Pelgrom М. / Пелгром М. - Analog-to-Digital Conversion / Аналого-цифровое преобразование [2010, PDF, ENG]

1 Introduction ................................ 1
1.1 About this Book ........................... 3
2 Components and Definitions ....................... 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 The z-transform ....................... 19
2.1.6 Statistics........................... 20
2.2 Resistivity .............................. 25
2.2.1 Temperature ......................... 28
2.2.2 VoltageandTemperatureCoefficient ............ 29
2.2.3 Measuring Resistance . ................... 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 Straight Wire Inductance .................. 38
2.3.4 SkinEffectandEddyCurrent ................ 40
2.3.5 Transformer ......................... 40
2.3.6 Capacitors .......................... 42
2.3.7 Energy in Capacitors . . ................... 43
2.3.8 PartialCharging ....................... 44
2.3.9 DigitalPowerConsumption................. 45
2.3.10 Coaxial Cable ........................ 45
2.4 Semiconductors ........................... 47
2.4.1 Semiconductor Resistivity .................. 48
2.4.2 VoltageandTemperatureCoefficient ............ 49
2.4.3 MatchingofResistors .................... 50
2.4.4 MOS Capacitance . . . ................... 51
2.4.5 Capacitance Between Layers ................ 54
2.4.6 VoltageandTemperatureCoefficient ............ 56
2.4.7 Matching of Capacitors ................... 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 Drain Voltage Influence ................... 69
2.5.4 Large Signal and Small Signal ............... 70
2.5.5 High-frequency Behavior .................. 71
2.5.6 Gate Leakage ........................ 73
2.5.7 TemperatureCoefficient................... 73
2.5.8 Noise............................. 75
2.5.9 Latch-up........................... 76
2.5.10 Enhancement and Depletion ................. 77
2.5.11 Models ............................ 78
2.6 Network Theory ........................... 79
2.6.1 Kirchhoff’s Laws . . . ................... 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-capacitor Circuits ................. 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 Source Follower .......................103
2.7.5 TheDifferentialPair.....................104
2.7.6 Degeneration .........................107
2.7.7 CurrentMirror........................107
2.7.8 DarlingtonPair........................109
2.7.9 Cascode and Regulated Cascode ..............110
2.7.10Single-stageAmplifier....................113
2.7.11 Miller Amplifier .......................114
2.7.12 Choosing the W/L Ratios in a Miller Opamp ........118
2.7.13 Dominant-pole Amplifier ..................119
2.7.14 Feedback in Electronic Circuits ...............120
2.7.15BiasCircuits.........................122
2.7.16 Oscillators ..........................123
3 Sampling .................................133
3.1 Sampling in Time and Frequency ..................133
3.1.1 Folding Back of Spectra ...................137
3.1.2 Sampling and Modulation ..................140
3.1.3 SamplingofNoise......................141
3.1.4 Jitter of the Sampling Pulse .................143
3.2 Time-discrete Filtering ........................146
3.2.1 FIR Filters ..........................146
3.2.2 Half-band Filters .......................151
3.2.3 Down Sample Filter . . ...................152
3.2.4 IIR Filters ..........................153
4 Sample and Hold .............................155
4.1 Track-and-Hold and Sample-and-Hold Circuits . . .........155
4.2 Artifacts ...............................159
4.3 Capacitor and Switch Implementations ...............160
4.3.1 Capacitor ...........................160
4.3.2 Switch Topologies . . . ...................161
4.3.3 BottomPlateSampling ...................164
4.3.4 The CMOS Bootstrap Technique ..............165
4.3.5 Buffer ............................167
4.4 Track-and-Hold Circuit Topologies .................168
4.4.1 Basic Configurations . . ...................168
4.4.2 Amplifying Track-and-Hold Circuit .............171
4.4.3 Correlated Double Sampling ................171
4.4.4 ABipolarExample .....................172
