Equalization and Clock and Data Recovery Techniques for 10-G(6)

(7)(8)

and

(9)

9Simulations

indicatethatiftheproposedmodelisalteredtoincuronemore

dBoferror,theequalizeroutputsuffersfrom2.6dBofadditionalverticalclo-sureand0.03UIofadditionaljitter.

Fig.27.(a)Errorduetoadditivenoisebasedonthesamplingpointsintheeye.(b)BERasafunctionofclockskew.

where

denotesthermsvalueofnoise.Carryingouttheinte-grationin(6)andneglectinghigher-orderterms,wehave

(10)

Forexample,with

mV,mV,mV,10andsamplinginthemiddleoftheeye,weobtain.

Inthepresenceofclockskewandjitter,thesamplingpointde-viatesfromthemaximumeyeopening,rapidlyraisingtheBER.(SincetheISI-inducedjitterinthedatawaveformcontainspre-dominantlyhigh-frequencycomponents[19],theCDRcircuitfailstotrackthecorrespondingphasevariations.)FortoinFig.27(a),weapproximatetheeyeopeningas

andplotasafunctionofthe

clockskew[Fig.27(b)].Here,theabovevaluesof,,areusedand.

Wecannowincorporatetheeffectofclockjitterbyweighting

(10)accordingtothejitterdistribution,

,wheredenotestherandomdepartureofthesamplingpointfromthe

centeroftheeye.AsillustratedinFig.28(a),if

placesthesamplinginstantat,then

islowerandtheeffectofmorepronounced.Theerrorprobabilitydensityfunctionacrossthebitperiodcanthereforebeexpressedas

(11)

PlottedinFig.28(b)foraGaussianjitterdistributionhavinganrmsvalueofps,thisresultrevealsthaterrorsaremostlikelytooccurinthevicinityofps,wherethe

dramaticriseinstillcompensatesforthefallin

.Beyondthispointtheclockjitterbecomessoimprobablethaterrorsarelessandlesslikelytooccur.

Theframeworkdevelopedabovecanbeusedtoformulatethetrade-offsbetweenrequiredswings,additivenoise,ISI,and

tolerableclockjitter.Forexample,with

mVand,theplotsinFig.29canbegenerated,where

10The

additivenoiseisobtainedbyintegratingthenoiseattheoutputofthe

equalizerpathupto100GHz.

2010Fig.28.(a)Errorduetoadditivenoiseandclockskew.(b)Errorprobabilitydensityacrossthebitperiod.

Fig.29.BERcurvesfordifferentcombinationofreceivedswingsandclockjitter.

eachcurverepresentstheacceptablecombinationofand

thatyieldsagivenBER.Worthnotinghereisthesharpriseintherequiredswingastheclockjitterexceeds3ps.Also,theexperimentalresultinFig.23(b)indicatesanrmsjitterof2.2ps,whichfromFig.29,woulddictateaminimumswingof

520mVforBER

.Thisvalueisfairlyclosetothemeasuredresultof640mVinFig.22.

ACKNOWLEDGMENT

TheauthorswishtothankV.PathakandKawasakiMicro-electronicsAmericaforsupportofthiswork,Dr.J.Leeforde-signassistance,andTSMCforfabricationsupport.

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