A Compressed Multivariate Macromodeling Framework for Fast Transient Verification of System-Level Power Delivery Networks

Abstract

This paper discusses a reduced-order modeling and simulation approach for fast transient power integrity verification at full system level. The reference structure is a complete power distribution network (PDN) from platform voltage regulator module (VRM) to multiple cores, including board, package, decoupling capacitors, and per-core fully integrated voltage regulators (FIVR). All blocks are characterized and known through high-fidelity models derived from first-principle solvers (full-wave electromagnetic and circuit-level extractions). The complexity of such detailed characterization grows very large and becomes intractable, especially for power integrity verification of massive multicore platforms subjected to real workload scenarios. We approach this problem by exploiting a multi-stage macromodeling and compression process, leading to a compact representation of the system dynamics in terms of a linearized state-space structure with multiple feedback loops from the FIVR controllers. The PDN macromodel is obtained through a data-driven approach starting from reference smallsignal frequency responses, obtaining a sparse and structured representation specifically designed to match the behavior of the reference system. The resulting compact model is then solved in time-domain very efficiently. Results on mobile and enterprise server benchmarks demonstrate a speedup in runtime up to 50× with respect to HSPICE, with negligible loss of accuracy.