Systematic approach to the synthesis of continuous-time cascaded Sigma-Delta modulators

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 cancellation filters for continuous-time cascaded architectures is presented in order to achieve maximum signal- to-noise ratio together with optimal anti-aliasing performance. By the same model, an exact equation for the performance loss of any cascaded architecture is derived. 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.