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ABaker’sDozen
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ABaker’sDozen
RealAnalogSolutionsforDigitalDesigners byBonnieBaker
AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Newnes is an imprint of Elsevier
NewnesisanimprintofElsevier 30CorporateDrive,Suite400,Burlington,MA01803,USA LinacreHouse,JordanHill,OxfordOX28DP,UK Copyright©2005,ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmittedinanyformorbyanymeans,electronic,mechanical,photocopying, recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher. PermissionsmaybesoughtdirectlyfromElsevier’sScience&TechnologyRights DepartmentinOxford,UK:phone:(+44)1865843830,fax:(+44)1865853333, e-mail:[email protected].Youmayalsocompleteyourrequeston-linevia theElsevierhomepage(http://elsevier.com),byselecting“CustomerSupport”andthen “ObtainingPermissions.” Recognizingtheimportanceofpreservingwhathasbeenwritten, Elsevierprintsitsbooksonacid-freepaperwheneverpossible. LibraryofCongressCataloging-in-PublicationData Baker,Bonnie. ABaker’sdozen:real-worldanalogsolutionsfordigitaldesigners/byBonnieBaker. p.cm. ISBN0-7506-7819-4 1.Digitalintegratedcircuits--Designandconstruction.2.Logicdesign.I.Title. TK7874.B3432005 621.3815--dc22
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Contents Preface.....................................................................................................ix Acknowledgments......................................................................................xi AbouttheAuthor.................................................................................... xiii Chapter1:BridgingtheGapBetweenAnalogandDigital.............................. 1 TrytoMeasureTemperatureDigitally....................................................................................... 6 RoadBlocksAbound................................................................................................................. 8 TheUltimateKeytoAnalogSuccess...................................................................................... 14 HowAnalogandDigitalDesignDiffer................................................................................... 15 TimeandItsInversion.............................................................................................................. 20 OrganizingYourToolbox......................................................................................................... 21 SetYourFoundationandMoveOn,OutoftheBox................................................................ 22 Chapter1References............................................................................................................... 23
Chapter2:TheBasicsBehindAnalog-to-DigitalConverters.......................... 25 TheKeySpecificationsofYourADC...................................................................................... 28 SuccessiveApproximationRegister(SAR)Converters........................................................... 40 Sigma-Delta(Σ−∆)Converters................................................................................................ 46 Conclusion............................................................................................................................... 59 Chapter2References............................................................................................................... 60
Chapter3:TheRightADCfortheRightApplication................................... 63 ClassesofInputSignals.......................................................................................................... 65 UsinganRTDforTemperatureSensing:SARConverterorSigma-DeltaSolution?............. 72 RTDSignalConditioningPathUsingtheSigma-DeltaADC................................................ 76 MeasuringPressure:SARConverterorSigma-DeltaSolution?............................................. 77 ThePressureSensorSignalConditioningPathUsingaSARADC....................................... 79 PressureSensorSignalConditioningPathUsingaSigma-DeltaADC................................... 80 PhotodiodeApplications.......................................................................................................... 81 PhotosensingSignalConditioningPathUsingaSARADC................................................... 81 PhotosensingSignalConditioningPathUsingaSigma-DeltaADC....................................... 82 MotorControlSolutions.......................................................................................................... 83 v
Contents Conclusion.............................................................................................................................. 88 Chapter3References............................................................................................................... 89
Chapter4:DoIFilterNow,LaterorNever?............................................... 91 KeyLow-PassAnalogFilterDesignParameters..................................................................... 95 Anti-AliasingFilterTheory................................................................................................... 103 AnalogFilterRealization....................................................................................................... 105 HowtoPickYourOperationalAmplifier............................................................................... 108 Anti-AliasingFiltersforNearDCAnalogSignals................................................................ 109 MultiplexedSystems.............................................................................................................. 112 ContinuousAnalogSignals.................................................................................................... 114 MatchingtheAnti-AliasingFiltertotheSystem................................................................... 115 Chapter4References............................................................................................................. 116
Chapter5:FindingthePerfectOpAmpforYourPerfectCircuit................. 117 ChoosetheTechnologyWisely.............................................................................................. 121 FundamentalOperationalAmplifierCircuits......................................................................... 122 UsingtheseFundamentals..................................................................................................... 129 AmplifierDesignPitfalls....................................................................................................... 131 Chapter5References............................................................................................................. 133
Chapter6:PuttingtheAmpIntoaLinearSystem...................................... 135 TheBasicsofAmplifierDCOperation.................................................................................. 137 EveryAmplifierisWaitingtoOscillate,andEveryOscillatoris WaitingtoAmplify............................................................................................................. 151 DeterminingSystemStability............................................................................................... 157 TimeDomainPerformance.................................................................................................... 161 GoForth................................................................................................................................ 163 Chapter6References............................................................................................................. 164
Chapter7:SPICEofLife........................................................................ 165 TheOldPencilandPaperDesignProcess............................................................................. 172 IsYourSimulationFundamentallyValid?.............................................................................. 175 Macromodels:WhatCanTheyDo?...................................................................................... 179 ConcludingRemarks.............................................................................................................. 183 Chapter7References............................................................................................................. 184
Chapter8:WorkingtheAnalogProblemFromtheDigitalDomain............. 185 PulseWidthModulators(PWM)UsedasaDigital-to-AnalogConverter............................. 188 UsingtheComparatorforAnalogConversions..................................................................... 194 vi
Contents WindowComparator.............................................................................................................. 196 CombiningtheComparatorwithaTimer.............................................................................. 197 UsingtheTimerandComparatortoBuildaSigma-DeltaA/DConverter........................... 199 Conclusion............................................................................................................................. 207 Chapter8References............................................................................................................. 208
Chapter9:SystemsWhereAnalogandDigitalWorkTogether................... 209 SelectingtheRightBatteryChemistryforYourApplication................................................. 212 TakingtheBatteryVoltagetoaUsefulSystemVoltage......................................................... 213 DefiningPowerSupplyEfficiency........................................................................................ 214 ComparingTheThreePowerDevices................................................................................... 219 WhatistheBestSolutionforBattery-OperatedSystems?.................................................... 221 DesigningLow-PowerMicrocontrollerSystemsisaStateofMind..................................... 222 Conclusion............................................................................................................................. 228 Chapter9References............................................................................................................. 229
Chapter10:Noise–TheThreeCategories:Device,ConductedandEmitted.. 231 DefinitionsofNoiseSpecificationsandTerms...................................................................... 234 DeviceNoise......................................................................................................................... 238 ConductedNoise.................................................................................................................... 254 Chapter10References........................................................................................................... 260
Chapter11:Layout/Grounding(Precision,HighSpeedandDigital)............ 261 TheSimilaritiesofAnalogandDigitalLayoutPractices...................................................... 263 WheretheDomainsDiffer–GroundPlanesCanBeaProblem.......................................... 266 WheretheBoardandComponentParasiticsCanDotheMostDamage............................... 267 LayoutTechniquesThatImproveADCAccuracyandResolution....................................... 274 TheArtofLayingOutTwo-LayerBoards............................................................................ 277 CurrentReturnPathsWithorWithoutaGroundPlane......................................................... 281 LayoutTricksfora12-BitSensingSystem........................................................................... 282 GeneralLayoutGuidelines–DevicePlacement................................................................... 284 GeneralLayoutGuidelines–GroundandPowerSupplyStrategy....................................... 284 SignalTraces.......................................................................................................................... 287 DidISayBypassandUseanAnti-AliasingFilter?............................................................... 287 BypassCapacitors.................................................................................................................. 287 Anti-AliasingFilters.............................................................................................................. 288 PCBDesignChecklist........................................................................................................... 288 Chapter11References........................................................................................................... 290
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Contents
Chapter12:TheTroubleWithTroubleshootingYourMixed-SignalDesigns WithouttheRightTools....................................................................... 291 TheBasicToolsforYourTroubleshootingArsenal............................................................... 293 Youask,“DoesmyCircuitA/DConverterWork?”............................................................... 295 PowerSupplyNoise............................................................................................................... 298 ImproperUseofAmplifiers................................................................................................... 301 Don’tMisstheDetails........................................................................................................... 303 Conclusion............................................................................................................................. 305 Chapter12References........................................................................................................... 306
Chapter13:CombiningDigitalandAnalogintheSameEngineer,andonthe SameBoard........................................................................................ 307 TheSignalChaintotheRealWorld...................................................................................... 309 ToolsoftheTrade.................................................................................................................. 310 ThrowingtheDigitalInWiththeAnalog.............................................................................. 314 Conclusion............................................................................................................................. 318
AppendixA:Analog-to-DigitalConverterSpecificationDefinitions andFormulas...................................................................................... 319 AppendixB:ReadingFFTs...................................................................... 329 ReadingtheFFTPlot............................................................................................................. 331
AppendixC:OpAmpSpecificationDefinitionsandFormulas...................... 337 Index.................................................................................................... 343
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Preface Iwenttoananaloguniversitywherethecorecourseswere,ofcourse,allanalog.ThenI startedmycareeratahigh-quality,premier,analoghouse;Burr-Brown.Mindyou,myobjectivewasnottoworkatananaloghouse,myobjectivewastohaveajob.Nonetheless,there Irubbedshoulderswiththebestanalogengineersinindustry.Afterthirteenyears,Idecided toexpandmyhorizonsandworkforadigitalcompany.Forme,thirteenwasaluckynumber becausethisiswhenmyrealeducationbegan. WhatdidIlearn?Ilearnedthatyoudesignyourcircuitsothatitworksintheapplication,not sothatyouhavethemostelegantsolutioninindustry.Ialsolearnedthatyoucanusedigital circuitsaswellasanalogcircuitstogetthejobdone.Moreover,Ilearnedthatsometimes ignoranceisbliss.ManyofthedigitalengineersthatIhaveworkedwithdon’tknowthat sometasksareimpossible.Forinstance,atBurr-Brownwetrimmedourprecisionanalog circuitswiththehightechnologyofNicrome.Thistrimprocessisveryspecifictoanalog siliconcircuitsandisaccurate.ItoldtheengineersthattheycouldnothaveprecisionproductswithoutaNicromeprocess.BoywasIwrong.Microchiptrimsinanalogcircuitprecision withtheirdigitalFlashprocess. Ihavealwaysbeena“diedinthewool”analogengineer,butIamstartingtochange.Ihaven’t madeatotaltransitiontothe“dark(digital)side,”butdigitalislookingmoreattractiveall thetime.ThisattractionisenhancedbythefactthatIamveryfamiliarwithanalogandhave adiversesetofanalog,andnowdigital,toolstosolvemycircuitproblems.Thisbookisfor yousothatyoucanalsohavethesamesetoftoolsandcanbecomemorecompetitiveinyour designendeavors. Digitalcircuitryandsoftwareisencroachingintotheanaloghardwaredomain.Analogwill neverdisappearatthesensorconditioningcircuit,powersupply,orlayoutstrategies.Iknow thedigitalengineerwillcontinuetobechallengedbyanalogissues,eveniftheydenythat theyexist. Nowlet’saddtothecomplexityofthedigitalengineer’schallenges.Theadvancesinmicrocontrollerandmicroprocessorchipdesignsaregrowingineverydirection.Increasedspeedand memoryisjustoneexampleofthedirectionthatthesedevicesaretaking.However,themost interestingchangeistheadditionofperipherals,includinganalogandinterfacecircuitry.Not onlyistheengineerrequiredtoknowthedetailsoftheimplementationoftheseperipherals,
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Preface butalsoknowthebasicsoflayoutstrategies.Today,thedigitalengineerneedsanaddeddimensionofknowledgeinordertosolveproblemsbeyondthefirmwaredesignchallenges. Goingforward,thedigitalengineerneedssomebasictoolsintheirtoolbox.Iwrotethisbook forpracticingdigitalengineers,students,educatorsandhands-onmanagerswhoarelooking fortheanalogfoundationthattheyneedtohandletheirdailyengineeringproblems.Itwill serveasavaluablereferenceforthenuts-and-boltsofsystemanalogdesigninadigitalword. Thetargetaudienceforthisbookistheembeddeddesignengineerthathasthegoodfortune towanderintotheanalogdomain.
