Analog-to-Digital Conversion (eBook)

Preface 5
Acknowledgments 6
Contents 8
List of Symbols 15
Reference Tables and Figures 17
Introduction 19
About this Book 21
Components and Definitions 22
Mathematical Tools 22
The Fourier Transform 26
Fourier Analysis 27
Distortion 30
Laplace Transform 32
The z-transform 36
Statistics 37
Resistivity 42
Temperature 45
Voltage and Temperature Coefficient 46
Measuring Resistance 46
Electromigration 47
Noise 48
Maxwell Equations 50
Inductors 54
Energy in a Coil 55
Straight Wire Inductance 55
Skin Effect and Eddy Current 57
Transformer 57
Capacitors 59
Energy in Capacitors 60
Partial Charging 61
Digital Power Consumption 62
Coaxial Cable 62
Semiconductors 64
Semiconductor Resistivity 65
Voltage and Temperature Coefficient 66
Matching of Resistors 67
MOS Capacitance 68
Capacitance Between Layers 71
Voltage and Temperature Coefficient 73
Matching of Capacitors 73
The pn-junction 73
The Bipolar Transistor 77
The MOS Transistor 79
Weak Inversion 83
Matching 85
Drain Voltage Influence 86
Large Signal and Small Signal 87
High-frequency Behavior 88
Gate Leakage 90
Temperature Coefficient 90
Noise 92
Latch-up 93
Enhancement and Depletion 94
Models 95
Network Theory 96
Kirchhoff's Laws 96
Two-port Networks 97
Energy and Power 98
Feedback 100
Opamps and OTAs 103
Differential Design 105
Switched-capacitor Circuits 107
Filters 109
Electronic Circuits 115
Classification of Amplifiers 115
One-transistor Amplifier 117
The Inverter 119
Source Follower 120
The Differential Pair 121
Degeneration 124
Current Mirror 124
Darlington Pair 126
Cascode and Regulated Cascode 127
Single-stage Amplifier 130
Miller Amplifier 131
Choosing the W/L Ratios in a Miller Opamp 135
Dominant-pole Amplifier 136
Feedback in Electronic Circuits 137
Bias Circuits 139
Oscillators 140
Sampling 150
Sampling in Time and Frequency 150
Folding Back of Spectra 154
Sampling and Modulation 157
Sampling of Noise 158
Jitter of the Sampling Pulse 160
Time-discrete Filtering 163
FIR Filters 163
Half-band Filters 168
Down Sample Filter 169
IIR Filters 170
Sample and Hold 172
Track-and-Hold and Sample-and-Hold Circuits 172
Artifacts 176
Capacitor and Switch Implementations 177
Capacitor 177
Switch Topologies 178
Bottom Plate Sampling 181
The CMOS Bootstrap Technique 182
Buffer 184
Track-and-Hold Circuit Topologies 185
Basic Configurations 185
Amplifying Track-and-Hold Circuit 188
Correlated Double Sampling 188
A Bipolar Example 189
Distortion and Noise 190
Quantization 192
Linearity 194
Integral Linearity 194
Differential Linearity 195
The Quantization Error 197
One-bit Quantization 197
2-6 bit Quantization 198
7-bit and Higher Quantization 200
Signal-to-Noise 201
Related Definitions 204
Non-uniform Quantization 204
Dither 205
DNL and SNR 206
Reference Circuits 208
General Requirements 208
Bandgap Reference Circuits 209
Bipolar Bandgap Circuit 213
CMOS Bandgap Circuit 214
Low-voltage Bandgap Circuits 217
Alternative References 218
Digital-to-Analog Conversion 220
Unary and Binary Representation 220
Digital Representation 222
Physical Domain 224
Digital-to-Analog Conversion Schemes 226
DA Conversion in the Voltage Domain 226
R-2R Ladders 230
Digital-to-Analog Conversion in the Current Domain 231
Semi-digital Filter/Converters 237
DA Conversion in the Charge Domain 238
DA Conversion in the Time Domain 241
Class-D Amplifiers 244
Accuracy 244
Limits to Accuracy 244
Methods to Improve Accuracy 248
Current Calibration 250
Dynamic Element Matching 251
Data-weighted Averaging 252
Digital-to-Analog Conversion: Implementation Examples 256
