Look-Ahead Based Sigma-Delta Modulation (eBook)
XII, 248 Seiten
Springer Netherland (Verlag)
978-94-007-1387-1 (ISBN)
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.
Contents 6
List of Symbols and Abbreviations 11
Chapter 1: Introduction 13
Chapter 2: Basics of Sigma-Delta Modulation 16
2.1 AD, DD, and DA Sigma-Delta Conversion 19
2.1.1 AD Conversion 19
2.1.2 DD Conversion 20
2.1.3 DA Conversion 20
2.2 Sigma-Delta Structures 21
2.3 Linear Modeling of an SDM 23
2.4 Sigma-Delta Modulator Performance Indicators 28
2.4.1 Generic Converter Performance 28
2.4.1.1 SNR and SINAD 28
2.4.1.2 SFDR 30
2.4.1.3 THD 30
2.4.1.4 Implementation and Resource Costs 30
2.4.1.5 Figure-of-Merit 31
2.4.2 SDM Specific Functional Performance 33
2.4.2.1 Stability 33
2.4.2.2 Limit Cycles and Idle Tones 34
2.4.2.3 Noise Modulation 34
2.4.2.4 Transient Performance 36
2.4.3 SDM Specific Implementation Costs 37
2.4.4 Figure-of-Merit of an SDM 38
Chapter 3: Transient SDM Performance 40
3.1 Measuring Signal Conversion Quality 40
3.1.1 Steady-State 40
3.1.2 Non-steady-State 41
3.2 Time Domain SINAD Measurement 42
3.3 Steady-State SINAD Measurement Analysis 44
3.3.1 Obtaining the Linearized STF 45
3.3.2 Time Domain SINAD Measurement 48
3.4 Non-steady-State SINAD Measurement Analysis 48
3.5 Conclusions 51
Chapter 4: Noise-Shaping Quantizer Model 53
4.1 Generic Quantizer 53
4.2 Noise-Shaping Quantizer 54
4.3 Noise-Shaping Quantizer with Multiple Cost Functions 56
4.4 Specific Realization Structures 57
Chapter 5: Look-Ahead Sigma-Delta Modulation 59
5.1 Noise-Shaping Quantizer with Look-Ahead 59
5.2 Look-Ahead Enabled SDM Model 61
5.3 Look-Ahead Principle 62
5.3.1 Quantizer Cost Function 64
5.4 Obtaining Information About the Future 65
5.4.1 Approximated Future Input 65
5.4.2 Actual Future Input 66
5.5 Full Look-Ahead Algorithm 66
5.6 Linear Modeling of a Look-Ahead SDM 69
5.6.1 Boundary Conditions and Assumptions 69
5.6.2 Feed-Forward Look-Ahead SDM 70
5.6.2.1 NTF 70
5.6.2.2 STF 71
5.6.3 Feed-Back Look-Ahead SDM 72
5.6.3.1 NTF 72
5.6.3.2 STF 72
5.7 Benefits and Disadvantages of Look-Ahead 74
5.7.1 Benefits 75
5.7.1.1 Improved Stability 75
5.7.1.2 Increase in Linearity 75
5.7.1.3 Improved Transient Response 76
5.7.2 Disadvantages 77
5.8 Look-Ahead AD Conversion 78
5.8.1 Potential Benefits and Disadvantages of Look-Ahead in AD Conversion 78
5.8.2 Feasibility of a Look-Ahead ADC 79
5.8.2.1 Obtaining the Future Input Signal 79
5.8.2.2 Calculation of Solutions 79
5.8.2.3 Calculation of the Cost 81
5.8.2.4 Selection of the Best Solution 81
5.8.3 Hybrid Look-Ahead ADC 81
5.8.4 Conclusion 82
5.9 Look-Ahead DD Conversion 82
5.10 Conclusions 85
Chapter 6: Reducing the Computational Complexity of Look-Ahead DD Conversion 86
6.1 Full Look-Ahead 86
6.1.1 Complete Response Calculation with Reuse of Intermediate Results 87
6.1.2 Select and Continue with Half of the Solutions 87
6.1.3 Linear Decomposition of the Filter Response 88
6.1.4 Conditional Computation of the Solutions 89
6.1.5 Calculating Multiple Output Symbols per Step 89
6.1.6 Summary 91
6.2 Pruned Look-Ahead 91
6.2.1 Motivation for Pruning 92
6.2.2 Basic Pruned Look-Ahead Modulation 93
6.2.3 Pruned Look-Ahead Modulation with Reuse of Results 95
6.2.3.1 Algorithmic Structure 99
6.2.3.2 Algorithm Steps 100
6.2.3.3 Start and End of a Conversion 101
6.2.3.4 Potential Convergence Issues 102
6.2.3.5 Conversion Quality as a Function of the Number of Paths 103
6.2.3.6 Required Resources per Parallel Solution 104
6.2.4 Summary 104
6.3 Pruned Look-Ahead Modulator Realizations 104
6.3.1 Trellis Sigma-Delta Modulation 105
6.3.2 Efficient Trellis Sigma-Delta Modulation 106
6.3.3 Pruned Tree Sigma-Delta Modulation 107
6.3.4 Pruned Tree Sigma-Delta Modulation for SA-CD 109
6.4 Conclusions 110
Chapter 7: Trellis Sigma-Delta Modulation 111
7.1 Algorithm - Kato Model 112
7.1.1 Hidden Markov Model 112
7.1.2 Algorithm Steps 114
7.1.2.1 Step 1: Calculate the Cost for Appending a Bit 114
7.1.2.2 Step 2: Calculate the Path Metric 115
7.1.2.3 Step 3: Sequence Selection 115
7.1.2.4 Step 4: Bounding the Path Metric 116
7.1.2.5 Step 5: Output Code Selection 116
7.2 Algorithm - Pruned Look-Ahead Model 117
