Mode-Decomposition-Based Equivalent Model of High-Speed Vias up to 100 GHz

Via transitions in high-speed channels critically influence the signal integrity and power integrity of high-speed systems. In this article, a mode-decomposition-based equivalent model of a high-speed via that can be applied at frequencies up to 100 GHz is proposed for the first time. The equivalent model for modeling the via transition consists of upper and lower via-to-plate capacitances and equivalent parallel-plate impedances, owing to the fundamental mode and higher order modes for parallel-plate, all of which can be calculated from physical geometrical parameters. The via-to-plate capacitances are calculated by using the domain decomposition method in the antipad domain and via domain. The parallel-plate impedances representing via and parallel-plate coupling are calculated with the mode decomposition method for different parallel-plate modes (fundamental and higher order modes) in the parallel-plate domain. The proposed equivalent via model provides more accurate results in the high-frequency range than previously proposed methods. Because the impact of higher order modes on parallel-plate impedance is considered in the proposed mode-decomposition-based via model, and the effects of higher order modes are prominent at high frequencies for printed circuit board (PCB) vias with typical dimensions. The proposed model is validated with numerical examples, which show good correlation at frequencies as high as 100 GHz. The proposed model can be applied to high-speed via transitions in PCBs and packages.