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Understanding Delta-Sigma Data Converters

ISBN: 978-0-471-46585-0
464 pages
November 2004, Wiley-IEEE Press
Understanding Delta-Sigma Data Converters (0471465852) cover image

Description

Learn how to harness the power of delta-sigma data converters

Understanding Delta-Sigma Data Converters brings readers a clear understanding of the principles of delta-sigma (DeltaSigma) converter operation--analog to digital and digital to analog. It introduces the best computer-aided analysis and design techniques available. With an understanding of the great versatility of the DeltaSigma converter, readers can apply their new knowledge to a wide variety of applications, including digital telephony, digital audio, wireless and wired communications, medical electronics, and industrial and scientific instrumentation. The authors make the material accessible to all design engineers by focusing on developing an understanding of the physical operation rather than getting mired in complex mathematical treatments and derivations.

Written for entry-level readers, the publication has a natural flow that begins with basic concepts, enabling the readers to develop a solid foundation for the book's more complex material. The text, therefore, starts with a general introduction to the DeltaSigma converter, including a brief historical overview to place it in context. Next, the publication introduces the first-order DeltaSigma modulator, covering oversampling, noise-shaping, decimation filtering and other key concepts. Then, using the first-order modulator as a foundation, second and higher-order modulators are presented and analyzed. Finally, the authors delve into implementation considerations and present several design examples using the Delta-Sigma Toolbox.

Everything needed to facilitate quick comprehension and help readers apply their newly learned principles is provided:Simplified methods to understand complicated concepts such as spectral estimation and switched noiseReferences that lead to in-depth analysis of specialized topicsFigures and charts that illustrate complex design issuesConclusion section at the end of each chapter that highlights the key pointsReference manual for the Delta-Sigma Toolbox, along with numerous practical examples that illustrate the use of the Toolbox

This is essential reading for all design engineers who want to learn and fully harness the powerful capabilities of DeltaSigma data converters. Upper-level undergraduates and graduate students will find the book's logical organization and clear style, coupled with numerous practical examples, a great entry into the field.
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Table of Contents