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Acknowledgments I’dliketothankalloftheengineerswhogavetheirtimetoreviewthematerialinthevolume. Aprimaryreviewer,KumenBlake(MicrochipTechnologyengineer)wasmeticulousand alwaysprovidedexcellent,relevantfeedback.PaulMcGoldrick(AnalogZone,editor-in-chief) gavesignificanttimetoensurethatsectionsofthisbookwereaccurateandconciselywritten.NumerousengineersatMicrochipTechnology,TexasInstrumentsandBurr-Brownalso reviewedthematerialfortechnicalaccuracy. ThanksalsotoNewnesacquisitioneditorHarryHelmsandKellyJohnsonofBorrego Publishing.Harrypesteredmeforoverayeartojustsitdownandwrite.Ithensaidtohimit wouldtaketwoyearstofinishthisbook,andhesaiditwouldtakeoneyear.Itactuallytook tenmonthsfromstarttofinishonlybecauseofHarry’senthusiasticencouragementatthe beginning.Kellydidanoutstandingjobofeditingmyfinal-author’scopy. Andespecially,thankstomysupportsysteminTucson,Arizona.Theyweremycheerleaders inthissolitaryendeavor.Andtogether,wefinishedit!
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AbouttheAuthor BonnieBakerwritesthemonthly“Baker’sBest”forEDNmagazine.Shehasbeeninvolved withanaloganddigitaldesignsandsystemsfornearly20years.BonniestartedasamanufacturingproductengineersupportinganalogproductsatBurr-Brown.Fromthere,Bonnie moveduptoICdesign,analogdivisionstrategicmarketer,andthencorporateapplications engineeringmanager.In1998,shejoinedMicrochipTechnologyandhasservedastheir analogdivisionanalog/mixed-signalapplicationsengineeringmanagerandstaffarchitect engineerforoneoftheirPICmicrodivisions.Thishasexpandedherbackgroundtonotonly includeanalogapplications,butmicrocontrollersolutionsaswell. BonnieholdsaMastersofScienceinElectricalEngineeringfromtheUniversityofArizona (Tucson,AZ)andabachelor’sdegreeinmusiceducationfromNorthernArizonaUniversity (Flagstaff,AZ).Inadditiontoherfascinationwithanalogdesign,Bonniehasadrivetoshare herknowledgeandexperienceandhaswrittenover200articles,designnotes,andapplication notesandsheisafrequentpresenterattechnicalconferencesandshows.
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CHAPTER
1 BridgingtheGapBetween AnalogandDigital
1
CHAPTER
BridgingtheGapBetween AnalogandDigital Afewyearsago,Iwasapproachedbyanewgraduate,engineeringapplicantattheEmbedded SystemsConference(ESC),2001inSanFrancisco.WhenhefoundoutthatIwasamanager, heexplainedthathewaslookingforajob.HesaidheknewofMicrochipTechnology,Inc. andwantedtoworkforthemifhecould.Heimmediatelyproducedhisresume.Igavehima fewmoredetailsaboutmyroleatMicrochip.Atthetime,Imanagedthemixedsignal/linear applicationsgroup.Mydepartment’sroleswereproductdefinition,technicalwriting,customertraining,andtravelingallovertheworldvisitingcustomers.Attheconclusionofthis “sales”pitch,heproudlytoldmethatitsoundedlikeagreatjob.IreemphasizedthatIwas intheAnalogarmatMicrochip.Heobviouslythoughtthathedidhishomeworkbecausehe toldmethatanalogisdyinganddigitalwilleventuallytakeover.Anyonewhoknewanything aboutMicrochipwouldagree!Wow,Ihadaliveone. Iwasthere,doingmyobligatoryMicrochipboothdutyfortheafternoon.Therewasalot ofactiononthefloor,andtheroomwasfullofexhibits.Thelightswereon,thesoundof conversationswereprojectingacrosstheroom.Theheatingandcoolingsystemwasdoing asplendidjobofkeepinguscomfortable.Exhibitorsintheboothswere(believeitornot) demonstratingtheoperationofsensors,powerdevices,passivedevices,RFproducts,andso forth.Theremusthavebeenseveralhundredbooths,allofwhichweretryingtopromotetheir engineeringmerchandise. Figure1.1:TheEmbedded SystemsConferenceexhibit hallin2001hadhundreds ofbooths,manyofwhich werealreadyshowing signsofinterestinanalog systems.Thiswasdoneeven thoughtheemphasisofthe conferencewasdigital.
3
Chapter1 Someofthevendorexhibitshadanalogsignalconditioningdemonstrations.Asamatterof fact,rightinfrontofus,Microchiphadatemperaturesensorconnectedtoacomputerthrough theparallelport.Thetemperaturesensorboardwouldself-heat,andthesensorwouldmeasure thischangeandshowtheresultsonthePCscreen.Oncethetemperaturereachedathreshold of85°C,theheatingelementwasturnedoff.Youcouldthenwatchthetemperaturegodown onthePCuntilitreached40°C,atwhichpointtheheatingelementwouldbeturned-onagain. Atasecondcounter,wealsohadacomputerrunningthenewFilterLab®analogfilterdesign program.Withthistool,youcanspecifyananalogfilterintermsofthenumberofpoles,cutofffrequencyandapproximationtype(Butterworth,BesselandChebyshev).Onceyoutypein yourinformation,thesoftwarespitsoutafiltercircuitdiagram,suchasthefiltercircuitshown inFigure1.2.Youcantheoreticallybuildthecircuitandtakeittothelabfortestingandverification.Therewasacustomeratthecounter,playingaroundwiththefiltersoftware.
Figure1.2:OneoftheviewsoftheFilterLabprogramfromMicrochip providedanalogfiltercircuitdiagrams.Thisparticularcircuitisa5th order,low-passButterworthfilterwithacut-offfrequencyof1kHz. TheFilterLabprogramfromMicrochipisjustoneexampleofafilter programfromasemiconductorsupplier.TexasInstruments,Linear Technology,andAnalogDeviceshavesimilarprogramsavailableonthe WorldWideWeb.
Atexhibitcounternumberthree,therewasaCANbusdemonstrationwithtemperaturesensing,pressuresensingandDCmotornodes.CANbusnetworkshavebeenaroundforover15 years.Initially,thisbuswasusedinautomotiveapplicationsrequiringpredictable,error-free 4
BridgingtheGapBetweenAnalogandDigital communications.Recentfallingpricesofcontrollerareanetwork(CAN)systemtechnologies havemadeitacommodityitem.TheCANbusnetworkhasexpandedpastautomotiveapplications.Itisnowmigratingintosystemslikeindustrialnetworks,medicalequipment,railway signalingandcontrollingbuildingservices(tonameafew).Theseapplicationsareusingthe CANbusnetwork,notonlybecauseofthelowercost,butbecausethecommunicationwith thisnetworkisrobust,atabitrateofupto1Mbits/sec. ACANbusnetworkfeaturesamultimastersystemthatbroadcaststransmissionstoallof thenodesinthesystem.Inthistypeofnetwork,eachnodefiltersoutunwantedmessages. Anadvantagefromthistopologyisthatnodescaneasilybeaddedorremovedwithminimal softwareimpact.TheCANnetworkrequiresintelligenceoneachnode,butthelevelofintelligencecanbetailoredtothetaskatthatnode.Asaresult,theseindividualcontrollersare usuallysimpler,withlowerpincounts.TheCANnetworkalsohashigherreliabilitybyusing distributedintelligenceandfewerwires. Youmightsay,“Whatdoesthishavetodowithanalogcircuits?”Andtheansweriseverything.Thecommunicationchannelisimportantonlybecauseyouareshippingdigitizedanalog informationfromonenodetoanother.WiththisESCexhibit,threeCANbusnodescommunicatedthroughthebustoeachother.Onenodemeasuredtemperature.Thetemperaturevalue wasusedtocalibratethepressuresensoronthesecondnode.Youcouldapplypressuretothe pressure-sensingnodebymanuallysqueezingaballoon.(Thistypeofdemonstrationwasput togethertogettheobservermoreinvolved.)Thesensorcircuitrydigitizedthelevelpressure appliedandsentthatdatathroughtheCANbusnetworktoaDCmotor.TheDCmotorwas configuredsothatincreasedpressurewouldincreasetherevolutionperminute(RPM)ofthe motor.Figure1.3showsabasicblockdiagramcontainingthepressure-sensingnode. +5V • • •
CAN Controller
CAN Driver
PWM
• • •
Output LED • • •
Figure1.3:The CANbussystemat the2001Embedded SystemsConference hasthreedifferent analogfunctionnodes. Thenodeillustratedin thisfiguremeasured thepressureapplied toaballoonandsent thedataacrossthe CANbusnetwork toaDCmotor(not illustratedhere).
SPI™ 4
Microcontroller
SPI CAN bus
SPI
12-bit ADC
Low-pass Analog Filter
Amplifier
Pressure Sensor
MPX2100AP
5
Chapter1 ThentofinishouttheMicrochipdisplaysinthebooth,therewerethreecountersthathad microcontrollerdemos. Iaskedtheengineeringapplicant,givinghimachancetoredeemhimself,“Outofcuriosity, doyouseeanythinganalog-ishlikeinthisroom?”Helookedaroundtheconventionroom thoughtfully.Iwasamusedwhenhesympatheticallylookedatmeandanswered,“No,notreally.”IthinkthathethoughtIwasabitold-fashioned,behindthetimes.Noregretsfromhim. Hewasconfidentthathegavemeaninsightful,informedanswer. Youguessedit.Hisresumewentintothecircularfile.
TrytoMeasureTemperatureDigitally No,thisisnotabookaboutinterviewtechniques.Thisbookisneitherabouthowtowin pointsandclimbthecorporateladder.Thisisabookabouttheanalogdesignopportunitiesthatsurrounduseveryday,alldaylong,andhowwecansolvetheminasingle-supply environment.Reflectingontheapplicant’sanswer,Ithinkthathewaspartiallyright.Digital solutionsareencroachingintotheanaloghardwareinamajorityofapplications. Solet’strytomeasuretemperaturedigitally.Thesimple,lowresolutionanalog-to-digital (A/D)convertercaneasilybereplacedwitharesistor/capacitor(R/C)pairconnectedtoa microcontrollerI/Opin.TheR/Cpairwouldsupplyasignalthatoperateswithasingle-pole, rise-timefunction.ThecontrollercountsmilV liseconds,withitsoscillator/timercombination R measurestheinputsignal.Whywouldyouwant V GP2 todothis?Maybeyouaremeasuringtemperature NTC Thermistor withasensorthatchangesitsresistancevaluewith 10kΩ @ 25(°C) changesintemperature. DD
REF
REF
GP1
ThetemperaturesensingcircuitinFigure1.4 isimplementedbysettingGP1andGP2ofthe microcontrollerasinputs.Additionally,GP0isset lowtodischargethecapacitor,CINT.AsthevoltageonCINTdischarges,theconfigurationofGP0 ischangedtoaninputandGP1issettoahigh output.Aninternaltimercountstheamountof time(t1inFigure1.5)beforethevoltageatGP0 reachesthethreshold(VTH),whichchangesthe recognizedinputfrom0to1.Inthiscase,RNTC (anegativetemperaturecoefficientthermistor)is placedinparallelwithRPARorRNTC||RPAR.This parallelcombinationinteractswithCINT.Afterthis happens,GP1andGP2areagainsetasinputsand 6
RPAR = 10kΩ ( +/–1% tolerance, metal film) GP0 CINT
Microcontroller
Figure1.4:Thiscircuitswitchesthe voltagereferenceonandoffatGP1and GP2.Inthismanner,thetimeconstant oftheNTCthermistorinparallelwitha standardresistor(RNTC||RPAR)and integratingcapacitor(CINT)iscomparedto thetimeconstantofthereferenceresistor (RREF)andintegratingcapacitor.
Figure1.5:TheR/Ctimeresponse ofthecircuitshowninFigure1.4 allowsforthemicrocontroller countertobeusedtodetermine therelativeresistanceofthe negativetemperaturecoefficient (NTC)thermistorelement.
Voltage at GPO, VOUT (V)
BridgingtheGapBetweenAnalogandDigital
R NTC ||R PAR
R REF
V TH
0
t1
Time (s)
t2
GP0asanoutputlow.OncetheintegratingcapacitorCINThastimetodischarge,GP2isset toahighoutputandGP0asaninput.AtimercountstheamountoftimebeforeGP0changes to1again,butthisprovidesthetimedamountoft2,perFigure1.5.Inthiscase,RREFisthe componentinteractingwithCINT. Theintegrationtimeofthiscircuitcanbecalculatedusing:
VOUT=VREF(1–e–t/RC)or
t=RCln(1–VTH/VREF)
whereVOUTisthevoltageattheI/Opin,GP0,
VREFistheoutput,logic-highvoltageoftheI/Opin,GP1orGP2;
VTHistheinputvoltagetoGP0thatcausesalogic1totriggerinthemicrocontroller.
