MSH: A Multi-Stage HiZ-Aware Homotopy Framework for Nonlinear DC Analysis

Nonlinear DC analysis is one of the most important tasks in transistor-level circuit simulation. Homotopy gains great success to eliminate non-convergence problem occurred in the Newton-Raphson (NR) based methods. However, nonlinear circuits with DC-path available high impedance (HiZ) nodes may fail to converge with homotopy methods due to sufficiently large resistance compared to homotopy insertions, leading to an insufficiently close enough initial-guess. In this paper, we propose a HiZ-aware homotopy framework, MSH, enabling multi-stage continuation for HiZ nodes and others separately to enhance simulation convergence. In addition, a brand-new homotopy function with limited current gain variation for MOS transistors is utilized to ensure smoother solution curve and better efficiency. Moreover, we trace the solution curve with arclength by considering homotopy parameters as unknown variables to better ensure convergence. The effectiveness of our proposed homotopy framework is demon-strated on large-scale industrial-level circuits.