Foreword xi

References xii

Chapter 1 Introduction 1

1.1 The Need for Oversampling Converters 1

1.2 Delta and Delta-Sigma Modulation 4

1.3 Higher-Order Single-Stage Noise-Shaping Modulators

1.4 Multi-Stage (Cascade, MASH) Modulators 10

1.5 Bandpass ΔΣ Modulators 13

1.6 ΔΣ Modulators with Multi-Bit Quantizers 15

1.7 Delta-Sigma Digital-to-Analog Converters 16

1.8 History; Performance and Architecture Trends 17

CHAPTER 2 The First-Order Delta Sigma Modulator 21

2.1 Quantizers and Quantization Noise 21

2.1.1 Binary Quantization 28

2.2 MODI as an ADC 29

2.3 MODI as a DAC 34

2.4 MODI Linear Model 36

2.5 Simulation of MODI 38

2.6 MODI under DC Excitation 41

2.6.1 Idle Tone Generation 42

2.6 2 Graphical Visualization 45

2.7 Stability of MODI 49

2.8 The Effects of Finite Op-Amp Gain 50

2.8.1 Linear Systems Perspective- Degraded Noise Shaping 50

2.8.2 Nonlinear Systems Perspective- Dead Zones 51

2.9 Decimation Filters for MODI 54

2.9.1 The Sine Filter [9] 55

2.9.2 The Sine1 Filter 58

2.10 Conclusions 60

CHAPTER 3 The Second-Order Delta-Sigma Modulator 63

3.1 The Second-Order Modulator: MOD2 63

3.2 Simulation of MOD2 67

3.3 Nonlinear Effects in MOD2 71

3.3 1 Signal-dependent quantizer gain 71

3.3.2 Stability o/MOD2 74

3.3.3 Dead-band behavior 77

3.4 Alternative Second-Order Modulator Structures 79

3.4.1 The Boser- Wooley Modulator 79

3.4.2 The Silva-Steensgaard Structure 80

3.4.3 The Error-Feedback Structure 81

3.4.4 Generalized Second-Order Structures 82

3.4.5 Optimal Second-Order Modulator 84

3.5 Decimation Filtering for Second-Order ΔΣ Modulators 86

3.6 Conclusions 89

CHAPTER 4 Higher-Order Delta-Sigma Modulation 91

4.1 High-Order Single-Quantizer Modulators 91

4.2 Stability Considerations in High-Order Modulators 97

4.2.1 Single-Bit Modulators 98

4.2.2 Multi-Bit Modulators [12] 104

4.3 Optimization of the NTF Zeros and Poles 107

4.3.1 NTF Zero Optimization 107

4.3.2 NTF Pole Optimization 111

4.4 Loop Filter Architectures 115

4.4.1 Loop Filters with Distributed Feedback and Input Coupling- The CIFB and CRFB Structures 115

4.4.2 Loop Filters with Distributed Feedforward and Input Coupling- The CIFF and CRFF Structures 121

4.5 Multi-Stage Modulators 122

4.5.1 The Leslie-Singh (L-0 Cascade) Structure [16] 123

4.5.2 Cascade (MASH) Modulators 127

4.5.3 Noise Leakage in Cascade Modulators 132

4.6 Conclusions 136

CHAPTER 5 Bandpass and Quadrature Delta-Sigma Modulation 139

5.1 The Need for Bandpass and Quadrature Modulation 139

5.2 Bandpass NTF Selection 145

5.2.1 Pseudo N-path transformation 149

5.3 Architectures for Bandpass Delta-Sigma Modulators 151

5.3.1 Topology Choices 151

5.3.2 Resonator Implementations 154

5.4 Bandpass Modulator Example 161

5.5 Quadrature Signals 166

5.6 Quadrature Modulation 172

5.7 Conclusions 176

CHAPTER 6 Implementation Considerations For AZ ADCs 179

6.1 Modulators with Multi-Bit Internal Quantizers 179

6.2 Dual-Quantizer Modulators 182

6.2.1 Dual-Quantization MASH Structure 182

6.2.2 Dual-Quantization Single-Stage Structure 183

6.3 Dynamic Element Randomization 184

6.4 Mismatch Error Shaping 186

6.4.1 Element Rotation or Data-Weighted Averaging 189

6.4.2 Individual Level Averaging 191

6.4.3 Vector-Based Mismatch Shaping 192

6.4.4 Element Selection Using a Tree Structure 196

6.5 Digital Correction of DAC Nonlinearity 199

6.5.1 Digitally-Corrected Multi-Bit AS Modulator with Power-Up Calibration 200

6.5.2 Digitally-Corrected Multi-Bit AS ADC with Background Calibration 202

6.6 Continuous-Time Implementations 205

6.6.1 A Continuous-Time Implementation ofMOD2 207

6.6.2 Inherent Anti-Aliasing in CT AS ADCs 212

6.6.3 Design Issues for Continuous-Time Modulators 213

6.7 Conclusions 216

CHAPTER 7 Delta-Sigma DACs 219

7.1 System Architectures for ΔΣ DACs 220

7.2 Loop configurations for ΔΣ DACs 222

7.2.1 Single-Stage Delta-Sigma Loops 223

7.2.2 The Error Feedback Structure 224