IftheratioofVTH:VREFiskeptconstant,theunknownresistanceoftheRNTC||RPARcanbe determinedwith: RNTC||RPAR=RREF(t2/t1) Noticethatinthisconfiguration,theresistancecalculationoftheparallelcombinationof RNTC||RPARisindependentofCINT,buttheabsoluteaccuracyofthemeasurementisdependent ontheaccuracyofyourresistors. Oops,didIsayyoucanusealinearresistorandachargingdevicelikeacapacitortoreplace anA/Dconverterinatemperaturemeasurementsystem?IguessmyapplicantattheESC showwasalsowrong.Analogwillneverdisappearandthedigitalengineerwillcontinueto bechallengedtodelveintothesetypesofissues.Theanalogsolutionismanytimesmore efficientandusuallymoreaccurate.Forinstance,thepreviousR/Cexampleisonlyas accurateasthenumberofbitsinthetimer,thespeedoftheoscillator,andhowaccuratelyyou knowthevalueofyourresistors. 7
Chapter1
RoadBlocksAbound Ihaveworkedwithawidespectrumofanaloganddigitaldesigners.Eachoneofthemhas theirownquirksandreasonswhytheycan’tdoeverything,butherearesomestatementsthat Ihavereceivedfrommydigitalclienteleconcerningtheiranalogchallenges.
NotMyJob! Thisstatementcameaboutwithsurprisingfrankness.“Peopleinmydepartmentareavoiding analogcircuitryintheirdesignasmuchaspossible,nomatterhowimportantitis.Manyof themhavehadexperienceswhereanalogcircuitperformancewashardtopredict.Therefore, almosteveryengineerwillfindanexistinganalogcircuitandusethatasapointofreference. Iftheyhavethemisfortuneofbeingaskedtodesignpartoralloftheanalogcircuitfrom scratch,theywilltrytousefactsthattheyrememberfromtheirschooldays.Andintheir schooldaystheystudiedmostlydigital.” Goodluck.Itseemsfromthisstatementthatthedied-in-the-wooldigitaldesignerhasno interestinhowtogetfromAtoB,butmoreinterestinwhatthecookbooksuggests. Itturnsoutthatthedesignerswhooperateinthismodearelikeacarpenterwithahammer lookingforanail.Thedesignerhasacircuitsolutionandtriestomakeitfittheirapplication. Agoodexampleofapplyingthecookbooksolutiontoaplacewhereitwon’tfitistotrytouse astandard12-bitsuccessiveapproximationregister LOAD (SAR)inapowersensingapplication.ThistypeofapDeltaplicationactuallyrequiresasigma-deltaconverter.As sigma SPI Interface A/D youwillfindlaterinthisbook(Chapter3),thesigmaConverter delta(Σ−∆)convertercanreacharesolutionlevelin thesub-nanovoltregion.Thisisanadvantagebecause L2 L1 younotonlyeliminatetheinput,analog-gainstage,but 240V youreducethenoiseinthebandpassregionofyour Figure1.6:Apowermeterapplication signal.Figure1.6showsthispowermetersolution. Inthiscircuit,thecurrentthroughthepowerlineis sensedusinganinductoronthelow-sideoftheload. Asaresult,thevoltagedropacrossthissensingelementmustbelow.
ShowMetheBeef
requires INDigital 0010 Output 0001 Code 0000 1111 1110 IN+ < IN1101 1100 1011 Negative Full 1010 Scale Output = − VREF 1001 1000 –FS –1/2 FS 0 FS 1/2 FS FS Analog Input Voltage
Figure2.3:Thetransferfunctionofa4-bitADCbipolaranalog inputwillproduceatwo’scomplementcodeasadigitaloutput.
Thissystemhasanoddnumberofcodesandonlyonezerostate.DifferentialinputADCs (Figure2.1c)aredevicesthatcanbeoperatedinasingle-ended,positivevoltageinputmodeor afull-differentialinputmode.Inthefull-differentialmode,theFSRofthedeviceisequalto: FSR={+INMAX–(–INMIN)}+{–INMAX–(+INMIN)} AndtheADC’sinputvoltagerangeisequalto: AIN=(+IN–(–IN)) Theconverterwillproducedigitalcodethatrepresentsthebothnegativeandpositiveanalog inputsasshowninTable2.2.
ThroughputRateversusResolutionandAccuracy Ioncehadacustomeraskmeonthecompanyhotlinefora32-bitconverter.Iwastakenoff guardwithhisrequest.Whydidheneed32-bits?Ifinallyfoundoutthatheonlyneeded1mV resolutionoutof4.096V.Wellthatiseasy.Youcandothiswitha12-bitconverterthathasa 4.096Vreference.Withthisconverter,theFSRwouldbe4.096andtheLSBsizewouldbe VREF/212=4.096V/4096=1mV.Whywashehavingproblemsfindingaconverter? Hetoldmethathisbuswas32-lineswide.Somyadvicebecame,“Usea12-bitconverterand tiebuslines0through29toground.”HeaskedmeifyoucoulddothatandIsaid,“Absolutely,andwiththissolutionyouwillcontrolyoursystemnoiseasanaddedbenefit!” Athroughputratespecification(alsoknowasdatarateforsigma-deltaADCs)definesthat amountoftimeittakesforaconvertertocompleteanentireconversion.Theactivitiesthat 33
Chapter2 areincludedinthethroughputratetimearesetuptime,sampletime,conversiontimeanddata transmissiontime.Thetwoconvertertopologiesthatwewillcenterourattentiononwillbe thesuccessiveapproximationregister(SAR)andsigma-delta.Whenyouthinkofthetypical conversiontimesofthesetopologies,youcaneasilyseparatethemintoapplicationclasses (Figure2.4).Ingeneralterms,thefasterthethroughputrateoftheconverter,thelowerthe resolutionwillbe.Butimpliedinthisdiagramisthesametrendinaccuracy.Theresolutionofaconverterissimplythenumberofbitsthattheconverteriscapableofhandlingper conversion.Theaccuracydescribesthenumberofbitsthatarerepeatablefromconversionto conversion.Inallcases,thespecifiedaccuracywillbeequaltoorlessthantheresolutionof theconverter. Sigma-Delta
Accuracy (bits)
24 20
SAR
16 12 10 8 10
100
1k 10k 100k 1M 10M Throughput Rate (SAR Converters) Data Rate (sigma-delta converters) (samples per second)
100M
Figure2.4:ThethroughputrateoftheSARconverter isfasterthanasigma-deltaconverter.Incontrast,the sigma-deltaconverterisabletoachievehigheraccuracy asatrade-offfortheslowerspeeds.
Thedatarateofthesigma-deltaconverterisgenerallyslowerthanthethroughputrateofthe SARconverter.Aswewillseelateroninthisdiscussion,theSARconverteronlysamplesthe inputsignalonceandconvertstoadigitalcode,accordingtothesampledsignal.Thesigmadeltaconvertersamplestheinputsignalmultipletimes.Itthenimplementsvariousnoise reductionalgorithmstoimprovethenumberofbitsintheconverter,aswellasthesignal-tonoiseratio(SNR),butthetrade-offwiththistypeofsamplingstrategyistime.
AccuracyversusResolution Thereareafewkeyspecificationsthatyoushouldbecomefamiliarwith.Knowingthese figuresofmeritwillhelpyouchoosetherightconverterforyourapplicationandalsoidentifiestheimpostors.Forinstance,“2.7V16-BitADCwithSPI®SerialInterface”isanexample ofwhatyoumightseeatthetopofadatasheet.Doesitmean16-bitsaccurate,noise-freefor 34
TheBasicsBehindAnalog-to-DigitalConverters everyconversion,accuratewithrespecttotheinputvoltage,ordoesitmean16-bitsresolution whereyouareguaranteedthat16-bitswillbetransmittedoutoftheconverterattheconclusionofaconversion?Thelatteriscorrect.Thephrase“2.7V16-BitADCwithSPISerial Interface”asthetitleoftheconverter’sdatasheetonlymeansthatyouwillsee16-bitstransmittedfromtheoutputoftheconverter. Youwillfindthatthose16-bitscanallbeaccurateornot,dependingonthemanufacturer. MorethanonceinmycareerIhaveseenthelastcoupleofcodesortheLSBs(leastsignificantbits)ofa16-bitconverterditherallovertheplacefromconversiontoconversion.So,I woulddefineaconverterlikethisashaving16-bitresolution,not16-bitaccurate.Thisisnota badthing,aslongasyouknowwhattoexpect. So,resolutionisdefinedasthenumberofbitsthataretransmittedoutoftheconverteratthe conclusionoftheconversion.Ifyouknowthisinformationaboutaconverteryoucanquickly calculatethetheoreticalLSBsizewiththefollowingformula:
LSB=FSR/2n
Wheren=numberofbits
Foraconverterthathas16-bitresolutionandanFSRof5V,theLSBsizeis76.29µV. OneofthemorecommonquestionsaboutADCsthatIhearis,“HowdoIknowthatanADC willgivemeagood,reliablecodeandcanIdeterminethisfromtheconverter’sdatasheet?” Ofcoursethisdependsonyourdefinitionof“reliable,”butifyouarelookingforarepeatable outputfromconversion-to-conversion,youshouldrefertoACdomainspecifications.Ifyou arelookingforaconvertedcodethatrepresentsthatactualinputvoltage,DCspecifications aremoreuseful.But,don’tforgetaboutthenoise.DCspecificationsimplyaverageaccuracy (notrepeatability).Fromconversion-to-conversionthesecodeswillvary,dependentonthe internalnoiseoftheconverter. ACSpecificationsImplyRepeatability ACdomainspecifications,suchasSNR,effectiveresolution(ER),signal-to-(noise+ distortion)(SINAD),oreffectivenumberofbits(ENOB),provideinformationaboutADCrepeatability.Nowthesespecificationswilltellyouhowrepeatableyourconversionis,butthey willnottellyouiftheconversionisaccurate.Ontheotherhand,DCdomainspecifications, suchasoffseterror,gainerror,differentialnonlinearityandintegralnonlinearityprovide informationabouthowclose,onaverage,theinputsignalismatchedtoanactualoutputcode. Thesespecificationsdonotimplyrepeatability,andnoisecouldgiveyouvaryingresultsfrom conversion-to-conversion. Ideally,theSNRofaconverterindecibelsisequalto6.02n+1.76dB,where“n”isequalto thenumberofconverterbits.Thistheoreticalnoiseisaresultofthequantizationnoiseinherentintheconverter.Inpractice,SNRisequalto20log(rmssignal)/(rmsnoise),whererms 35
Chapter2 meansroot-mean-square,equaltoonestandarddeviationinanormaldistribution.Inorderto determinethermsnoise,theresultsofmanyconversionsneedtobecollected. AswiththeSNR,ERismeasuredbycollectingastatisticalsampleofmanyconversions, butthistimewedon’thaveanACinputsignaltotheconverter.Theinputsignalisaclean, “noiseless”DCsignal.IfthisDCsignalhaslessnoisethanyourconverter(about3×),you aregoodtogo.TheunitsofmeasureforERarebits,whichisreferredtotheoutputofthe converter.Ifyouwanttoreferthisnumbertotheinput,youcanchangetheunitstovolts.This isinterchangeablewiththefollowingformula: ER(inbitsrms)={20log(FS/ERinVrms)–1.76}/6.02, sincetheunitofERisinbits,younowknowwhichbitsarerepeatableinyourADCoutput code. WhileSNRorERprovidesinformationaboutthedevicenoiseoftheconverter,SINADand ENOBprovidemoreinformationaboutADCfrequencydistortions.SINADistheratioof thermsamplitudeofthefundamentalinputfrequencyoftheinputsignaltothermssumof allotherspectralcomponentsbelowonehalfofthesamplingfrequency(excludingDC).The theoreticalminimumforSINADisequaltotheSNRor6.02n+1.76dB.Butinpractice,an ADCwillhavesomeharmonicdistortionofthisinputsignalthatisgeneratedwithintheconverter.ThecomplementaryspecificationtoSINADisENOB.TheunitofmeasureforSINAD isdB,andtheunitsofmeasureforENOBsisbits.SINADcanbeconvertedtoENOBwith thefollowingcalculation: ENOB=(SINAD–1.76)/6.02 Tothispointinourdiscussion,thespecificationunitsareintermsofrms.Statisticallyspeaking,rmstoonestandarddeviationofdatashapedasanormaldistribution.Whenthenoise unitsaredefinedwithrmsunits,theprobabilitythattheconverterwillgiveyouavalueof plusorminusonermsis~68%.Therelationshipbetweentheoutputnoiseoftheconverter, thenormaldistributionofasetofsampledoutputsandthesestatisticalvaluesareillustrated inFigure2.5aand2.5b. Anrmsspecificationisastatisticalcalculationfrommanysamplesorapopulation.The formulaforonestandarddeviationis: σ2=Σ(y−η)2/Ν
whereσisthepopulationstandarddeviation
yisasamplefromthepopulation
ηisthepopulationmeanand
Nisthesetofpopulationobservations
36
TheBasicsBehindAnalog-to-DigitalConverters A68%probabilityofgettingyourexpectedoutputmaynotbetheoddsyouwanttowork with.Youmightwanttoconsiderconvertingthespecificationlimitstopeak-to-peak(p-p) values.Fromthermsnumber,youcanquicklycalculatethep-pspecification,whichisvery convenientifyouaretryingtogetgoodrepeatableresults.Thisconversioniseasilydone withERandENOBspecificationsbymultiplyingyourrmsspecification(involtages)by twotimesthecrestfactor(CF,Figure2.5c),orsubtractingthebitcrestfactor(BCF,Figure 2.5c)fromyourrmsspecification(inbits).Withthisnewcalculation,yourADChasabetter chanceofproducingyourexpectedoutput.Theindustrystandardcrestfactorfornonmilitary applicationsis3.3.Also,becarefulthatthedatayouselectedhastheattributesofanormal distribution,otherwisethesecalculationswillnotbeasaccurateaspromised. Thecalculationfortheconversionofrmstop-pis:
V(p-p)=V(rms)*2*CF
Bits(p-p)=Bits(rms)−BCF
or
Formoredetailsaboutthesespecifications,refertoAppendixA.