7.3 Verification of the Linearized NTF and STF 118
7.3.1 NTF 118
7.3.2 STF 120
7.4 Relation Trellis Order and Trellis Depth 121
7.4.1 Simulation Setup 122
7.4.2 Trellis Depth as a Function of the Trellis Order and the Signal Amplitude 122
7.4.3 Trellis Depth as a Function of the Signal Frequency 124
7.4.4 Trellis Depth as a Function of the Loop-Filter Configuration 125
7.4.5 Summary 126
7.5 Functional Performance 127
7.5.1 SNR, SINAD, THD and SFDR 127
7.5.1.1 SDM1 127
7.5.1.2 SDM1FB 128
7.5.1.3 SDM2 and SDM2FB 128
7.5.1.4 SDM3 and SDM3FB 130
7.5.1.5 SDM4 and SDM4FB 130
7.5.1.6 Summary 131
7.5.2 Converter Stability 132
7.5.2.1 Maximum Stable Input Amplitude 132
SDM2 132
SDM4 133
7.5.2.2 Maximum Loop-Filter Corner Frequency 134
SDM2 134
SDM4 135
7.5.2.3 Summary 135
7.5.3 Noise Modulation 136
7.5.4 Summary 138
7.6 Implementation Aspects 139
7.6.1 Required Computational Resources 139
7.6.2 Look-Ahead Filter Unit 140
7.6.2.1 Latency 140
7.6.2.2 Resource Sharing 141
7.6.2.3 Dither 141
7.6.3 Output Symbol Selection 142
7.7 Conclusions 143
Chapter 8: Efficient Trellis Sigma-Delta Modulation 145
8.1 Reducing the Number of Parallel Paths 145
8.2 Algorithm 148
8.3 Relation Between N and M 149
8.4 Required History Length 151
8.5 Functional Performance 153
8.5.1 SNR, SINAD, THD and SFDR 153
8.5.1.1 SDM1 153
8.5.1.2 SDM2 154
8.5.2 Converter Stability 157
8.5.3 Noise Modulation 158
8.5.4 Summary 160
8.6 Implementation Aspects 161
8.6.1 Selection Step 162
8.7 Conclusions 164
Chapter 9: Pruned Tree Sigma-Delta Modulation 166
9.1 Removing the Test for Uniqueness 166
9.2 Algorithm 168
9.2.1 Initialization Phase 169
9.2.2 Operation Phase 169
9.3 Required History Length 170
9.4 Functional Performance 172
9.4.1 SNR, SINAD, THD and SFDR 172
9.4.1.1 SDM1 172
9.4.1.2 SDM2 173
9.4.2 Converter Stability 175
9.4.2.1 Maximum Stable Input Amplitude 175
9.4.2.2 Maximum Loop-Filter Corner Frequency 176
9.4.3 Noise Modulation 177
9.4.4 Summary 179
9.5 Implementation Aspects 181
9.6 Conclusions 182
Chapter 10: Pruned Tree Sigma-Delta Modulation for SA-CD 185
10.1 Requirements of an SA-CD Modulator 185
10.2 SA-CD Lossless Data Compression 187
10.3 Dual Optimization 190
10.3.1 Predictor Cost Function 191
10.3.2 Combining the Cost Functions 193
10.3.3 Spectral Shaping 194
10.4 Algorithm 196
10.5 Functional Performance 199
10.5.1 Lossless Data Compression 199
10.5.2 SNR, SINAD, THD and SFDR 200
10.5.2.1 SDM1 201
10.5.2.2 SDM2 202
10.5.3 Converter Stability 202
10.5.3.1 Maximum Stable Input Amplitude 202
10.5.3.2 Maximum Loop-Filter Corner Frequency 203
10.5.4 Noise Modulation 203
10.5.5 Summary 206
10.6 Implementation Aspects 207
10.7 Conclusions 208
Chapter 11: Comparison of Look-Ahead SDM Techniques 210
11.1 Alternative Look-Ahead Techniques 210
11.2 Algorithm Comparison 211
11.3 Functional Performance Comparison 214
11.3.1 SNR, SINAD, THD and SFDR 214
11.3.1.1 SDM1 215
11.3.1.2 SDM2 217
11.3.2 Converter Stability 218
11.3.2.1 Maximum Stable Input Amplitude 218
11.3.2.2 Maximum Loop-Filter Corner Frequency 220
11.3.3 Noise Modulation 221
11.3.4 Lossless Data Compression 223
11.3.5 Summary 225
11.4 Conclusions 226
Chapter 12: Maximum SNR Analysis 229
12.1 Experiment 1 229
12.2 Experiment 2 231
12.3 Analysis 232
12.3.1 Second Order Filter Stability 233
12.3.2 High Order Filter Stability 235
12.4 Obtaining the Maximum SNR 237
12.5 Theoretical Maximum SNR 239
12.6 Conclusions 241
Chapter 13: General Conclusions 242
Appendix A FFT Calculations - Coherent and Power Averaging 244
Appendix B Description of the Used Sigma-Delta Modulators 246
References 248
| Erscheint lt. Verlag | 2.4.2011 |
|---|---|
| Reihe/Serie | Analog Circuits and Signal Processing | Analog Circuits and Signal Processing |
| Zusatzinfo | XII, 248 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik ► Netzwerke |
| Technik ► Elektrotechnik / Energietechnik | |
| Schlagworte | Analog Circuit Design • Data Converters • Digital Circuit Design • Sigma Delta Modulators |
| ISBN-10 | 94-007-1387-8 / 9400713878 |
| ISBN-13 | 978-94-007-1387-1 / 9789400713871 |
| Haben Sie eine Frage zum Produkt? |
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