Influence of frequency errors in the variance of the cumulative histogram [in ADC testing]

University of Lisbon, Lisboa, Lisbon, Portugal
IEEE Transactions on Instrumentation and Measurement (Impact Factor: 1.79). 05/2001; 50(2):461 - 464. DOI: 10.1109/19.918166
Source: IEEE Xplore


In this paper, the calculation of the variance in the number of
counts of the cumulative histogram used for the characterization of
analog-to-digital converters (ADCs) with the histogram method is
presented. All cases of frequency error, number of periods of the
stimulus signal, and number of samples are considered, making this
approach more general than the traditional one, used by the IEEE
1057-1994 standard, where only a limited frequency-error range is
considered, leading to a value of 0.2 for the variance. Furthermore,
this value is an average over all cumulative histogram bins, instead of
a worst-case value, leading to an underestimation of the variance for
some of those bins. The exact knowledge of this variance allows for a
more efficient test of ADCs and a more precise determination of the
uncertainty of the test result. This calculation was achieved by
determining the dependence of the number of counts on the sample phases,
on the transition voltage between codes, and on the stimulus signal

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    • "This knowledge allows the proper choice of amplification and filtering to use in order to minimize the effects of noise. Knowing the amount of random noise is also very important in ADC testing in two instances: first, when noise itself is used as the stimulus signal [1] [3] and its standard deviation has to be accurately controlled; and second, when it is required to compute the uncertainty of the estimation results, be it in the Histogram Test [4] [5], the Ramp Vernier Test [6], or aperture uncertainty test [7], for instance. In signal processing, where sinusoids are fitted to experimental data points, the value of random noise present can be used to compute the bias [8] and precision [9] of its parameters, like amplitude. "
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    ABSTRACT: An exact expression for the expected value of the mean square difference of the two data sets acquired during the IEEE 1057 Standard Random Noise Test of analog to digital converters is derived. This expression can be used to estimate exactly the amount of random noise present which is an improvement over the heuristically derived estimator suggested in the standard. A study of the influence of stimulus signal amplitude and offset on the existing estimator is carried out.
    Full-text · Article · Dec 2009 · Metrology and Measurement Systems
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    • "This, in turn, is extremely important in accessing the quality of the system and ultimately the application it serves. The authors have extensively worked in determining the precision of estimates of ADC characteristics obtained with the Standard Histogram Test and other ADC test methods [1] [2] [3] [4] [5]. Other authors have also published valuable contributions in this area [6] [7] [8] [9] which is a very active field of research. "
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    ABSTRACT: Extensive dynamic testing of Analog to Digital Converters is often carried out using the Standard Histogram Test. With this test one can estimate the converter transfer function, including gain, offset error, integral and differential non-linearity. Since the Histogram Test is inherently a statistic test, the estimated parameters are random variables affected by bias and uncertainty. This paper verses specifically the precision of terminal based gain and offset error precision
    Preview · Conference Paper · Jun 2005
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    • "The analytical approach taken in [6] is not easily extrapolated for other situations, so, in this work, we present a different formulation accompanied by a graphical interpretation that will help, in the future, to determine a limit for the frequency ratio that guarantees a maximum for the variance of the number of counts of the histogram. In [8]–[10], we have presented previous developments of this work; however, here, a new formulation is used that better illustrates the ideas we wish to transmit, allowing the reader an easier understanding of our work. "

    Preview · Article · Jan 2003
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