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Andrea Baschirotto · Pieter Harpe Ko  A.A. Makinwa Editors

Wideband Continuous-time

ADCs, Automotive Electronics, and Power Management

Design

Editors

UniversityofMilan Milano,MI,Italy

KofiA.A.Makinwa

ElectronicInstrumentationLaboratory DelftUniversityofTechnology Delft,Zuid-Holland TheNetherlands

PieterHarpe DepartmentofElectricalEngineering EindhovenUniversityofTechnology Eindhoven,Noord-Brabant TheNetherlands

ISBN978-3-319-41669-4ISBN978-3-319-41670-0(eBook) DOI10.1007/978-3-319-41670-0

LibraryofCongressControlNumber:2016947073

©SpringerInternationalPublishingSwitzerland2017

Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.

Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse.

Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.

Printedonacid-freepaper

ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland

Preface

ThisbookispartoftheAnalogCircuitDesignseriesandcontainsthecontributions fromall18speakersofthe25thWorkshoponAdvancesinAnalogCircuitDesign (AACD).Thisyear,thesponsorsoftheworkshopwereInfineon(mainsponsor), JoanneumResearchCenter,INTEL,andIEEESolid-StateCircuitsSocietyAustrian andItalianChapters.TheworkshopwasheldattheInfineonsiteinVillach(Austria), fromApril26to28,2016.Thebookcomprisesthreeparts,coveringtopicsin advancedanalogandmixed-signalcircuitdesignthatweconsidertobeofgreat interesttothecircuitdesigncommunity:

•Continuous-TimeSigma-DeltaModulatorsforTransceivers

•AutomotiveElectronics

•PowerManagement

Eachpartconsistsofsixchapterswrittenbyexpertsinthefield.Theaimof theAACDworkshopistobringtogetheragroupofexpertdesignerstodiscuss newdevelopmentsandfutureoptions.Eachworkshopisthenfollowedbythe publicationofabookbySpringeraspartoftheirsuccessfulseriesonAnalogCircuit Design.Thisbookisthe25thinthisseries(afulllistoftheprevioustopicscanbe foundonthefollowingpage).Theseriescanbeseenasareferenceforallpeople involvedinanalogandmixed-signaldesign.Weareconfidentthatthisbook,like itspredecessors,willprovetobeavaluablecontributiontoouranalogandmixedsignalcircuitdesigncommunity.

Milano,ItalyAndreaBaschirotto Eindhoven,TheNetherlandsPieterHarpe Delft,TheNetherlandsKofiA.A.Makinwa v

TheTopicsCoveredBeforeinThisSeries

2015Neuchatel(Switzerland)EfficientSensorInterfaces AdvancedAmplifiers LowPowerRFSystems

2014Lisbon(Portugal)High-PerformanceADandDAConverters

ICDesigninScaledTechnologies Time-DomainSignalProcessing

2013Grenoble(France)FrequencyReferences PowerManagementforSoC SmartWirelessInterfaces

2012Valkenburg(TheNetherlands)NyquistA/DConverters CapacitiveSensorInterfaces BeyondAnalogCircuitDesign

2011Leuven(Belgium)Low-VoltageLow-PowerDataConverters

Short-RangeWirelessFront-Ends PowerManagementandDC-DC

2010Graz(Austria)RobustDesign SigmaDeltaConverters RFID

2009Lund(Sweden)SmartDataConverters FiltersonChip MultimodeTransmitters

2008Pavia(Italy)High-SpeedClockandDataRecovery High-PerformanceAmplifiers PowerManagement

2007Oostende(Belgium)Sensors,ActuatorsandPowerDrivers fortheAutomotiveandIndustrial Environment IntegratedPAsfromWirelinetoRF VeryHighFrequencyFrontEnds

2006Maastricht(TheNetherlands)High-SpeedADConverters

AutomotiveElectronics:EMCIssues UltraLowPowerWireless

2005Limerick(Ireland)RFCircuitsWideBand,Front-Ends,DACs DesignMethodologyandVerificationof RFandMixed-SignalSystems LowPowerandLowVoltage

2004Montreux(Switzerland)SensorandActuatorInterfaceElectronics

IntegratedHigh-VoltageElectronicsand PowerManagement Low-PowerandHigh-ResolutionADCs

2003Graz(Austria)Fractional-NSynthesizers

DesignforRobustness LineandBusDrivers

2002Spa(Belgium)StructuredMixed-ModeDesign Multi-bitSigma-DeltaConverters Short-RangeRFCircuits

2001Noordwijk(TheNetherlands)ScalableAnalogCircuits High-SpeedD/AConverters RFPowerAmplifiers

2000Munich(Germany)High-SpeedA/DConverters Mixed-SignalDesign PLLsandSynthesizers

1999Nice(France)XDSLandOtherCommunication Systems

RF-MOSTModelsandBehavioural Modelling

IntegratedFiltersandOscillators

1998Copenhagen(Denmark)1-VElectronics Mixed-ModeSystems LNAsandRFPowerAmpsforTelecom

1997Como(Italy)RFA/DConverters

SensorandActuatorInterfaces Low-NoiseOscillators,PLLsand Synthesizers

1996Lausanne(Switzerland)RFCMOSCircuitDesign BandpassSigmaDeltaandOtherData Converters

TranslinearCircuits

1995Villach(Austria)Low-Noise/Power/Voltage Mixed-ModewithCADTools Voltage,CurrentandTimeReferences

1994Eindhoven(TheNetherlands)Low-PowerLow-Voltage IntegratedFilters SmartPower

1993Leuven(Belgium)Mixed-ModeA/DDesign SensorInterfaces CommunicationCircuits

1992Scheveningen(TheNetherlands)OpAmps ADCs AnalogCAD

Contents

PartIContinuous-Time † ModulatorsforTransceivers

1WiFiReceiverEvolutioninaDenseBlockerEnvironment ............3 PatrickTorta,AntonioDiGiandomenico, LukasDörrer,andJoseLuisCeballos

2High-ResolutionWidebandContinuous-Time † Modulators .......23 LucienBreemsandMuhammedBolatkale

3Sigma-DeltaADCswithImprovedInterfererRobustness .............45 RudolfRitter,JiazuoChi,andMauritsOrtmanns

4DesignConsiderationsforFilteringDeltaSigmaConverters .........65 ShanthiPavanandRadhaRajan

5BlockerandClock-JitterPerformanceinCT † ADCs forConsumerRadioReceivers ............................................89 SebastiánLoeda

6Continuous-TimeMASHArchitecturesforWidebandDSMs ........105 HajimeShibata,YunzhiDong,WenhuaYang, andRichardSchreier

PartIIAutomotiveElectronics

7TrendsandCharacteristicsofAutomotiveElectronics

HermanCasier

8NextGenerationofSemiconductorsforAdvancedPower DistributioninAutomotiveApplications .................................141 AndreasKucherandAlfonsGraf

9High-VoltageFast-SwitchingGateDrivers ..............................155 BernhardWicht,JürgenWittmann,AchimSeidel, andAlexisSchindler

10ASelf-CalibratingSARADCforAutomotiveMicrocontrollers ......177 CarmeloBurgio,MauroGiacomini,EnzoMicheleDonze, andDomenicoFabioRestivo

11AdvancedSensorSolutionsforAutomotiveApplications ..............205 PaoloD’Abramo,AlbertoMaccioni,GiuseppePasetti, andFrancescoTinfena

12ALow-PowerContinuous-TimeAccelerometerFront-End ...........215 PieroMalcovati,MarcelloDeMatteis,AlessandroPezzotta, MarcoGrassi,MarcoCroce,MarcoSabatini, andAndreaBaschirotto

PartIIIPowerManagement

13Switched-CapacitorPower-ConverterTopologyOverview andPerformanceComparison ............................................239 RaviKaradi,GerardVillarPiqué,andHenkJanBergveld

14ResonantandMultimodeSwitchedCapacitorConverters forHigh-DensityPowerDelivery .........................................263 JasonT.Stauth,ChristopherSchaef,andKapilKesarwani

15HeterogeneousIntegrationofHigh-SwitchingFrequency InductiveDC/DCConverters ..............................................281 BrunoAllard,FlorianNeveu,andChristianMartin

16ElectricalCompensationofMechanicalStressDrift inPrecisionAnalogCircuits ...............................................297 MarioMotzandUdoAusserlechner

