Analysis, Estimation and Compensation of Mismatch Effects in A/D Converters

266 Pages·2003·1.91 MB·English

Linko(cid:127)ping Studies in Science and Technology. Dissertations
No. 811
Analysis, Estimation and
Compensation of Mismatch E(cid:11)ects
in A/D Converters
Jonas Elbornsson
Department of Electrical Engineering
Linko(cid:127)pings universitet, SE{581 83 Linko(cid:127)ping, Sweden
Linko(cid:127)ping 2003
Analysis, Estimation and Compensation of Mismatch E(cid:11)ects in A/D
Converters
(cid:13)c 2003 Jonas Elbornsson
[email protected]
http://www.control.isy.liu.se
Division of Control & Communication,
Department of Electrical Engineering,
Linko(cid:127)pings universitet,
SE{581 83 Linko(cid:127)ping,
Sweden.
ISBN 91-7373-621-X ISSN 0345-7524
Printed by Bokakademin AB, Link(cid:127)oping, Sweden 2003
This page is intentionally left blank.

Abstract
The trend in modern communication systems is to replace as much analog circuits
as possible with digital ones, to decrease size, energy consumption and cost. An
analog to digital converter (ADC) is the interface between the analog and digital
parts. Replacing analog parts, such as mixers, with digital ones requires higher
sampling rates. The bottleneck in a digital communication system is often the
ADC. Requirements on low power consumption, small chip area and high sample
ratesareoftencontradictorytorequirementsonhighaccuracyinthemanufacturing
process.
The traditional way to improve the accuracy is to calibrate the ADC before
use. However, calibration is time consuming and costly. Furthermore, the errors
usually change during the lifetime of the ADC due to, for instance, temperature
variation and aging. This means that the ADC must be recalibrated at regular
intervals.
In this thesis, we investigate how the errors in an ADC can be estimated and
compensatedforwhiletheADCisused. Theestimationmustthenbedonewithout
any special calibration signal.
Two di(cid:11)erent types of errors are discussed in this thesis. The (cid:12)rst type of
error is static errors in the reference levels, caused by resistor mismatch. Two
methods are proposed for estimation and correction of these errors. The most
general method requires only that the amplitude distribution is smooth, while the
other one requires knowledge of the amplitude distribution of the input signal but
gives a little better performance.
ThesecondtypeoferroroccursintimeinterleavedADCs, whereseveralADCs
are used in parallel. Due to component mismatch, three di(cid:11)erent static errors
appear: Time errors (static jitter), amplitude o(cid:11)set errors and gain errors. A
method for estimation and compensation of these errors is proposed. The method
requiresbasicallyonlythattheinputsignalisbandlimitedtotheNyquistfrequency
for the system.
Anotherwaytodecreasetheimpactofthemismatcherrorsinatimeinterleaved
ADC is to randomize the selection of which order the ADCs should be used. This
randomizationspreadsthedistortiontoamorenoiselikeshape. Howthemismatch
errors a(cid:11)ect the spectrum of a randomly interleaved ADC is also analyzed in this
thesis.
Tocon(cid:12)rmthattheanalysisandestimationmethodsworkinpractisethemeth-
ods are evaluated on both simulated data and data from real ADCs.
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ii
Acknowledgments
Several persons have contributed to this thesis. First of all, I would like to thank
mysupervisor,ProfessorFredrikGustafsson,forguidanceandsupportinthework
that has lead to the thesis. I am also grateful to Professor Lennart Ljung for
drafting me to the Control & Communication group in Linko(cid:127)ping.
All the people in the Control & Communication group are gratefully acknowl-
edged. Especially I want to thank M.Sc. Thomas Scho(cid:127)n and Lic.Eng. Rickard
Karlsson who have proofread various parts of the thesis and given valuable com-
ments and suggestions for improvement.
During my graduate studies, I have had the opportunity to share ideas and
discussions with the people at In(cid:12)neon Technologies Wireless Solutions Sweden
AB and the Electronic Devices group at Linko(cid:127)ping University. Especially I want
to thank Dr. Jan-Erik Eklund, Prof. Christer Svensson, Lic.Eng. Darius Jakonis
and M.Sc. Kalle Folkesson for helping me understand how the A/D converters
work and helping me with the measurements. I also want to thank M.Sc. Martin
Anderson from Lund University for providing measurement data.
This work was (cid:12)nancially supported by ECSEL (Excellence Center in Com-
puterScienceandSystemsEngineeringinLinko(cid:127)ping)graduateschoolinLinko(cid:127)ping,
which is gratefully acknowledged.
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Contents