Magnitude
Vp-p Vrms
mean (η)
a.
Time
Occurrences outside the crest factor limits
Occurrences outside the crest factor limits
Percentage of Crest Crest Factor Factor Occurrences where (CF) (BCF,bits) Peaks are Exceeded 2.6 3.3 3.9 4.4 4.9
1% 0.1% 0.01% 0.001% 0.0001%
2.38 2.72 2.96 3.14 3.29
b. Vp-p
Noise P-P volts = Noise rms * 2 * Crest Factor Noise P-P bits = Noiserms bits - Crest Factor in bits
c.
rms or one standard deviation ( σ)
Figure2.5:AsampleofanADC’soutputcanbecollectedintime(a)andtranslated intoahistogram(b)wherethemeanandstandarddeviationofthesamplescanbe calculated.Withthestandarddeviationofthesesamples,apeak-to-peakvaluecan bedetermined(c)withamultipleof2timesthecrestfactor(CF)foroutputsignal referredtoinputcalculationsoranadditivebitcrestfactor(BCF).
37
Chapter2 DCSpecificationsImplyAccuracy Ifyouarelookingforaconversionfromyourconverterthataccuratelyrepresentstheanalogvoltage,youshouldbelookingattheDCspecifications.TheDCspecificationsthatIam referringtoareoffsetvoltage,gainerror(orFSerror),differentialnonlinearity,andintegral nonlinearity.Ifyourconversionsarenotrepeatableasdiscussedinthe“ACSpecifications ImplyRepeatability”sectioninthischapter,thentheaccuracyofyourconverterisdeterminedbytheaverageofmultiplesamples.Inthisdiscussion,wearegoingtoassumethatthe converterisnoise-free. Whatdotheleastsignificantbit(LSB)specificationsmeanwhenyouarelookingatADCs? Onedayafellowengineertoldmethata12-bit,ConverterX(manufacturerwillremain unnamed)hadjust7usablebits.Soessentially,the12-bitconverterwasonlya7-bitconverter.Hebasedthisconclusiononthedevice’soffsetandgainspecifications.Themaximum specificationswere: Offseterror=±3LSB, Gainerror=±5LSB, Atfirstglance,Ithoughthewasright.Fromthelistabove,theworstspecificationisgain error(±5LSB).Applyingsimplemathematics,12-bitsofresolutionminusfiveisequalto 7-bits,right?WhywouldanADCmanufacturerintroducesuchadevice?Thegainerror specificationmotivatesmetopurchasealower-cost,8-bitconverter.However,thatdoesn’t seemright.Well,asitturnedout,itwasn’tright. Let’sstartoutbylookingatthedefinitionofLSB.Thinkofaserial12-bitconverter;it producesastringoftwelveonesorzeros.Typically,theconverter’sfirsttransmitteddigital bitistheMSB(orLSB+11).SomeconverterstransmittheLSBfirst.Wewillassume thattheMSBisfirstinthischapter.ThesecondbitisMSB–1(orLSB+10);thethirdbit isMSB–2(orLSB+9),andsoon.Attheendofthisstringofbits,theconverterfinally transmitsasMSB–11(orLSB). Theterminology,LSB,isveryspecific.Itdescribesthelastpositioninthedigitalstream.It alsorepresentsafractionofthefull-scaleinputrange.Fora12-bitconverter,theLSBvalue isequivalenttotheanalogfull-scaleinputrangedividedby212or4096.IfIputthisinterms ofrealnumbers,IhaveanLSBsizeof1mVwitha12-bitconverterthathasafull-scaleinput rangeof4.096V.However,themostinstructivedefinitionofLSBisthatitcanrepresentone codeoutofthe4096codespossible. Goingbacktothespecificationsandtranslatingthemintoa12-bitconverterthathasaninput FSRof4.096V: Offseterror=±3LSB=±3mV, Gainerror=±5LSB=±5mV, 38
TheBasicsBehindAnalog-to-DigitalConverters Thesespecificationsactuallyclaimthattheconvertercanhave(worstcase)an8mV(or 8code)errorintroducedthroughtheconversionprocess.Thisisnottosaythattheerroroccurs attheLSB,LSB–1,LSB–2,LSB–3,LSB–4,LSB–5,LSB–6andLSB–7positionsin theoutputbitstreamoftheconverter.TheerrorscanbeuptoeighttimesoneLSB,or8mV. Preciselystated,thetransferfunctionoftheconvertercouldhaveuptoeightcodesmissing outof4096codes.Thesecodeswillbemissingatthelowerorupperrangeofthecodes.For example,aconverterwithanerrorof+8LSB((+3LSBoffseterror)+(+5LSBgainerror)) willproducepossibleoutputcodesofzeroto4088.Thelostcodesarefrom4088upto4095. Thisisasmall,incrementalerrorof0.2%atfull-scale.Incontrast,aconverterwithanerrorof –3LSB((–3LSBoffseterror)–(–5LSBgainerror))willproducecodesfrom3upto4095. Thegainerrorinthissituationproducesanaccuracyproblem,notalossofcodes.Thelost codesare0,1,and2.Bothoftheseexamplesillustratetheworstpossiblescenario. Thedifferencebetweenthefirstmeasuredtransitionpointandthefirstidealtransitionpointis theoffsetvoltageoftheconverter.Iftheoffseterrorisknownitcaneasilybecalibratedoutof theconversioninhardwareorsoftwarebysubtractingtheoffsetfromeverycode.Gainerror (full-scaleerror)isthedifferencebetweentheidealslopefromzerotoFSandtheactualslope betweenthemeasuredzeropointandFS.Offseterrorsarezeroedoutwiththiserrorcalculation.GainerrorisanotherADCcharacteristicthatcanbecalibratedoutofthefinaldigital codefromtheconverter.Multiplyingthefinalconversionbyaconstantdoesthis.Although thiscalibrationispossible,thesoftwareoverheadmaybetoomuch.Typically,theoffset errorsandgainerrorsdonottrackthiscloselyinactualconverters. Thereal-lifeperformanceenhancementsduetoincrementalimprovementsinanADC’s offsetorgainspecificationsarenegligibletononexistent.Tosomedesigners,thisseemslike aboldassumption,ifprecisionisoneofthedesignobjectives.Itiseasytoimplementdigital calibrationalgorithmwithyourfirmware.However,moreimportantly,thefront-endamplification/signalconditioningsectionofthecircuittypicallyproduceshighererrorsthanthe converteritself. Thisdiscussionputsanewlightontheconclusionsreachedatthebeginningofthissection. Infact,the12-bitconverterasspecifiedabovehasanaccuracyofapproximately11.997bits. Thegoodnewsisthatamicroprocessorormicrocontrollercanremovethisoffsetandgain errorwithasimplecalibrationalgorithm. Differentialnonlinearity(DNL)isthemaximumdeviationincodewidthfromtheideal 1LSB(FS/2n)codewidth.Thedifferenceiscalculatedforeachtransition.Thisconverter characteristicisverydifficulttocalibrateout.Evenifyoutakethetimetomeasureone converterforthiserror,thenextconverterfromthesameproductfamilywillhaveaslightly differentDNLerrorfromcodetocode.Integralnonlinearity(INL)isthemaximumdeviationofatransitionpointfromthecorrespondingpointoftheidealtransfercurvewithoffset andgainerrorszeroed.TheINLperformanceofanADCisactuallyderivedfromDNLtests. 39
Chapter2 Onceagain,theINLerrorisdifficulttocalibrateoutofthefinalconversion,particularlyfrom part-to-partofaproductfamily. Formoredetailsaboutthesespecifications,seeAppendixA.
SuccessiveApproximationRegister(SAR)Converters TheSARADCaroseoutofindustrialapplicationrequirements.Thistriedbuttrueconverter solutionhasspreadacrossavarietyofapplicationsincludingprocesscontrol,medicaland earlieraudiosystems.Intheseapplications,8-to16-bitconversionresultswererequired. TheSARADCisnothingnewtothedataacquisitionworld.Inthe1970s,thestate-of-theartSARADCwastoutedasalowerpower,moreaccurateandlessexpensivedevice.These convertersutilizedR-2Rresistiveladdersintheirdesigninordertoachievethedifferential linearity,integrallinearity,offsetandgainspecifications.Theywereabletoachievethe promisedperformancebecauseofcarefulIClayoutpracticesandwaferlevelresistorlaser trimming.ThecoreofthisfirstgenerationSARADCsrequiredanexternalsample-and-hold circuitbutwasexclusivelybuiltusingabipolartransistorprocess.Thiswasagoodmarriage becausethebipolartechnologywasbestsuitedforlow-noiseandhigh-speedperformance.A goodexampleofthistypeofconverterwouldbetheindustrystandard,ADC700,manufacturedbyTexasInstruments. Intoday’sstandards,thishybridADCwouldbeconsideredtoopowerhungry.Thecurrent CMOSgenerationofSARshassucceededintakingovertheall-bipolarSAR.Thearchitectureofthisconverterusesacapacitiveredistributioninputsection,whichinherentlyincludes thesample/holdfunction.Thecapacitorarraysaremorecompactandmucheasiertomatch thantheoldernicromeR-2Rladdernetworks,whichusuallyrequiresanexternalsampleand-holdcircuitontheanalogfrontend.Thisnewchiptopologyhaslowerpoweroperation, higherfunctionalityandasmallerchipsize. Allthisisgoodnewstothesystemsdesignerwhoislookingforimprovedperformance, higherintegrationandanoverallexcellentcost/performanceratio.ThisgenerationofSAR convertersnotonlyincludesthesample-holdfunction,butalsodifferentialinputsandvoltagecontrolledgaincapabilitythroughthevoltagereferenceinputs.Sincetheintegratedcircuit designisimplementedprimarilywithcapacitorsratherthanresistors,thepowerdissipation andthechipsizeislowerthaneverachieved.TheSARconverteralsohastakenasteptowards increasedfunctionality.InpriorSARADCdesigns,thevoltagereferencecircuitcouldbe internalorexternal,butinallcaseswaslimitedinvoltagerange.Withthisnewtopology,the devicevoltagereferenceisusuallyexternalanditsrangeismuchwider.Thisgivesflexibility whenselectingthedesiredLSBsize.Asmentionedbefore,theLSBsizeofaconverteris:
LSB=FSR/2n wheren=numberofbits, andFSR=thevoltagereferencevoltage. 40
TheBasicsBehindAnalog-to-DigitalConverters Undernormalsingle-supplyconditions,thevoltagereferencewouldbeequalto5V.Ifthis isthecase,theLSBsizeofa12-bitconverterisequalto1.22mV(5V÷4096codes).Ifthe voltagereferencefortheconverterisequalto100mV,theLSBsizenowbecomes0.0244mV. Thisisa50×reductionintheLSBsize.Ifyouhaveaverycleanlayoutandvoltagereference, thistypeofchangecouldeliminateananaloggainstage. AfinaladvantageoftheCMOSversionoftheSARconverteristhatitispossibletointegrate thiscircuitontothemicrocontrollerorprocessorchip.Thisisnotfeasiblewiththebipolar SARconverterunlessyouproducedanexpensivemultichip,mixed-signalversion.
