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

Dept. of Electr. & Comput. Eng., Tech. Univ. Lisbon
IEEE Transactions on Instrumentation and Measurement (Impact Factor: 1.71). 05/2001; DOI: 10.1109/19.918166
Source: IEEE Xplore

ABSTRACT 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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    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.
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    ABSTRACT: In this paper an overview of the uncertainty in the results obtained with the histogram test of Analog to Digital Converters is presented. The effect of phase noise, input equivalent additive noise and random phase difference on the number of counts of the cumulative histogram is shown. Theoretical and experimental results are presented. I. INTRODUCTION The histogram test method is a tool widely used for the characterization of analog to digital converters (ADCs). This test gives information about the deterministic characteristics of the converters through the transfer function from which the gain, offset, transition voltages and code bin widths can be obtained. A signal with a known amplitude density function is used to stimulate the converter. Usually a sinusoidal stimulus signal is used because it is the signal that can be more easily generated with a low distortion. Several samples are taken and the converter transfer characteristic is determined by comparing the output codes experimentally obtained with the ones expected from an ideal converter. The results of the characterization suffer from errors caused by different non idealities in the test setup, namely the stimulus signal amplitude, offset, frequency, additive noise, phase noise, and in the sampling signal frequency and phase noise. Also the presence of additive noise and of aperture uncertainty in the ADC itself, that are not characterized with this test method, have an adverse influence in the results obtained. The errors referenced in the previous paragraph can be classified in two types: deterministic errors, that results in a inaccuracy of the results, and can be corrected if determined; and random errors that lead to an uncertainty in those same results and can not be corrected but should be specified. The results can thus be seen as random variables with a statistical distribution that can be considered normal. The knowledge of its mean and variance allow the determination of a confidence interval that contains the exact value of the ADC characteristic with a certain degree of confidence. In the following sections the determination of the variance of the transition voltages is studied.


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