Elements Redundancy in Reorderings of Switching-Based Calibration for DACs

This paper is devoted to the assessment of redundancy introduction in switching-based calibration with elements reordering for digital-to-analog converters. The simulation covers a full range of redundancy level of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{0 \% - 1 0 0 \%}$</tex> and is performed for a primary array with random errors. The number of primary arrays is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 0 0 0}$</tex> for even resolutions from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{6}$</tex> to 12. According to redundancy level, a certain part of elements from primary arrays is selected after sorting. For the research, several reorderings are applied to the selected elements: 1F1D, Parity-Split, Mirrored and Mirrored Symmetric. For redundancy estimation only, Unreordered array is considered, where no reordering is applied for the selected elements. The selected elements are used for transfer curves obtaining and further calculation of differential and integral nonlinearities. Then, maximum nonlinearities are averaged across the ensemble and normalized on Unreordered array results. The simulation showed that introduction of redundancy is approximately 2 times more effective in nonlinearity reduction than increment of area at a 100 % redundancy. Redundancy level of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10 \%-100 \%$</tex> reduces both differential and integral nonlinearities by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$20 \%-60 \%$</tex>. Further reordering application enhances the obtained results for only integral nonlinearity. The best results are shown by the Mirrored Symmetric reordering, achieving reduction by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$70 \%-80 \%$</tex> at redundancy level of only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 0 \%}$</tex> for resolutions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{6 - 1 2}$</tex> correspondingly.