I 1
1 Introduction 3
1.1 Outline of Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Outline of Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Published Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Background 9
2.1 Sample-and-hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 A/D Converter Structures . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Flash ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Pipelined ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Successive Approximation ADC . . . . . . . . . . . . . . . . . . 15
2.2.4 Sigma-Delta ADC . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.5 Integrating A/D Converters . . . . . . . . . . . . . . . . . . . . 18
2.2.6 Interleaved ADCs . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Speci(cid:12)cations of A/D Converters . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 DC Speci(cid:12)cations . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Amplitude O(cid:11)set . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.4 Time Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.5 Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.6 Gain Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.7 Dynamic Speci(cid:12)cations . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 ADC Applications in Communication Systems . . . . . . . . . . . . . 26
2.4.1 Digital Subscriber Line Technology . . . . . . . . . . . . . . . . 27
2.4.2 Software Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Blind Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6.1 Reference level errors . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6.2 Mismatch errors in time interleaved ADCs . . . . . . . . . . . . 36
A Sample-and-hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
v
vi Contents
A.1 Nonlinearities in sample-and-hold . . . . . . . . . . . . . . . . . 37
A.2 Dynamic error correction methods . . . . . . . . . . . . . . . . 39
3 Mismatch Compensation of Static Nonlinearities in SA-ADC 41
3.1 A/D Converter Description . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.1 SA-ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.2 Binary Search Algorithm. . . . . . . . . . . . . . . . . . . . . . 43
3.1.3 Subranging Technique . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.1 Resistance Errors . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Subranging Mismatch . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Equalization with known Input Distribution . . . . . . . . . . . . . . 49
3.3.1 Assumptions and Notation. . . . . . . . . . . . . . . . . . . . . 49
3.3.2 Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.3 Criterion Functions . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.4 Amount of Data . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.5 Parameter Update . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.6 Initial Value Estimation . . . . . . . . . . . . . . . . . . . . . . 58
3.3.7 Reference Level Estimation Algorithm . . . . . . . . . . . . . . 59
3.4 Equalization with Unknown Input Distribution . . . . . . . . . . . . 61
3.4.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.2 Estimation Overview . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.3 Amplitude Distribution Estimation . . . . . . . . . . . . . . . . 61
3.4.4 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . 63
3.4.5 Estimation Algorithm . . . . . . . . . . . . . . . . . . . . . . . 64
3.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5.1 Known Amplitude Distribution . . . . . . . . . . . . . . . . . . 65
3.5.2 Unknown Amplitude Distribution . . . . . . . . . . . . . . . . . 73
3.5.3 Subranging ADC . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6.1 ADC Description . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6.2 Algorithm Modi(cid:12)cation . . . . . . . . . . . . . . . . . . . . . . 85
3.6.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.6.4 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.6.5 Implementation Aspects . . . . . . . . . . . . . . . . . . . . . . 90
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4 Time Interleaved A/D Converters 95
4.1 Notation and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2 O(cid:11)set Error Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2.1 Sinusoidal input. . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3 Gain Error Distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3.1 Sinusoidal input. . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4 Time Error Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.1 Sinusoidal signal . . . . . . . . . . . . . . . . . . . . . . . . . . 106