Systematic approach to the synthesis of continuous-time cascaded sigma–delta modulators

Abstract

This paper deals with a systematic approach to the synthesis of continuous-time cascaded sigma---delta modulators. Based on a system-theoretical model, a detailed derivation of the digital cancelation filters for continuous-time cascaded architectures is presented in order to achieve maximum signal-to-noise ratio together with optimal anti-aliasing performance. By using the same model, an exact equation for the performance loss of any cascaded architecture is derived. The latter is due to the scaling for stability and given relative to an ideal high-pass filter of the overall modulator order. Finally, an analytical calculation of optimal scaling coefficients in between the stages is performed, resulting in a limited search-space for these coefficients. Theoretical results are verified by simulations.