Measuring the static characteristic of dithered A/D converters

Abstract

Dithering is a useful technique that removes quantization error and part of the linearity error in A/D converters. Removing the remaining static error requires a periodical fast measurement of the characteristic, which is a rather difficult task because of the intrinsic very high resolution of the dithered device. Focusing on this issue, the paper examines three possible test methods: statistical analysis, time domain analysis, and, with more detail, frequency domain analysis. The peculiar nature of the static characteristic of dithered converters makes the third method particularly attractive. The frequency domain technique is proposed, therefore, as a good practical tool for implementing linearization in A/D converters with dither.

Introduction

Dithering is a common and well-known technique more and more employed with modern analog-to-digital converters (ADCs) for measurement applications [1], [2]. In dithered converters the input is added to a small ‘noise’ (dither signal) before the digitization. More specifically (Fig. 1), in the subtractive topology a pseudorandom dither signal is synchronously added to the analog input and subtracted from the digital output; in the non-subtractive topology the dither signal is only added at the input. In both cases, effective resolution improvement is obtained by filtering or averaging, at the cost of bandwidth or speed reduction. Non-subtractive dither is especially appealing and more common in practice, because it does not need costly hardware for generating a precisely known signal and perform synchronous analog and digital additions. Besides, it can be sometimes implemented by simply exploiting the intrinsic analog noise of the converter, or other small stable signals inherently present in the digitizing hardware. In this paper we will refer always to the non-subtractive dither, but the final results apply without substantial differences also to the subtractive topology.

The dither technique is essentially aimed at reducing systematic conversion errors, including quantization, but there are not standard techniques to measure the static characteristic of the converter for this particular case. The problem lies mainly in the very high (theoretically infinite) resolution of the ADC, and is therefore caused just by the main advantage provided by the dither. An accurate measurement of the characteristic is useful to assess the uncertainty of the device, and is necessary when the aim is to obtain a highly linear converter by further linearization, for example implementing a look-up linearization table like suggested in Ref. [3]. The present paper is therefore focused on this measurement, with special attention to the problem of its velocity: this is indeed a critical point when one must use its results for the periodical automatic recalibration of a look-up table. Section 2 of the paper deals, under a theoretical viewpoint, with linearity errors in ADCs and effect of dither on them. In Section 3 three possible methods for measuring the static characteristic of an ADC with dither are examined, i.e. the statistical analysis (histogram test), the time-domain analysis, and the much faster frequency-domain analysis. Theoretical considerations suggest that the frequency domain approach, usually too imprecise for ordinary converters, is well suited for use with dithered converters. Section 4 reports experimental results that show the practical advantages and drawbacks of each test method with dithered converters, and demonstrates the special effectiveness of the frequency-domain approach.