17PowerElectronicsforLEDBasedGeneralIllumination ...............327 StefanDietrichandStefanHeinen

18AnUltra-Low-PowerElectrostaticEnergyHarvesterInterface ......343 StefanoStanzione,ChrisvanLiempd,andChrisvanHoof

Continuous-Time † Modulatorsfor Transceivers

Thefirstpartofthisbookisdedicatedto recentdevelopmentsinwidebanddeltasigma(† )ADCsforuseintransceivers.Thesehavebeendrivenbythespread ofmobiledevices,mostofwhichmustcommunicatewirelesslywiththeoutside world.Toenablewidebandandfilter-lessradiofront-ends,continuous-time(CT) † modulatorswithhighdynamicandveryhighlinearityarerequired.Thefirsttwo chaptersbeginbydiscussingvarious † modulatorarchitectures,rangingfromthe traditionalsinglelooparchitecturetomorerecentMASHstructures.Thenexttwo chapterspresentvariouswaysofmodifyingthemodulator’ssignaltransferfunction (STF)sothatitalsosuppresstheout-of-bandinterferersorblockersthatmayalso bepresent.Thefinaltwochaptersdiscusstheconsiderationsassociatedwiththe designofreceiverchainsforWIFI,andforuseinhand-heldmobileapplications.

Thefirstchapter,byPatrickTorta,AntonioDiGiandomenico,LukasDörrerand JoseLuisCeballos,comparesthreedifferentWiFireceiverchainsbasedonahigh dynamic-rangeCT † ADC.Twoimplementanactivefilterstagebetweenthe mixerandtheADC:oneusesatrans-impedanceamplifierandtheotheroneaGm stage.Athirdobviatestheneedforan activefilteringstageandreplacesitwith apassivepole.Measurementsshowthatallthreechainsachieveroughlythesame chainperformance,butprovidedifferenttradeoffsintermsofblockerrejection,area andpowerconsumption.

Thesecondchapter,byLucienBreemsandMuhammedBolatkale,provides anintroductiontothedesignofhigh-resolutionwideband † modulators,from architecturalchoicestofilterimplementationandcircuitdesign.Itconcludeswitha discussionofsomerecentcontinuous-time † modulatordesignsthathavepushed theenvelopeintermsoftheirbandwidthandlinearity.

Thethirdchapter,byRudolfRitter,JiazuoChiandMauritsOrtmanns,also discussesvariouswaysofattenuatinginterfererswithintheloopfilterofa † modulator.Itisshownthathybridcombinationsoffeed-forwardandfeedback architecturescanbemadetoexhibitenhanced filteringcharacteristics.Alternatively, amixed-signalinterferersuppressionloopcanbeappliedaroundamodulator.Here, adigitalfilterextractsout-of-bandsignalsfromthemodulator’sdigitaloutputand thencancelsthembyfeedingthembacktothemodulator’sinputviaaDAC.

Thefourthchapter,byShanthiPavanandRadhaRajan,exploresthepossibility ofusingthebuilt-infilteringofacontinuous-time † modulatortoattenuateout-ofbandinterferers.Adesignexampleispresentedthatdemonstratesthatsuchfiltering isindeedquitepossible,thussavingthepowerrequiredbyadedicatedfilter,while alsoimprovingout-of-bandlinearityandreducingactivearea.

Thefifthpaper,bySebastianLoeda,describesthechallengesanddesign techniquesusedtoexploitthewell-knownenergy-efficiencyofFFarchitecturesin thecontextofamodernconsumerradio.Techniquesaredescribedtocopewiththe resultingout-of-bandpeakingandtomake themodulatorrobusttoclockjitterand toout-of-bandblockers.

Thesixthchapter,byHajimeShibata,YunzhiDong,WenhuaYang,andRichard Schreier,contraststheuseofconventionalsingle-loopwithMASH † modulator architecturesinthecontextofwidebandwirelessapplicationssubjecttoout-of-band blockers.TheperformanceoftwowidebandMASHimplementationsina28nm CMOSprocessarecomparedanddiscussed.

Chapter1

WiFiReceiverEvolutioninaDenseBlocker Environment

1.1Introduction

Themostdemandingscenariothatareceiverchainmustsustainisadense blockerenvironmentwheremanycontiguousreceivingchannelsareallocatedand simultaneouslyinusebymanyusers.Insuchascenariothesignaltobeconverted inthebandofinterestcanbetransmittedfromafarstationandcanthereforebe veryweakcomparedtothetransmittedsignalofanearuser.TheWiFitransceiver canbeembeddedintoaplatformwhichservesalsootherstandardslikecellular, GNSS,BTorFMradioinaco-runningmode.Astheisolationoftheantennais limitedtoapproximately10–12dB,itisimportanttoensurethatothersignalsdo notdegradethewantedsignalduetoalias,foldingordistortion.Theanalysisof allpossibledisturbercombinationsisadifficulttask,inparticularwhentheA/D clockfrequencyislowanditsmultiplescan generateintermodulationproductsand foldingeffectstogetherwiththereceiverchainmixerclock.Figure 1.1 showsa basebandspectrumscenarioandareceiverchaincomposedbymanyconsecutive filter-and-gainstagesfollowedbyamediumresolutionADC.TheADCisclocked attwiceoftheNyquistrateofthewantedsignalbandwidth.Averyhighchaingain isneededtoprovidesufficientsignaltonoiseanddistortionratio(SNDR)atthe ADCinput:thissetsstringentconstraintstoallthebasebandblocks.Inparticular thechainstronglyamplifiesthenon-idealitiesoftheblocksimmediatelyfollowing themixer.Thefrequencybehavioroftheanalogactivecomponentscanbestrongly affectedbypoorlycontrollableparasiticsandevenbytheconfigurationsettingsfor theblockbandwidthandthegain.Forinstance,theDCoffsetofthemixeraswell astheI-Qskewofthedirectconversionreceiverneedtobecarefullycontrolledand

P.Torta( )•A.DiGiandomenico•L.Dörrer•J.L.Ceballos IntelAustriaGmbH,Villach,Austria e-mail: patrick.torta@intel.com

©SpringerInternationalPublishingSwitzerland2017 A.Baschirottoetal.(eds.), WidebandContinuous-time ˙ ADCs,Automotive Electronics,andPowerManagement,DOI10.1007/978-3-319-41670-0_1

Fig.1.1 AfilterandgainreceiverchainandthespectrumattheADCinput

mappedtoallchainconfigurationstoguaranteehighchainresolution.Alownoise DCoffsetcancellationmayberequired.Thisleadstocomplexgainandcalibration schemes.

WhenanoversampledhighresolutionADCisused,thechaincankeepthe requiredinbandSNDRand,atthesametime,absorbthepoweroftheoutofband signalsemployingalowerchaingain.Thisrelaxessomeanalogblocksrequirements andtheamountofdigitalcalibrationsneeded.Thereceiverlineupspresentedin Fig. 1.2 areminimalreceiverarchitectures implementinghighdynamicrange(DR) continuoustimesigmadeltaADC(SD-ADC).Theupperoneimplementsonlyone activefilterstagewithtrans-impedanceamplifier(TIA)betweenthepassivemixer andtheSD-ADC.Thisstructuretargetstominimizeareaandpowerconsumption comparedtothefilter-and-gainchainandislessexposedtothecircuitimperfections oftheblocksinterconnections.IthasaRF-to-basebandinterfacethatcanbeeasily simulatedwithcommonknowntechniques.Afurthersteptoreducetheareaandthe powerconsumptionavoidstheinstantiationoftheTIAstage,asshowninFig. 1.2 (middle),andreplacestheactivestage byasmallpassiveattenuationstageand alowerpoleinthefirststage.AhighorderSD-ADCisachaoticsystemandit isingeneralnotpossibletousedirectlyharmonicbalancetosimulatethischain performanceandalinearizedmodelcanbeusedinstead.Bothlowgainproposed chainshaveincommonthatthefirstactivestageafterthemixersuffersofnoisegain duetotheequivalentsmallimpedanceintheRFchain.Thethirdpresentedlineup inFigure(bottom)usesapassivemixerinvoltagemodefollowedbyaGmstage havingahighoutputimpedanceinterfacetotheSD-ADC.

