Beta Expansions: a New Approach to Digitally Corrected A/d Conversion

We introduce a new architecture for pipelined (and also algorithmic) A/D converters that give exponentially accurate conversion using inaccurate comparators. An error analysis of a sigma-delta converter with an imperfect comparator and a constant input reveals a self-correction property that is not inherited by the successive refinement quantization algorithm that underlies both pipelined multistage A/D converters as well as algorithmic A/D converters. Motivated by this example, we introduce a new A/D converter— the Beta Converter—which has the same self-correction property as a sigma-delta converter but which exhibits higher order (exponential) accuracy with respect to the bit rate as compared to a sigma-delta converter, which exhibits only polynomial accuracy.