Optimal design of delta-sigma modulators via generalized KYP lemma

Abstract

In this paper, we propose a new method for designing delta-sigma modulators via H-infinity optimization. In delta-sigma modulators, the accumulator is conventionally used in a feedback loop to reduce quantization noise. In contrast, we propose an H-infinity design to shape the frequency response of the noise transfer function. The design is formulated as frequency domain inequalities in finite frequency ranges, which is reduced to linear matrix inequalities via generalized Kalman-Yakubovic-Popov (KYP) lemma. A design example is presented to show that our design is superior to conventional ones.