Stochastic testing of ADC—Step-Gauss method

doi:10.1016/j.csi.2003.09.001

Computer Standards & Interfaces

Volume 26, Issue 3, May 2004, Pages 251-257

https://doi.org/10.1016/j.csi.2003.09.001 Get rights and content

Abstract

The article describes theoretical background and practical results of Analog-to-Digital Converters (ADC) stochastic test method “Multi-Gauss” that has been designed, developed and verified at the Department of Measurement of the Czech Technical University, FEE in Prague. It is suitable for testing of high-resolution AD converters (e.g. Σ–Δ or dither-based) or on the contrary ultra high-speed AD converters. The method is based on the histogram test driven by stochastic signal with defined probability density function (p.d.f.). Further enhancement that allows an estimation of frequency dependency of effective number of bits (ENOB) is also presented.

Introduction

Low sampling frequency, high-resolution AD converters (e.g. Σ–Δ or dither-based) or on the contrary ultra high-speed AD converters (e.g. with opto-electronic core) testing by means of deterministic testing signal is a problem due to the lack of (pure) testing signals. In such cases, stochastic input signals seem to be better applied for testing [1], [2], see also Fig. 1.

Histogram test can use various input signals and principally allows the use of noise as the input signal. To overcome difficulties related to generation of large-scale uniformly distributed stochastic signal, a method based on superposition of Gaussian noises with equidistantly spaced DC shifts (Fig. 2) has been proposed in Ref. [3] and theoretical analysis has been provided there. Practical applicability of this method has been verified by comparison of results obtained by this method and by standard histogram test using deterministic (ramp) testing signal for an internal Analog-to-Digital Converter (ADC) of digitizing oscilloscope [4], plug-in card for PC [5] and portable ADC transfer device [4], [5], [6], [7]. One has to carefully design the test setup to obtain enough code words covered by each particular test signal.

Section snippets

Histogram stochastic test

Each particular testing signal is Gaussian noise with probability density function (p.d.f.) f_G(μ,σ) where μ is the mean value and σ means standard deviation. It is easy to show that $lim Δ→0 ∑ k=−∞ ∞ f_{G} (μ+kΔ,σ) − 1 Δ =0,k integer$ Independently on the value of μ and σ. In other words, the superposition of Gaussian distributed noises with the equidistantly spaced DC values by step Δ is for suitably small values of Δ, an excellent approximation of uniformly distributed signal. Measurement is provided for each

Required number of samples

The following formula should be used to calculate the necessary amount of samples to achieve a required accuracy [3]: $k=m a^{2} ε^{2}$ where k is number of required samples, m is number of code words of the tested ADC, a=1.96 for 5% confidence level of Differential Nonlinearity (DNL) evaluation and ε is the statistical error of DNL evaluation (5% in our case).

ENOB calculation

Effective number of bits (ENOB) calculation follows the usual way that is described in Ref. [2] or in Ref. [3]. In the concrete, DNL values are estimated from the measured histogram and Integral Nonlinearity (INL) values are then calculated using DNL: $DNL_{i} = O_{i} −O O$ $INL_{j} =− ∑ i=1 j DNL_{i}$ where O_i is the value of the i-th code of cumulative histogram and O is its ideal value that can be achieved by the following way (the common way of indexing of code words 0,1,…,m−1 is expected): $O= ∑ i=1 m−2 O_{i} m−2$ Assuming

Measurement results

Two tested objects have been selected to confirm practical applicability. The results of testing of digital oscilloscope HP54645A are shown in Table 3. Since the testing system operates up to several MHz and the sampling rate of the internal flash 8-bit ADC is 200 MSa/s sample rate, no differences have been found. Small variations of ENOB values shown in Table 3 fall within uncertainty level that is given by finite number of samples, as indicated by formula (7). Practical applicability of this

Conclusions

A special type of stochastic testing signal for ADC tests has been introduced. It allows substitution of difficult-to-generate but easy-to-process uniformly distributed stochastic signal with a cumulation of Gaussian signals that are easy to generate. Two other modifications of this method are presented. They allow estimation of the dependency of effective number of bits on the frequency content of input signal. Experimental results that confirm the method applicability are available.

Acknowledgements

This project is supported by the Grant Agency of Czech Republic No. 102/01/D087 New Methods of Digitizers Testing by means of Stochastic Signals.

References (7)

P Carbone et al.
Noise sensitivity of the ADC histogram test
IEEE Std. 1241-2000
IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters
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J Holub et al.
Signal source for statistical testing of ADC, XVI

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