7.2.3 Cascade (MASH) Structures 226

7.3 ΔΣ DACs Using Multi-Bit Internal DACs 229

7.3.1 Dual-Truncation DAC Structures 230

7.3.2 Multi-bit Delta-Sigma DACs with Mismatch Error Shaping 232

7.3.3 Digital Correction of Multi-Bit Delta-Sigma DACs 236

7.3.4 Comparison of Single-Bit and Multi-Bit ΔΣ DACs 238

7.4 Interpolation Filtering for ΔΣ DACs 239

7.5 Analog Post-Filters for ΔΣ DACs 243

7.5.1 Analog Post-Filtering in Single-Bit ΔΣ DACs 244

7.5.2 Analog Post-Filtering in Multi-Bit ΔΣ DACs 251

7.6 Conclusions 253

CHAPTER 8 High-Level Design and Simulation 257

8.1 NTF Synthesis 257

8.1.1 How synthesize NTF works 260

8.1.2 Limitations of synthes i zeNTF 262

8.2 NTF Simulation, SQNR Calculation and Spectral Estimation 263

8.3 NTF Realization and Dynamic Range Scaling 266

8 3.1 The ABCD Matrix 271

8.4 Creating a SPICE-Simulatable Schematic 273

8.4.1 Voltage Scaling 273

8.4.2 Timing 274

8.4.3 kT/C Noise 280

8.5 Conclusions 281

CHAPTER 9 Example Modulator Systems 283

9.1 SCMOD2: General-Purpose Second-Order Switched-Capacitor ADC 283

9.1.1 System Design 284

9.1.2 Timing 286

9.1.3 Scaling 288

9.1.4 Verification 289

9.1.5 Capacitor Sizing 292

9.1.6 Circuit Design 294

9.2 SCM0D5: A Fifth-Order Single-Bit Noise-Shaping Loop 298

9.2.1 NTF and Architecture Selection 298

9.2.2 Implementation 302

9.2.3 Instability and Reset 311

9.3 A Wideband 2-0 Cascade System 311

9.3.1 Architecture 312

9.3 2 Implementation 315

9.4 A Micropower Continuous-Time ADC 317

9.4.1 High-Level Design 318

9.4.2 Circuit Design 322

9.5 A Continuous-Time Bandpass ADC 326

9.5.1 Architecture/Analysis 328

9.5.2 Subcircuits 333

9.6 Audio DAC 337

9.6.1 Modulator Design 338

9.6.2 Interpolation Filter Design 344

9.6.3 DAC and Reconstruction Filter Design 355

9.7 Conclusions 357

9.7.1 The ADC State-of-the-Art 357

9.7.2 FOM Justification 359

9.7.2 References 362

APPENDIX A Spectral Estimation 365

A.I Windowing 366

A.2 Scaling and Noise Bandwidth 373

A.3 Averaging 377

A.4 An Example 379

A.5 Mathematical Background 383

APPENDIX B The Delta-Sigma Toolbox 389

Demonstrations and Examples 390

Summary of Key Functions 391

synthesizeNTF 393

predictSNR 395

simulateDSM 396

simulateSNR 398

realizeNTF 400

stuffABCD, mapABCD 401

scaleABCD 402

calculateTF 403

sirnulateESL 404

designHBF 405

simulateHBF 408

findPIS 409

Modulator Model Details 410

APPENDIX C Noise in Switched-Capacitor Delta-Sigma Data Converters 417

C.I Noise Effects in CMOS Op Amps 419

C.2 Sampled Thermal Noise 423

C.3 Noise Effects in an SC Integrator 425

C.4 Integrator Noise Analysis Example 433

C.5 Noise Effects in Delta-Sigma ADC Loops 435

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Author Information

RICHARD SCHREIER, PhD, is a Senior Design Engineer for Analog Devices in Wilmington, Massachusetts. He has published numerous papers relating to delta-sigma modulation including one which received the Lewis Winner Outstanding Paper award at the 2002 ISSCC, and is the creator of the Delta-Sigma Toolbox for MATLAB®.

GABOR C. TEMES, PhD, is a Professor in the Department of Electrical and Computer Engineering at Oregon State University. He is a Life Fellow of the IEEE and a recipient of the 1998 IEEE Graduate Teaching Award.

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Reviews

"…a comprehensive introduction to data converters…novice engineers…[and] students who specialize in circuit design, signal processing, and communications will find this book very useful." (E-STREAMS, February 2006)

"...a 'one-stop shop' for engineers who want a comprehensive introduction...an excellent starting point for engineers entering the field, as well as a useful reference for experts." (IEEE Solid-State Circuits Society Newsletter, September 2005)

"…a comprehensible tutorial describing the design of base-band, band-pass, and quadrature delta-sigma modulators…" (CHOICE, April 2005)

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