Look-ahead Sigma-Delta Modulation and its application to Super

339 Pages·2010·4.42 MB·English

Look-ahead Sigma-Delta Modulation
and its application to Super Audio CD
Erwin Janssen
The work described in this thesis has been carried out at the Philips
Research Laboratories and NXP Semiconductors, Eindhoven,
the Netherlands, as part of the Philips/NXP research program.
Janssen, E.
Look-ahead Sigma-Delta Modulation
and its application to Super Audio CD
Proefschrift Technische Universiteit Eindhoven, 2010
Trefwoorden: 1-bitaudio,digital-to-digitalconversion,linearization,look-
ahead, noise shaping, sigma-delta modulation, signal processing
A catalogue record is available from the Eindhoven University of Tech-
nology Library
ISBN: 978-90-386-2364-1
(cid:176)c E. Janssen 2010
All rights reserved.
Reproduction in whole or in part is prohibited
without the written consent of the copyright owner.
Look-ahead Sigma-Delta Modulation
and its application to Super Audio CD
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
rector magnificus, prof.dr.ir. C.J. van Duijn, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen
op woensdag 1 december 2010 om 16.00 uur
door
Erwin Janssen
geboren te Ede
Dit proefschrift is goedgekeurd door promotor:
prof.dr.ir. A.H.M. van Roermund
Samenstelling promotiecommissie:
prof.dr.ir. A.H.M. van Roermund Technische Universiteit Eindhoven
prof.dr.ir. A.C.P.M. Backx Technische Universiteit Eindhoven
dr.ir. J.A. Hegt Technische Universiteit Eindhoven
dr.ir. P.C.W. Sommen Technische Universiteit Eindhoven
prof.dr.ir. B. Nauta Universiteit Twente
prof.dr.ir. G. Gielen Katholieke Universiteit Leuven
dr. D. Reefman Philips Research
dr.ir. L.J. Breems NXP Semiconductors

Contents
List of symbols and abbreviations vii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Aim of the thesis . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Scope of the thesis . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Organization of the thesis . . . . . . . . . . . . . . . . . . 4
2 Basics of sigma-delta modulation 7
2.1 AD, DD, and DA Sigma-Delta conversion . . . . . . . . . 11
2.1.1 AD conversion . . . . . . . . . . . . . . . . . . . . 11
2.1.2 DD conversion . . . . . . . . . . . . . . . . . . . . 12
2.1.3 DA conversion . . . . . . . . . . . . . . . . . . . . 12
2.2 Sigma-Delta structures . . . . . . . . . . . . . . . . . . . . 13
2.3 Linear modeling of an SDM . . . . . . . . . . . . . . . . . 16
2.4 SDM performance indicators . . . . . . . . . . . . . . . . 22
2.4.1 Generic converter performance . . . . . . . . . . . 23
2.4.2 SDM specific functional performance . . . . . . . . 29
2.4.3 SDM specific implementation costs . . . . . . . . . 34
2.4.4 Figure-Of-Merit of an SDM . . . . . . . . . . . . . 36
3 Transient SDM performance 39
3.1 Measuring signal conversion quality. . . . . . . . . . . . . 39
3.1.1 Steady-state. . . . . . . . . . . . . . . . . . . . . . 39
3.1.2 Non-steady-state . . . . . . . . . . . . . . . . . . . 40
3.2 Time domain SINAD measurement . . . . . . . . . . . . . 41
3.3 Steady-state SINAD measurement analysis . . . . . . . . 44
3.3.1 Obtaining the linearized STF . . . . . . . . . . . . 45
3.3.2 Time domain SINAD measurement . . . . . . . . . 49
3.4 Non-steady-state SINAD measurement analysis . . . . . . 50
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 52
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Contents
4 Noise-shaping quantizer model 55
4.1 Generic quantizer . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Noise-shaping quantizer . . . . . . . . . . . . . . . . . . . 57
4.3 Noise-shaping quantizer with multiple cost functions . . . 59
4.4 Specific realization structures . . . . . . . . . . . . . . . . 60