TheCMOSSARTopology TheCMOSSARADCisasamplingsystemthattakesonesampleforeveryconversion.The analoginputsignaltoaSARconverterfirstseesaswitchandacapacitivearray,asshownin Figure2.6.Theinputnodeconnectsacapacitivearrayononeside,andthenoninvertinginput toacomparatorontheother. CS
VIN S1
R SAMPLE (1 kΩ ) 16C
SCLK
Cap array is both the sample cap and a DAC 2C
C
C
S DOUT
Shift Register SC
+ _
S A R
1/2 V DD Control Logic V REF
V SS
Figure2.6:ThemoderndaySARconverterusesacapacitivearray attheanaloginput.Thiscapacitivearrayandtheremainderof thedeviceareeasilymanufacturedinCMOS,makingiteasyto integrateitwithmicrocontrollersormicroprocessors.
41
Chapter2 Whentheswitch(S1)isclosed,thevoltageinputsignalissampledontotheinternalcapacitive arrayoftheconverter.Afterthesamplingtimeiscompleted,S1isopenedandthebottomside oftheMSB(mostsignificantbit)capacitorisconnectedtoVREFwhiletheothercapacitorsare tiedtoVSS(orthesystemground).ThechargefromtheMSBcapacitorisredistributedamong theothercapacitors.Thechargeisdistributedacrossthecapacitorarray,andthenoninverting inputofthecomparatormovesupordownaccordingtothevoltagepresentedatitsinput. Thevoltageatthenoninvertinginputofthecomparator,withrespecttoVSS,isequalto (1/2VDD–VIN)+1/2VREF.Ifthisvoltageisgreaterthan1/2VDD,theMSBisequaltozero, whichistransmittedoutoftheserialport,andtheMSBcapacitorislefttiedtoVREF.The transmissionofallbitstotheserialportissynchronizedwithsystemclock(SCLK)through SDOUT(serialdataout).Ifthevoltageatthenoninvertinginputofthecomparatorislessthan 1/2VDD,theMSBcapacitorisconnectedtoVSSandanMSBbitequaltooneistransmittedout oftheserialport. AssoonastheMSBvalueisdetermined,theconverterstartstodeterminetheMSB–1value. ConnectingtheMSB–1capacitortoVREFwhiletheothercapacitorsaretiedtoVSS(exceptfor theMSBcapacitor)doesthis.NotethattheMSB–1capacitorisnotillustratedinFigure2.6, butitsvalueis8C.Withthischangeinthecapacitivearrayconnections,thevalueofthevoltageatthenoninvertinginputofthecomparatoris[1/2VDD–VIN]+1/2VREF(MSB)+1/4VREF. Nowthevoltageonthecapacitivearrayiscomparedtothevoltageattheinvertingoftheinput comparator,1/2VDD.Intheanalysisofthisbit,ifthisvoltageisgreaterthan1/2VDD,the MSB–1isequaltozero,whichistransmittedoutoftheserialport.Additionally,theMSB–1 capacitorislefttiedtoVREF.Ifthevoltageacrossthecapacitivearrayislessthan1/2VDD,the MSB–1bitisequaltoone.Thisbitvalueistransmittedoutthroughtheserialport.Oncethis isdonetheMSB–1capacitorisconnectedtoVSS.Thisprocessisrepeateduntilthecapacitive arrayisfullyutilized. Therearetwocriticalpointsduringtheconversiontime.Thefirstpointiswherethesampleis actuallyacquiredbytheconverter.Duringthistime,theinputsignalmustbestablewithin¼ ofanLSB.Otherwise,theconverterwillgiveanoutputthatislessthanaccurate.Thesecond criticalpointduringtheconversiontimeiswheretheconverterisfinishinguptheconversion. Atthisparticulartime,theconverterisconvertingtheLSB,whichrequiresthemostaccuracy. Generallyspeaking,itisgoodpracticetokeeptheconverter’spowersupplyandinputsignal asquietaspossibleduringtheentireconversion. Figure2.7showsanotherwayofthinkingabouttheSARconversionbylookingatthedigitalto-analogconverter(DAC)output.Inthisfigure,theinputissampledbetweentime(a)and (b).Startingattime(b),theanalogvoltageistestedagainsttheDACoutputvoltage,whichis nowequalto½FS.Iftheanaloginputvoltageishigherthan½FS,adigitaloutputcodeof “1”issentoutoftheserialdigitaloutput.Ifthechargefromtheanaloginputvoltageislower than½FS,adigitaloutputcodeof“0”issentoutoftheserialdigitaloutput.Inthiscase, theMSBvalueis“1”.ThecapacitivearrayisswitchedtotestMSB–1asdiscussedabove. 42
TheBasicsBehindAnalog-to-DigitalConverters Figure2.7:Anotherway oflookingattheSAR conversionprocessis toexaminetheinternal DACoutputofthe converter.Theconverter startsbyconvertingthe MSBoftheanaloginput signalandthensteps througheachbit.Each bitconversionistimed withthesystemclock.
Digital Output Code = 1010 FS
Bit = 0
3/4FS
Bit = 1 Bit = 0
Analog input
Bit = 1
VIN 1/2FS
TEST TEST TEST TEST MSB MSB –1MSB –2 LSB 1/4FS
0
a b DAC Output
c
d e Time (s)
f
g
Betweentime(c)and(d)theanaloginputchargeisnowcomparedto¾FS.IftheMSBwas foundtobea“0”theMSB–1bitwouldbecomparedto¼FS.Butasyoucanseeinthis case,withtheMSBequalto“1”,theMSB–1isdeterminedtoequal“0”.ThisprocesscontinuesuntilthefinalLSBcodeisdetermined.
InterfacingWiththeInputoftheSARConverter DrivinganyA/Dconvertercanbechallengingifallissuesandtrade-offsarenotwellunderstoodfromthebeginning.WiththeSARconverter,thesamplingspeedandsourceimpedance shouldbetakenintoconsiderationifthedeviceistobefullyutilized.Herewewilldiscuss theissuesthatsurroundtheSARconverter’sinputandconversiontoensurethattheconverter ishandledproperlyfromthebeginningofthedesignphase.Wearealsogoingtoreviewthe specificationsavailableinmostA/Dconverterdatasheets,andidentifytheimportantspecificationsfordrivingyourSAR.Fromthisdiscussion,techniqueswillbeexploredwhichcan beusedtosuccessfullydrivetheinputoftheSARA/Dconverter.SincemostSARapplicationsrequireanactivedrivingdeviceattheconverter’sinput,thefinalsubjectistoexplorethe impactofanoperationalamplifierontheanalog-to-digitalconversionintermsofDCaswell asACresponses.AtypicalsystemblockdiagramoftheSARconverterapplicationisshown inFigure2.8.SomecommonSARconvertersystemsaredataacquisitionsystems,transducerssensingcircuits,batterymonitoringapplicationsanddatalogging.Inallofthesesystems, DCspecificationsareimportant.Additionally,therequiredconversionrateisrelativelyfast Figure2.8:Aninputsignalto theSARconvertershouldbe bufferedtoreduceimpedance matchingproblemsandafilter toreducealiasingerrorsinthe converter.Theamplifierstage andfilterstageinthisdiagram canbecombined.
Input Signal Source
Amp
Filter
Analog to Digital Converter
Filter Output
43
DAC or PWM
Microcontroller Engine
Chapter2 (ascomparedtosigma-deltaconverters)andhavingalowernumberofbitsthatarereliably convertedisacceptable. FortheinputstageoftheconvertershowninFigure2.9,theinputsignalcouldbeAC,DCor both.Theoperationalamplifierisusedforgain,impedanceisolationanditsdrivecapability.A filterofsomesort(passiveoractive)isneededtoreducenoiseandtopreventaliasingerrors. AmodeloftheSARADCinternalinputsamplingmechanismisshowninFigure2.9.CriticalvaluesinthismodelareRS,CSAMPLEandRSWITCH.CSAMPLEisequivalenttothesummationof thecapacitivearrayshowninFigure2.6.Pincapacitanceandleakageerrorsareminimal.The externalsourceresistanceandsamplecapacitorcombineswithinternalswitchresistanceand internalsamplecapacitortoformanR/Cpair.ThisdistributedR/Cpairrequiresapproximately 9.5timeconstantstofullychargeto12-bitsovertemperature.TheMCP3201(fromMicrochip),12-bitADCrequires938nsectofullysampletheinputsignal,assumingRS 1 LSB
001
000
Narrow code, < 1 LSB Analog Input Voltage
A DNL error of zero would imply that every code was exactly 1 LSB wide A missing code means DNL = –1 LSB
FigureA.3:Thedifferentialnonlinearityisthedifference betweenanidealcodewidthandthemeasuredcodewidth.
EffectiveNumberofBits(ENOB)–TheunitsofmeasureforSINADisdBandtheunits ofmeasureforENOBsisbits.YoucanchangeSINADintoENOBwiththefollowing calculation: ENOB=(SINAD–1.76)/6.02 Full-ScaleInput(FS)–WithA/Dconvertersthisinputsignalisanalog.Thefull-scale inputvoltageisdeterminedbythevoltagereferencevaluethatisappliedtheconverter referencepin.Inmanycases,thefull-scaleinputrangeisequaltogroundtothevoltage referencevalue.Inothercases,thefull-scaleinputrangeisequaltogroundtotwicethe voltagereferencevalue.RefertospecificADCdatasheetfordetails. GainError(Full-ScaleError)–Thedifferencebetweentheidealslopebetweenzeroand fullscaleandtheactualslopebetweenthemeasuredzeropointandfullscale.Youzero outtheOffseterrorswiththiserrorcalculation.SeeFigureA.4. Full scale range = Difference Between the First and Last Code Transition Points
111 110 101
Digital Output 100 Code 011 010
Actual transfer function
Gain Error = Full-Scale Ideal transfer Error − Offset Error function
001
000
Ideal full scale range Actual full scale range
Gain Errors can be corrected in firmware
FigureA.4:Gainerroristhedifferencebetweentheideal gaincurveandtheactualgaincurvewithoffsetremoved.
323
AppendixA IdealA/DConverterTransferFunction–Ananalogvoltageismappedintoann-bitdigital valuewithnooffset,gain,orlinearityerrors.SeeFigureA.2. IdleTones–Causedbytheinteractionbetweenthesigma-deltaA/Dconvertermodulatorand digitalfilter.Idletonesusuallyoccurwith2ndordermodulatorsand3rdorderdigitalfilters. Theyalsooccuraroundananaloginputofzerovoltsplusorminustheconverter’soffset voltage.Asthenameimplies,idletonesappearasafrequencyintheoutputconversion withmultipleDCinputconversionsataconstantdatarate. IntegralNonlinearity(INL)–Themaximumdeviationofatransitionpointfromthe correspondingpointoftheidealtransfercurve,withoffsetandgainerrorszeroed.See FigureA.5.
111 110
Digital Output Code
101
Actual transfer function
INL = maximum deviation between an actual code transition point and its corresponding ideal transition point, after offset and gain error have been removed
INL < 0
100
Ideal transfer Positive INL means function transition(s) later than ideal
011 010
Negative INL means transition(s) earlier than ideal
001
000
INL < 0 Analog Input Voltage
FigureA.5:INListheaggregateofDNLerrorsandisequaltothe maximumdeviationforanidealA/Dconvertertransferfunction.
InternalBuffer–TheA/Dconverterinputhasahighimpedanceinputthat“isolates”the inputsignalfromtheconverter. LeastSignificantBit(LSB)–Theleastsignificantbitisthebitrepresentationofthesmallest analoginputsignalthatisconverted.Itisalsoreferredtothefurthestrightbitinabinary digitalword. Monotonic–Impliesthatanincrease(ordecrease)intheanalogvoltageinputwillalways producenochangeoranincrease(ordecrease)indigitalcode.Monotinicitydoesnot implytherearenomissingcodes.SeeFigureA.6. MostSignificantBit(MSB)–Themostsignificantbitisoftenthoughtasthefurthestleftbit inabinarydigitalword. NoMissingCode–Impliesthatanincrease(ordecrease)intheanalogvoltageinputwill alwaysincrease(ordecrease)indigitaloutputconvertercode.Aconverterwithnomissingcodeisalsomonotonic. 324
Analog-to-DigitalConverterSpecificationDefinitionsandFormulas 111 110
Non-monotonic
101
Digital Output 100 Code
If the Output Code Always Increases when the Input Increases the Device is called Monotonic
011 010 001
000 0
1/4 FS
1/2 FS
3/4 FS
Analog Input Voltage
FigureA.6:Thiscurveisnonmonotonicbecauseanincreasein theanalogvoltagecanproduceasmallerdigitaloutputcode.