1.2TheReceiverChainasaFullFeaturedandFairADC VerificationEnvironment

Allpresentedreceiverarchitecturesareabletoconvertsignalspresentinthetwo WiFiRFbands.Thesignalattheantennaisamplifiedbyacascadeddifferential lownoiseamplifier(LNA)anddownconvertedtozeroIF.Apassiveswitchin

Fig.1.2 Thethreeminimalgain,highdynamicrangelineupspresentedinthisworkandthe typicalPSDplotscenarioinbaseband.Theoutofbandsignalsdoesnotsaturatethechain.Less foldinginbandisachievedduetothehighclkfrequency

serieswiththeswitchingquadmixerselectsthebandofinterestandthesignal isroutedtotheIandQbasebandpaths.TheWiFistandarddefinesthepossibility toallocateforeachuserachannelcontainingadifferentnumberofcarriers.Asa resultallproposedlineupsareabletoprocessabasebandsignalswithbandwidth of8.9,18.3and38.3MHz.AttheoutputoftheADCachainofdecimatorsand digitalfiltersprocessestheconvertedsignal.Theimplementedanaloggaincontrol adaptstheLNAgainproportionallytothesignalstrengthdetectedattheADC output.InthedigitaldomainitisalsopossibletocollecttheundecimatedSD-ADC datastreamstoredintoaninternalmemory.Asidesoftheactivepolethereisa significantdifferencethatdistinguishthesystems:theADCclockcanbederived fromthemixerlocaloscillator(LO)orfromaseparatedPLL.ALOderivedclock isparticularlyhelpfulwhentheisolationofanactiveblockismissing.Inthiscase avariablerateconverterneedstobeaddedattheendofthedecimationchainto interpolatethedecimatedsamplestothefixedfrequencyofthesystem.Thevariable rateconvertercanbeskippedifamultipleofthesystemclockisusedfortheADC. Thethreechipshaveacompatiblepinout;inparticulartheprogrammingofthe devices,theroutingoftheRFsignalstotheLNAandofthesupplylinesarethesame andthusthesamemotherboardisusedtomeasureandcomparethem(Fig. 1.3).

Fig.1.3 ClocksourcesinthefullreceiverincludingdecimatorsandAGC

1.2.1TheTIA-ADCLineup

ThefunctionalblockofthereceiverispresentedinFig. 1.4.InthisSD-ADC,aswell asintheotherpresentedSD-ADC,thechosencontinuoustimefilterisimplemented asathird-orderchainofintegratorsinfeedback.Anadvantageofthisstructureis thattheresistorbetweenTIAandADCcan beprogrammedtoachieveanadditional gainandDRboostoffewdBsatthecostofaddedgaincomplexity.Ablock-level noisebudgetisusedtosizeanddesigntheblocksandit’scalculatedbyreplacing theantenna,theLNAandthemixerwithagreatlysimplifiedmodelasshown inFig. 1.5.Themodelreplacestheantennabyanidealvoltagesourcedrivinga noiselessvoltagegainelementofvalueGconnectedtoanoiselessresistor Rmix , whichrepresentsthemixer’soutputimpedance.Thisresistorvalueisaffectedby thechosenRFfrontendarchitectureandinourdesignhasavalueoffewhundred Ohms.Asafurthersimplificationthenoiseof allpassiveelementsinthebasebandis neglected,sincethenoiseoftheamplifiersistheonethatdominatesthetotalnoise and,asaconsequence,thesystemareaandpowerconsumption.Tofairlycompare thelineupsweassumethatbothGand Rmix arefixedinallsystems.Thetransfer function(TF)oftheTIAandtheoneoftheADCareflatinthebandofinterest. ThereforeinthenoisebudgetmodelwecanskiptheTIAcapacitorandthehigh frequencysuppressionoutofbandoftheADCSTF.ThecompleteADCisthus reducedtoasimpleinvertingamplifier:thefeedbackresistor Rdac istheequivalent resistorofthefirstcurrentsteeringDAC,whichtogetherwiththeresistor R2 sets theADCgain. Nop1 and Nop2 mimictheinputreferrednoiseoftheOPAMPsand Nq replacestheADCquantizationnoise.

Wecanusethesuperpositionprincipletocalculatetheinputreferrednoiseofthe systemundertheassumptionthatthegainoftheOPAMPsisveryhigh.Thesystem gainfrominputXtooutputYisgivenby: Y X D Rdac R1 G Rmix R2

BycalculatingtheTFofeachnoisesourcetotheoutputanddividingthembythe systemgainweobtaintheinputreferrednoisecontributionequation:

Fig.1.4 Conceptualdrawingofthefirstproposedlowgainhighdynamicrangelineup.TheTIA filtersthehighfrequencysignals

Fig.1.5 SimplifiedDCnoisemodeloftheTIAandADCcascade

Thevalueofthequantizationnoise Nq isdrivenbytheclock.Ononeside,toreduce thepowerconsumptiontheclockneedstobeminimized,ontheothersidealower frequencydecreasestherateoftheDACfeedbackandreducestheloopstability.The polesoftheADChavealimitedhighestfrequencyconstraintforthesamereasons. Asthequantizationnoiseisaddedattheendofthechainitcanbeminimizedby risingthegainthroughanincreasingof R1 and Rdac .Thesupplyvoltagelimits thetotalgainofthefirststageandsetsconstraintsontheADCgain Rdac =R2 . Thushavingaflattransferfunctionontwostagesandasmall R2 setsequivalent stringentconstraintstoboththeTIAnoiseandtotheADCfirststagenoise.Itis possibletocalculatetheinputreferrednoisebudgetforeachfrequencyandwith

Fig.1.6 ChaingainandSTF(top)andinputreferrednoisebudget(bottom).Thisincludesthe contributionofthequantizationnoise,oftheTIAandofthefirstADCopampnoise.IfR2equals Rdacthentheopamp1noisecanbegreatlyrelaxed

lesssimplificationsbyusingmathtoolstosolvethesystemequations.Anexample forthebreakdownisshowninFig. 1.6.Theareaandthepowerconsumptionof thesetwoblocksisconsiderable.

Toreduceataminimumthethermalnoisecontributionofthefirststage,the multipathOPAMPstructure[1]wasusedintheTIAstage.ThedifferentialOPAMP conceptisdepictedinFig. 1.7.The gm stagescanbeprogrammedtofindabetter tradeoffbetweenthenoise(gm1 and Cg1 ),the GBW andthepowerconsumption. Thetwocascaded gm stagesallowtoachieveveryhighgainatlowerandmedium frequencies.AsinglestageversionoftheclassABoutputstageasreportedin[2]is usedtoefficientlydrivetheintegratorfeedbackcapandtheload.

ThefollowingOPAMPsinthedesignneedtoachieveahigherbandwidthbutnot muchinbandgainandatwostagemillercompensatedstructurewasused.

Theclockofthislineuphasbeenderivedfromthemixerclock.Thelocal oscillator(LO)isdividedbyanintegerfactorwhichchangeswiththeWiFimode. Theclockcanthusspanoverawiderange,andtheADCneedstofulfillallstability andDRrequirementsforthelowestclock,butalsoneedstobeabletorunatthe highestclockfrequency.ThedatapathbetweenquantizerandDACsneedstobe designedtoavoidthemetastabilityregionwhenthesampleiscapturedintheDAC latch.

