Application of the Foldy–Lax multiple scattering method to the analysis of vias in ball grid arrays and interior layers of printed circuit boards

The authors applied the method of Foldy–Lax multiple scattering equations to multiple vias in ball grid arrays and the interior layers of printed circuit boards. The method gives the scattering parameters of the array. The results are verified with Ansoft's HFSS with very little difference between the Foldy–Lax approach and the HFSS results. The CPU required for the method is only a small fraction of the time that HFSS requires. For a 16 × 16 array of vias, the method calculates all the S‐parameters of the 512 ports in 4 min for 10 frequencies on a Pentium 3.2 GHz PC.