Normal-ModeRejection–Theattenuationofaspecificfrequencythroughtheconversion process. NumberofConverterBits(n)–ThenumberofoutputcodesofanA/Dconverterproduces 2npossiblecodes. OffsetError–Thedifferencebetweenthefirstmeasuredtransitionpointandthefirstideal, transitionpoint.SeeFigureA.7.
111 110
Offset Error = Difference Between the Actual First Transition Point and Ideal First Transition Point.
Ideal transfer function
101
Digital Output 100 Code
1st code transition
011
Actual transfer function
010 001
Offset Errors can be corrected in Firmware
Offset Error
000 0
1/4 FS
1/2 FS
3/4 FS
FS
Analog Input Voltage
FigureA.7:OffseterroristhedifferencebetweenanIdeal 1stcodetransitionandameasured1stcodetransition.
QuantizationNoise–ThenoisethatanA/Dconvertergeneratesasaconsequenceofdividingtheinputsignalintodiscrete“buckets.”Thewidthofthese“buckets”isequaltothe LSBsizeoftheconverter.Thequantizationnoiseofaconverterdeterminesthemaximum signal-to-noiseratio(SNRIDEAL=6.02n+1.76dB). 325
AppendixA Resolution–ThenumberofpossibleoutputbitsanA/Dconvertercanproduceinone conversion. SampleandHold–Theanalogswitchedinputtoacircuitwithasampleandholdfunction open(samples)forashortdurationtocapture(hold)theanaloginputvoltage. SamplingTime–Thetimerequiredtoaccuratelysampleananaloginputsignal. SampleRate–Thespeedthataconvertercancontinuouslyconvertseveralconversions. Typicallyspecifiedassamplespersecond(sps)orHertz(Hz) SettlingTime(asitrelatestoSigma-DeltaA/DConverters)–Thesettlingtimeofthedigitalfilterinasigma-deltaA/Dconverterreflectstheorderofthedigitalfilterinternaltothe converter.This“time”isunit-lessandequaltothenumberoffilterstages. Signal-to-NoiseRatio(SNR)–Acalculatedvaluethatrepresentstheratioofsignalpowerto noisepower.TheidealSNRofanA/Dconverteris6.02n+1.76dB.Formoreinformation,refertoAppendixB(ReadingFFTs). Signal-to-NoiseRatioplusDistortion(SINADorSNR+D)–Thecalculatedcombinationof SNRandtotalharmonicdistortion(THD).SINADistheratiooftheRMSamplitudeof thefundamentalinputfrequencyoftheinputsignaltotheRMSsumofallotherspectral componentsbelowonehalfofthesamplingfrequency(excludingDC).Thetheoretical minimumforSINADisequaltotheSNRor6.02n+1.76dB.Formoreinformation, refertoAppendixB(ReadingFFTs). Single-EndedInputs–AnA/Dconverterthatisconfiguredforoneinputvoltagethatis referencedtoground. SpuriousFreeDynamicRange(SFDR)–ThedistanceindBonanFFTplotfromthe fundamentalinputsignaltothefirstspur.Formoreinformation,refertoAppendixB (ReadingFFTs). StraightBinaryCode–Withthelowestinputvoltage,thedigitalcountbeginswithallzeros andcountsupsequentiallyalloneswithafull-scaleinput.Straightbinaryisadigitalcodingschemeforunipolarvoltagesonly. SuccessiveApproximationRegisterConverter(SAR)–TheSARconverterusesacapacitivearrayattheanaloginput.Youcanmanufacturethiscapacitivearrayandthe remainderofthedeviceinaCMOSprocess,makingiteasytointegrateitwithmicrocontrollersormicroprocessors. ThroughputTime–Thetimerequiredfortheconvertertosample,acquire,digitize,and prepareforthenextconversion. TotalHarmonicDistortion(THD)–Thermssumofthepowersoftheharmoniccomponents(spurs)ratioedtotheinputsignalpower.Formoreinformation,refertoAppendixB (ReadingFFTs). 326
Analog-to-DigitalConverterSpecificationDefinitionsandFormulas
FigureA.8:Thestraight binarycode(alsoknownas unipolarstraightbinarycode) representationofzerovoltsis equaltoadigital(0000).The analogfull-scaleminusoneLSB digitalrepresentationisequal to(1111).Withthiscode,there isnodigitalrepresentationfor analogfull-scale.
Mediananalogvoltage(V) 0.9375FS(15/16FS) 0.875FS(14/16FS) 0.8125FS(13/16FS) 0.75FS(12/16FS) 0.6875FS(11/16FS) 0.625FS(10/16FS) 0.5625FS(9/16FS) 0.5FS(8/16FS) 0.4375FS(7/16FS) 0.375FS(6/16FS) 0.3125FS(5/16FS) 0.25FS(4/16FS) 0.75FS(3/16FS) 0.1875FS(2/16FS) 0.0625FS(1/16FS) 0
Digitalcode 1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
TotalUnadjustedError–Thesumofoffset,gain,andintegralnon-linearityerrors. TransitionPoint–Theanaloginputvoltageatwhichthedigitaloutputswitchesfromone codetothenext. Two’sComplement–SeeFigureA.9.
FigureA.9:Thetwo’scomplement (alsoknownasbinarytwo’s complement)representationof zerovoltsisalsoequaltoadigital (0000).Theanalogpositive full-scaleminusoneLSBdigital representationisequalto(0111) andtheanalognegativefull-scale representationis(1000).
MedianVoltage(V) 0.875FS(7/8FS) 0.75FS(6/8FS) 0.625FS(5/8FS) 0.5FS(4/8FS) 0.375FS(3/8FS) 0.25FS(2/8FS) 0.125FS(1/8FS) 0 –0.125FS(–1/8FS) –0.25FS(–2/8FS) –0.375FS(–3/8FS) –0.5FS(–4/8FS) –0.625FS(–5/8FS) –0.75FS(–6/8FS) –0.875FS(–7/8FS) –1FS
Code 0111 0110 0101 0100 0011 0010 0001 0000 1111 1110 1101 1100 1011 1010 1001 1000
UnipolarInputMode(Single-EndedInput)–Aninputrangethatonlyallowspositive analoginputsignals. 327
AppendixA VoltageReference(alsoknowasAnalogVoltageReference)–Theinputrange(VIN)and LSBsizedisdeterminedbythevoltagereference(VREF)totheconverter.Dependingon theconverter,VIN=VREForVIN=2VREF.LSB=VREF/2norLSB=2VREF/2n(were“n”is thenumberofbits).
328
APPENDIX
B ReadingFFTs
B
APPENDIX
ReadingFFTs YouwouldusethefastFouriertransform(FFT)tooltoevaluatetheacperformanceofdigitizingsystemsinthefrequencydomain.ThetheoryoftheFourierseriesissomewhatcomplex, buttheapplicationissimple.TheFouriertransformoperatesonthepremisethatyoucan reconstructanysignalorwaveformbyjustaddingtogetheroneormorepuresinewaveswith theirappropriateamplitude,frequency,andphase. Forexample,asquarewavecanbeconstructedfromtheFourierseries,sin(x)+1/3sin(3x) +1/5sin(5x)+1/7sin(7x).Theadditionofeachelementofthisseries,thefundamentalpure sinewave(sin(x)),beginstotransformintoasquarewave. a square wave can be made by adding..... the fundamental plus 1/3 of the third harmonic plus 1/5 of the fifth harmonic plus 1/7 of the seventh harmonic
FigureB.1:Youcanconstructasquarewaveusingafundamental sinewaveandaddingtheoddharmonicsofthatsinewave.
ReadingtheFFTPlot YougenerateanFFTplotbycollectingalargenumberofdigitalsamplesfromtheoutput oftheA/D,inaperiodicfashion.Typically,A/Dconvertermanufacturersuseasingletone, full-scaleanalogsignal,attheinputoftheA/Dconverter,fortheirtypicalperformancecurves fortheirspecificationsheets.Undertheseconditions,youexercisethefulldynamicrangeof theconverter.ThisdataisthenconvertedtotheplotshowninFigureB.2.Thefrequencyscale 331
Amplitude (dB)
AppendixB 0 –10 –20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 –130
VDD = VREF = 5 V FSAMPLE = 100 ksps FINPUT = 9.985 kHz 4096 points
A: Fundamental Input Signal Magnitude B: Headroom = –0.5 db C: Signal-to-Noise Ratio = 72 db D: Spurious Free Dynamic Range = 78.5 db E: Average Noise Floor = –107 db F: First Harmonic Magnitude = –79 db G: Second Harmonic Magnitude = –89 db
0
10000
20000
30000
40000
50000
Frequency (Hz)
FigureB.2:BasicelementsoftheFFTplotincludethefundamentalinputsignal(A), signalheadroom(B),signal-to-noiseratio(C),spurious-freedynamicrange(D)and theaveragenoisefloor(E).
ofthisplotisalwayslinear,fromzerotonyquist/2.WithFFTplots,thenyquistfrequencyis equaltothesamplingfrequencyoftheconverter. Themagnitudeaxisrangesfromzerodowntoanappropriatenegativevalue,dependingon thenumberofconverterbits,andthenumberofsamplesincludedintheFFTcalculation. Whenananaloginputsignalgeneratesafull-scaleoutputfromtheA/Dconverter,itwill appearaszerodBontheFFTplot.Anymagnitudelessthanfull-scalecaneasilybeconverted intothedigitalcoderepresentationwiththeseformulas:
DOUT=(2n-1)*10(MAGNITUDE/20) VOUTRTI=DOUT*FSR/2n
where,DOUTisadecimalrepresentationofthedigitaloutputcode.DOUTshouldbe roundedtothenearestinteger,
MAGNITUDEistakenfromtheFFTplotandisindB,
VOUTRTIisamathematicalcalculationthatconvertsDOUTintothesameunitsasthe analoginputvoltage.RTI=ReferredtoInput.Thisnumbershouldbeequivalenttotheanaloginputvoltage,VIN, nisthenumberofA/Dconverterbits, FSRistheanalogfull-scaleinputrangeinvolts
TherearefiveelementsofparticularinterestintheFFTplot,thatprovidesinsightintothe systemperformance.FigureB.2illustratesthesefiveelements.
332
ReadingFFTs
FundamentalInputSignal TheFFTplotinFigureB.2usestheoutputsignalofa12-bit,SAR,A/Dconverter.The12-bit converterhasasamplingfrequencyof75kHzwithaclockrateof1.2MHz.Theanaloginput signalis36kHz(FigureB.2(A)).Atotalof409612-bitwordsaretakenfromtheconverter togeneratethisplot.
InputSignalHeadroom InreferencetoFigureB.2,thehighestspur(A)representsthefundamentalinputsignalto theconverter.Thissignalexercisestheconverter’scodes.Inthiscase,theinputsignalis exercisingtheconverteroverasmuchofitsinputrangeaspossible.Theamplitudeofthe fundamentalfrequencyinfigureB.2is0.5dBor94.4%lowerthanfull-scale,givingheadroom(B)fortheconverter’soutput.Thisisdonetoinsurethattheconverterisnotoverdriven, whichwillcausesignalclipping.Ifsignalclippingoccurs,theFFTplotwillshowdistortion ofthatsignalintheformofspursatfrequenciesotherthanthefundamentalfrequency.
Signal-to-NoiseRatio AusefulwayofdeterminingnoiseinthecircuitoftheA/Dconverteriswiththesignal-tonoiseratio(C).Thesignal-to-noiseratio(SNR)isacalculatedvalue.Itistheratioofsignal powertonoisepower.ThetheoreticallimitofSNRisequalto6.02n+1.76dB,wherenis thenumberofbits.Anideal12-bitA/DconvertershouldhaveaSNRof74dB.Allspursand thenoisefloorareincludedintheFFTcalculation.