Fig.1.7 TheTIAandthefirstADCopampisaGmCmultipathstructurecascadedtoaclassAB stage(left ).Opampopenloopfrequencyresponse(right )

Fig.1.8 Thereferenceandoffsetsamplingphase(left ),andtheinputsignaltrackingphase(right ) foracomparatorinthequantizer

Thequantizerdesignimplementsanevolutionoftheoffsetcompensatedcomparatorspresentedin[3].Thebasicdifferentialcomparatorslicecircuitincluding thereferencegenerationcapacitivenetworkandthepreamplifierforthelatchis showninFig. 1.8.Itoperatesessentiallyintwonon-overlappingphasesdrivenby theADCclock.Inthefirstphase,depictedontheleft,thedifferentialpairoutputs andinputsareshorted.Thereferencefullscalevoltage,commontoallcomparators, isconnectedtothecomparatorcapacitorarray.Inthisway,thevoltagestoredinthe capacitorsissampledagainsttheoperatingpointofthedifferentialpair.Assuming adifferentialpreamplifiergainG,theoutputvoltageinthisoperatingconditionis:

1 D GVOffs G C 1

Thismeansthatalsotheoffsetvoltage VOffs ofthecomparatorisstoredinthe capacitors.Inthesecondphase,depictedontherightofFig. 1.8,aswitchconnected totheSD-ADCfilterisclosed.Inthiswaychargeredistributionbetween C1 and C2 occurs.Thevoltageattheoutputofthepreamplifieristhengivenby:

2

1

Voutdiffph2 D G Vindiff C

Voutdiffph

Fig.1.9 Afullquantizerarrayoffourcomparators(left )andanoptimizedversionthatenables afasterchargeredistributionduetothereducedamountofcapacitors(right ).TheVINpswitches canbeboostedtoachievehigherfrequency

Ifthegainishighenoughthenthelasttwotermsarecanceledandtheoffsetis compensated.AlthoughthecapacitorscanbealtogetherintherangeoftenthsoffF thespeedofthisstructureislimitedinphaseonebytheparasiticcapacitorsatthe differentialinputpair.Forthisreasonitisessentialtobuildanextremelycompact layoutforthiscell.Thetotalparasiticcapacitancestemsfromparasiticsalongthe routedlinestogetherwiththedifferentialpairgatecapacitanceandtheparasitic capacitancethattheresistiveloadsshowversusthesubstrate.

Thelattertermappearsduetothefactthatinadvancedtechnologiesthe minimumresistorwidthiswidecomparedtothetransistors.Inthesetechnologies theallowedminimumdistancebetweentransistorsisshortcomparedtotheone betweenatransistorandapolyresistor.Tomitigatealltheseparasiticeffects twolongPMOStransistorsdrivenintheohmicregionareusedasloadinstead oftheresistors.Duetotheembeddedoffsetcompensationofthestructurethe mismatchbetweenthetwoPMOSloadsisnotofconcern.Anadditionalspeedlimit comesfromthechargeredistributionswitchesinthesecondphase.Contrarytothe referenceswitches,theinputswitchesdonotsitatapotentialneartothesupply.The issueisthat Vinp and Vinn areoftenclosetocommonmodevoltageandthiscanbe solvedusingtwotricksimplementedasshowninFig. 1.9.Comparingtheleftand therightpart:threeboostedswitches sw canbeusedinsteadoftwotoreducetheir seriesresistance Ron .Moreover,wherethecomparatorlevelallowsit,thenumber ofunitcapacitor Cu canbereducedtotheminimumrequiredratiobasedonratio matchingandgainrequirements.

TheoutputofthequantizerisfedtotheDACsafterasmalldelayofseveral hundredsofpicoseconds.ToincreasetheperformanceoftheADCtheDACtransfer functionshallbelinear.AstheDACcellssufferfrommismatchabackground calibrationhasbeenimplemented.Theliteraturereportsseveralwaystolinearize theDAC.Thescramblingofthecellsusedbydynamicelementmatchingtechnique

isveryefficientinsimulation,butdifficulttobeimplementedoutoftheboxdueto theaddeddelayintheloopandduetothecommonmodeglitchenergy,generated atthefirstOPAMPinput.Thisglitchmodulateswiththeinputsignalgenerating distortiontones.AnotherwaytolinearizetheDACistocalibratethemismatch ofthecells.Itispossibletocalibratethemismatchinadigitalcontrolledfashion [4],oritisalsopossibletodoitwithinananalogloop[5].Theadvantageofthe digitalcalibrationisthattheobservabilityandmanipulationiswellcontrolledin thedigitaldomainandtherefreshrateinbackgroundcanbeperformedseldom; theimplementationiscomplexandtheresidualerrorislimitedbytheimplemented LSB.Ontheotherhandtheanalogcalibrationloopneedsacontinuousrefreshand thecalibrationisvirtuallyabletoreducetheresidualerrortoasmall ".

InthisADCdesigntheanalogcalibrationwaschosenbecausethecomplexity isreduced.ThecircuitideaofthecalibrationisshownFig. 1.10 andthebasic techniqueisknownsinceverylongtime[6].Todecreasetheamountofnoise injectedintheintegratorstheunusedDACcellsaredisconnectedfromthefilterand connectedtoafloatingnode dump.Ifacellisinusethenthedigitalwordcoming fromthequantizerisroutedtotheswitches DPx =DN x .TheDACsinjectthecurrent pulsesinanonreturn-to-zerofashion.ThecurrentsteeringPMOSandNMOSare splitintwoparts:awidetransistorpartisconnectedtoafixedbiasvoltagethat grantstoinjectacurrentofabout90%ofthewantedcurrent.Additionallyasmaller transistorinparallelinjectstheresidual calibratedcurrentofabout10%.Itsbias voltageisstoredintoalocalcapacitor.Ifacellisincalibrationitsquantizerdata isroutedtoasparecellthatcantakeoverthetaskofinjectingtherequiredcurrent inthefilterintegrators.Thecellincalibrationactivatestheswitchesmarkedwith CALsw and DC x .Inthiswayareferencecurrentcellisconnectedandcompared againstthecellincalibration.Asbothreferencecellandin-calibrationcurrent steeringcellshowsahighimpedanceoutput 1=gds thevoltageatthenode CALsw settlestotherequiredvoltageneededtoproducethereferencecurrent.Aftersettling isachievedthecellisreinsertedbackintheSD-ADCloop.Asthedisconnectionand thereinsertionofthecellcanaffectthestoredbiasvoltagethisoperationisdonein anon-overlappingfashion.

Thefunctionalityofthecircuithasbeentestedwithmeasurementsshownin Fig. 1.11 andthecircuitisabletolinearizetheDACbyreducingthethirdharmonic.

1.2.2TheRF-ADCLineup

ThelineupisshowninFig. 1.12.Asdemonstratedintheprevioussectionthe presenceofanactivestagebetweenmixerandADCistighteningthenoise requirementsforbothTIAandthefirstADCstage.Theideaistoassigntheportion ofnoisegeneratedfromtheTIAintothetotalADCnoisebudget,actuallyrelaxing itsrequirements.

Fig.1.10 TheDACbiasandacurrentsteeringDACcellincludingtheswitchesfortheoperation, forthedumpingandforthecalibrationagainstareferencecurrent

Fig.1.11 MeasuredFFTspectrumperformedinjectinga 3dBFStonewithandwithoutcalibration.Withcalibrationthethirdharmonicissuppressedby9dBFS

GiventhesimplifiednoisemodelofFig. 1.13,thechainDCgainwithhighgain amplifiersAis

andtheinputnoisepower

Y X D Rdac G Rmix

Fig.1.12 Conceptualdrawingofthesecondproposedlowgainhighdynamicrangelineup.The SD-ADCandthemixerareconnecteddirectly

Fig.1.13 SimplifiedDCnoisemodeloftheRFADC

Thefinalgoalistoreducetheoverallareaandpowerconsumption.TheSD-ADC coefficientsetneedstofulfilltheoutofbandsignalrejectionrequirements:thiscan bepartlyachievedbyusingapassivepoleinfrontoftheADCandalowercut-off frequencyinthefirststagewhichlimitsthequantizationnoise.Adisadvantageof thislineupisthatchangingthelowfrequencygainoftheSTFwouldrequirethe DAC1currentandthefirstfiltercapacitor C1 ,orthesecondstageinputresistor R2 ,tobereprogrammedtokeepthepolepositionatthesamefrequency.Theinput referrednoisebreakdownisshowninFig. 1.14.

ThebuildingblocksofthisADCarethesameastheonesofthepreviousdesign. TheinterfacebetweenmixerandADCneeds carefulattention.Iftheclockofthe LOandtheclockofthefirstDACarenotsynchronizedspurscanpollutethe

Fig.1.14 NoisebudgetbreakdownfortheRFADC.Thedominantnoiseisgeneratedinthefirst opampandatthequantizer

inbandspectrum.TheDACactsasadifferentialcurrentsource,butwhenacell changesitsstatethegenerationofasmallcommonmodeglitchcannotbeavoided. ThecommonmodeglitchcontainsseveralharmonicsatthemultiplesoftheADC clock.Adifferentialsignalproducedbythemixeratthesamefrequencyisdownconvertedtobaseband:itsamplitudeatthedigitalADCoutputdependsonthefirst stageperformance,whichisusuallylimitedathigherfrequencies.Inthislineupthe clockisderivedfromtheLO;thismakestheanalysisandtheassessmentofthe potentialproblematicscenariosmucheasier.Forhighfrequencyisolationpurposes itisadvisabletoaddasmallandnon-dominantRCpassivepoleattheADCinput. Atoobigcapacitorbooststhefirststagenoise.

