuitsConference


• Wehavepresentedthefirstcontinuous-timehybridcomputingunit.

• Arbitrarynonlinearfunctionsareimplementedbyacontinuous-timehybridarchitecture(ADC+SRAM+DAC).

• Wehaveusedthechiptosuccessfullysolveseveralbenchmarkequationsanddemonstratedtheuseofthechipinaroboticapplication.

• Weexpectthistechniquetofindapplicationsinlow-powerapproximatecomputationandinaccelerationofdigitalcomputation.

Conclusions



WethankChien-TangHu,Doyun Kim,Jianxun Zhu,Teng Yang,YangXu,YuChenandZhe Caoforvaluablediscussions.

ThisworkhasbeensupportedbyNationalScienceFoundationgrantCNS1239134.

Acknowledgement



[1]G.Cowan,R.Melville,andY.Tsividis,“AVLSIanalogcomputer/mathco-processorforadigitalcomputer”,DigestIEEE2005ISSCC,pp.82-83.[2]B.SchellandY.Tsividis,“AclocklessADC/DSP/DACsystemwithactivity-dependentpowerdissipationandnoaliasing”,Digest2008IEEEISSCC,pp.550-551

[3]D.Kimetal.,“A1.85fW/bitultralowleakage10TSRAMwithspeedcompensationscheme”,Proc.IEEEISCAS,pp.69-72,May2011.[4]G.Klancar andI.Skrjanc,"Tracking-errormodel-basedpredictivecontrolformobilerobotsinrealtime,"RoboticsandAutonomousSystems,vol.55,no.6,pp.460-469, 2007.

[6]G.A.Korn,T.M.Korn,ElectronicAnalogandHybridComputers,McGrawHill,1964.[7]B.Gilbert,"Current-mode,voltage-mode,orfreemode?Afewsagesuggestions”,AnalogIntegratedCircuitsandSignalProcessing,vol.38,pp.83-101, February2004

References



Thankyou!

Questions?





Comparisondetails

[8] D.Bol,etal,“SleepWalker: A25-MHz0.4-VSub-mm27-µW/MHzMicrocontroller in65-nmLP/GPCMOSforLow-CarbonWireless SensorNodes”, IEEEJSSC,vol.48,pp.20-32,2013.

Timestepsize

Total clockcycles

Timeneededforonesolution

Energyconsumption foronesolution

Our hybridchip N/A N/A 0.84μs 0.48nJ

0.4VRISCmicroprocessor [8] 0.1s 734 29μs 5.14nJ

35Xbetter 11Xbetter

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Continuous-Time Hybrid Computation with Programmable ...yipenghuang.com/wp-content/uploads/2016/07/ESSCIRC...Continuous-Time Hybrid Computation with Programmable Nonlinearities Columbia