High Accuracy Sigma-Delta Modulator implementations via Suboptimal Quasi-Sliding Mode Control

Abstract

Two novel Sigma-Delta modulator algorithms based on discretized suboptimal second order sliding mode concepts for high resolution analog-to-digital conversion purposes are proposed. Let $\boldsymbol{f_{s}}$ be the finite over-sampling frequency of the modulator, novel schemes that convert to a 1-bit signal, resp., the first, or the second time-derivative of the signal to be modulated are suggested to reduce the error of the conversion process, at the demodulation side, to an $\boldsymbol{\mathcal{O}}(1/\boldsymbol{f_{s}}^{2})$, instead of $\boldsymbol{\mathcal{O}}(1/\boldsymbol{f_{s}}^{0.5})$ of the traditional scheme. The algorithms are discussed and analyzed in the discrete-time setting, and a comparative analysis illustrates the effectiveness of these solutions.