Understanding and Predicting Vmin Failures in Power Delivery Networks through Multi-Order Droop Signatures

As voltage margins continue to shrink in modern high-performance ICs, circuits become increasingly vulnerable to power supply noise, making the minimum supply voltage ($V_{\text {min }}$) a critical metric for reliable operation. These voltage fluctuations arise from the multi-level characteristics of the power delivery network (PDN), whose frequency-dependent impedance induces multi-order voltage droops under dynamic loads. This paper presents a systematic framework for understanding and predicting $V_{\text {min }}$ failures in PDNs through multi-order droop signatures. We examine how varying input current profiles affect the relative impact of each PDN level and conduct a comprehensive statistical study to quantify the relationship between droop characteristics and multi-level contributions to $V_{\text {min }}$. A machine-learning model is further developed to rapidly and accurately predict multilevel contribution ratios from input current profiles and droop signatures, offering insights into $V_{\text {min }}$ failures and facilitating efficient PDN optimization for improved power integrity.