Understanding Delta-Sigma Data Converters

1 The Magic of Delta-Sigma Modulation 1

1.1 The Need for Oversampling Converters 1

1.2 Nyquist and Oversampling Conversion by Example 3

1.3 Higher-Order Single-Stage Noise-Shaping Modulators 11

1.4 Multi-Stage and Multi-Quantizer Delta-Sigma Modulators 12

1.5 Mismatch Shaping in Multi-Bit Delta-Sigma Modulators 14

1.6 Continuous-Time Delta-Sigma Modulation 15

1.7 Bandpass Delta-Sigma Modulators 17

1.8 Incremental Delta-Sigma Converters 18

1.9 Delta-Sigma Digital-to-Analog Converters 18

1.10 Decimation and Interpolation 19

1.11 Specifications and Figures of Merit 19

1.12 Early History, Performance, and Architectural Trends 21

References 25

2 Sampling, Oversampling, and Noise-Shaping 27

2.1 A Review of Sampling 28

2.2 Quantization 30

2.3 Quantization Noise Reduction by Oversampling 39

2.4 Noise-Shaping 42

2.5 Nonlinear Aspects of the First-Order Delta-Sigma Modulator 52

2.6 MOD1 with DC Excitation 54

2.7 Alternative Architectures: The Error-Feedback Structure 60

2.8 The Road Ahead 60

References 61

3 Second-Order Delta-Sigma Modulation 63

3.1 Simulation of MOD2 67

3.2 Nonlinear Effects in MOD2 70

3.3 Stability of MOD2 73

3.4 Alternative Second-Order Modulator Structures 77

3.5 Generalized Second-Order Structures 80

3.6 Conclusions 82

References 82

4 High-Order Delta-Sigma Modulators 83

4.1 Signal-Dependent Stability of Delta-Sigma Modulators 85

4.2 Improving MSA in High-Order Delta-Sigma Converters 92

4.3 Systematic NTF Design 95

4.4 Noise Transfer Functions with Optimally Spread Zeros 97

4.5 Fundamental Aspects of Noise Transfer Functions 98

4.6 High-Order Single-Bit Delta-Sigma Data Converters 100

4.7 Loop Filter Topologies for Discrete-Time Delta-Sigma Converters 104

4.8 State-Space Description of Delta-Sigma Loops 114

4.9 Conclusions 115

References 115

5 Multi-Stage and Multi-Quantizer Delta-Sigma Modulators 117

5.1 Multi-Stage Modulators 117

5.2 Cascade (MASH) Modulators 120

5.3 Noise Leakage in Cascade Modulators 123

5.4 The Sturdy-MASH Architecture 126

5.5 Noise-Coupled Architectures 128

5.6 Cross-Coupled Architectures 131

5.7 Conclusions 131

References 133

6 Mismatch-Shaping 135

6.1 The Mismatch Problem 135

6.2 Random Selection and Rotation 136

6.3 Implementation of Rotation 141

6.4 Alternative Mismatch-Shaping Topologies 145

6.5 High-Order Mismatch-Shaping 151

6.6 Generalizations 156

6.7 Transition-Error Shaping 158

6.8 Conclusions 162

References 162

7 Circuit Design for Discrete-Time Delta-Sigma ADCs 165

7.1 SCMOD2: A Second-Order Switched-Capacitor ADC 165

7.2 High-Level Design 166

7.3 Switched-Capacitor Integrator 168

7.4 Capacitor Sizing 174

7.5 Initial Verification 176

7.6 Amplifier Design 178

7.7 Intermediate Verification 186

7.8 Switch Design 191

7.9 Comparator Design 191

7.10 Clocking 195

7.11 Full-System Verification 197

7.12 High-Order Modulators 201

7.13 Multi-Bit Quantization 203

7.14 Switch Design Revisited 207

7.15 Double Sampling 209

7.16 Gain-Boosting and Gain-Squaring 211

7.17 Split-Steering and Amplifier Stacking 212

7.18 Noise in Switched-Capacitor Circuits 217

7.19 Conclusions 221

References 221

8 Continuous-Time Delta-Sigma Modulation 223

8.1 CT-MOD1 224

