Analog-to-Digital Conversion

470 Pages·2010·16.36 MB·English

by  Marcel J.M. Pelgrom (auth.)

Analog-to-Digital Conversion
Marcel J.M. Pelgrom
Analog-to-Digital
Conversion
MarcelJ.M.Pelgrom
NXPSemiconductors
HTC-32
Eindhoven5656AE
TheNetherlands
[email protected]
Additionalmaterialtothisbookcanbedownloadedfromhttp://extra.springer.com.
ISBN978-90-481-8887-1 e-ISBN978-90-481-8888-8
DOI10.1007/978-90-481-8888-8
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2010930616
©SpringerScience+BusinessMediaB.V.2010
Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby
anymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten
permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose
ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.
Coverillustration:courtesyPhilipsSemiconductors
Coverdesign:eStudioCalamar
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
A book is like a window that allows you to look into the world. The window is
shapedbytheauthorandthatmakesthateverywindowpresentsauniqueviewof
the world. This is certainly true for this book. It is shaped by the topics and the
projects throughout my career. Even more so, this book reflects my own style of
workingandthinking.
ThatstartsalreadyinChap.2.WhenIjoinedPhilipsResearchin1979,manyof
mycolleaguesusedlittlepapernotebookstokeeptrackofthemostusedequations
andotherpracticalthings.ThisnotebookwasthebeginningforChap.2:acollection
oftopicsthatformthebasisformuchoftheotherchapters.Chapter2isnotintended
toexplainthesetopics,buttorefreshyourknowledgeandhelpyouwhenyouneed
somebasicstosolvemorecomplexissues.
Inthechaptersdiscussingthefundamentalprocessesofconversion,youwillrec-
ognizemypreoccupationwithmathematics.Ireallyenjoyfindinganequationthat
properly describes the underlying mechanism. Nevertheless mathematics is not a
goalonitsown:theequationshelptounderstandthewaythevariablesareconnected
totheresult.Realinsightcomesfromunderstandingthephysicsandelectronics.In
thechaptersoncircuitdesignIhavetriedtoreducethecircuitdiagramstothesim-
plest form, but not simpler... I do have private opinions on what works and what
should not be applied. Most poor solutions have simply been left out, sometimes
youmightreadawarninginthetextonacertainaspectofaninterestingcircuit.
Anotherofmyfavoritesisthesearchforaccuracy.InChap.11youwillfindade-
taileddescription,butalsointheearlierchapters,thereisalotofmaterialreferring
toaccuracy.
Circuitdesignandanalog-to-digitalcircuitdesignisaboutbridgingthegapbe-
tween technology and systems. Both aspects have been treated less than they de-
serve.StillIhopeitwillbesufficienttocreateaninteresttoprobefurther.
Thisbookisbasedonmylecturesforgraduatestudentswhoarenoviceinanalog-
to-digitaldesign.Intheclassesmyaimistobringthestudentstoalevelwherethey
canread and interpret theliterature (such as IEEE Journal of Solid-StateCircuits)
andjudgethereportedresultsontheirmerits.Stillthatleavesaknowledgegapwith
thedesignerofanalog-to-digitalconverters.Forthosedesignersthisbookmayserve
asareferenceofprinciplesandbackground.
v
vi Preface
Inevitablythisbookhassomestrongpointsbutalsoweakpoints.Therearestill
so many wonderful ideas, that are not addressed here but certainly would deserve
some space, but simply did not fit in this volume. Still I hope this book will let
you experience the same thrill that all analog-to-digital designers feel, when they
talkabouttheirpassion.Becausethatisthegoalofthisbook:toencourageyouto
proceedontheroutetowardsevenbetteranalog-to-digitalconverters.
Acknowledgments
Archimedessaid:“GivemeonefixedpointandIwillmovetheEarth”.Homehas
always served for me as the fixed point from which I could move forward in my
work. I owe my wife Elisabeth a debt of gratitude for creating a wonderful home.
She herself was once part of this semiconductor world and understands its crazy
habits.Yet,theencouragementandsupportshegavemeisinvaluable.
Thisbookreflectspartsofmy30yearsofworkinthePhilipsNatuurkundigLab-
oratorium and its successor. If there is anything I would call “luck” in my life, it
wastheopportunitytoworkinthisplace.Thecreativity,energy,opportunities,and
peopleinthislaboratoryareunique.Itisnottrivialtocreatesuchresearchfreedom
inafinanciallydrivenindustry.Mysevenyearsasamixed-signaldepartmenthead
havetaughtmethat.ThereforeIamtrulygratefultothosewhoservedintheman-
agement of Philips Research and backed me when working on things outside the
projectscopeorlookinginunusualdirections.Justnaminghere:TheovanKessel,
KeesWouda,GerardBeenker,HansRijnsandLeoWarmerdam.