4.4.5 DistortionandNoise.....................173
5 Quantization ...............................175
5.1 Linearity . . .............................177
5.1.1 Integral Linearity . . . ...................177
5.1.2 Differential Linearity . ...................178
5.2 TheQuantizationError .......................180
5.2.1 One-bitQuantization ....................180
5.2.2 2–6bitQuantization.....................181
5.2.3 7-bit and Higher Quantization ................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 Reference Circuits ............................191
6.1 General Requirements ........................191
6.2 Bandgap Reference Circuits . . ...................192
6.2.1 Bipolar Bandgap Circuit ...................196
6.2.2 CMOS Bandgap Circuit ...................197
6.2.3 Low-voltage Bandgap Circuits ...............200
6.3 Alternative References ........................201
7 Digital-to-Analog Conversion ......................203
7.1 UnaryandBinaryRepresentation..................203
7.1.1 DigitalRepresentation....................205
7.1.2 PhysicalDomain.......................207
7.2 Digital-to-Analog Conversion Schemes ...............209
7.2.1 DAConversionintheVoltageDomain ...........209
7.2.2 R-2R Ladders ........................213
7.2.3 Digital-to-Analog Conversion in the Current Domain . . . 214
7.2.4 Semi-digital Filter/Converters ................220
7.2.5 DAConversionintheChargeDomain ...........221
7.2.6 DAConversionintheTimeDomain ............224
7.2.7 Class-DAmplifiers .....................227
7.3 Accuracy . . .............................227
7.3.1 Limits to Accuracy . . ...................227
7.4 Methods to Improve Accuracy . ...................231
7.4.1 CurrentCalibration .....................233
7.4.2 Dynamic Element Matching .................234
7.4.3 Data-weightedAveraging ..................235
7.5 Digital-to-AnalogConversion:ImplementationExamples .....239
7.5.1 Resistor Ladder Digital-to-Analog Converter ........239
7.5.2 CurrentDomainDigital-to-AnalogConversion.......242
7.5.3 AComparison........................243
7.5.4 An Algorithmic Charge-based Digital-to-Analog Converter 244
8 Analog-to-Digital Conversion ......................249
8.1 TheComparator ...........................251
8.1.1 The Dynamics of Transistor Comparator . .........253
8.1.2 Hysteresis ..........................254
8.1.3 Accuracy ...........................256
8.1.4 Metastability and Bit-Error Rate ..............258
8.1.5 Kick-back ..........................259
8.1.6 Comparator Schematics ...................260
8.1.7 Auto-zeroComparators ...................262
8.2 Full-flashConverters.........................264
8.2.1 Ladder Implementation ...................267
8.2.2 ComparatorYield ......................267
8.2.3 Decoder ...........................272
8.2.4 AveragingandInterpolation.................274
8.2.5 Technology Scaling for Full-flash Converters ........277
8.2.6 FoldingConverter ......................277
8.3 Sub-ranging Methods ........................280
8.4 PipelineConverters .........................284
8.4.1 Error Sources in Pipeline Converters . . . .........286
8.4.2 DigitalCalibration......................288
8.5 1.5BitPipelineAnalog-to-DigitalConverter ............289
8.5.1 DesignofaStage ......................291
8.5.2 Redundancy .........................293
8.5.3 PipelineVariants.......................294
8.6 Successive Approximation Converters ...............296
8.6.1 Charge-redistributionConversion..............298
8.6.2 AlgorithmicConverters ...................300
8.7 Linear Approximation Converters ..................304
8.8 Time-interleavingTime-discreteCircuits ..............305
8.9 AnImplementationExample ....................308
8.9.1 AnAuto-zeroComparator..................309
8.9.2 Full-flashAnalog-to-DigitalConverter ...........310
8.9.3 Successive-approximation Analog-to-Digital Converter . . 311
8.9.4 Multi-step Analog-to-Digital Converter . . .........312
8.9.5 AComparison........................313
8.10 Other Conversion Ideas .......................314
8.10.1Level-crossingAnalog-to-DigitalConversion........314
8.10.2 Asynchronous Conversion ..................315
8.10.3Time-relatedConversion...................316