SNR=rmsSignal/rmsNoise =(LSB2n–1/√2)/(LSB√12) =6.02n+1.76dB
TheSNRoftheFFTcalculationisacombinationseveralnoisesources.Thepossiblenoise sourcesincludethequantizationerroroftheA/Dconverter,internalnoiseoftheA/Dconverter,noisefromthevoltagereference,differentialnon-linearityerrorsfromtheA/Dconverter andnoisefromthedrivingamplifier.
Spurious-FreeDynamicRange Thespurious-freedynamicrange(D)quantifiestheamountofdistortioninthesystem.The spurious-freedynamicrange(SFDR)isthedistancefromthefundamentalinputsignaltothe firstspur(indB).
333
AppendixB SpursresultingfromthenonlinearityoftheA/Dconverterwillappearasamultiple(b)ofthe inputsignal’sfrequency(fundamentalfrequency),i.e.,Asin(bx),unlesstheyarearesultof aliasing.Ifthespursarearesultofthealiasingphenomena,theyareequalto:
finterference=±(Kfsample-faliased)
wherefinterferenceisthecalculatedpossibilitiesofhighfrequencyinterference
Kinapositivewholenumber fsampleisthesamplingfrequencyoftheA/Dconverter faliasedthealiasedsignalthatappearsontheFFTgraph
Ingeneral,harmonicallyrelatedspurscomefromerrorsintheA/Dconverter.Nonharmonicallyrelatedspursarearesultofotherdevicesorexternalnoisesources. IftheA/Dconvertercreatesspurs,itisprobablethattheconverterhasadegreeofintegral nonlinearity.Thedrivingamplifierofthesignalsourcecanalsocreatethesespurs.The frequenciesofthesespursarenotrelatedtothefrequencyofthefundamentalfrequencyper theformulaabove.Ifthedrivingamplifieristheculprititmayhavecrossoverdistortion,be unabletodrivetheA/Dconverter,orbebandwidthlimited.Injectednoisecanalsocausethese spursfromotherplacesinthecircuit,suchasdigitalclocksourcesorthemainsfrequency.
AverageNoiseFloor Theaveragenoisefloor(E)inFigureB.2isacombinationofthenumberbitsandthenumberofpointsusedintheFFT.ItisnotareflectionoftheperformanceoftheA/Dconverter. RegardlessthenumberofbitsthattheA/Dconverterhas,thenumberofsamplesshouldbe chosensothatthenoisefloorisbelowanyspursofinterest.
AverageFFTNoiseFloor(dB)=6.02n+1.76dB+10log(3*M/(π*ENBW)),
whereMisthenumberofdatapointsintheFFT.
ENBWistheequivalentnoisebandwidthofthewindowfunction(seenext sectiononhowFFTsaregenerated) nisthenumberofbitsoftheA/Dconverter
AreasonablenumberofsamplesfortheFFTofa12-bitconverteris4096.
OtherSpecificationsfromtheFFT TherearetwootherspecificationofinterestthattheFFTcalculationsproduce;totalharmonic distortion(THD)andsignal-to-noiseplusdistortion(SINAD).THDisthermssumofthe powersoftheharmoniccomponents(spurs)ratioedtotheinputsignalpower.
THDrms=20log(sqrt((102ndHAR/20)2+(103rdHAR/20)2+(104thHAR/20)2+...))
334
ReadingFFTs Significantintegral,non-linearityerrorsoftheA/DconvertertypicallyappearintheTHD results.MostmanufacturersspecifyTHDbyincludingthefirstnineharmoniccomponentsin thiscalculation.
SINADisacalculatedcombinationofSNRandTHDwhere,
SINAD=–20log(sqrt(10–SNR/10+10+THD/10)
FFTAccuracy TheFFTcalculationisaneffectivetooltouseinthissituation.WithanFFT,youcanusethe appropriatenumberofsamplestocalculatefairlyreliableestimates.Thissamplesizeisassociatedwiththelevelof“accuracy”orbitsyouareinterestedinaccountingfor.Theformula belowwillgiveyougoodFFTresultsifthecorrectwindowisused:
FFTAccuracy(dB)=±4dB/(n√K) ;unitsindB FFTAccuracy(%)=±10(4/(20n√K))–1)×100% ;unitsis% Wherenisthenumberofbits andKisthenumberofdatapointaccumulatedfortheFFT
Withthisformula,youcandeterminehowmanysamplesyouwanttotakeasyouevaluateyourcircuitnoise.Forinstance,ifIcollect256samplesfromacircuitwitha12-bitA/D ConverterIcanonlyexpectanFFTaccuracyof0.021dBor0.24%.Theaccuracyofagood 12-bitconverterisequalto1/212or0.024%;10xbetter.Iwouldsaythat256samplesarenot enoughtomakegoodnoisedecisions!Amoresuitablesamplenumberwouldbe4096,which hasanFFTAccuracyof0.06%.Notethatthesquarerootofthenumberofsamples,K,will preventhugeaccuracygains.
Windowing Blackman/Harris–Bell-shapedwindow.Typicallyusedforharmonicanalysisofcontinuous timesignals.Tapersdataatendsofrecordtozero.Mainlobewidthiswidestcomparedto otherWindows.Haslowestadjacentsidelobesaswellaslowestfarthersidelobesfrom mainlobe. Hamming–Bell-shapedwindow.Typicallyusedforharmonicanalysisofcontinuoustime signals.Tapersdatatosmallervalues,butnotzero,atendsofrecord.Haslowerside lobesadjacenttomainlobethanHanningWindow. Hanning–Bell-shapedwindow.Typicallyusedforharmonicanalysisofcontinuoustime signals.Tapersdataatendsofrecordtozero.Sidelobesfartherfrommainlobearelower thanHammingwindow. Rectangular–Rectangularshapedwindow.Typicallyusedforimpulseresponsetesting. Equivalenttomultiplyingalldatarecordpointsbyone.Givesbestfrequencyresolution withnarrowestlobewidth.Amplitudeaccuracyerrorsoccuriffrequencyofobserved signalhasanon-integernumberofcyclesintheFFTtimerecord. 335
APPENDIX
C OpAmpSpecification DefinitionsandFormulas
C
APPENDIX
OpAmpSpecification DefinitionsandFormulas AbsoluteMaximumRatings–Maximumconditionswheretheamplifierwillfundamentally operateandnotexperienceshorttermorlongtermdamage.Amplifierspecificationsare notguaranteedundertheseconditions. Beta(β)–Thefeedbackfactorinaclosed-loopsystem.Insimplesystems,1/βistheinverse oftheclosed-loopgainoftheamplifiercircuitfromthenoninvertinginputtotheoutput. Betaisalsoaconstantusedtodescribebipolartransistors.Inthisinstancebetaisthegain factorthatdescribestherelationshipofthecollector,emitter,andbasecurrents.Inbipolar transistorsIC=IE+IBandIC=(1+β)*IB. Closed-loopOutputResistance–Approximatelyequalstheopen-loopoutputresistance dividedbythe1/betaoroneoverthefeedbackfactoroftheamplifiercircuit. Common-modeInputVoltageRange(VIN)–Seeinputvoltagerange. Common-modeRejectionRatio(CMRR)–Theratioofthedifferentialchangeinthe common-modevoltagetotheresultingchangesinoffsetvoltage.CMRR=20log (∆VCOMMON-MODEVOLTAGE/∆VOS).CMRRisindecibelsordB. Common-modeInputResistanceandCapacitance(ZCM,CCM–,RCM–,CCM+,RCM+)–The effectiveresistanceandcapacitancebetweeneachinputandground.SeeFigureC.1. FigureC.1:Thecommon-mode resistanceandcapacitanceonthe inputoftheamplifierisin-between theinputpinsandground.
–
VIN–
VDD
CCM– RCM– VOUT
+
VIN+ RCM+ CCM+
339
VSS
AppendixC DifferentialInputResistanceandCapacitance(ZDIFF,CDIFF,RDIFF)–Theeffectiveresistanceandcapacitancebetweenthetwoinputs.SeeFigureC.2. FigureC.2:Differentialinput impedanceistheeffective resistanceandcapacitance betweenthetwoinputpins oftheamplifier.
VIN–
VDD
– RCM–
VIN+
CCM–
+
VOUT VSS
FullPowerResponse–Themaximumfrequencyatwhichtheamplifiercanswingtothe open-loopgainratedoutputvoltagewithoutsignificantdistortion.Theamplifier’sslew ratelimitsthisperformancespecificationbyinsertingdistortionasthesignalfrequency increases.SeeFigureC.3. Full-Scale Output Voltage Swing (V)
5.5
VDD = 5V
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
1K
10K
100K
1M
10M
Frequency (Hz)
FigureC.3:Thefullpowerbandwidthofthis amplifierisapproximately75kHz.
GainBandwidthProduct(GBWP)–Theopen-loopgain(V/V)timesthefrequencyinthe regionwheretheopen-loopgainisattenuating20dB/decade.Foraunity-gain,stable amplifiertheGBWPisequaltothe0dBcrossingoftheopen-loopgaincurve. 340
OpAmpSpecificationDefinitionsandFormulas InputBiasCurrent(IIN–andIIN+)–Thecurrentflowinginoroutoftheinverting(VIN–)or noninverting(VIN+)inputterminalsofanoperationalamplifier.Thisbiascurrentoriginatesintheinputtransistor,gate,orESDcellstructures. InputNoise(CurrentandVoltage)–Thenoisethatprimarilyoriginatesintheinputstructureoftheamplifier.Inputnoiseisspecifiedacrossabandwidth.Theunitsofinputnoise isVrms,Vpeak-to-peak,ampsrms,orampspeak-to-peak. InputNoiseSpectralDensity(CurrentandVoltage)–Agraphicalrepresentationofthe culminationofspotnoiseacrossafrequencyspectrum.Thex-axisunitsareHz;they-axis unitsareV/√HzorAmps/√Hz.SeeFigureC.4. Input Voltage Noise Density (nV/√Hz)
10000 RL = 10kΩ
1000
100
10 0.1
1
10
100
1k
10k
100k
1M
Frequency (Hz)
FigureC.4:Agraphicalrepresentationofanamplifier voltagenoisedensityoverfrequency.
InputOffsetCurrent(IOS)–Thedifferencebetweenthetwoinputbiascurrentsor(IIN+−IIN–). InputOffsetCurrentDrift(IOS/TEMP)–Therateofchangeoftheinputbiascurrentwith temperature. InputOffsetVoltage(VOS)–ThedifferentialDCinputvoltagerequiredtoprovideazero outputvoltage. InputOffsetVoltageDrift(VOS/TEMP)–Therateofchangeoftheinputoffsetvoltage withtemperature. InputVoltageRange(VIN)–Themaximumandminimuminputvoltagesatwhichtheamplifierwilloperateinitslinearregionasdefinedbytheopen-loopgainspecification. OperatingTemperatureRange–Temperaturerangewheretheamplifierwilloperatebut notnecessarilymeetspecificationscalledoutinthetableofspecifications. 341
AppendixC Open-loopGain(AOL)–Themagnitudeofthegainoftheoperationalamplifierblock.OpenloopGainlessenswithincreasingfrequency.AOL=20log(∆VOUT/∆VOS).Theunitsof measureforOpen-loopgainisdBorvolts/volts. OutputResistance–SeeClosed-loopOutputResistanceandOpen-loopOutputResistance. OutputSwingBandwidth–SeeFullPowerResponse. OutputVoltageSwing(VOUT)–Themaximumandminimumoutputvoltagesthatunder specifiedloadconditions. PhaseMargin–Thephaseoftheopen-loopgainatits0dBcrossingplus180degrees,with respecttothenoninvertinginputoftheamplifier.Theoretically,aphasemargingreater thanzerodegreesindicatesastablesystem.Inpractice,aphasemarginmustbegreater thanorequalto45°. PowerSupplyCurrent(IDD)–SeeQuiescentCurrent. PowerSupplyRejectionRatio(PSRR)–Theratiothedifferenceoftwopower-supplysettingtothechangeinoffsetvoltage.PSRR=20log(∆VPOWERSUPPLY/∆VOS).PSRRreduces withincreasingfrequency. PowerSupplyVoltage–Allowablevoltagerangeforthepositivepowersupplyinreference tothenegativepowersupply. QuiescentCurrent(IDD)–Amountofcurrentthatwillbesourcedfromthepositivepower supplyorsinkedintothenegativepowersupplywithnoloadontheoutputofanamplifier. RatedOutput–SeeOutputVoltageSwing. SettlingTime–Givenastepinput,thetimerequiredfortheoutputvoltagetosettlewithina specifiedpercentageofitsfullvalue. StorageTemperatureRange–Maximumtemperaturerangeforstorageoftheoperational amplifier.Ifthetemperatureexceedsthisrange,damagetotheamplifiermayoccur. SpecifiedTemperatureRange–TemperatureRangewheretheamplifierwillmeetspecificationscalledoutinthetableofspecifications. Short-CircuitCurrent(ISC)–Whentheoutputisshortedmid-betweenthepowersupplythis isthemaximumoutputcurrent. SlewRate(SR)–Themaximumrateofchangeoftheoutputvoltage. SpotNoise–Noiseamplitudewithinabandwidthof1Hz. UnityGainBandwidth–ThefrequencyrangefromDCtothefrequencyatwhichtheopenloopgaincrossesunity.
