Analysis of Residue Probability Density Function and Comparator Offset Error in Pipelined ADCs

Abstract

This paper presents a new approach to analyze the convergence of residue probability density function (pdf) in pipelined ADCs. Compared to the previous approaches, in the proposed approach, in addition to the analysis of residue pdfs for different input densities, the analysis of the sub-ADC comparator offsets impact on output pdf is possible. Using Fourier analysis, it will be shown that the residue density converges to uniformity. In the half-bit redundant structure, residue pdf concentrates in the center half of the stage full-scale range and 6 dB of extra resolution can be gained. Also, the share of each stage in this resolution improvement is investigated. Examining the sub-ADC threshold offsets impact on residue pdfs, it is observed that with respect to the impact on converter additional resolution, the final stages offset errors are more significant than the first stages offsets.