ThedesignoftheRFcomponentsrequiresagoodmodelofthebaseband circuitry.DuetothecoarsequantizationofthesignalattheoutputoftheADC filter,itisnotgrantedthatthedatastreamisperiodic.Thisnon-periodicbehavior ofaSDADCisablockingpointforallharmonicbalancebasedsimulators.Afull transistorlevellinearmodeloftheADCisneeded.Forthispurposethequantizer andtheDACcanbereplacedbyasimplevoltagecontrolledcurrentsourceasshown inFig. 1.15.ThismodelfitswelltherealSTFandNTFathigheroversamplingratio andcanbeusedtoverifytheoverallchainperformance.Goodmatchingbetween simulationsandmeasurementshasbeenachieved.Inthemodelitispossibleto emulatethenoisecontributionofthequantizer.Thenoisegeneratedbyaresistor

Fig.1.15 LinearizedmodeloftheSD-ADC(top)andequivalentquantizationnoisegeneratorfor transientsimulations(bottom)

canbesizedtofittotheonedeterminedbythenumberofbitsandbytheADCclock frequency.ThequantizationnoiseintherealADCissampledatfclkandthusitis filteredatitsmultiples.Thethermalnoiseofaresistorshowsaflatcharacteristic: itisthereforeadvisabletostronglyfiltertheresistornoisewithanLCfilterpriorto theinjectionatthefilteroutput.

1.2.3TheGm-ADCLineup

HavingaclockfrequencysynchronizedwiththeLOissimplifyingtheanalysisof thepossibleblockerscenariosbutrequirestheuseofavariablerateconverterinthe digitaldomain,whichisaverypowerhungryblock.Onewaytoavoidthisadditional digitalblockistokeeptheSD-ADCclockinsynchwiththesystemandindependent oftheLO.InsuchanarchitectureitisveryimportanttoimplementastrongantialiasfunctionincascadewiththeADCSTFwhichavoidsintermodulationbetween themixerandtheDAC.Thisisachievedintroducinga gm stageinthechain.Inall thepresentedarchitecturesthemixeris passiveandcomposedofsimpleswitches drivenatthecommonmodevoltage.Themixertobasebandinterfaceinthiscaseis notfixedatcommonmodeasitisinthevoltagedomain.Thisisanopportunityto

Fig.1.16 Conceptualdrawingofthethirdproposedlowgainhighdynamicrangelineup.AGm stagefilterstheoutofbandsignalswithacapacitorattheinputandattheoutput

Fig.1.17 SimplifiedDCnoisemodeloftheGmADC

filtertheinputsignalwithacapacitor.The gm cellisdirectlyfeedingtheADCin currentmode,anditcanbeseenattheinputoftheopampasahighimpedanceinput load Rg .ComparedtotheTIAlineupthe gm inter-stagerelaxesthefirstOPAMP noisebudget.Theequivalentcircuitforthebasicnoisebudgetcalculationdoesnot containanymorethemixerimpedance;justtheLNAgainG(Figs. 1.16 and 1.17). Thechaingain,undertheassumptionofahighgainamplifiersA,isgivenby:

andtheinputreferrednoiseis

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plants. ↑

Hopoe was said to be a woman that was turned into stone by Pele in a fit of jealous anger. ↑

This mele of Kamapuaa’s seeks to imply that Pele knew him only in spirit. ↑

This likely has reference to some bird traits or habits, there being no known birds of this name whose home at high elevations, like the koae, or bos’n bird, is in a region of cold temperature ↑

Referring to the Kaliuwaa episode where his forces climbed up his body and escaped. ↑

Haleaha, a place in Makua, opposite the Kaliuwaa valley, near the main road. ↑

Sore or inflamed eyes to which Pele is likened from her fires. The chant throughout is a series of irritating slurs. ↑

This is the first instance where the Hiiaka family name of Pele’s eight sisters is given to any of the brothers, and is a grave error. ↑

A case of love soothing the way. ↑ Lonomakua as Pele’s agent ↑ Pele. ↑

Pohakea, a section of Kilauea ↑ Thunder is frequently referred to as rolling stones in the heavens. ↑

This, then, would be the accompanying lightning ↑

Referring to the Hilo rains. ↑

Volcanic eruption ↑

Abbreviation of Kamapuaa, a not infrequent habit of the race with their names, not restricted to their stories ↑

Hia was the term used for rubbing the two sticks aulima and aunaki together, producing a powder which became ignited by friction ↑

Summary treatment for a discourteous act. ↑

The same Makalii that had escaped alone on several occasions to tell Olopana of his defeat. ↑

Aalii (Dodonaea viscosa), a mediumsized, common forest tree of hardgrained, dark wood. ↑

This is a play on the latter part of Kualele, a practice common to chants and meles; a poetic license. ↑

First use of this name in full, probably through his higher rank and claiming possession of Kauai. As an epithet it embodies nothing complimentary. ↑

Aimoku is rendered creator of the isles rather than devourer, as connected with volcanic origin. ↑

Nananuu, the place of offering in the temple, as was experienced at the heiau of Kawaewae, where the tables were turned on Olopana. ↑

Mahiki in the sense used here is thought to mean a leap, to indicate the proximity of the two islands, rather than Kauai being pried from Oahu ↑

Kamapuaa here warns Makalii that he is an easy mark ↑

Names indicative of various cloud formations, the latter “a large cloud standing close to the heavens ” ↑

The early part of this story locates this person with Olopana in Koolau, Oahu. ↑

Kahikiula, father of Kamapuaa, a reason for shielding him from certain death at the hand of his antagonist, as also to test him for recognition. ↑

This denial was probably based on the supposed death of Kamapuaa in the encounter with Pele. ↑

This is the first mention of the demigod having a brother. Kahikihonuakele, lit., muddy foundation foreign land. ↑

Reviving his brother by the lomilomi process, a rubbing, pressing method to relieve pain and bruises. ↑

Further insight in Kamapuaa’s family history. The failure of father and brother and subsequently the mother to recognize him shows he had assumed a form which they were unfamiliar with ↑

“Their own mother,” a customary complimentary term, rendered more applicable in this case owing to the

bond of relationship existing between the men ↑

This throws light perhaps on a tendency in ancient times of falsely claiming or asserting kinship for the sake of personal gain ↑

These two had been assigned to the uplands with Makalii, but are prepared to “eat humble pie” and own Kamapuaa ↑

A complimentary, figurative name to sooth Kamapuaa’s anger; a play on Iliahi, the fragrant sandalwood ↑

A condition that arises from the excessive use of awa, sacred to the gods. ↑

Ka ua kilinoe hau might be better defined as “the fine dewy rain,” or probably “the cold misty rain.” ↑

Prostrating at one’s feet is indicative of contrition for past wrongs, but the sitting on Hina and then trampling on them all shows Kamapuaa was not to be placated. ↑

An act of abandon; abject submission, appealing for forgiveness. ↑

Resuming his hog form he revenges his insults at the fisherman’s hands. ↑

[Contents]

L K.

K S H K B

—E G

O O. H D

S. A M

A. K F. S

K T S

R O H

L E F

O.—M,

W, K.

Kaulu was a very young boy who once lived in Kailua, Koolau, Oahu. His father was Kukaohialaka.1 At the birth of Kaulu,2 he was in the form of a piece of cord. He had two older brothers. Kaholeha was the name of the brother who loved him, while the other brother did not like him at all, in fact he hated him. Some time after this the brother that thought a good deal of Kaulu was taken away by

K K.

I K K O

P U L

P. I O K. H

M K. H

K. M,

K H

K N H H

L L E —

M M, K.

