Continuous-Time Sigma-Delta A/D Conversion

Fundamentals, Performance Limits and Robust Implementations

By: Maurits Ortmanns, Friedel Gerfers

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Hardcover | 8 December 2005

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268 Pages

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Sigma-delta A/D converters are a key building block in wireless and multimedia applications. This comprehensive book deals with all relevant aspects arising during the analysis, design and simulation of the now widespread continuous-time implementations of sigma-delta modulators. The results of several years of research by the authors in the field of CT sigma-delta modulators are covered, including the analysis and modeling of different CT modulator architectures, CT/DT loop filter synthesis, a detailed error analysis of all components, and possible compensation/correction schemes for the non-ideal behavior in CT sigma-delta modulators. Guidance for obtaining low-power consumption and several practical implementations are also presented. It is shown that all the proposed new theories, architectures and possible correction techniques have been confirmed by measurements on discrete or integrated circuits. Quantitative results are also provided, thus enabling prediction of the resulting accuracy.

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You Can Find This Book In

Non-Fiction Engineering & Technology Energy Technology & Engineering Electrical Engineering Other Technologies & Applied Sciences Applied Optics Electronics & Communications Engineering Communications Engineering & Telecommunications Science Science in General Electronics Engineering Electronic Devices & Materials

Technology in General Engineering in General Computing & I.T.Computer Science Digital Signal Processing (DSP)