Resistor Ladder Digital-to-Analog Converter 256
Current Domain Digital-to-Analog Conversion 259
A Comparison 260
An Algorithmic Charge-based Digital-to-Analog Converter 261
Analog-to-Digital Conversion 265
The Comparator 267
The Dynamics of Transistor Comparator 269
Hysteresis 270
Accuracy 272
Metastability and Bit-Error Rate 274
Kick-back 275
Comparator Schematics 276
Auto-zero Comparators 278
Full-flash Converters 280
Ladder Implementation 283
Comparator Yield 283
Decoder 288
Averaging and Interpolation 290
Technology Scaling for Full-flash Converters 293
Folding Converter 293
Sub-ranging Methods 296
Pipeline Converters 300
Error Sources in Pipeline Converters 302
Digital Calibration 304
1.5 Bit Pipeline Analog-to-Digital Converter 305
Design of a Stage 307
Redundancy 309
Pipeline Variants 310
Successive Approximation Converters 312
Charge-redistribution Conversion 314
Algorithmic Converters 316
Linear Approximation Converters 320
Time-interleaving Time-discrete Circuits 321
An Implementation Example 324
An Auto-zero Comparator 325
Full-flash Analog-to-Digital Converter 326
Successive-approximation Analog-to-Digital Converter 327
Multi-step Analog-to-Digital Converter 328
A Comparison 329
Other Conversion Ideas 330
Level-crossing Analog-to-Digital Conversion 330
Asynchronous Conversion 331
Time-related Conversion 332
The Vernier/Nonius Principle 334
The Floating-point Converter 334
Sigma-delta Modulation 336
Oversampling 336
Noise Shaping 340
Sigma-delta Modulation 344
Sigma-delta Digital-to-Analog Conversion 349
Time-discrete Sigma-delta Modulation 349
A First Order Modulator 349
A Second Order Modulator 352
Cascaded Sigma-delta Modulator 354
Time-continuous Sigma-delta Modulation 356
A First-order Modulator 356
Higher Order Sigma-delta Converters 360
Time-discrete and Time-continuous Sigma Delta Conversion 363
Multi-bit Sigma-delta Conversion 365
Various Forms of Sigma-delta Modulation 368
Complex Sigma-delta Modulation 368
Asynchronous Sigma-delta Modulation 368
Input Feed-forward Modulator 369
Band-pass Sigma-delta Converter 370
Sigma Delta Loop with Noise-shaping 371
Incremental Sigma-delta Converter 371
Characterization and Specification 374
The Test Hardware 374
Measurement Methods 378
INL and DNL 378
Harmonic Behavior 380
Self Testing 383
Technology 384
Technology Roadmap 384
Power Supply and Signal Swing 385
Feature Size 386
Process Options 387
Variability: an Overview 388
Deterministic Offsets 390
Offset Caused by Electrical Differences 391
Offset Caused by Lithography 392
Proximity Effects 393
Temperature Gradients 395
Offset Caused by Stress 396
Offset Mitigation 400
Random Matching 401
Random Fluctuations in Devices 401
MOS Threshold Mismatch 404
Current Mismatch in Strong and Weak Inversion 407
Mismatch for Various Processes 409
Application to Other Components 411
Modeling Remarks 412
Consequences for Design 413
Analog design 413
Digital Design 414
Drift 415
Limits of Power and Accuracy 416
Packaging 418
Substrate Noise 421
System Aspects of Conversion 428
System Aspects 430
Specification of Functionality 431
Signal Processing Strategy 433
Input Circuits 435
Conversion of Modulated Signals 437
Comparing Converters 438
Limits of Conversion 442
Exercises 444
Bibliography 448
1 Introduction 448
2 Components and Definitions 448
3 Sampling 451
4 Sample-and-Hold 451
5 Quantization 452
6 Reference Circuits 452
7 Digital-to-Analog Conversion 453
8 Analog-to-Digital Conversion 455
9 Sigma-delta Conversion 458
10 Characterization and Specification 459
11 Physical Restrictions 459
12 System Aspects 461
Index 462