He keiki opiopio o Kaulu, no Kailua, i Koolau, Oahu. O Kukaohialaka, ka makuakane. He pauku kaula ia i kona hanau ana, a he mau kaikuaana kona elua. O Kaholeha, ka mea aloha ia ia, hookahi kaikuaana huhu loa ia ia. A o ke kaikuaana aloha ia ia, oia kai lilo ia Kane laua o Kanaloa, lawe ia a ka moku o Kuaihelani, noho. A mahope imi o Kaulu a hiki i Kuaihelani. Ma keia hele ana a Kaulu, he nui

Kane and Kanaloa,3 to the island of Kuaihelani,4 where he was kept. Being attached to this brother, because of his great kindness, Kaulu concluded that he would go to Kuaihelani in search of him. On the voyage Kaulu encountered several obstacles.5 First he encountered large and terrible waves; secondly, he encountered the long waves; thirdly, he encountered Kuilioloa; fourthly he encountered Keaumiki and Keauka, and fifthly he encountered the gods or ghosts.

When Kaulu arrived in the land of Kuaihelani, he went up to a loulu6 palm tree and hid in the leaves. That evening he saw his brother coming out of the house, so he went to meet him. Kaulu then asked him: “How are you getting along?” Kaholeha replied: “I am not happy.” Kaulu again asked him: “What do you all do in the evening?” The brother replied: “We drink awa.” “Yes,” said Kaulu, “when it is time to drink awa, you tell the gods that they can go ahead and drink their’s and that you will take

kona mau hoapaio. O ka mua o ka nalu nui; o ka lua o ka ale moe; o ke kolu o Kuilioloa; o ka ha o Keaumiki a me Keauka; o ka lima o ke ’kua.

A hiki o Kaulu i Kuaihelani, hele aku la ia a loko o ka ao loulu hou e owili ana, pee iho la ia. A ahiahi, hemo mai la kona kaikuaana i waho, hele aku la o Kaulu e launa pu. Ninau aku o Kaulu: “Pehea kou noho ana?” Olelo mai o Kaholeha: “Aohe pono.” I aku o Kaulu: “I ka wa ahiahi heaha ka oukou hana?” I mai ke kaikuaana: “He inu awa.” “Ae,” wahi a Kaulu. “Ina inu ka awa, olelo aku oe i ke ’kua, o ko lakou awa mua ke inu, a mahope kou. A inu oe i kou apu awa, e papa aku oe i ke ’kua,

your’s later. When it comes to your turn to drink awa, you order the gods not to talk, and when they are quiet then you call out to me as follows: ‘Say, my god, here is our awa.’ I will then answer back: ‘Drink it. I will take the intoxicating portion.’ ” The brother returned into the house and in time carried out the orders given him. When the gods heard the reply from without, they said: “What a loud voiced god you have. It even calls differently.” This was continued so often that Kane and Kanaloa became vexed and so they sent their messengers to fly up to Makalii7 and inquire of him of the nature of this thing, whether it is a human being or a god.

When the messengers came in the presence of Makalii, they informed him of the nature of their mission. He replied: “The voice is not the voice of a god; it is the voice of a man, Kaulu by name.” When the messengers arrived back in the presence of Kane and Kanaloa, they reported what they had been told by Makalii. When the two [366]heard

aole make walaau, a noho malie lakou, alaila, kahea ae oe, penei: ‘E ke ’kua e! eia ka awa o kaua.’ Na’u ia e olelo aku: ‘Inu hia. O ka ona wale ana ko’u.’ ”

Hoi aku la ke kaikuaana a hana pela. I mai la ke ’kua: “He oi ka hoi kou o ke ’kua leo nui. He hea okoa mai no.” Pela no ka hana ana, a uluhua o Kana a me Kanaloa. Hoouna i na elele, e lele i luna e ninau ia Makalii i ke ano o keia mea. He kanaka paha, he ’kua paha.

A hiki ua elele i o Makalii la, olelo aku la ia ia, a lohe ia, olelo mai la: “Aohe akua, he kanaka, o Kaulu ka inoa.” A hiki na elele i mua o Kane laua o Kanaloa. Hai [367]aku la i na olelo a Makalii. A lohe laua, huhu iho la laua i ke kaikuaana o Kaulu, nolaila, imi hala laua ia Kaholeha. Nolaila, hoowalewale o Kane laua me Kanaloa ia Kaholeha, e hele e

the report, they became very angry with the brother of Kaulu, and so the two devised a way of getting Kaholeha into trouble. After they had thought out a plan they tempted Kaholeha to go down with them into the sea for a bath and to ride the surf. When they came to the place where the surf was breaking Kaholeha was caught by a shark and eaten. Therefore Kaulu went down to the seashore [in search of him].

.

When Kaulu arrived at the beach he stooped down and drank up the sea until the whole ocean was dried up and all the fish were exposed. Kaulu then proceeded to kill all the sharks and other kinds of fish. In this search for Kaholeha, Kaulu killed several fish without being able to find him, so he flew up to Makalii and asked him. When Kaulu arrived at the home of Makalii, he found him asleep with his face turned up, for Makalii was a

auau kai, e heenalu. I ka hiki ana i kahi heenalu, ua pau o Kaholeha i ka ai ia e ka mano, nolaila, hele o Kaulu a hiki i ke kai.

.

Wehe ae la o Kaulu i ka waha ona, omo ia ke kai a pau i loko a maloo iho la ke kai, ahuwale na ia a pau loa. Noke o Kaulu i ka luku i ka mano, a me na i’a e ae. Ma keia imi ana a Kaulu, aole i loaa o Kaholeha. Nolaila, lele aku la ia i luna i o Makalii la e ninau ai. A hiki o Kaulu i o Makalii la, e moe ana o Makalii i luna ke alo, nokamea, he elemakule ia, aka, he mana nae, a me ka ikaika loa. Lele iho la o Kaulu iniki i ka opi o na uha, a

very old man, but possessed of great powers and was very strong. When Kaulu saw him, he went up to him and pinched his leg, causing Makalii to wake up and cry out in pain.

puoho ae la o Makalii me ka uwe i ka eha.

. .

Kaaona was the younger brother of Makalii and he was very ill tempered. When he saw Kaulu he took up a large rock called Ikuwa,8 being about as large as the island of Maui. When Kaulu saw this, he asked of Makalii: “Who is this man holding a large rock?” Makalii replied: “It is my ill tempered younger brother.” When Kaaona came up to Kaulu, he hurled the rock at Kaulu, thinking to crush him with it. Kaulu then stuck up his poi finger9 and held the rock up. Kaulu then said: “Say, the rock from the strong man is held up. When is it to fall down?” At seeing this Kaaona ran off fearful of being put to death by Kaulu.

Sometime after this Kaulu inquired of Makalii, saying:

Oia ke kaikaina huhu o Makalii, ike mai la ia ia Kaulu. Amo mai la ia i ka pohaku nui, o Ikuwa ka inoa, ua like me Maui ka nui o ka pohaku. Nana aku la o Kaulu a ike. Ninau aku la ia Makalii: “Owai keia kanaka me ka pohaku nui e amo mai nei?” I mai la o Makalii: “O kuu kaikaina huhu.” A hiki o Kaaona i mua o Kaulu, hoonee iho la i ka pohaku i luna o Kaulu, me ka manao e pepe i ka pohaku. E koo ae ana o Kaulu: “Ea! paa ka pohaku a ua kanaka ikaika, a hea hoi haule iho?” Holo aku la o Kaaona me ka makau o make ia Kaulu.

A mahope o keia, ninau aku o Kaulu ia Makalii: “Auhea kuu

“Where is my older brother? Tell me who killed him, that I may know the person.” Makalii replied: “Your older brother is within the king of all the sharks.” Kaulu again asked him: “Tell me clearly who eat my brother.” Makalii replied: “He is in the great mound of coral rock which has an opening at the top, which is in reality a shark.”

.

Kalakeenuiakane was a very large shark; he was the king of all the sharks in the sea, and it was this shark that swallowed alive the brother of Kaulu. At the conclusion of the conversation between Makalii and Kaulu, Kaulu returned and proceeded to the presence of Kalakeenuiakane10 and asked him: “Say, have you seen my brother?” “Yes, I have seen him; he is no more; he has turned into hair and into filth.” Kaulu then asked him: “Are you strong?” “Yes,” said the shark. “What is your strength?” Kalakeenuiakane replied: “If I open my mouth my

kaikuaana, e hai mai oe i ka mea nana i pepehi i ike au.” Olelo aku o Makalii: “Aia ko kaikuaana i loko o ke ’lii o na mano a pau loa.” Ninau aku o Kaulu: “E hai pono mai oe i ka mea nana i ai kuu kaikuaana?” Wahi a Makalii: “Aia i ka pukoa nui, e hamama ana o luna, he mano ia.”

