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A surface integral equation (SIE) formulation under the magneto-quasi-staticassumption is proposed to efficiently and accurately model arbitrarily shapedinterconnects in packages. Through decently transferring all electromagneticquantities into circuit elements, the loop analysis is used to carefullyconstruct matrix equations with an independent and complete set of unknownsbased on graph theory. In addition, an efficient preconditioner is developed,and the proposed formulation is accelerated by the pre-corrected Fast FourierTransform (pFFT). Four practical examples, including a rectangular metallicinterconnect, bounding wire arrays, interconnects in a real-life circuit andthe power distribution network (PDN) used in packages, are carried out tovalidate its accuracy, efficiency and scalability. Results show that theproposed formulation is accurate, efficient and flexible to model complexinterconnects in packages.

An SIE Formulation with Triangular Discretization and Loop Analysis for Parameter Extraction of Arbitrarily Shaped Interconnects