Janssen / Roermund Look-Ahead Based Sigma-Delta Modulation

1. Auflage 2011
ISBN: 978-94-007-1387-1
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 248 Seiten

Reihe: Analog Circuits and Signal Processing

The aim of this book is to expand and improve upon the existing knowledge on discrete-time 1-bit look-ahead sigma-delta modulation in general, and to come to a solution for the above mentioned specific issues arising from 1-bit sigma-delta modulation for SA-CD. In order to achieve this objective an analysis is made of the possibilities for improving the performance of digital noise-shaping look-ahead solutions. On the basis of the insights obtained from the analysis, several novel generic 1-bit look-ahead solutions that improve upon the state-of-the-art will be derived and their performance will be evaluated and compared. Finally, all the insights are combined with the knowledge of the SA-CD lossless data compression algorithm to come to a specifically for SA-CD optimized look-ahead design.

Autoren/Hrsg.

Janssen, Erwin

Roermund, Arthur van

Inhaltsverzeichnis

1;Contents;6
2;List of Symbols and Abbreviations;11
3;Chapter 1: Introduction;13
4;Chapter 2: Basics of Sigma-Delta Modulation;16
4.1;2.1 AD, DD, and DA Sigma-Delta Conversion;19
4.1.1;2.1.1 AD Conversion;19
4.1.2;2.1.2 DD Conversion;20
4.1.3;2.1.3 DA Conversion;20
4.2;2.2 Sigma-Delta Structures;21
4.3;2.3 Linear Modeling of an SDM;23
4.4;2.4 Sigma-Delta Modulator Performance Indicators;28
4.4.1;2.4.1 Generic Converter Performance;28
4.4.1.1;2.4.1.1 SNR and SINAD;28
4.4.1.2;2.4.1.2 SFDR;30
4.4.1.3;2.4.1.3 THD;30
4.4.1.4;2.4.1.4 Implementation and Resource Costs;30
4.4.1.5;2.4.1.5 Figure-of-Merit;31
4.4.2;2.4.2 SDM Specific Functional Performance;33
4.4.2.1;2.4.2.1 Stability;33
4.4.2.2;2.4.2.2 Limit Cycles and Idle Tones;34
4.4.2.3;2.4.2.3 Noise Modulation;34
4.4.2.4;2.4.2.4 Transient Performance;36
4.4.3;2.4.3 SDM Specific Implementation Costs;37
4.4.4;2.4.4 Figure-of-Merit of an SDM;38
5;Chapter 3: Transient SDM Performance;40
5.1;3.1 Measuring Signal Conversion Quality;40
5.1.1;3.1.1 Steady-State;40
5.1.2;3.1.2 Non-steady-State;41
5.2;3.2 Time Domain SINAD Measurement;42
5.3;3.3 Steady-State SINAD Measurement Analysis;44
5.3.1;3.3.1 Obtaining the Linearized STF;45
5.3.2;3.3.2 Time Domain SINAD Measurement;48
5.4;3.4 Non-steady-State SINAD Measurement Analysis;48
5.5;3.5 Conclusions;51
6;Chapter 4: Noise-Shaping Quantizer Model;53
6.1;4.1 Generic Quantizer;53
6.2;4.2 Noise-Shaping Quantizer;54
6.3;4.3 Noise-Shaping Quantizer with Multiple Cost Functions;56
6.4;4.4 Specific Realization Structures;57
7;Chapter 5: Look-Ahead Sigma-Delta Modulation;59
7.1;5.1 Noise-Shaping Quantizer with Look-Ahead;59
7.2;5.2 Look-Ahead Enabled SDM Model;61
7.3;5.3 Look-Ahead Principle;62
7.3.1;5.3.1 Quantizer Cost Function;64
7.4;5.4 Obtaining Information About the Future;65
7.4.1;5.4.1 Approximated Future Input;65
7.4.2;5.4.2 Actual Future Input;66
7.5;5.5 Full Look-Ahead Algorithm;66
7.6;5.6 Linear Modeling of a Look-Ahead SDM;69
7.6.1;5.6.1 Boundary Conditions and Assumptions;69
7.6.2;5.6.2 Feed-Forward Look-Ahead SDM;70
7.6.2.1;5.6.2.1 NTF;70
7.6.2.2;5.6.2.2 STF;71
7.6.3;5.6.3 Feed-Back Look-Ahead SDM;72
7.6.3.1;5.6.3.1 NTF;72
7.6.3.2;5.6.3.2 STF;72
7.7;5.7 Benefits and Disadvantages of Look-Ahead;74
7.7.1;5.7.1 Benefits;75
