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This study shows that placing four NFPs in selective PCB layers significantly improves signal integrity, reducing minimum jitter from 18.28 ps to 12.81 ps and maximum jitter from 27.66 ps to 22.03 ps. 

The accuracy of mixed-mode S-parameter conversion is important for crosstalk mitigation in high-speed digital systems. However, the conventional mixed-mode S-parameter formulation assumes equal even-mode and odd-mode impedances ( Zoo=Zoe ), which limits its applicability, particularly in tightly coupled differential structures. In this article, we propose a novel mixed-mode S-parameter generalization (generalized M1/M2 approach) using an N-differential port network, which allows for multipair (i.e., pair-to-pair) crosstalk analysis on coupled differential systems, given by: [Smm]i×i= ([M1]i×i×[Ss]i×i+[M2]i×i)×([M1]i×i+ [M2]i×i×[Ss])−1. The proposed M1/M2 formulation eliminates the need for renormalization by integrating mode-dependent coupling factors koo and koe, ensuring a more physically meaningful representation of mixed-mode S-parameters, thereby improving the accuracy of both intrapair and interpair crosstalk analysis in high-speed digital systems. The effectiveness of the proposed M1/M2 approach is demonstrated through intrapair and interpair analysis on tightly coupled striplines, revealing peak-to-peak variations in differential return loss, interpair near-end crosstalk, and far-end crosstalk. Validation using a differential setup with commercial tools (Balun approach) confirmed the formulation's accuracy, with errors below 1%. In addition, measurement validation on a microstrip differential pair highlighted the model's scalability and precision, emphasizing the importance of incorporating mode-dependent impedance variations. 

A high-speed via model considering equivalent high-order-mode inductance for frequencies above 70 GHz is proposed in this article. The proposed via model, which considers the equivalent high-order-mode inductance, is a high-accuracy and high-bandwidth via model, improved from the previously proposed mode-decomposition-based equivalent via (MEV) model. The equivalent high-order-mode inductance is an inductance produced by the magnetic fields of high-order modes in the via domain. By including the empirical equivalent high-order-mode inductance, the proposed via model accurately predicts the insertion and return losses of the via with a large antipad size up to the frequency of 150 GHz, which expands the application range of the previously proposed MEV model. In this article, the limitation of the previously proposed MEV model is analyzed by comparing the input impedance extracted from the MEV model and the full-wave simulation. An empirical closed-form formula is proposed to calculate the equivalent high-order-mode inductance at high frequencies to improve the accuracy of the previously proposed model. In addition, the proposed single high-speed via model was expanded to a differential via pair model. The proposed high-speed via model was verified using simulation and measurement results.