The mismatch-noise PSD from a tree-structured DAC in a second-order ΔΣ modulator with a midscale input

Mismatch-shaping DAC have become widely used in high-performance delta-sigma data converters in recent years. Nevertheless, no theoretical results have been published to date that quantify their performance, so designers have been forced to rely on simulation-based analyses. This paper presents the first theoretical performance analysis of a mismatch-shaping DAC. Specifically, the PSD of the mismatch noise introduced by a first-order tree-structured DAC within a second-order ADC delta-sigma modulator with a midscale constant input signal is derived. This particular mismatch-shaping DAC and delta-sigma modulator configuration was chosen for analysis because it has been demonstrated experimentally to achieve state-of-the-art ADC performance. The choice of a constant midscale input was made because simulation and experimental results suggest that it yields the worst-case performance