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Modeling Analog to Digital Converters at Radio Frequency
KTH, School of Electrical Engineering (EES), Signal Processing.
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [sv]

Det här arbetet handlar om att ta fram beteendemodeller av analog till digital omvandlare avsedda för tillämpningar i radiofrekvensområdet. Det gäller tillämpningar inom telekommunikation men även in test- och mätinstrument där omvandlingen från analoga till digitala signaler ofta är en prestandamässig flaskhals. Modellerna är avsedda att användas för att efterbehandla utdata från omvandlaren och på så sätt förbättra prestanda på den digitala signalen. Genom att skapa modeller av verkliga omvandlare och hur dessa avviker från ett idealt beteende kan ofullständigheter korrigeras genom så kallad postkorrigering.

Beteendemodeller innebär att genererar en lämplig insignal, mäta utdata och beräkna en modell. För omvandlare i radiofrekvensområdet ställs höga krav på instrumentering. Den testutrustningen som används är baserad på moderna högprestanda instrument som har kompletterats med specialbyggd utrustning för signalkonditionering och datainsamling. I avhandlingen har även olika insignaler utvärderats med såväl teoretisk som experimentell analys.

Det finns ett flertal olika varianter av modeller för att modulera ett olinjär, dynamisk system. För att få en parametereffektiv modell har utgångspunkten varit att utgå från en Volterramodell som på ett optimalt sätt beskriver svagt olinjära dynamiska system, så som analog till digital omvandlare, men som är alltför omfattande i antal parametrar. Volterramodellens har sedan reducerats till en mindre parameterintensiv, modellerstruktur på så sätt att Volterrakärnans symmetriegenskaper jämförts med symmetrierna hos andra modeller. En alternativ metod är att använda en Kautz-Volterramodell. Den har samma generella egenskaper som Volterramodellen, men är inte lika parameterkrävande. I den här avhandlingen redovisas experimentella resultat av Kautz-Volterramodellen som i framtiden kommer att vara intressanta att använda för postkorrigeringen.

För att kunna beskriva beteenden som en dynamiska olinjära modellen inte klarar av har modellen kompletterats med en statisk styckvis linjär modellkomponent. I avhandlingen presenteras en sluten lösning för att identifiera samtliga paramervärden i modellen. Vidare har det i avhandlingen genomförs en analys av hur respektive komponent påverkar prestanda på utsignalen. Därigenom erhålls ett mått på den maximala prestandaförbättring som kan uppnås om felet kan elimineras.

Abstract [en]

This work considers behavior modeling of analog to digital converters with applications in the radio frequency range, including the field of telecommunication as well as test and measurement instrumentation, where the conversion from analog to digital signals often is a bottleneck in performance. The models are intended to post-process output data from the converter and thereby improve the performance of the digital signal. By building a model of practical converters and the way in which they deviate from ideal, imperfections can be corrected using post-correction methods.

Behavior modeling implies generation of a suitable stimulus, capturing the output data, and characterizing a model. The demands on the test setup are high for converters in the radio frequency range. The test-bed used in this thesis is composed of commercial state-of-the-art instruments and components designed for signal conditioning and signal capture. Further, in this thesis, different stimuli are evaluated, theoretically as well as experimentally.

There are a large number of available model structures for dynamic nonlinear systems. In order to achieve a parameter efficient model structure, a Volterra model was used as a starting-point, which can describe any weak nonlinear system with fading memory, such as analog to digital converters. However, it requires a large number of coefficients; for this reason the Volterra model was reduced to a model structure with fewer parameters, by comparing the symmetry properties of the Volterra kernels with the symmetries from other models. An alternative method is the Kautz-Volterra model, which has the same general properties as the Volterra model, but with fewer parameters. This thesis gives experimental results of the Kautz-Volterra model, which will be interesting to apply in a post-correction algorithm in the future.

To cover behavior not explained by the dynamic nonlinear model, a complementary piecewise linear model component is added. In this thesis, a closed form solution to the estimation problem for both these model components is given. By gradually correcting for each component the performance will improve step by step. In this thesis, the relation between a given component and the performance of the converter is given, as well as potential for improvement of an optimal post-correction.

Place, publisher, year, edition, pages
Stockholm: Signalbehandling , 2007.
Series
Trita-EE, ISSN 1653-5146 ; 2007:062
Keyword [en]
ADC, Analog to Digital Converters, Signal processing
National Category
Telecommunications
Identifiers
URN: urn:nbn:se:kth:diva-4523ISBN: 978-91-7178-777-4 (print)OAI: oai:DiVA.org:kth-4523DiVA: diva2:12672
Public defence
2007-11-30, 99:131, Högskolan i Gävle, Kungsbäcksvägen 47, Gävle, 13:00
Opponent
Supervisors
Note
QC 20100629Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2010-06-29Bibliographically approved
List of papers
1. Truncated Gaussian Noise in ADC Histogram Tests
Open this publication in new window or tab >>Truncated Gaussian Noise in ADC Histogram Tests
2007 (English)In: Measurement, ISSN 0263-2241, E-ISSN 1873-412X, Vol. 40, no 1, 36-42 p.Article in journal (Refereed) Published
Abstract [en]