.

He mano nui ia, oia ke ’lii o na mano a pau loa o loko o ke kai, a nana i moni ola ke kaikuaana o Kaulu. A pau ka Makalii olelo ana ia Kaulu, hoi mai la o Kaulu a hiki i mua o Kalakeenuiakane. Ninau aku la: “Ea! Ua ike auanei oe i kuu kaikuaana?” “Ae, ua ike, ua pau, ua hulu, ua kukae.”

I aku o Kaulu: “He ikaika no?” “Ae.” “Pehea kou ikaika?” I mai o Kalakeenuiakane: “Ina e hamama kuu waha, o ke a luna i ka lani, o ke a lalo i ka honua.” Alaila, ninau iho o Kaulu i na lima ona: “E Limakaukahi a me Limapaihala, he ikaika io [369]anei keia?” Hoole mai na

upper jaw can reach the heaven while my lower jaw rests at the bottom of the earth.” Kaulu then asked of his own hands: “Say, Limakaukahi and Limapaihala,11 is he really strong?” The hands replied: [368]“No.” The shark then opened its mouth and Kaulu stepped in and held the jaws open. He then called those in the belly of the shark to come out, and Kaholeha came forth; his hair was all gone, but he was still alive. Shortly after this Kaulu and his brother returned home.

.

When they were ready to come away, Kaulu said to his brother: “You go on ahead, I will follow behind.” Kaulu then urinated and the sea was restored to its former condition. But it was salty and has smelled bad to this day; it was not so before.

lima: “Aole!” Hamama ka waha o ka mano, paa no ke a luna i ka lani, o ke a lalo i ka honua. Kahea aku la o Kaulu ia loko o ka opu e hele mai, oili mai ana o Kaholeha, ua pau ka lauoho i ka helelei, e ola ana no nae. Mahope o laila, hoi mai la o Kaulu me ke kaikuaana.

.

I aku o Kaulu i ke kaikuaana: “Mamua aku oe, mahope aku nei au.” Ia wa mimi o Kaulu i ke kai, a hoi hou ke kai e like me mamua. Eia nae, ua hohono a awaawa ke kai a hiki i keia la, aole pela mamua.

. .

Kaulu and his brother then returned from Kuaihelani and Hoi mai la o Kaulu ma mai Kuaihelani mai me kona

stopped at Moanalua,12 where Kaholeha remained, while Kaulu went off to Niuhelewai13 to see the place. Niuhelewai is a place at Kapalama, where Haumea lived.

Haumea14 was a ghost [or akua] and no one who fell in its way was saved; all would be eaten up. Haumea was a woman. When Kaulu came to the home of Haumea, he found the ghost asleep, so Kaulu woke her up. Haumea then asked Kaulu: “Where are you going?” Kaulu replied: “Sightseeing.” “You cannot go any further; this place is sacred to me and death shall meet those who disobey.” Kaulu then asked the ghost: “Are you strong?” Haumea replied: “Yes.” Kaulu again said: “Yes, I will return and tomorrow I will come again, when we will fight.” Haumea assented to this.

The reason why Kaulu deferred the fight with Haumea was because he wished to get some nets (koko) to catch Haumea with. These were the nets of Makalii,15 called “Maoleha” and

kaikuaana a hiki i Moanalua.

Hoonoho o Kaulu i ke kaikuaana i laila, hele mai la oia i ka makaikai a hiki i Niuhelewai, Kapalama, e noho ana o Haumea i laila.

He ’kua o Haumea, aohe mea koe ia ia i ka ai ia, he wahine. A hiki o Kaulu, e moe ana o Haumea, hoala ae la o Kaulu a ala o Haumea. Ninau mai la o Haumea: “E hele ana oe i hea?” I aku o Kaulu: “I ka makaikai.” “Aole pono ke hele, he kapu keia wahi ia’u, he make.” I aku o Kaulu: “He ikaika no oe?” “Ae!” pela mai o Haumea. I aku o Kaulu: “Ae, e hoi au, a popo hiki mai au, hakaka kaua.” Ae mai o Haumea.

Eia ko Kaulu manao ia Haumea ma laila i loaa ona koko e paa ai o Haumea, oia na koko a Makalii, o Maoleha ma. Lele aku la o Kaulu a hiki ia Makalii, nonoi aku la i na koko. Ae mai la o

its mate. Kaulu then flew up to Makalii and asked for the nets. Makalii allowed him to take them, and Kaulu returned with the nets and he again found Haumea asleep. Kaulu then surrounded the house with four thicknesses of real fish nets and two thicknesses of the nets of Makalii, Maoleha and its mate. When Kaulu saw that the house of Haumea was completely encompassed with nets, he called out in a loud voice:

Wake up Haumea, It is daylight, the cock has crowed, Darkness has fled, Pleiades has risen. Here I am, Kaulu, Your opponent. You must wake up.

When Haumea heard the call, she woke up and looking about saw that she was entirely surrounded with nets. She then began to tear them with her teeth. After cutting through the four thickness of fish nets she came to the nets of Makalii, Maoleha and its mate. At these

Makalii, hoi mai la o Kaulu a hiki, ia wa e moe ana o Haumea. Nolaila, hoopuni o Kaulu i na upena maloko o ka hale, a eha puni i ka upena, a elua hoi puni o ka hale i na koko a Makalii ia Maoleha ma. A ike o Kaulu ua puni ka hale o Haumea i ka upena. Kahea aku la o Kaulu me ka leo nui:

E ala e Haumea!

Ua ao, ua kani ka moa, Ua lele ka okai o ke ao, Aia i luna ka Huhui, Eia au la o Kaulu, Ko hoa hakaka. E ala oe.

A lohe o Haumea, ala mai la. I nana ae ka hana, ua paa o waho i ka upena. E noke aku ana i ke aki i ka upena, o ka hele ia a pau na upena eha, koe o na koko a Makalii, o Maoleha ma. Ia lalau ana aku o Haumea ia mau koko, e hao mai ana na koko paa o Haumea, pela no a luhi o

nets Haumea was unable to cut them, and became so entangled and exhausted that she went to sleep. While asleep Kaulu set the house on fire, which consumed Haumea, killing her [370]

.

After the death of Haumea, Kaulu went up from Niuhelewai to Nuuanu and from there to Koolau, where Lonokaeho was living. At this time Lonokaeho16 had charge of Koolau. This man had eight foreheads which were all sharp and very powerful. When Kaulu came in the presence of Lonokaeho, Lonokaeho asked him: “Where are you from?” Kaulu replied: “I came along this way.” Lonokaeho said: “No person is allowed to come this way, for the place is sacred and death will result, for I have placed a kapu over it, and because of this people fear me to this very time. If you are strong you shall live, but if not I will kill you.” Kaulu

Haumea hoi e hiamoe. Ma keia hiamoe ana, e puhi ae ana o Kaulu i ka hale o Haumea, pau o Haumea i ke ahi, a make iho la. [371]

.