Alaboratoryisjustasgoodasthepeoplethatworkinit.InmycareerImetalot
ofextraordinarypeople.Theyformedandshapedmywayofthinkingandanalyz-
ingproblems.Theychallengedmyideas,tookthetimetolistentomyreasoningand
pointedmeinpromisingdirections.Iamgratefulforbeingabletousetheinsights
andresultsoftheMixed-signalcircuitsandsystemsgroup.Withouttheusefuldis-
cussions and critical comments of the members of this group this book would not
exist.However,therearemanymorecolleaguesthathavecontributedinsomeform.
Withouttheillusionofbeingcomplete,Iwanttoexpressmygratitudeforapleasant
collaborationwith:CarelDijkmans,RudyvanderPlassche,EduardStikvoort,Rob
vanderGrift,ArthurvanRoermund,ErikvanderZwan,PeterNuijten,EdvanTu-
ijl, Maarten Vertregt, Pieter Vorenkamp, Johan Verdaasdonk, Anton Welbers, Aad
Duimaijer,JeannetvanRens,KlaasBult,GovertGeelen,StephaneBarbu,Laurent
Giry, Robert Meyer, Othmar Pfarkircher, Ray Speer, John Jennings, Joost Briaire,
RafRoovers,LucienBreems,RobertvanVeldhoven,KathleenPhilips,BramNauta,
Hendrik van der Ploeg, Kostas Doris, Erwin Janssen, Robert Rutten, Violeta Pe-
trescu,HarryVeendrick,HansTuinhout,JanvanderLinde,PetervanLeeuwenand
manyothers.
ThisbookisbasedonthelecturesinthePhilipsCenterforTechnicalTraining,
at universities and in the MEAD/EPFL courses. I want to thank prof. Bram Nauta
and prof. Kofi Makinwa for giving me the opportunity to teach at the universities
of Twente and Delft, prof. Bruce Wooley and prof. Boris Murmann of Stanford
Preface vii
University for their collaboration, prof. Gabor Temes and dr. Vlado Valence for
invitingmetolectureintheMEADandEPFLcourses.
Aspecialwordofthanksgoestoallthestudentsfortheirquestions,remarksand
stimulatingdiscussions.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 AboutthisBook . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 ComponentsandDefinitions . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 MathematicalTools . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 TheFourierTransform. . . . . . . . . . . . . . . . . . . . 9
2.1.2 FourierAnalysis . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 LaplaceTransform . . . . . . . . . . . . . . . . . . . . . . 15
2.1.5 Thez-transform . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.6 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.2 VoltageandTemperatureCoefficient . . . . . . . . . . . . 29
2.2.3 MeasuringResistance . . . . . . . . . . . . . . . . . . . . 29
2.2.4 Electromigration . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.5 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 MaxwellEquations . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.2 EnergyinaCoil . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.3 StraightWireInductance . . . . . . . . . . . . . . . . . . 38
2.3.4 SkinEffectandEddyCurrent . . . . . . . . . . . . . . . . 40
2.3.5 Transformer . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.6 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.7 EnergyinCapacitors. . . . . . . . . . . . . . . . . . . . . 43
2.3.8 PartialCharging . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.9 DigitalPowerConsumption . . . . . . . . . . . . . . . . . 45
2.3.10 CoaxialCable . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 SemiconductorResistivity . . . . . . . . . . . . . . . . . . 48
2.4.2 VoltageandTemperatureCoefficient . . . . . . . . . . . . 49
ix
x Contents
2.4.3 MatchingofResistors . . . . . . . . . . . . . . . . . . . . 50
2.4.4 MOSCapacitance . . . . . . . . . . . . . . . . . . . . . . 51
2.4.5 CapacitanceBetweenLayers . . . . . . . . . . . . . . . . 54
2.4.6 VoltageandTemperatureCoefficient . . . . . . . . . . . . 56
2.4.7 MatchingofCapacitors . . . . . . . . . . . . . . . . . . . 56
2.4.8 Thepn-junction . . . . . . . . . . . . . . . . . . . . . . . 56
2.4.9 TheBipolarTransistor . . . . . . . . . . . . . . . . . . . . 60
2.5 TheMOSTransistor . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.5.1 WeakInversion . . . . . . . . . . . . . . . . . . . . . . . 66
2.5.2 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.5.3 DrainVoltageInfluence . . . . . . . . . . . . . . . . . . . 69
2.5.4 LargeSignalandSmallSignal . . . . . . . . . . . . . . . 70
2.5.5 High-frequencyBehavior . . . . . . . . . . . . . . . . . . 71
2.5.6 GateLeakage . . . . . . . . . . . . . . . . . . . . . . . . 73
2.5.7 TemperatureCoefficient . . . . . . . . . . . . . . . . . . . 73
2.5.8 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.9 Latch-up . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.5.10 EnhancementandDepletion . . . . . . . . . . . . . . . . . 77
