A 3D full-wave approach, based on the Foldy-Lax multiple scattering equations, is successfully extended to model massively-coupled multiple vias using differential signaling and shared antipad in high speed vertical interconnects. For the first time, this method has been used and tested on via-pair with shared antipad in multilayered structure. The magnetic frill current source on the port is calculated by using the finite difference method. Banded matrix iterative method is applied to accelerate the finite difference calculation. Numerical example of 15 signal via-pairs and 20 ground shielding vias in 6-layer board demonstrates that this approach is able to model the via-pair with shared antipad and to include all the coupling effects among multiple vias. The electrical performances of different signal driving schemes are provided and discussed. The coupling crosstalk on various via-pairs is compared. The improvement of signal integrity is shown by using differential signaling and shared antipad for via-pair in multilayered structure. The results are compared with HFSS and SIwave in accuracy and CPU. The CPU using Foldy-Lax approach is three orders of magnitude faster than using HFSS, and two orders of magnitude faster than using SIwave. The accuracy of Foldy-Lax is within 2% difference from HFSS up to 20 GHz, and outperforms SIwave in accuracy.
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