Synthesis of robust digital correction filters for cascaded sigma-delta converters

Cascaded sigma-delta converters relax the requirements on the oversampling ratio for a given resolution. However, their performance is sensitive to mismatches in the analog components. Previous work has explored adaptive calibration schemes to address the mismatch problem, but such methods lead to an increase in the implementation complexity. In the present work an alternative strategy to the adaptive one is pursued in which robust digital correction filters are synthesised. The main contributions reported in this paper are the development and validation of the synthesis framework and preliminary solutions to the synthesis problem. A robust correction filter is synthesised for the 2–1 cascaded architecture which provides improved performance over the nominal correction filter for the worst case uncertainties in the analog parameter values. Since the filters are fixed at the design stage, the proposed scheme does not add an additional burden on the implementation.