342
Index Symbols .OPTION(.OP)statement,SPICE,175–78 1/fnoise,241,243–44,247
A absolutemaximumratings,339 acquisitiontime,321 activefilter,95,97–8,105–6,109,142–3,147–8, 312 ACinductionmotor,65,68,83–5,87 ADC accuracy,33–5,38–9,42,44–5,50,56,200 effectivenumberofbits(ENOB),35–7 effectiveresolution(ER),35–7 erroranalysis,203 full-scalerange(FSR),28 gainerror,31,35,38–9,46,56 inputrange,28–9,38 offseterror,31,35,38–9,46,56 repeatability,35,38 resolution,33–5,38,47,52–3,56,199–200, 202 settlingtime,57,58 signaltonoiseratio(SNR),34–6,52–3 signaltonoiseratioplusdistortion(SINAD), 35–6 throughputrate,33–4 Alexander,Bowersmacromodel,177 alkaline,212 amplifier designpitfalls,131 inputcapacitance,152 inputstage,138–41,144,148,150–1 outputdistortion,144–6 outputstage,146,148,152
analogfilter,4,8,10,14,20,70–1,73–81,83,88, 93–5,98,104–5,108,110,312 analogground(AGND),266,275–7,280,286 anti-alias,95,103,105,109–15 anti-aliasfilter,43–4,49,70–1,73–81,83,88,95, 142–3,147–8,238,258–9,286–8,310 approximationtypes,95,98 autorouter,277–8 averagenoisefloor,321,332,334
B batterychemistry,211–2 Bessel,95–6,98,100–3,110,112–3 beta(β)1/β,155–61,339 binarytwo’scomplement,29,31–2 bipolaramplifiers,121 bipolarinputmode,321 bipolartransistors,84 Blackman/Harriswindow,335 board capacitance,267–8 inductance,265,267,274 resistance,267,289 Bodeplot,152–3,156–7,161 Boltzman’sconstant,239 Boyle,Pedersonmacromodel,181 breadboard,294,304 brickwall,96 bridgesensor,11 broadbandnoise,243 Buck-SPC,215–6,219–20 bufferamplifier,121–4,140–2,148,150,162, 313 Butterworthfilter,95–6,98–101,110,112 bypasscapacitor,237–8,255–9,263–5,276, 286–7,289
343
Index
C CANbus,4–5 chargepump,213–6,219–24,228,239,250,252 Chebyshevfilter,95–6,98,100–1,110–2 clockstart-uptime,225–6 closed-loopamplifiersystem,154–5 closed-loopnoisegain,246 closed-loopoutputresistance,339 CMOSamplifiers,121,123,129,132 codewidth,321 common-modeinputresistanceandcapacitance (ZCM,CCM–,RCM–,CCM+,RCM+),245,339 common-modeinputvoltagerange(VIN),339 common-moderejection(CMR),322 common-moderejectionratio(CMRR),148–51, 339 comparator,187,194–7,199–202,204–7 componentslocation,263,267,284 conductednoise,233–4,238–9,252,254,259 constantcurrentsource,72–4,76,172–3 conversiontime,322 crestfactor,234–5,239,244 current-to-voltageconversion,122,128,310,313 currentreturnpath,277,280–2,285,288 cut-offfrequency,94–7,100,108–111
D DAC accuracy,189,192,194 resolution,189,192,194 datarate,322 DCoperatingpoint,175–6 dependentsources,179,182 devicenoise,233–4,238–9,249,252–4 differenceamplifier,122,126–7,129–30,313 differentialinput,28–9,33,40,50,321–2 differentialinputresistanceandcapacitance (ZDIFF,CDIFF,RDIFF),245,340 differentialnonlinearity(DNL),31,35,38–9,322 digital-to-analogconverter(DAC),188–90,193, 200–1,269–70,272–3 digitalcodeout,322 digitalfilter(decimation,FIR,IIR),11,13,47–8, 50–2,54,56–8,93–5,312 digitalground(DGND),275–8,280,286 digitalinterface,322
digitalpotentiometer,269–73 digitalsignalprocessor(DSP),84
E effectivenumberofbits(ENOB),35–7,323 effectiveresolution(ER),35–7 efficiency,213–7,219–23 electro-magneticinterference(EMI),213,221, 265–6,274,277,281,286,316 energydensity,212–3
F FastFourierTransform(FFT),190–1,293–4, 298–303,305,314,335 ferritebead,237,252,258–9 filterpassband,96–7,99–102,113–4 filterstopband,96,98,101–2,111 filtertransitionband,96,98,100–2,104 FIRfilter,95 floatingcurrentsource,131,173 full-scaleerror,323 full-scaleinput(FS),323 fullpowerresponse,340 fundamentalinputsignal,332–3
G gainbandwidthproduct(GBWP),8–11,105, 108–9,340 gainerror,31,35,38–9,46,56,323 GMIN,178 groundplane,266–7,275–7,280–2,284–6,288, 314,318 groundtrace,265–6,269,278,281
H Halleffectsensor,83,86,88 hammingwindow,335 hanningwindow,335 headroom,332–3 high-passfilter,93,105 histogram,295–6,301,314 hysteresis,194–6
I I/OgatesorI/Oports,187–8,190,199,207 idealA/Dconvertertransferfunction,324
344
Index idealopamp,120 idletones,324 IGBT,84 IIRfilter,95 independentsources,179 input-offsetdistortion,137–8,141–2,148 inputbiascurrent(IIN–andIIN+),341 inputcapacitance,amplifier,152 inputnoise(currentandvoltage),341 inputnoisespectraldensity(currentandvoltage), 341 inputoffsetcurrent(IOS),341 inputoffsetcurrentdrift(IOS/TEMP),341 inputoffsetvoltage(VOS),341 inputoffsetvoltagedrift(VOS/TEMP),341 inputstage,amplifier,138–41,144,148,150–1 inputvoltagenoise,237–8,243–4 inputvoltagerange(VIN),341 instrumentationamplifier,11–3,69–70,72, 79–80,129–30,140,142,236,238,241–3, 253–4,259,310 integralnonlinearity(INL),31,35,38–9,324 integratedsilicontemperaturesensor,66–7 internalbuffer,324 invertinggainamplifier,122,125
L leastsignificantbit(LSB),324 LEDdisplay,314,316 Li-Poly,212 Lithion-Ion,Li-Ion,211–3,221,223 lithium,212 load-cellcircuit,283,297,301,314,316 low-passfilter,70–1,73–81,83,88,93,95–97, 99–101,103–8,110–15,142–43,147–48, 189–94,200,238,258,259,312 lowdropoutregulator(LDO),213–4,217–22, 250–1,253–4
M macromodel,167,169–70,175–83 maximallyflat,98–9,101 mean,234–5 microcontrollerΣ−∆converter,194,199–201, 203,205–7 metaloxidesemiconductorfieldeffecttransistor
(MOSFET),68,83–6,216,218 monotonic,324 mostsignificantbit(MSB),324 motorcontrol,65,68,83–5,87 multimeter,293–5,314 multiplexer,95,99,112–3,162–3 multiplefeedbacklow-passfilter,108–9
N negativetemperaturecoefficient(NTC)thermistor,6–7 NiCd,212–3 NiMH,212–3 noise,28–9,31,33,35,312–4,317–8 noise-shapingfilter,50,52–3 noisestatistics,36–7 noninvertinggainamplifier,122,125–6 normal-moderejection,325 normaldistribution,234–5,237 nomissingcode,324 numberofconverterbits(n),325 Nyquist,94,103
O offseterror,31,35,38–9,46,56,325 offsetvoltage,138,140–1,144,148–51 open-loopgain(AOL),148,150,152–8,162, 246–7,342 operatingtemperaturerange,341 operationalamplifiernoise,243,247–9,253–4 optocoupler,83,87–8 opampinputstage,119,121,129 opampstability,16–9,173,175 oscilloscope,293–4,302,314 outputdistortion,144–6 outputresistance,342 outputstage,146,148,152 outputswingbandwidth,342 outputvoltageswing(VOUT),342 overshoot,97–9,101,103,112,114–5,159, 162–3
P parasiticcapacitance,168–9,174–5 passivefilter,95,105–6 peak-to-peaknoise,235,252
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Index perfboard,304 phasemargin,97,152,154,157–63,342 phaseshift,152,154,157–63 photodetector,sensing,diode,65,67,81–3,114 photodiodepre-amp,146–7 poles,95–101,106–8,112 powerconnectionplan,317 powermeter,8 powerplane,263,266,27–7,284–6,314 powersupplycurrent(IDD),342 powersupplyfilter,254,257–8 powersupplynoise,250,252,256–8 powersupplyrejectionratio(PSR)(PSRR), 148–51,342 powersupplytrace,26–6,284 powersupplyvoltage,342 pressuresensor,69,78–80,295–7,301 primarybatterycell,212 propagationdelay,97,115 pseudo-differentialinput,28 pulsefrequencymodulation(PFM),252 pulsewidthmodulation(PWM),252 pulsewidthmodulator(PWM),84–6,187–94 PWMdutycycle,188
Q quantizationnoise,325,333 quiescentcurrent,342
R radiatednoise,233–4,254 radio-frequencyinterference(RFI),277 randomnoise,234,239,298–9,301 ratedcapacity,212 ratedoutput,342 rectangularwindow,335 referred-to-input(RTI),243,247–8,251 referred-to-output(RTO),248 regulatedchargepump,219,228 repeatability,ADC,35,38 resistancetemperaturedetector(RTD)sensor, 66–8,72–7,95,109–10 resistornoise,239–42,253–4 resolution,326 resolution,ADC,33–5,38,47,52–3,56, 199–200,202
resolution,DAC,189,192,194 ripple,96,100–1,112 root-mean-square(rms),234–5,239–40,244,313 RS-232transmitter,316
S Sallen-keylow-passfilter,107–9 sampleandhold,326 samplerate,326 samplingtime,326 SARconverterlayout,274–6 SARconverter,311 secondarycell,212–3 settlingtime,57–8,162,326,342 short-circuitcurrent(ISC),342 sigma-deltaADC(Σ−∆),194,199–201,203, 205–7,311,313,322 sigma-deltaboardlayout,274,276–7 signal-to-noiseratio(SNR),34–6,52–3,249–50, 326,332–3 signal-to-noiseratioplusdistortion(SINADor SNR+D),35–6,326,334–5 single-endedinput,28–9,321,326–7 slewrate(SR),8,10–1,145,162,342 specifiedtemperaturerange,342 SPICEsimulation,241–2,248–9,313 spotnoise,342 spuriousfreedynamicrange(SFDR),326,332–3 stabilityanalysis,152,157 standarddeviation,234–5 starlayoutconfiguration,281–2 storagetemperaturerange,342 straightbinary,28–30,32 straightbinarycode,326–7 successiveapproximationregister(SAR) converter,311,326,333 summingamplifier,122,127–8,313 switched-capacitorfilter,70–1 switchedpowerconverter(SPC),213–6,219–22, 251–2
T temperaturesensors,66–7,69,72–3,76–7 thermistor,66–7,72 thermocouple,66–8 throughputrate,ADC,33–4
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Index throughputtime,326 timer,187,194,197,199–200 timedomain,300,303 totalharmonicdistortion(THD),326,334 totalunadjustederror(TUE),327 touchscreen,65,68–9 transimpedanceamplifier,17,121,146–7 transistorlevelmodel,170–1,179–82 transitionpoint,327 two’scomplement,327 two-clockstart-up,222,227 two-layerboard,277,289
unipolarstraightbinary,28–30,32 unitygainbandwidth,342
V voltagefolloweramplifier,122,140–2,148,150, 162 voltagereference,328
W wallcube,238,252,257,315 Wheatstonebridge,69,78 windowcomparator,187,196–7
U unipolarinputmode,327
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