Introduction	p. 1
Motivation and History	p. 1
Intention of this Work	p. 3
Further Recommended Literature	p. 3
Organization of this Book	p. 5
Basic Understanding of [Sigma][Delta] A/D Conversion	p. 7
Basics of A/D Conversion	p. 7
Sampling and Quantization	p. 7
Quantizer White Noise Model	p. 10
Performance Metrics	p. 11
Frequency Domain Metrics	p. 12
Noise and Power Metrics	p. 13
Used Tools and Program Code	p. 15
Performance of Nyquist Rate Converters	p. 16
Performance of Oversampled Converters	p. 17
Oversampled Noise-Shaping Converters: [Sigma][Delta] ADC	p. 18
The First-Order [Sigma][Delta] Modulator	p. 20
Pattern-Noise and Dithering in [Sigma][Delta] Modulators	p. 21
Performance Increase in [Sigma][Delta] Modulators	p. 22
High OSR [Sigma][Delta] Modulators	p. 23
Higher Order [Sigma][Delta] Modulators	p. 23
Multibit [Sigma][Delta] Modulators	p. 24
Single-Loop, Single-Bit, Higher Order [Sigma][Delta] Modulators	p. 25
Distributed Feedback Topology	p. 25
Feed-Forward Topology	p. 27
Local Feedback Loops	p. 28
[Sigma][Delta] Modulator Loop Filter Stability and Scaling	p. 29
Effective Quantizer Gain in [Sigma][Delta] Modulators	p. 32
Multiloop, Cascaded [Sigma][Delta] Modulators	p. 33
Specialized Architectures	p. 36
Loop Filters with Bandpass Characteristic	p. 37
Continuous-Time [Sigma][Delta] Modulators	p. 39
CT [Sigma][Delta] Modulator Issues	p. 39
Sampling Operation	p. 40
Filter Realization	p. 41
Quantizer Realization	p. 42
Feedback Realization	p. 43
DT/CT Modulators Trade-offs	p. 47
DT-to-CT Conversion of [Sigma][Delta] Modulators	p. 47
The Impulse-Invariant Transformation	p. 48
Modified Z-Transform	p. 52
Differences of the Two Transformations	p. 54
DT-to-CT Conversion of Cascaded [Sigma][Delta] Modulators	p. 55
Direct Filter Synthesis	p. 61
STF and NTF in CT [Sigma][Delta] Modulators	p. 63
Implicit Antialiasing Filter in CT [Sigma][Delta] Modulators	p. 65
Implicit AAF of the CT Third-Order Modulator	p. 66
Implicit AAF of the CT SOFO Modulator	p. 69
Calculations with the CT Loop Filters	p. 71
Alternatives for CT Filter Implementation	p. 71
gmC-Integrator	p. 71
LC-Resonator	p. 73
Active gmC-Integrator	p. 74
Current-mode Integrator	p. 75
Log-Domain Integrator	p. 75
Active RC-Integrator	p. 76
Active MOSFET-C-Integrator	p. 77
Conclusion on the Commonly Used CT Integrators	p. 77
Classification of Non-Idealities in CT [Sigma][Delta] Modulators	p. 78
Input Referred Errors	p. 81
Organization of the Following Chapters	p. 83
DAC Nonidealities in Continuous-Time [Sigma][Delta] Modulators	p. 85
Feedback DAC Error Classification	p. 85
Excess Loop Delay in Continuous-Time [Sigma][Delta] Modulators	p. 85
Coefficient Mismatch through Excess Loop Delay	p. 86
Increased Modulator Order through Excess Loop Delay	p. 87
Alternative Approach to the Effect of Excess Loop Delay	p. 88
Compensation for Excess Loop Delay in CT [Sigma][Delta] Modulators	p. 89
Simulation Results on Excess Loop Delay	p. 92
Extension to Other Architectures	p. 94
Clock Jitter in Continuous-Time [Sigma][Delta] Modulators	p. 94
Jitter Effects in CT [Sigma][Delta] Modulators	p. 94
Calculation of the Jitter Influence for Rectangular Feedback	p. 96
Reduction of Clock Jitter Influence Using Multibit DACs	p. 99
Reduction of Clock Jitter Influence Using Shaped Feedback Waveform DACs	p. 100
Further Possibilities for CT [Sigma][Delta] Modulators with Reduced Clock Jitter Sensitivity	p. 106
CT Loop Filters Employing Shaped Feedback Waveforms	p. 107
Trade-off for Reduced Clock Jitter Sensitivity	p. 108
Discussion on the White Clock Jitter Model	p. 109
Simulation Results on Clock Jitter	p. 110
DAC Slew Rate Limitation	p. 113
DAC Nonlinearity	p. 114
Filter Nonidealities in Continuous-Time [Sigma][Delta] Modulators	p. 117
Analytical Description	p. 117
Analytical Description of the Nonideal CT Filter Behavior	p. 117
Quantitative Impact of Nonideal CT Filter Behavior	p. 118
Finite OpAmp Gain	p. 119
Simulation Results	p. 121
Integrator Gain or Time-Constant Error	p. 121
Effective Quantizer Gain and Integrator Gain Errors	p. 122
Single-Loop Modulators	p. 123
Cascaded Modulators	p. 124
Simulation Results	p. 125
Compensation of Gain Errors in Single-Loop [Sigma][Delta] Modulators	p. 126
Compensation of Gain Errors in Cascaded [Sigma][Delta] Modulators	p. 126
Finite Amplifier Gain-Bandwidth Product	p. 128
Basic Analytical Description of Finite GBW	p. 129
Extended Model for Single-Loop Modulators	p. 131
Compensation for Finite GBW-Induced Errors in CT [Sigma][Delta] Modulators	p. 134
Influence on Different Feedback Implementations	p. 139
Finite Amplifier Slew Rate	p. 141
Slew Rate in CT [Sigma][Delta] Modulators	p. 141
Influence of Different Feedback Waveforms and [Sigma][Delta] Architectures	p. 142
Simulation Results	p. 143
Other Integrator Nonidealities	p. 146
Limited Output Swing	p. 146
Circuit Noise	p. 147
Integrator Nonlinearity	p. 150
Quantizer Nonidealities in Continuous-Time [Sigma][Delta] Modulators	p. 155
CT [Sigma][Delta] Modulator Design Examples	p. 157
FOM Based Design Strategy for CT [Sigma][Delta] Modulators	p. 157
Generic Figure of Merit Calculation	p. 158
Single-Loop Architectures	p. 160
Multibit Single-Loop Architectures	p. 161
Cascaded Architectures	p. 162
FOM Based Design Example: A 12-Bit 25 kHz [Sigma][Delta] Modulator	p. 163
Expansion Features of the FOM Based Design Strategy	p. 164
Low-Power Limits in Analog Circuits	p. 165
Low-Power Limits in Noise-Dominated Circuits	p. 165
Low-Power Limits in Noise-Dominated and Distortion-Dominated Circuits	p. 166
Low-Power Limits in Matching-Dominated Circuits	p. 166
Low-Power Limits in [Sigma][Delta] Modulators	p. 167
Implementation Example I: A 12-Bit 25 kHz 1.5 V CT [Sigma][Delta] Modulator	p. 169
Loop Filter Design	p. 170
Circuit Blocks	p. 174
Modulator Design	p. 178
Measurements	p. 181
Implementation Example II: A CT [Sigma][Delta] Modulator with SCR-Feedback	p. 185
SCR-Feedback Implementation	p. 185
SCR Time Constant and Loop Filter Scaling	p. 186
Experimental Results	p. 188
CT [Sigma][Delta] Modulator with SCR-I-Feedback	p. 189
Implementation Example III: A 12-Bit 2 MHz 1 V CT [Sigma][Delta] Modulator	p. 191
Modulator Architecture	p. 191
Loop Filter	p. 192
Circuit Implementation	p. 195
Layout Consideration	p. 203
Experimental Results	p. 203
Implementation Example IV: A 2-1-1 Cascaded CT [Sigma][Delta] Modulator	p. 205
Circuit Realization of the Cascaded Modulator	p. 207
Measured Ideal Modulator Performance	p. 207
Verification of the Digital Gain-Error Cancellation	p. 209
Program Code	p. 213
General Loop Filter Pole Transformation for the Exponential Feedback	p. 215
On the CT Integrator, Sampling Frequency fs and the Amplifier GBW	p. 217
References	p. 221
Index	p. 239
Table of Contents provided by Ingram. All Rights Reserved.

Continuous-Time Sigma-Delta A/D Conversion

Fundamentals, Performance Limits and Robust Implementations

At a Glance

Hardcover

Shipping

How to return your order

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