Generalized Comb Decimation Filters for <formula formulatype="inline"><tex>$\Sigma\Delta$</tex></formula> A/D Converters: Analysis and Design

Abstract

This paper addresses the design of generalized comb decimation filters, proposing some novel decimation schemes tailored to SigmaDelta modulators. We present a mathematical framework to optimize the proposed decimation filters in such a way as to increase the SigmaDelta quantization noise (QN) rejection around the so called folding bands, frequency intervals whose QN gets folded down to baseband because of the decimation process. Comparisons are given in terms of passband drop and selectivity with respect to classic comb filters with orders ranging from 3 to 6. As far as the practical implementation of the proposed filters is concerned, we present two different architectures, namely a recursive and a nonrecursive implementation, the latter of which constitutes the basis for realizing multiplier-less generalized comb filter (GCF) realizations. We propose a mathematical framework for evaluating the sensitivity of GCFs to the approximation of the multipliers embedded in the filter architectures. The considerations deduced from the sensitivity analysis, pave the way to an optimization algorithm useful for approximating the multipliers with power-of-2 coefficients