5 Look-ahead sigma-delta modulation 63
5.1 Noise-shaping quantizer with look-ahead . . . . . . . . . . 63
5.2 Look-ahead enabled SDM model . . . . . . . . . . . . . . 65
5.3 Look-ahead principle . . . . . . . . . . . . . . . . . . . . . 67
5.3.1 Quantizer cost function . . . . . . . . . . . . . . . 69
5.4 Obtaining information about the future . . . . . . . . . . 70
5.4.1 Approximated future input . . . . . . . . . . . . . 71
5.4.2 Actual future input . . . . . . . . . . . . . . . . . 71
5.5 Full look-ahead algorithm . . . . . . . . . . . . . . . . . . 72
5.6 Linear modeling of a look-ahead SDM . . . . . . . . . . . 75
5.6.1 Boundary conditions and assumptions . . . . . . . 76
5.6.2 Feed-forward look-ahead SDM . . . . . . . . . . . 78
5.6.3 Feed-back look-ahead SDM . . . . . . . . . . . . . 80
5.7 Benefits and disadvantages of look-ahead. . . . . . . . . . 82
5.7.1 Benefits . . . . . . . . . . . . . . . . . . . . . . . . 82
5.7.2 Disadvantages. . . . . . . . . . . . . . . . . . . . . 86
5.8 Look-ahead AD conversion . . . . . . . . . . . . . . . . . 87
5.8.1 Potentialbenefitsanddisadvantagesoflook-ahead
in AD conversion . . . . . . . . . . . . . . . . . . . 87
5.8.2 Feasibility of a look-ahead ADC . . . . . . . . . . 88
5.8.3 Hybrid look-ahead ADC . . . . . . . . . . . . . . . 90
5.8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . 92
5.9 Look-ahead DD conversion . . . . . . . . . . . . . . . . . 92
5.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6 Reducing the complexity of LA DD conversion 97
6.1 Full look-ahead . . . . . . . . . . . . . . . . . . . . . . . . 97
6.1.1 Completeresponsecalculationwithreuseofinter-
mediate results . . . . . . . . . . . . . . . . . . . . 98
6.1.2 Select and continue with half of the solutions . . . 98
6.1.3 Linear decomposition of the filter response . . . . 99
6.1.4 Conditional computation of the solutions . . . . . 101
6.1.5 Calculating multiple output symbols per step . . . 101
6.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Pruned look-ahead . . . . . . . . . . . . . . . . . . . . . . 104
6.2.1 Motivation for pruning . . . . . . . . . . . . . . . . 104
6.2.2 Basic pruned look-ahead modulation . . . . . . . . 105
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Contents
6.2.3 Pruned look-ahead modulation with reuse of results108
6.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . 120
6.3 Pruned look-ahead modulator realizations . . . . . . . . . 120
6.3.1 Trellis sigma-delta modulation . . . . . . . . . . . 121
6.3.2 Efficient Trellis sigma-delta modulation . . . . . . 122
6.3.3 Pruned Tree sigma-delta modulation . . . . . . . . 124
6.3.4 Pruned Tree sigma-delta modulation for SA-CD . 126
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Trellis sigma-delta modulation 129
7.1 Algorithm - Kato model . . . . . . . . . . . . . . . . . . . 130
7.1.1 Hidden Markov model . . . . . . . . . . . . . . . . 131
7.1.2 Algorithm steps. . . . . . . . . . . . . . . . . . . . 133
7.2 Algorithm - pruned look-ahead model . . . . . . . . . . . 137
7.3 Verification of the linearized NTF and STF . . . . . . . . 139
7.3.1 NTF . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.3.2 STF . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.4 Relation Trellis order and Trellis depth . . . . . . . . . . . 142
7.4.1 Simulation setup . . . . . . . . . . . . . . . . . . . 143
7.4.2 TrellisdepthasafunctionoftheTrellisorderand
the signal amplitude . . . . . . . . . . . . . . . . . 144
7.4.3 Trellis depth as a function of the signal frequency. 146
7.4.4 Trellis depth as a function of the loop-filter con-
figuration . . . . . . . . . . . . . . . . . . . . . . . 147
