Delta-Sigma Modulators Modeling, Design and Applications George I Bourdopoulos University ofpatras, Greece Aristodemos Pnevmatikakis Athens Information Technology, Greece Vassilis Anastassopoulos University of Patras, Greece Theodore L Deliyannis University of Patras, Greece Imperial College Press
Contents Preface v 1. Introduction 1 1.1 Modulation - Demodulation 1 1.2 AI Modulation 2 1.3 Design and Implementation of AS Modulators 4 1.4 Applications 6 1.5 Book Organization 7 10 2. Analog to Digital Conversion 12 2.1 Introduction 12 2.2 The Basic Concept of A/D Conversion 14 2.3 Uniform Sampling 15 2.4 Quantization Error and the Linear Model 20 2.5 Sampling ofband-pass Signals 25 2.6 Oversampling Principles 27 2.7 The Delta Modulator 29 2.8 Performance of the Delta Modulator 33 2.9 The Exponential DM 34 2.10 The Concept ofnoise Shaping 36 ix
X AS Modulators 2.11Summary 37 Problems 3g 4Q 3. AS Modulators Architectures 41 3.1 Introduction 4i 3.2 First-Order AS Modulators 42 3.2.1 Input and output waveforms 45 3.2.2 SNR and PSD diagrams, ' '. 46 3.3 Comparison of Delta and AS Modulators 48 3.3.1 Linear DM 48 3.3.2 Exponential DM 4g 3.3.3 AS Modulator 49 3.4 Second-Order AS Modulators 49 3.5 High-Order AS Modulators 5! 3.6 Stability of Single-Stage AS Modulators 58 3.7 Multi-Stage AS Modulators 59 3.8 Multi-Bit AS Modulators 64 3.9 Hybrid AS Modulators 68 3.10 Adaptive AS Modulators 69 3.11 Band-Pass AS Modulators 70 3.12Summary 73 Problems 73 75 4. Single-Bit Single-Stage AS Modulators, Modeling and Design 77 4.1 Introduction 77 4.2 Modeling of AS Modulators 78 4.2.1 Linear model 79 4.2.2 Quasi-Linear model 1 4.3 NTF Characteristics 33 4.4 Stability of AS Modulators 85 4.5 Stability Criteria g7 4.6 Noise Transfer Function Determination 89 4.6.1 Optimizing the position ofzeros 90 4.6.2 Optimizing the position of poles 93
Contents xi 4.7 AS Modulator Assessment 95 4.8 Summary 96 Problems 97 99 5. Implementation of AS Modulators 100 5.1 Introduction 100 5.2 Basic Blocks of a AS Modulator for Analog-to-Digital Conversion 100 5.2.1 The loop filter 102 5.2.2 Local ADC and DAC 106 5.3 Continuous-Time Loop Filter Implementation 108 5.4 Circuit Design ofa First-Order AS Modulator 113 5.5 Circuit Design ofa Second-Order AS Modulator 114 5.6 Circuit Design of a Third-Order AS Modulator 119 5.7 Circuit Design of a Fourth-Order Band-pass AS Modulator 124 5.8 Testing the Operation of AS Modulators Experimentally. 127 5.9 Low-Power, Low-Voltage AS Modulators 131 5.10 Summary 134 Problems 135 137 Appendix 138 6. Practical Limitations of AS Modulators 139 6.1 Introduction 139 6.2 Practical Circuit Limitations 139 6.2.1 Noise sources in the AS loop 140 6.3 Effect of Thermal Noise 144 6.3.1 SCcircuits 144 6.3.2 CT active RC circuits 146 6.4 Effects of the Opamp Non-ldealities 147 6.4.1 Thermal and flicker noise and DC offset of the opamp 147 6.4.2 Finite opamp gain 149 6.4.3 Finite bandwidth and slew-rate of the opamp.... 151
xii AS Modulators 6.5 Effect ofjitter, 6.5.1 SCcircuits, 6.5.2 CT active RC circuits i54 6.6 Effect of Rise and Fall Times of DAC Pulses in CT Circuits, <- fi 6.7 A Comparison of SC and CT active RC Circuits 158 6.8 DACErrors 159 6.8.1 Single-bit DAC 160 6.8.2 Multibit DAC.. i AI 6.9 Summary,,., Problems 164 165 7. Stabilization and Suppression of Tones for Higher-Order Single-Stage AS Modulators 167 7.1 Introduction 7.2 Bounds on Quantizer Input Using the Variable Gain Method 167 16g 7.3 Stabilization Methods 1 y 0 7.3.1 Resetting the integrators 171 7.3.2 Clipping the integrators 171 7.3.3 Activation of local feedback loops around the integrators y]2 73.4 Reducing the order of the loop filter 173 7.4 Comparison of the Stabilization Methods 175 7.5 Tones in AS Modulators 182 7.6 Fixed Techniques ^4 7.6.1 Dithering.. 104 7.6.2 Chaotic AS modulators 185 7.6.3 Bit-flipping 18g 7.6.4 Comparison of fixed techniques 191 7.7 Adaptive Techniques 192 7.7.1 Adaptive dithering 192 7.7.2 Adaptive bit-flipping 193 7.7.3 Comparison of the adaptive techniques 193
Contents xiii 7.8 Summary 193 5. Decimation, Interpolation and Converters 8.1 Introduction 8.2 Rate Conversion 8.2.1 Decimation 19 6 197 197 1 QS 8.2.2 Interpolation 8 3 Decimation and Interpolation filters 201?rv3 ZUJ> 8.3.1 Multi-stage rate conversion LVJ 8.3.2 Comb filters 8 3 3 Fractional rate conversion 207 8.4 AS Modulators for ADC 211 8.5 AI Modulators for DAC 212 8.6 Summary Problems 213 214 9. Applications 9.1 Introduction 214 9.2 AI Modulation in Digital Radio 9 2 1 Conversion bandwidth and resolution 217 919 9.2.2 Sampling rate 221 9.3 Frequency Synthesis 9.3.1 Principles of the PLL Operation 221 9.3.2 AI modulation in frequency synthesis 224 9.3.3 Analysisof the frequency divider 226 9.4 Clock Generators Using AI Modulation 229 9.5 AI Modulation in Analog-Input Digital Phase-Locked Loops for Frequency and Phase Demodulation 232 9.6 AI Modulation in Analog Oscillators 234 936 241 9.7 Summary Index