7.7.1.1;5.7.1.1 Improved Stability;75
7.7.1.2;5.7.1.2 Increase in Linearity;75
7.7.1.3;5.7.1.3 Improved Transient Response;76
7.7.2;5.7.2 Disadvantages;77
7.8;5.8 Look-Ahead AD Conversion;78
7.8.1;5.8.1 Potential Benefits and Disadvantages of Look-Ahead in AD Conversion;78
7.8.2;5.8.2 Feasibility of a Look-Ahead ADC;79
7.8.2.1;5.8.2.1 Obtaining the Future Input Signal;79
7.8.2.2;5.8.2.2 Calculation of Solutions;79
7.8.2.3;5.8.2.3 Calculation of the Cost;81
7.8.2.4;5.8.2.4 Selection of the Best Solution;81
7.8.3;5.8.3 Hybrid Look-Ahead ADC;81
7.8.4;5.8.4 Conclusion;82
7.9;5.9 Look-Ahead DD Conversion;82
7.10;5.10 Conclusions;85
8;Chapter 6: Reducing the Computational Complexity of Look-Ahead DD Conversion;86
8.1;6.1 Full Look-Ahead;86
8.1.1;6.1.1 Complete Response Calculation with Reuse of Intermediate Results;87
8.1.2;6.1.2 Select and Continue with Half of the Solutions;87
8.1.3;6.1.3 Linear Decomposition of the Filter Response;88
8.1.4;6.1.4 Conditional Computation of the Solutions;89
8.1.5;6.1.5 Calculating Multiple Output Symbols per Step;89
8.1.6;6.1.6 Summary;91
8.2;6.2 Pruned Look-Ahead;91
8.2.1;6.2.1 Motivation for Pruning;92
8.2.2;6.2.2 Basic Pruned Look-Ahead Modulation;93
8.2.3;6.2.3 Pruned Look-Ahead Modulation with Reuse of Results;95
8.2.3.1;6.2.3.1 Algorithmic Structure;99
8.2.3.2;6.2.3.2 Algorithm Steps;100
8.2.3.3;6.2.3.3 Start and End of a Conversion;101
8.2.3.4;6.2.3.4 Potential Convergence Issues;102
8.2.3.5;6.2.3.5 Conversion Quality as a Function of the Number of Paths;103
8.2.3.6;6.2.3.6 Required Resources per Parallel Solution;104
8.2.4;6.2.4 Summary;104
8.3;6.3 Pruned Look-Ahead Modulator Realizations;104
8.3.1;6.3.1 Trellis Sigma-Delta Modulation;105
8.3.2;6.3.2 Efficient Trellis Sigma-Delta Modulation;106
8.3.3;6.3.3 Pruned Tree Sigma-Delta Modulation;107
8.3.4;6.3.4 Pruned Tree Sigma-Delta Modulation for SA-CD;109
8.4;6.4 Conclusions;110
9;Chapter 7: Trellis Sigma-Delta Modulation;111
9.1;7.1 Algorithm - Kato Model;112
9.1.1;7.1.1 Hidden Markov Model;112
9.1.2;7.1.2 Algorithm Steps;114
9.1.2.1;7.1.2.1 Step 1: Calculate the Cost for Appending a Bit;114
9.1.2.2;7.1.2.2 Step 2: Calculate the Path Metric;115
9.1.2.3;7.1.2.3 Step 3: Sequence Selection;115
9.1.2.4;7.1.2.4 Step 4: Bounding the Path Metric;116
9.1.2.5;7.1.2.5 Step 5: Output Code Selection;116
9.2;7.2 Algorithm - Pruned Look-Ahead Model;117
9.3;7.3 Verification of the Linearized NTF and STF;118
9.3.1;7.3.1 NTF;118
9.3.2;7.3.2 STF;120
9.4;7.4 Relation Trellis Order and Trellis Depth;121
9.4.1;7.4.1 Simulation Setup;122
9.4.2;7.4.2 Trellis Depth as a Function of the Trellis Order and the Signal Amplitude;122
9.4.3;7.4.3 Trellis Depth as a Function of the Signal Frequency;124
9.4.4;7.4.4 Trellis Depth as a Function of the Loop-Filter Configuration;125
9.4.5;7.4.5 Summary;126
9.5;7.5 Functional Performance;127
9.5.1;7.5.1 SNR, SINAD, THD and SFDR;127
9.5.1.1;7.5.1.1 SDM1;127
9.5.1.2;7.5.1.2 SDM1FB;128
9.5.1.3;7.5.1.3 SDM2 and SDM2FB;128
9.5.1.4;7.5.1.4 SDM3 and SDM3FB;130
9.5.1.5;7.5.1.5 SDM4 and SDM4FB;130
9.5.1.6;7.5.1.6 Summary;131
9.5.2;7.5.2 Converter Stability;132
9.5.2.1;7.5.2.1 Maximum Stable Input Amplitude;132
9.5.2.1.1;SDM2;132
9.5.2.1.2;SDM4;133
9.5.2.2;7.5.2.2 Maximum Loop-Filter Corner Frequency;134
9.5.2.2.1;SDM2;134
9.5.2.2.2;SDM4;135
9.5.2.3;7.5.2.3 Summary;135
