This paper presents a new method to design the digital filters for correcting uncertain 2-1 cascaded sigma-delta (ΣΔ) modulators. The main contribution of this paper consists of two parts. First, we develop a new filter design method, based on H∞ loop shaping technique, to deal with a certain weighted matching condition with polytopic uncertainties in parameters. The feature of the proposed method is to show the filter order can be independent of the weighting function and determined beforehand. Therefore, in contrast to the conventional H∞ loop shaping design method, lower-order filters can be obtained by using the proposed method. The second contribution is the application of the proposed method. For uncertain cascaded ΣΔ modulators, a low-order filter with the same order of the nominal filter is designed, which can efficiently reduce the H∞ norm of the noise transfer function in the signal frequency band. Consequently, the signal-to-noise ratio (SNR) performance is improved. We compare the proposed method with other existing designs and establish its efficacy.
International Journal of Innovative Computing, Information and Control (IJICIC) 8(10A), pp.6761-6775