Necessary and sufficient conditions for mismatch shaping in a general class of multibit DACs

Multibit digital-to-analog converters (DACs) are often constructed by combining several 1-bit DACs of equal or different weights in parallel. In such DACs, component mismatches give rise to signal dependent error that can be viewed as additive DAC noise. In some cases these DACs use dynamic element matching techniques to decorrelate the DAC mismatch noise from the input sequence and suppress its power in certain frequency bands. Such DACs are referred to as mismatch-shaping DACs and have been used widely as enabling components in state-of-the-art ΔΣ data converters. Several different mismatch-shaping DAC topologies have been presented, but theoretical analyses have been scarce and no general unifying theory has been presented in the previously published literature. This paper presents such a unifying theory in the form of necessary and sufficient conditions for a multibit DAC to be a mismatch-shaping DAC and applies the conditions to evaluate the DAC noise generated by several of the previously published mismatch-shaping DACs and qualitatively compare their behavior.