One method to characterize analogue to digital converters (ADCs) is to use a histogram, where Gaussian noise may be used as stimulus signal. However, a Gaussian noise signal that excites all transition levels also generates input values outside working range of the ADC. Modern signal generators can generate arbitrary signals. Hence, excluding undesired values outside the ADC full scale can minimize test sequences. Truncating the signal to the working range gives further advantages, which are explored in this paper. The Cramer-Rao lower bound and a minimum variance estimator for histogram tests with an arbitrary stimulus are derived. These are applied for truncated Gaussian noise and the result is theoretically evaluated and compared to untruncated noise. It is shown that accuracy increases for a fixed sample length and that variation over transition levels decrease.

Keyword
ADC; histogram tests; CRLB; MVE; testing; signal processing
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-7590 (URN)10.1016/j.measurement.2006.05.005 (DOI)000243833500006 ()2-s2.0-33845450590 (Scopus ID)
Note
QC 20100629Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2017-12-14Bibliographically approved
2. Histogram Tests for Wideband Applications
Open this publication in new window or tab >>Histogram Tests for Wideband Applications
2008 (English)In: IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456, E-ISSN 1557-9662, Vol. 57, no 1, 70-75 p.Article in journal (Refereed) Published
Abstract [en]

Characterization and testing of analog-to-digital converters (ADCs) are important for many reasons. A histogram test is a common method to characterize the linearity features of an ADC. Two commonly used stimulus signals are sine waves and Gaussian noise. This paper presents a metrological comparison between Gaussian and sine-wave histogram tests for wide-band applications, that is, we evaluate the performance of the characterization of the ADC and the usability of postcorrection. A postcorrection procedure involves the characterization of the ADC nonlinearity and then the use of this information by processing the ADC output samples to remove the distortion. The results show that the Gaussian histogram test gives reasonable accuracy in measuring nonlinearities. However, it does not result in a suitable model for postcorrection in wideband applications. A single-tone sine-wave histogram will be a better basis for postcorrection. The best result can be obtained if the lookup table is trained with several single-tone sine waves in the frequency band.

Keyword
analog-to-digital converters (ADCs); histogram; measurements; test
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-7591 (URN)10.1109/TIM.2007.908274 (DOI)000251947400010 ()2-s2.0-43949129589 (Scopus ID)
Note
QC 20100629Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2017-12-14Bibliographically approved
3. Measuring Volterra Kernels of Analog To Digital Converters Using a Stepped Three-Tone Scan
Open this publication in new window or tab >>Measuring Volterra Kernels of Analog To Digital Converters Using a Stepped Three-Tone Scan
2008 (English)In: IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456, E-ISSN 1557-9662, Vol. 57, no 4, 666-671 p.Article in journal (Refereed) Published
Abstract [en]

The Volterra theory can be used to mathematically model nonlinear dynamic components such as analog-to-digital converters (ADCs). This paper describes how frequency-domain Volterra kernels of an ADC are determined from measurements. The elements of the Volterra theory are given, and practical issues are considered, such as methods for signal conditioning and finding the appropriate test signals scenario and suitable sampling frequency. The results show that, for the used pipeline ADC, the frequency dependence is significantly stronger for second-order difference products than for sum products and the linear frequency dependence was not as pronounced as that of the second-order Volterra kernel. It is suggested that the Volterra kernels have the symmetry properties of a specific box model, namely, the parallel Hammerstein system.

Keyword
analog-to-digital converter (ADC), measurements, test, Volterra kernels
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-7592 (URN)10.1109/TIM.2007.911579 (DOI)000254029600001 ()2-s2.0-41549085064 (Scopus ID)
Note
QC 20100922Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2017-12-14Bibliographically approved
4. Achievable ADC Performance by Post-Correction Utilizing Dynamic Modeling of the Integral Nonlinearity
Open this publication in new window or tab >>Achievable ADC Performance by Post-Correction Utilizing Dynamic Modeling of the Integral Nonlinearity
2008 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1110-8657, 497187-1-497187-10 p.Article in journal (Refereed) Published
Abstract [en]

There is a need for a universal dynamic model of analog-to-digital converters (ADC’s) aimed for postcorrection. However, it is complicated to fully describe the properties of an ADC by a single model. An alternative is to split up the ADC model in different components, where each component has unique properties. In this paper, a model based on three components is used, and a performance analysis for each component is presented. Each component can be postcorrected individually and by the method that best suits the application. The purpose of postcorrection of an ADC is to improve the performance. Hence, for each component, expressions for the potential improvement have been developed. The measures of performance are total harmonic distortion (THD) and signal to noise and distortion (SINAD), and to some extent spurious-free dynamic range (SFDR).

