Estimation of ADC Nonlinearities from the Measurement in Input Voltage Intervals

Transcription

1 Estiation of ADC Nonlinearities fro the Measureent in Input Voltage Intervals M. Godla, L. Michaeli, 3 J. Šaliga, 4 R. Palenčár,,3 Deptartent of Electronics and Multiedia Counications, FEI TU of Košice, Slovak Republic 4 Institute of autoation, easureent and applied inforatics, SjF STU Bratislava, Slovak Republic Eail: arek.godla@tuke.sk Abstract. This paper present proposal for fast testing ethod of AD converters aied for estiation of INL as the error function and superiposed uncertainty based on two diensional ADC error odel. INL function is being deterined by curve fitting of approxiation function fro the easureent of INL( in chosen code bins of the full scale range of ADC under test. Proposed testing ethod is suitable for approval of final accuracy of assebled data acquisition syste. Keywords: Analog to Digital Converters (ADC), Curve Fitting, Integral Nonlinearity (INL), Error Function, Uncertainty. Introduction This paper presents a siple experiental ethod of testing INL characteristics of AD converters which can be perfored in laboratories of end user. Test ethod works with several code bins which are iportant to approxiate of integral nonlinearity as a basic paraeter describing deviation in the transfer characteristic. Integral nonlinearity INL( and average code bin width Q are defined according to [], []. Taking into account Terinal based definitions transient code levels idea and real at both ends are equal T id (0) = T(0) and T id (N-)= T (N-) The characteristic of a real AD converter could be described by the two diensional odel []. INL is being described by the forula LCF HCF INL( INL( INL( (3) Where low code frequency coponent LCF INL represents sothered coponent of INL function while high code frequency coponent HCF INL describes deterinistic and stochastic effects of ADC nonlinearities. There are various atheatical ethods proposed in the literature which approxiate LCF INL( with sufficient accuracy [4], [5]. The optial type of approxiating function depends on shape resulting error function conditioned by the ADC architecture and utilized technology. Fro the etrological point of view, with increasing approxiation order the LCF INL( convert to the systeatic ADC error and reaining HCF INL( covers all reaining stochastic error sources. Ipact of all those error sources could be described by cobined uncertainty.. Curve fitting ethod for approxiation of the INL characteristics The proposed test ethod is based on the approxiation of the ADC error characteristics by a polynoial. k... ak 0 (4) INL( a k a a 8

2 The paraeters a 0, a,, a, are estiated using the least ean square (LMS) criteria k n E in kk INL( a k a k... a k a The nuber n of codes (k k n ) where the integral nonlinearity INL( have to be easured is lower than all ADC codes, which allows to speed up testing procedure. The transient code levels T( in the L interleaved nodes (k, k n- ) are easured by standardized testing ethod [3]. 3. Uncertainties and Errors of Measuring of Code Bins The INL easured in chosen code bins gives inforation just about systeatic error. Uncertainty deterines the argin of error of the tested error function by giving a range of values likely to enclose the true value. The cobined uncertainty consists fro following coponents in our case. The first one u represents the testing uncertainty caused by the utilized testing ethod. It belongs to the uncertainty of type A and could be deterined by the repetition of easureent of code bins. We have used 0 easureent for any code bin k. Uncertainty u ( of transient code level testing deterines uncertainty of INL( in the nodal code bin. l u ( 3 ( Ti ( T ( ) l( l ) i The total uncertainty of INL estiation in the L nodal points is being deterined by the geoetrical su. Uncertainty in nodes k=0 and k= N - are zero. L L u u i u i u( j). L i i j j where r ij represents the cross correlation between testing results in any nodal point k n. The second uncertainty coponent is deterined by the uncertainty of the precise digital volteter, which is responsible for traceability of easured code levels. This value could be estiated by the u uncertainty of type B taken fro the volteter data sheet. The third coponent is connected with approxiation uncertainty expressed by the u 3. Q. E approxiation ean square error 3. This coponent has no correlation to the other uncertainty coponents. The uncertainty expressed in the codes ust be transfored in voltage. The total cobined uncertainty of testing procedure u c is being deterined by all three contributions. No correlation between the is considered. 3 c 3 u i i r ij u (8) Cobined uncertainty is an optial indicator of test confidence. Deterination of INL( systeatic error is reliable when final uncertainty is lower than axial value INLax. This figure of erit allows end user to iprove its testing procedure in two directions. 0 (6) (7) (5) 9

