Signal Integrity Analysis of Package and Printed Circuit Board With Multiple Vias in Substrate of Layered Dielectrics

This paper successfully extends the Foldy-Lax multiple scattering approach to model massively-coupled multiple vias in substrate of layered dielectrics between two horizontal power/ ground plates. The dyadic Green's functions of layered dielectrics are expressed in vector cylindrical waves and modal representations. Formulations are derived for admittances and S-parameters of single via and multiple vias structures. The CPUs and results of S-parameters are illustrated for various sizes of via array. For the case of 16 × 16 via array through hybrid dielectrics in single interior layer, the CPU is about 0.8 s per frequency and is at least three orders of magnitude faster than Ansoft HFSS. The results are within 5% difference of accuracy up to 20 GHz. This full-wave method is able to include all the coupling effects among the multiple vias. It is also shown that the approach of using effective dielectric constant by assuming an effective homogeneous media does not give accurate results.