Keyword
Dynamic models; Electric network analysis; Harmonic distortion; Signal to noise ratio
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-7593 (URN)10.1155/2008/497187 (DOI)000255610900001 ()2-s2.0-43949088850 (Scopus ID)
Note
QC 20100629Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2011-11-08Bibliographically approved
5. High dynamic range test-bed for characterization of analog-to-digital converters up to 500 MSPS
Open this publication in new window or tab >>High dynamic range test-bed for characterization of analog-to-digital converters up to 500 MSPS
2005 (English)In: 14th Symposium on New Technologies in Measurement and Instrumentation and 10th Workshop on ADC Modelling and Testing, IMEKO-International Measurement Federation Secretariat , 2005, 601-604 p.Conference paper, Published paper (Refereed)
Abstract [en]

A measurement set-up of for the characterization of analog-to-digital converters (ADCs) is described. The measurement set-up characterizes ADCs up to 16 bits at 350 MHz (option for >500 MHz). Testing dynamic performance of high-speed ADCs is regarded as difficult and expensive. By using existing state-of-the-art instruments in combination with specially designed amplifiers and filters, a high performance, cost efficient test-bed has been built-up. Practical performance corresponds to ADC datasheet and exceeds the performance obtained if using commercial instruments only. Consequently, the measurement results represent the true performance of the ADC without impact from the test-bed

Place, publisher, year, edition, pages
IMEKO-International Measurement Federation Secretariat, 2005
Keyword
Analog to digital conversion, Instruments, Analog to digital converters, And filters, Commercial instruments, Cost-efficient, Dynamic performance, High dynamic range
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7594 (URN)2-s2.0-84899049387 (Scopus ID)9788389786371 (ISBN)
Conference
14th Symposium on New Technologies in Measurement and Instrumentation and 10th Workshop on ADC Modelling and Testing, Gdynia/Jurata, Poland, 12 September 2005 through 15 September 2005
Note

QC 20100630

Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2015-04-10Bibliographically approved
6. Model Based Dynamic Characterization of Analog-Digital-Converters at Radio Frequency
Open this publication in new window or tab >>Model Based Dynamic Characterization of Analog-Digital-Converters at Radio Frequency
2007 (English)In: 2007 9th International Symposium on Signal Processing and its Applications, Vol. 1-3, 2007, 1403-1408 p.Conference paper, Published paper (Refereed)
Abstract [en]

A dynamic characterization of analog-digital converter integral nonlinearity (INL) is considered. When using a plurality of test frequencies in the measurement set-up, the dynamic errors of the converter are characterized. The INL is modeled by low and high code components - LCF and HCF, respectively. The LCF and HCF are parameterized and a least squares method is derived for the estimation of the parameter values from obtained measurements. A closed form solution to the estimation problem is derived and its performance is illustrated by a numerical example. The proposed method is believed to be fruitful in wide-band characterization of analog-digital converters at radio frequency, and thus of importance for the evaluation of modem and future wireless communication systems.

Keyword
Analog-digital conversion, Closed-form solution, Frequency conversion, Frequency measurement, Least squares methods, Parameter estimation, Radio frequency, Testing, Wideband, Wireless communication
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-7595 (URN)10.1109/ISSPA.2007.4555623 (DOI)000259439900350 ()2-s2.0-51549088895 (Scopus ID)978-1-4244-0778-1 (ISBN)
Conference
9th International Symposium on Signal Processing and its Applications, Sharjah, U. Arab Emirates, Feb 12-15, 2007
Note
QC 20100630 Invited paperAvailable from: 2007-11-08 Created: 2007-11-08 Last updated: 2012-02-12Bibliographically approved
7. Kautz-Volterra modelling of analogue-to-digital converters
Open this publication in new window or tab >>Kautz-Volterra modelling of analogue-to-digital converters
2010 (English)In: Computer Standards & Interfaces, ISSN 0920-5489, E-ISSN 1872-7018, Vol. 32, no 3, 126-129 p.Article in journal (Refereed) Published
Abstract [en]

In many test and measurement applications, the analogue-to-digital converter (ADC) is the limiting component. Using post-correction methods can improve the performance of the component as well as the overall measurement system. In this paper an ADC is characterised by a Kautz–Volterra (KV) model, which utilises a model-based post-correction of the ADC with general properties and a reasonable number of parameters. It is also shown that the inverse model has the same dynamic properties as the direct KV model. Results that are based on measurements on a high-speed 12-bit ADC show good results for a third-order model.

Keyword
Kautz–Volterra model; Analogue-to-digital converter; Vector signal analyzers
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-7596 (URN)10.1016/j.csi.2009.11.007 (DOI)000275477300008 ()2-s2.0-75849128322 (Scopus ID)
Conference
XII International Workshop on ADC Modelling and Testing
Note
QC 20100630Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2017-12-14Bibliographically approved

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  • apa
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