9.5.3;7.5.3 Noise Modulation;136
9.5.4;7.5.4 Summary;138
9.6;7.6 Implementation Aspects;139
9.6.1;7.6.1 Required Computational Resources;139
9.6.2;7.6.2 Look-Ahead Filter Unit;140
9.6.2.1;7.6.2.1 Latency;140
9.6.2.2;7.6.2.2 Resource Sharing;141
9.6.2.3;7.6.2.3 Dither;141
9.6.3;7.6.3 Output Symbol Selection;142
9.7;7.7 Conclusions;143
10;Chapter 8: Efficient Trellis Sigma-Delta Modulation;145
10.1;8.1 Reducing the Number of Parallel Paths;145
10.2;8.2 Algorithm;148
10.3;8.3 Relation Between N and M;149
10.4;8.4 Required History Length;151
10.5;8.5 Functional Performance;153
10.5.1;8.5.1 SNR, SINAD, THD and SFDR;153
10.5.1.1;8.5.1.1 SDM1;153
10.5.1.2;8.5.1.2 SDM2;154
10.5.2;8.5.2 Converter Stability;157
10.5.3;8.5.3 Noise Modulation;158
10.5.4;8.5.4 Summary;160
10.6;8.6 Implementation Aspects;161
10.6.1;8.6.1 Selection Step;162
10.7;8.7 Conclusions;164
11;Chapter 9: Pruned Tree Sigma-Delta Modulation;166
11.1;9.1 Removing the Test for Uniqueness;166
11.2;9.2 Algorithm;168
11.2.1;9.2.1 Initialization Phase;169
11.2.2;9.2.2 Operation Phase;169
11.3;9.3 Required History Length;170
11.4;9.4 Functional Performance;172
11.4.1;9.4.1 SNR, SINAD, THD and SFDR;172
11.4.1.1;9.4.1.1 SDM1;172
11.4.1.2;9.4.1.2 SDM2;173
11.4.2;9.4.2 Converter Stability;175
11.4.2.1;9.4.2.1 Maximum Stable Input Amplitude;175
11.4.2.2;9.4.2.2 Maximum Loop-Filter Corner Frequency;176
11.4.3;9.4.3 Noise Modulation;177
11.4.4;9.4.4 Summary;179
11.5;9.5 Implementation Aspects;181
11.6;9.6 Conclusions;182
12;Chapter 10: Pruned Tree Sigma-Delta Modulation for SA-CD;185
12.1;10.1 Requirements of an SA-CD Modulator;185
12.2;10.2 SA-CD Lossless Data Compression;187
12.3;10.3 Dual Optimization;190
12.3.1;10.3.1 Predictor Cost Function;191
12.3.2;10.3.2 Combining the Cost Functions;193
12.3.3;10.3.3 Spectral Shaping;194
12.4;10.4 Algorithm;196
12.5;10.5 Functional Performance;199
12.5.1;10.5.1 Lossless Data Compression;199
12.5.2;10.5.2 SNR, SINAD, THD and SFDR;200
12.5.2.1;10.5.2.1 SDM1;201
12.5.2.2;10.5.2.2 SDM2;202
12.5.3;10.5.3 Converter Stability;202
12.5.3.1;10.5.3.1 Maximum Stable Input Amplitude;202
12.5.3.2;10.5.3.2 Maximum Loop-Filter Corner Frequency;203
12.5.4;10.5.4 Noise Modulation;203
12.5.5;10.5.5 Summary;206
12.6;10.6 Implementation Aspects;207
12.7;10.7 Conclusions;208
13;Chapter 11: Comparison of Look-Ahead SDM Techniques;210
13.1;11.1 Alternative Look-Ahead Techniques;210
13.2;11.2 Algorithm Comparison;211
13.3;11.3 Functional Performance Comparison;214
13.3.1;11.3.1 SNR, SINAD, THD and SFDR;214
13.3.1.1;11.3.1.1 SDM1;215
13.3.1.2;11.3.1.2 SDM2;217
13.3.2;11.3.2 Converter Stability;218
13.3.2.1;11.3.2.1 Maximum Stable Input Amplitude;218
13.3.2.2;11.3.2.2 Maximum Loop-Filter Corner Frequency;220
13.3.3;11.3.3 Noise Modulation;221
13.3.4;11.3.4 Lossless Data Compression;223
13.3.5;11.3.5 Summary;225
13.4;11.4 Conclusions;226
14;Chapter 12: Maximum SNR Analysis;229
14.1;12.1 Experiment 1;229
14.2;12.2 Experiment 2;231
14.3;12.3 Analysis;232
14.3.1;12.3.1 Second Order Filter Stability;233
14.3.2;12.3.2 High Order Filter Stability;235
14.4;12.4 Obtaining the Maximum SNR;237
14.5;12.5 Theoretical Maximum SNR;239
14.6;12.6 Conclusions;241
15;Chapter 13: General Conclusions;242
16;Appendix A FFT Calculations - Coherent and Power Averaging;244
17;Appendix B Description of the Used Sigma-Delta Modulators;246
18;References;248