8.2 STF of CT-MOD1 230

8.3 Second-Order Continuous-Time Delta-Sigma Modulation 234

8.4 High-Order Continuous-Time Delta-Sigma Modulators 239

8.5 Loop-Filter Topologies 246

8.6 Continuous-Time Delta-Sigma Modulators with Complex NTF Zeros 249

8.7 Modeling of Continuous-Time Delta-Sigma Modulators for Simulation 250

8.8 Dynamic-Range Scaling 253

8.9 Design Example 255

8.10 Conclusions 258

References 258

9 Nonidealities in Continuous-Time Delta-Sigma Modulators 259

9.1 Excess Loop Delay 259

9.2 Time-Constant Variations of the Loop Filter 271

9.3 Clock Jitter in Delta-Sigma Modulators 273

9.4 Addressing Clock Jitter in Continuous-Time Delta-Sigma Modulators 285

9.5 Mitigating Clock Jitter Using FIR Feedback 287

9.6 Comparator Metastability 293

9.7 Conclusions 298

References 298

10 Circuit Design for Continuous-Time Delta-Sigma Modulators 301

10.1 Integrators 302

10.2 The Miller-Compensated OTA-RC Integrator 305

10.3 The Feedforward-Compensated OTA-RC Integrator 306

10.4 Stability of Feedforward Amplifiers 309

10.5 Device Noise in Continuous-Time Delta-Sigma Modulators 312

10.6 ADC Design 316

10.7 Feedback DAC Design 320

10.8 Systematic Design Centering 331

10.9 Loop-Filter Nonlinearities in Continuous-Time Delta-Sigma Modulators 338

10.10 Case Study of a 16-Bit Audio Continuous-Time Delta-Sigma Modulator346

10.11 Measurement Results 358

10.12 Summary 359

References 360

11 Bandpass and Quadrature Delta-Sigma Modulation 363

11.1 The Need for Bandpass Conversion 363

11.2 System Overview 366

11.3 Bandpass NTFs 367

11.4 Architectures for Bandpass Delta-Sigma Modulators 372

11.5 Bandpass Modulator Example 380

11.6 Quadrature Signals 391

11.7 Quadrature Modulation 396

11.8 Polyphase Signal Processing 402

11.9 Conclusions 404

References 405

12 Incremental Analog-to-Digital Converters 407

12.1 Motivation and Trade-Offs 407

12.2 Analysis and Design of Single-Stage IADCs 408

12.3 Digital Filter Design for Single-Stage IADCs 411

12.4 Multiple-Stage IADCs and Extended Counting ADCs 415

12.5 IADC Design Examples 416

12.6 Conclusions 422

References 423

13 Delta-Sigma DACs 425

13.1 System Architectures for Delta-Sigma DACs 425

13.2 Loop Configurations for Delta-Sigma DACs 427

13.3 Delta-Sigma DACs Using Multi-Bit Internal DACs 431

13.4 Interpolation Filtering for Delta-Sigma DACs 438

13.5 Analog Post-Filters for Delta-Sigma DACs 441

13.6 Conclusions 449

References 449

14 Interpolation and Decimation Filters 451

14.1 Interpolation Filtering 452

14.2 Example Interpolation Filter 456

14.3 Decimation Filtering 461

14.4 Example Decimation Filter 463

14.5 Halfband Filters 467

14.5.1 Saramäki Halfband Filter 469

14.6 Decimation for Bandpass Delta-Sigma ADCs 471

14.7 Fractional Rate Conversion 472

14.8 Summary 480

References 480

A Spectral Estimation 483

A.1 Windowing 484

A.2 Scaling and Noise Bandwidth 488

A.3 Averaging 491

A.4 An Example 493

A.5 Mathematical Background 495

References 498

B The Delta-Sigma Toolbox 499

C Linear Periodically Time-Varying Systems 539

C.1 Linearity and Time (In)variance 539

C.2 Linear Time-Varying Systems 541

C.3 Linear Periodically Time-Varying (LPTV) Systems 543

C.4 LPTV Systems with Sampled Outputs 547

References 559

Index 561