An SIE Formulation With Loop Analysis for Large-Scale Arbitrarily Shaped Interconnects

A magneto-quasi-static (MQS) surface integral equation (SIE) formulation with loop analysis is proposed to extract the impedance of interconnects in packages. The loop analysis is developed with an independent and complete set of unknowns according to the graph theory, which can significantly reduce the dimension of the final matrix. With the pre-corrected fast Fourier Transform (pFFT), large-scale interconnects can be efficiently modelled. A practical example in packages is carried out to validate the effectiveness and scalability of the proposed formulation. Results show that the proposed formulation is accurate and flexible to model complex interconnects in packages compared with the industrial solver.