On the Synthesis of Continuous-Time Sturdy MASH Delta-Sigma Modulators

Sturdy multi-stage noise-shaping (SMASH) delta-sigma modulators (DSMs) achieve high-order noise-shaping while significantly alleviating the mismatch issue between analog and digital transfer functions. Based on the SMASH architecture, we propose a methodology of synthesizing its continuous-time (CT) architecture from its discrete-time (DT) counterpart by using loop-filter connections. The proposed methodology circumvents the necessity of a direct extraction of the quantization noise from the early stages, which is problematic for CT architectures with high sampling rate. Moreover, the proposed method allows to intuitively compensate the CT SMASH for the excess loop delay (ELD). Furthermore, an input feedforward path is introduced into the second stage to eliminate the STF peaking induced by the ELD. A 2–2 SMASH topology is analyzed as a case study to demonstrate the synthesis methodology. Besides, we present derivations for determining loop-filter coefficients. Simulation results confirm the efficacy of the synthesis methodology for the SMASH topology.