A SAR-Assisted Continuous-Time M-0 MASH Delta-Sigma Modulator With Digital-Domain Noise Leakage Shaping

Delta–sigma (<inline-formula> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula>) modulators are widely used in high-resolution analog-to-digital converters (ADCs). With continued technology scaling, digital-intensive <inline-formula> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> architectures are increasingly favored over traditional analog-centric designs. This work presents a successive approximation register (SAR)-assisted digital noise-coupling (DNC)-based noise-leakage shaping technique for continuous-time (CT) <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>–0 multi-stage noise-shaping (MASH) <inline-formula> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> modulators, complemented by a digital back-end integrator. The key building blocks for implementing DNC-based noise-leakage shaping, including the interface between the first and second stages, are efficiently realized through a SAR-assisted structure, while the DNC filter is implemented using simple digital delay cells, enabling a compact and hardware-efficient design. Extensive behavioral simulations demonstrate robustness against key nonidealities, including finite opamp gain, limited unity-gain bandwidth (UGBW), and wide coefficient variations, and circuit-level results validate the practicality and effectiveness of the proposed architecture for high-resolution, low-power applications.