3 The first one is based on the deterination of bottlenecks in the proposed ethod by selection of uncertainty coponents contributing doinantly to the cobined uncertainty. It allows enhancing nuber of testing attepts, iproving the quality of reference volteter or increasing order of approxiating polynoial. The second possibility how to achieve satisfying ratio between u c and INL ax is the enhanceent of the aount of the testing nodes and order of the polynoial approxiation. Ipossibility to achieve required liits of cobined uncertainty is a sign that standardized ethods has to be applied. As entioned in paper [6] the suitable error odels are dependent on ADC technology. Besides converter error the digital results at the ADC output are always corrupted by the u q Q' quantization noise which theoretical value is. When the testing cobined uncertainty and axial value of error function are lower than quantization uncertainty it has no sense to perfor correction using error function. 4. Experiental Results Proposed ethod was tested by two types of ADCs each one representing another internal architecture. First one is bit ADC of type TC709 A by Microchip based on the double slope integration principle with autozeroing phase. Second tested ADC was 8-bit ADC0804 by Intersil working on the successive approxiation principle. The (Fig..a.) shows results of approxiation of the first ADC (TC 709 A) by the polynoial of 5,0,3-th order when L=0 equidistant points in the transfer characteristic were taken for INL estiation. The integral nonlinearity by the standardized ethod is on (Fig..b). Fig.a.) Fig.. Measured INL of TC709 by standardized ethod b.) approxiated function with polynoial of 3,5,0 th order for 0 nods The (Fig. a). shows results of approxiation of ADC0804 with different order. The difference between approxiated polynoial and real INL easured by standardized ethods is shown on (Fig..b). Typical consequence of DAC in the feedback is periodical repetition of the characteristic values of INL over the full scale. The uncertainty coponents contributions and their ipact on cobined one are shown on (Tab.). 30

4 Table. Final uncertainties for both ADCs with use variety of nodal points Type of ADC 8 bit ADC ADC0804 bit ADC- TC709 Nod. points u 3 [µv] u u u c Order of pol. [µv] 0 [µv] [µv] pol. 0 6, , ,5 64, , ,79 630, , ,5 50 3, , 66,7 643,9 4946,5 5,5 0 8,58 50,57 3,473 67, ,7 30,469 99,86 40,56 377, ,55 50,404 4,3 76, ,50 43,7 Fig.a.). Measured INL of ADC0804 by standardized ethod b.) approxiated function with polynoial of 3,5,0 th order for 0 nods Conclusions Experiental results show that approxiation of ADCs INL by a polynoial function on the base of easureent in the reduce aount of easured points of its FSR is a suitable ethod which can speed up tie consuing procedure according to IEEE standards for ADC testing. Increasing resolutions of the produced ADCs increase contribution of analog coponents to the final error function. Especially, integrated sensor systes could be presented by the generalized analog to digital converter. Testing for the reduced aount of reference physical quantities fro the full easuring range is uch easier. Acknowledgent The work is a part of project supported by the APVV agency APVV , VEGA agency (No. /030/09 and /0555/) and KEGA agency (97-034STU-4/00, 3/75/09).This publication is the result of the project ipleentation Developent of Centre of Inforation and Counication Technologies for Knowledge Systes (project nuber: ) supported by the Research & Developent Operational Prograe funded by the ERDF. References [] Michaeli,L., Michalko,P., Šaliga,J.>Unified ADC nonlinearity error odel for SAR ADC /, 008.In: Measureent. - ISSN Vol. 4, no. (008), p [] IEEE Standard for digitizing wavefor recorders, Dec [3] IEEE Standard for terinology and test ethods for analog-to-digital converters, Dec [4] Janik, Jean-Marie: Estiation of A/D Converter Nonlinearities fro Coplex Spectru [5] Adao, F. Attivissio, F. Giaquinto, N. Kale, I.: Measuring Dynaic Nonlinearity of A/D Converters Via Spectral Methods, Proc of IMEKO IWADC 003, p

5 [6] Adao, F.,Andria,G.,Attivissio, F. Giaquinto, N.:.:Linearisation of A/D converters by dither and Chebyshev polynoials, /In: Measureent. - ISSN Vol. 35, no. (004), p [7] Stefani,F.,Moschitta,A.,Macii,D.,Carbone,P.,Petri,D.: Fast estiation of ADC nonlinearities using Sinewave Histogra Test, In: Measureent. - ISSN Vol. 39, no. 3 (006), p