A Matching Strategy Based on Full-Permutation Bisection for Data Converters

This paper presents a top-to-bottom element-matching strategy based on a full-permutation bisection algorithm for data converters. By bisecting the composing elements and recombining them for a minimal weight difference, the linearity of the data converter can be significantly improved. Three different approaches have been implemented for the proposed algorithm, and they are based on linear programming, stochastic quantization, and maximal linearly independent subset (MLIS) respectively. Their pros and cons have been discussed and simulated exhaustively, and all of them have been silicon proved via capacitive digital to analog converters in 180-nm technology. Measurement results of twenty dies for each approach verified the aforementioned theoretical analysis, and all three approaches could achieve sub-30 ppm for all codes after calibration. The worst integral nonlinearity at the most significant bit after calibration can be improved from 402 ppm to 10.9 ppm, which is equivalent to a 5.2-bit boost, indicating a promising potential of the proposed matching strategy. Besides, the MLIS-based approach is the first optimal-combination-algorithm-based matching strategy that achieves
$\mathcal {O}(N)$
time complexity, as the authors know.