A make o Haumea, pii aku la o Kaulu mai Niuhelewai aku a hiki i Nuuanu, mai laila aku a hiki i Koolau. E noho ana o Lonokaeho, ia ia o Koolau ia wa. Nona na lae ewalu, he mau lae oi a me ka ikaika loa. A hiki o Kaulu i mua o Lonokaeho, ninau mai o Lonokaeho: “Mahea mai oe?” I aku o Kaulu: “Maanei mai nei no wa’u.” Olelo mai o Lonokaeho: “Aole mea a maalo mai maanei, he kapu, he make, no ka mea, he kapu keia wahi ia’u, a he makau ia au a hiki i keia la e noho nei. Ina he ikaika oe, alaila ola oe i na la; ina aole make oe ia’u. I aku o Kaulu: “No kuu ikaika hiki au ianei.” Ia wa, hoike mai o Lonokaeho i na lae ewalu ona, he pohaku, he

replied: “It is because I am strong that I am able to reach here.” Lonokaeho then exposed his eight foreheads, one was of stone, another of sharp edged rock, another of wood, another of ohia, another of certain weeds, another of maile vines, another of ieie, another of hala. On each of these foreheads grew lehua trees. When Kaulu saw the foreheads of Lonokaeho, he asked of his two hands,17 Limakaukahi and Limapaihala: “How about the eight foreheads of Lonokaeho?” The hands made reply: “They will not escape us.” Kaulu then said to Lonokaeho: “Then why don’t your eight foreheads go ahead and cut me?” Lonokaeho replied: “If they cut you, you will be dead, you will not be saved.” The first forehead then came down, the one of sharp rock, but Kaulu dodged, missing him and the forehead struck the ground. The ieie and the maile vines crawled over and covered it, which prevented it from getting up again. When the forehead tried to get up it was unable to move.18 Thus were all of the

pahoa, he laau, he ohia, he nahele, he maile, he ieie, he hala, he lehua ko luna. A ike o Kaulu i na lae o Lonokaeho, ninau iho o Kaulu i na lima ona, ia Limakaukahi a me

Limapaihala: “Pehea na lae ewalu o Lonokaeho.” I ae na lima: “Aole e pakele ia maua.” Ia wa, olelo aku o Kaulu ia

Lonokaeho: “A hea la hoi ooki ou lae ewalu?” I mai o Lonokaeho: “Ooki no make oe, aole oe e ola.” E iho iho ana ka lae mua he pahoa oi ia, e alo ae ana o Kaulu hala, haule ka lae i lalo. E hao iho ana ka ieie me ka maile i ka hihi, me ke kolo paa i lalo. E oni ae ana ka lae, aole e hiki i luna. Pela no a pau na lae ewalu o Lonokaeho, lilo ae la o Koolau a puni ia Kaulu. Hele aku la o Kaulu a hiki i Kualoa ma ka lae o Kaoio, e noho ana o Mokolii i laila, he kupua, he iole ia.

eight foreheads of Lonokaeho overcome, and Kaulu thereby became possessed of all Koolau. Kaulu then proceeded on to Kualoa19 at the Kaoio point, where Mokolii20 was living, a wizard in the form of a rat.

. .

This wizard was a very evil person and no one, man or woman, was saved who came within its reach; all would be eaten. It was customary with this wizard to sit and watch by the wayside for people to cunningly coax and deceive them to come nearer.

When Kaulu arrived at the place, Mokolii inquired of him: “Where are you from?” Kaulu replied: “I came along this way.” “Yes, you will become my food for this day.” Kaulu made reply: “You can have me if you are strong.” Mokolii then jumped on Kaulu and held him with its teeth. Kaulu then flew up with Mokolii, and when they got into the blue sky Mokolii came falling down, breaking every bone in its body,

He kupua ino keia, aohe kanaka koe ia ia i ka ai ia, aohe wahine koe. He mea mau ia ia ka noho i ke alanui e kiai ai, a e hoopunipuni ai me na olelo maalea. A hiki o Kaulu, ninau mai la o Mokolii: “Mahea mai oe?” I aku o Kaulu: “Maanei mai nei no.” “Ae, he mea ai oe na’u no keia la.” I aku o Kaulu: “Aia no hoi paha i ka ikaika.” E hao mai ana o Mokolii ia Kaulu, paa i na niho. Ia wa o Kaulu i lele ai i luna me Mokolii, a ke ao uli, haule o Mokolii a okaoka liilii, a make iho la ia Kaulu. Lilo ae la ia wahi no Kaulu. [372]

killing it. The place thus became the property of Kaulu. [365]

This is the name of the god of dancers, represented by a branch of the ohia lehua, a species of ohia bearing beautiful blossoms. Laka, a god or goddess, was the presiding deity of the hula. ↑

Kaulu, born as a piece of cord, resembles the birth of Palila, of Mahinai, daughter of Hina and Kana. ↑

Kane and Kanaloa, two of the principal deities. ↑

The mythical hidden land of Kane ↑

The hoa paio obstacles were kupuas, demigods, and ghosts. The Keaumiki and Keauka mentioned were gods of the tides, ebb and flow ↑

The loulu palms were of two varieties, known as loulu lelo, or hawane from its nuts, and loulu hiwa ↑

Makalii, a veteran in the heavens, credited in this case with more discerning power than Kane and Kanaloa ↑

Ikuwa was a name of the month which differed on the different islands of the group in the olden time Hawaii’s calendar placed it in October, Molokai had it in January, Oahu in August, and April on Kauai. ↑

The fore or index finger ↑

A famous shark deity. The name lakee signifies circling or coiling as a serpent, and in its application to a shark may emphasize its size for flexibility ↑

Names of his right and left hands. ↑

Moanalua, between Kalihi and Halawa, Oahu. ↑

Niuhelewai, near Kapalama, below King street, Honolulu. ↑

Haumea was a resident deity of Kalihi valley and vicinity, as testified by the traditions of the locality ↑

The net of Makalii is from the story of Kila, son of Moikeha ↑

This celebrity was one of Kamapuaa’s antagonists, as also Kualii’s. ↑

The named right and left hands again show their power. ↑

Vanquished, similar to the Kamapuaa story ↑

Kualoa was a sacred land of high chiefs in ancient time; all canoes in passing recognized it by lowering their sails. ↑

Mokolii is the name of the small islet off Kualoa ↑

[Contents]

S P.

P N W H

S B.—O O

P’ T F

B.

Palila was a very brave man and very powerful, for in battle he could fight single handed against a multitude of people. He belonged to Alanapo, in Humuula, at Koloa, Kauai.

Alanapo was a kapued temple sacred to the gods from the time of darkness,1 and it was in this temple that Palila was brought up by the gods, and while here he received his instruction in all the arts of warfare.

K P.

P, K K K

K E A.—K K E

E O P.

He kanaka koa loa o Palila, a he kanaka ikaika loa, ma ke kaua ana, ua hiki ia ia ke ku imua o na kanaka he lehulehu, e kue mai ana. No Alanapo i Humuula, ma Koloa i Kauai o Palila. He heiau kapu o Alanapo na ke ’kua mai ka po mai. A ma laila o Palila i hanai kapu ia ai, e ke ’kua, me ke ao ia i ke ano o ke koa.

Kaluaopalena was the father of Palila and Mahinui was his mother. Hina was the grandmother2 of Palila and it was O Kaluaopalena ka makuakane o Palila, o Mahinui ka makuahine, o Hina ke kupunawahine o Palila, nana i

she that took him to Alanapo to be brought up by the gods. Namakaokalani3 was the king of one side of Kauai, while Kaluaopalena4 ruled the other side. These two were at war with one another constantly; and Kaluaopalena was seen to be losing and it became apparent that in a short time he would be defeated when Namakaokalani would have in his possession the whole of Kauai.

The place where the battle was being fought was called Paa and here the two kings with their chiefs and a great number of their warriors were gathered. While the battle was at its height, Palila rose and came out of Alanapo, took up his war club, Huliamahi5 by name, and went out until he came to a rise looking down on the lowlands of Paa. The name of this rise is Komoikeanu.6 While he stood meditating, looking at the battle that was raging below him, he concluded that it was a battle being fought against his father; so he twirled his club and threw it. The club flew through the air,

lawe i loko o Alanapo e noho ai. O Namakaokalani ke ’lii o kekahi aoao o Kauai, o Kaluaopalena, ko kekahi aoao. E kaua ana laua, a kokoke o Kaluaopalena e pio, a lilo loa o Kauai no Namakaokalani.

O kahi a na kanaka e kaua ana, o Paa ka inoa o ka aina, malaila na ’lii me na koa, a me na kanaka he lehulehu loa. Ia lakou e kaua ana, ala mai o Palila mai loko mai o Alanapo, a hopu i kana laau palau o Huliamahi ka inoa. Hele mai la a ku i ke ahua e nana ai ia kai o Paa, o Komoikeanu ka inoa o ia ahua. Nana aku la ia a noonoo, no ka makuakane kela kaua o kai. Ia wa, oniu hema keia i ka laau palau ana, o Huliamahi. A pahu aku la i kai o Paa. O ka honua, nei ka laau me ka hina i lalo. Na ka laau i luku na koa o Namakaokalani, a lohelohe hina iho la maluna o na kanaka ka

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