This paper proposes a general hierarchical analysis methodology, HiPRIME, to efficiently analyze RLKC power delivery systems. After partitioning the circuits into blocks, we develop and apply the IEKS (Improved Extended Krylov Subspace) method to build the multiport Norton equivalent circuits which transform all the internal sources to Norton current sources at ports. Since there are no active elements inside the Norton circuits, passive or realizable model order reduction techniques such as PRIMA can be applied. The significant speed improvement, 700 times faster than Spice with less than 0.2% error and 7 times faster than a state-of-the-art solver, InductWise, is observed. To further reduce the top-level hierarchy runtime, we develop a second-level model reduction algorithm and prove its passivity.

This paper proposes a general hierarchical analysis methodology, HiPRIME, to efficiently analyze RLKC power delivery systems. After partitioning the circuits into blocks, we develop and apply the IEKS (Improved Extended Krylov Subspace) method to build the Multi-port Norton Equivalent circuits which transform all the internal sources to Norton current sources at ports. Since there is no active elements inside the Norton circuits, passive or realizable model order reduction techniques such as PRIMA can be applied. To further reduce the top-level hierarchy runtime, we develop a second-level model reduction algorithm and prove its passivity. Experimental results show 400-700X runtime improvement with less than 0.2% error.