A model of mismatch-shaping D/A conversion for linearized DAC architectures

Mismatch-shaping DACs offer one way to overcome the linearity problems inherent in sigma-delta converters employing multibit quantization. This paper analyzes the spectral shaping of the noise introduced by circuit inaccuracies, providing a model valid for a class of DAC structures. This model is developed in two versions. The first is purely theoretical because it assumes that the actual DAC errors are known, but constitutes a reference against which the performance of alternative mismatch-shaping structures can be judged. The second model is a modification of the first, which dispenses with the need to know the absolute DAC errors if there exists a linear relationship between a set of unknown independent error sources and the DAC errors. The analysis leads to some properties that this class of DAC must possess in order to exploit mismatch-shaping and predicts the existence of alternative structures of mismatch-shaping DACs. In particular, a DAC consisting of nonunit elements is shown to be amenable to second-order lowpass mismatch shaping