Efficient Spectral-Aware Power Supply Noise Analysis for Low-Power Design Verification

The relentless pursuit of energy-efficient electronic devices necessitates advanced methodologies for low-power design verification, with a particular focus on mitigating power supply noise. The challenges posed by shrinking voltage margins in low-power designs lead to a significant demand for rapid and accurate power supply noise simulation and verification techniques. Too large supply noise inevitably results in the raise of supply level, thereby hurting the lower power design target. Spectral methods have demonstrated as a great alternative to produce a sparse sub-matrix with spectral-similarity property as the preconditioner to efficiently reduce the iteration number and solve the linear system for supply noise verification. However, existing methods either suffer from high computational complexity or rely on approximations to reduce computational time. Therefore, a novel approach is needed to efficiently generate high-quality preconditioners. In this paper, we propose a two-stage spectral-aware algorithm to address these challenges. Our approach has three main highlights. Firstly, by introducing spectral-aware weights, we can better assess the priority of edges and construct high-quality spanning trees with the minimum relative condition number. Secondly, by leveraging eigenvalue transformation strategies, we can quickly and accurately recover off-tree edges that are spectrally critical, avoiding time-consuming iterative computations. Thirdly, we proposed a fast computation method to further decrease the computational complexity of the effective resistance. Compared with two SOTA methods, GRASS and feGRASS, our approach demonstrates higher accuracy and efficiency in preconditioner generation (37.3x and 2.13x speedup, respectively) as well as significant improvements in accelerating the linear solver for power supply noise analysis in power grid simulation and other Laplacian graphs (5.16x and 1.70x speedup, respectively).