2.5.11 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.6 NetworkTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.6.1 Kirchhoff’sLaws . . . . . . . . . . . . . . . . . . . . . . 79
2.6.2 Two-portNetworks . . . . . . . . . . . . . . . . . . . . . 80
2.6.3 EnergyandPower . . . . . . . . . . . . . . . . . . . . . . 81
2.6.4 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.6.5 OpampsandOTAs . . . . . . . . . . . . . . . . . . . . . . 86
2.6.6 DifferentialDesign . . . . . . . . . . . . . . . . . . . . . 88
2.6.7 Switched-capacitorCircuits . . . . . . . . . . . . . . . . . 90
2.6.8 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.7 ElectronicCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.7.1 ClassificationofAmplifiers . . . . . . . . . . . . . . . . . 98
2.7.2 One-transistorAmplifier . . . . . . . . . . . . . . . . . . . 100
2.7.3 TheInverter . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.7.4 SourceFollower . . . . . . . . . . . . . . . . . . . . . . . 103
2.7.5 TheDifferentialPair . . . . . . . . . . . . . . . . . . . . . 104
2.7.6 Degeneration . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.7.7 CurrentMirror . . . . . . . . . . . . . . . . . . . . . . . . 107
2.7.8 DarlingtonPair. . . . . . . . . . . . . . . . . . . . . . . . 109
2.7.9 CascodeandRegulatedCascode . . . . . . . . . . . . . . 110
2.7.10 Single-stageAmplifier . . . . . . . . . . . . . . . . . . . . 113
2.7.11 MillerAmplifier . . . . . . . . . . . . . . . . . . . . . . . 114
2.7.12 ChoosingtheW/LRatiosinaMillerOpamp. . . . . . . . 118
2.7.13 Dominant-poleAmplifier . . . . . . . . . . . . . . . . . . 119
2.7.14 FeedbackinElectronicCircuits . . . . . . . . . . . . . . . 120
2.7.15 BiasCircuits . . . . . . . . . . . . . . . . . . . . . . . . . 122
2.7.16 Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Contents xi
3 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.1 SamplinginTimeandFrequency . . . . . . . . . . . . . . . . . . 133
3.1.1 FoldingBackofSpectra . . . . . . . . . . . . . . . . . . . 137
3.1.2 SamplingandModulation . . . . . . . . . . . . . . . . . . 140
3.1.3 SamplingofNoise . . . . . . . . . . . . . . . . . . . . . . 141
3.1.4 JitteroftheSamplingPulse . . . . . . . . . . . . . . . . . 143
3.2 Time-discreteFiltering. . . . . . . . . . . . . . . . . . . . . . . . 146
3.2.1 FIRFilters . . . . . . . . . . . . . . . . . . . . . . . . . . 146
3.2.2 Half-bandFilters . . . . . . . . . . . . . . . . . . . . . . . 151
3.2.3 DownSampleFilter . . . . . . . . . . . . . . . . . . . . . 152
3.2.4 IIRFilters . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4 SampleandHold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.1 Track-and-HoldandSample-and-HoldCircuits . . . . . . . . . . . 155
4.2 Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.3 CapacitorandSwitchImplementations . . . . . . . . . . . . . . . 160
4.3.1 Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
4.3.2 SwitchTopologies . . . . . . . . . . . . . . . . . . . . . . 161
4.3.3 BottomPlateSampling . . . . . . . . . . . . . . . . . . . 164
4.3.4 TheCMOSBootstrapTechnique . . . . . . . . . . . . . . 165
4.3.5 Buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
4.4 Track-and-HoldCircuitTopologies . . . . . . . . . . . . . . . . . 168
4.4.1 BasicConfigurations. . . . . . . . . . . . . . . . . . . . . 168
4.4.2 AmplifyingTrack-and-HoldCircuit . . . . . . . . . . . . . 171
4.4.3 CorrelatedDoubleSampling . . . . . . . . . . . . . . . . 171
4.4.4 ABipolarExample . . . . . . . . . . . . . . . . . . . . . 172
4.4.5 DistortionandNoise . . . . . . . . . . . . . . . . . . . . . 173
5 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.1 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.1.1 IntegralLinearity . . . . . . . . . . . . . . . . . . . . . . 177
5.1.2 DifferentialLinearity . . . . . . . . . . . . . . . . . . . . 178
5.2 TheQuantizationError . . . . . . . . . . . . . . . . . . . . . . . 180
5.2.1 One-bitQuantization . . . . . . . . . . . . . . . . . . . . 180
5.2.2 2–6bitQuantization . . . . . . . . . . . . . . . . . . . . . 181
5.2.3 7-bitandHigherQuantization . . . . . . . . . . . . . . . . 183
5.3 Signal-to-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.3.1 RelatedDefinitions . . . . . . . . . . . . . . . . . . . . . 187
5.3.2 Non-uniformQuantization. . . . . . . . . . . . . . . . . . 187
5.3.3 Dither . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.3.4 DNLandSNR . . . . . . . . . . . . . . . . . . . . . . . . 189
6 ReferenceCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.1 GeneralRequirements . . . . . . . . . . . . . . . . . . . . . . . . 191
6.2 BandgapReferenceCircuits . . . . . . . . . . . . . . . . . . . . . 192
6.2.1 BipolarBandgapCircuit . . . . . . . . . . . . . . . . . . . 196