  A surface integral equation (SIE) formulation under the magneto-quasi-static
assumption is proposed to efficiently and accurately model arbitrarily shaped
interconnects in packages. Through decently transferring all electromagnetic
quantities into circuit elements, the loop analysis is used to carefully
construct matrix equations with an independent and complete set of unknowns
based on graph theory. In addition, an efficient preconditioner is developed,
and the proposed formulation is accelerated by the pre-corrected Fast Fourier
Transform (pFFT). Four practical examples, including a rectangular metallic
interconnect, bounding wire arrays, interconnects in a real-life circuit and
the power distribution network (PDN) used in packages, are carried out to
validate its accuracy, efficiency and scalability. Results show that the
proposed formulation is accurate, efficient and flexible to model complex
interconnects in packages.