8.10.4TheVernier/NoniusPrinciple ................318
8.10.5TheFloating-pointConverter ................318
9 Sigma-delta Modulation .........................321
9.1 Oversampling ............................321
9.2 Noise Shaping ............................325
9.3 Sigma-delta Modulation .......................329
9.3.1 Sigma-deltaDigital-to-AnalogConversion .........334
9.4 Time-discrete Sigma-delta Modulation ...............334
9.4.1 A First Order Modulator ...................334
9.4.2 A Second Order Modulator .................337
9.4.3 Cascaded Sigma-delta Modulator ..............339
9.5 Time-continuous Sigma-delta Modulation .............341
9.5.1 A First-order Modulator ...................341
9.5.2 Higher Order Sigma-delta Converters . . . .........345
9.5.3 Time-discrete and Time-continuous Sigma Delta
Conversion..........................348
9.6 Multi-bit Sigma-delta Conversion ..................350
9.7 Various Forms of Sigma-delta Modulation .............353
9.7.1 Complex Sigma-delta Modulation ..............353
9.7.2 Asynchronous Sigma-delta Modulation . . .........353
9.7.3 Input Feed-forward Modulator ...............354
9.7.4 Band-pass Sigma-delta Converter ..............355
9.7.5 Sigma Delta Loop with Noise-shaping . . .........356
9.7.6 IncrementalSigma-deltaConverter .............356
10 Characterization and Specification ...................359
10.1TheTestHardware..........................359
10.2 Measurement Methods ........................363
10.2.1INLandDNL ........................363
10.2.2HarmonicBehavior .....................365
10.3SelfTesting .............................368
11 Technology ................................369
11.1 Technology Roadmap ........................369
11.1.1 Power Supply and Signal Swing ...............370
11.1.2 Feature Size .........................371
11.1.3 Process Options .......................372
11.2 Variability: an Overview .......................373
11.3DeterministicOffsets ........................375
11.3.1 Offset Caused by Electrical Differences . . .........376
11.3.2 Offset Caused by Lithography ................377
11.3.3ProximityEffects ......................378
11.3.4TemperatureGradients....................380
11.3.5OffsetCausedbyStress ...................381
11.3.6 Offset Mitigation .......................385
11.4 Random Matching ..........................386
11.4.1 Random Fluctuations in Devices ..............386
11.4.2MOSThresholdMismatch .................389
11.4.3CurrentMismatchinStrongandWeakInversion......392
11.4.4MismatchforVariousProcesses...............394
11.4.5 Application to Other Components ..............396
11.4.6ModelingRemarks......................397
11.5 Consequences for Design . . . ...................398
11.5.1Analogdesign ........................398
11.5.2DigitalDesign........................399
11.5.3Drift .............................400
11.5.4 Limits of Power and Accuracy ...............401
11.6 Packaging . .............................403
11.7 Substrate Noise ...........................406
12 System Aspects of Conversion ......................413
12.1 System Aspects ...........................415
12.1.1 Specification of Functionality ................416
12.1.2 Signal Processing Strategy .................418
12.1.3 Input Circuits ........................420
12.1.4 Conversion of Modulated Signals ..............422
12.2ComparingConverters........................423
12.3LimitsofConversion ........................427
Exercises ....................................429
Bibliography ..................................433
1 Introduction ..........................433
2 Components and Definitions .................433
3 Sampling............................436
4 Sample-and-Hold .......................436
5 Quantization..........................437
6 Reference Circuits .......................437
7 Digital-to-AnalogConversion.................438
8 Analog-to-DigitalConversion.................440
9 Sigma-deltaConversion....................443
10 Characterization and Specification ..............444
11 PhysicalRestrictions .....................444
12 System Aspects ........................446
Index ......................................447