On the Static Resolution of Digitally Corrected Analog-to-Digital and Digital-to-Analog Converters With Low-Precision Components

Abstract

Abstract-This semi-tutorial paper considers the effect of component mismatch on the static accuracy of analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) with digital correction. First, it is noted that the effective static resolution of flash ADCs is not much reduced by component mismatch: with proper digital correction, the loss due to mismatch is only about 1.3 bit, virtually independently of the mismatch level unless the mismatch is very small. Second, it is noted that current steering DACs may actually benefit from component mismatch. Moreover, with proper digital correction, current steering DACs can achieve an effective static resolution of bits with as few as +2 near-unit low-precision current sources.Index Terms-Analog-to-digital converter (ADC), calibration, digital-to-analog converter (DAC).

On sequential analog-to-digital conversion with low-precision components

“…The static accuracy of certain analog-to-digital converters (ADCs) with low-precision components and digital correction was studied in [1], [2]. In this paper, we continue the discussion in [2] and connect it with the work by Daubechies et al on ADCs based on beta expansions [3]- [5].…”

“…In this paper, we continue the discussion in [2] and connect it with the work by Daubechies et al on ADCs based on beta expansions [3]- [5]. As in [1], [2], we will consider only the static accuracy of ADCs; both noise and dynamic issues (including the thorny practical problem of accurate sampling) will be ignored in this paper.…”

“…Without loss of generality, we will assume 0 ≤ x < 1. As in [2], we will measure the accuracy of an ADC in terms of its effective resolution (in bits), which is defined as…”

“…The required accuracy (and thus the chip area and the power consumption) of each comparator is linear in K, i.e., exponential in the effective resolution. However, it was shown in [2] that the precision of the comparators can be reduced almost arbitrarily if digital calibration is used.…”

“…The necessary background and the motivation will be given in Section II. In particular, it will be pointed out that such an ADC (with attractive analog complexity) may be obtained by using the digital-to-analog converter (DAC) of [2] in a successive-approximation ADC scheme.…”