A symbolic approach toward high-level variation-aware topology synthesis of Delta-Sigma modulators

This article presents a methodology for automated high-level variation-aware topology synthesis of ΔΣ (Delta-Sigma) modulators. The methodology targets an optimal high-level ΔΣ modulator topology in terms of statistical signal-to-noise ratio (SNR) variation. In the proposed methodology, a systematic symbolic formulation of statistical SNR variation is made so that variations of capacitors are directly translated to SNR variation. The symbolic formulation of statistical SNR variation is then taken as the cost function guiding the topology synthesis process. A ΔΣ modulator template topology, which compactly represents all possible modulator topologies, is used so that the solution space is complete. To facilitate the search for an optimal topology, a mixed-integer non-linearly constrained programming (MINLP) program is formulated. By solving the MINLP program, an optimal solution with least statistical SNR variation can be obtained. A few experiments have shown the solved optimal topologies have less SNR variations compared to traditional ones.