7.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . 148
7.5 Functional performance . . . . . . . . . . . . . . . . . . . 149
7.5.1 SNR, SINAD, THD and SFDR . . . . . . . . . . . 149
7.5.2 Converter stability . . . . . . . . . . . . . . . . . . 155
7.5.3 Noise modulation . . . . . . . . . . . . . . . . . . . 160
7.5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . 163
7.6 Implementation aspects . . . . . . . . . . . . . . . . . . . 164
7.6.1 Required computational resources . . . . . . . . . 164
7.6.2 Look-ahead filter unit . . . . . . . . . . . . . . . . 164
7.6.3 Output symbol selection . . . . . . . . . . . . . . . 168
7.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8 Efficient Trellis sigma-delta modulation 173
8.1 Reducing the number of parallel paths . . . . . . . . . . . 174
8.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.3 Relation between N and M . . . . . . . . . . . . . . . . . 178
8.4 Required history length . . . . . . . . . . . . . . . . . . . 180
8.5 Functional performance . . . . . . . . . . . . . . . . . . . 183
8.5.1 SNR, SINAD, THD and SFDR . . . . . . . . . . . 183
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Contents
8.5.2 Converter stability . . . . . . . . . . . . . . . . . . 188
8.5.3 Noise modulation . . . . . . . . . . . . . . . . . . . 189
8.5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . 192
8.6 Implementation aspects . . . . . . . . . . . . . . . . . . . 194
8.6.1 Selection step . . . . . . . . . . . . . . . . . . . . . 194
8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 196
9 Pruned Tree sigma-delta modulation 199
9.1 Removing the test for uniqueness . . . . . . . . . . . . . . 199
9.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
9.2.1 Initialization phase . . . . . . . . . . . . . . . . . . 202
9.2.2 Operation phase . . . . . . . . . . . . . . . . . . . 203
9.3 Required history length . . . . . . . . . . . . . . . . . . . 204
9.4 Functional performance . . . . . . . . . . . . . . . . . . . 206
9.4.1 SNR, SINAD, THD and SFDR . . . . . . . . . . . 206
9.4.2 Converter stability . . . . . . . . . . . . . . . . . . 210
9.4.3 Noise modulation . . . . . . . . . . . . . . . . . . . 213
9.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . 215
9.5 Implementation aspects . . . . . . . . . . . . . . . . . . . 217
9.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 218
10 Pruned Tree sigma-delta modulation for SA-CD 223
10.1 Requirements of an SA-CD modulator . . . . . . . . . . . 224
10.2 SA-CD lossless data compression . . . . . . . . . . . . . . 226
10.3 Dual optimization . . . . . . . . . . . . . . . . . . . . . . 230
10.3.1 Predictor cost function . . . . . . . . . . . . . . . . 231
10.3.2 Combining the cost functions . . . . . . . . . . . . 232
10.3.3 Spectral shaping . . . . . . . . . . . . . . . . . . . 234
10.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
10.5 Functional performance . . . . . . . . . . . . . . . . . . . 240
10.5.1 Lossless data compression . . . . . . . . . . . . . . 240
10.5.2 SNR, SINAD, THD and SFDR . . . . . . . . . . . 242
10.5.3 Converter stability . . . . . . . . . . . . . . . . . . 245
10.5.4 Noise modulation . . . . . . . . . . . . . . . . . . . 247
10.5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . 249
10.6 Implementation aspects . . . . . . . . . . . . . . . . . . . 251
10.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 252
11 Comparison of look-ahead SDM techniques 255
11.1 Alternative look-ahead techniques . . . . . . . . . . . . . 255
11.2 Algorithm comparison . . . . . . . . . . . . . . . . . . . . 257
11.3 Functional performance comparison. . . . . . . . . . . . . 260
11.3.1 SNR, SINAD, THD and SFDR . . . . . . . . . . . 260
iv