Mixed-Port Scattering and Hybrid Parameters for High-Speed Differential Lines

High-speed transmission lines are commonly routed as differential lines to control sensitivity to noise on the reference planes at higher speeds. Differential lines are typically characterized in terms of mixed-mode scattering parameters, as they provide insight into the behavior of differential and common signals, as well as the mode conversion among them. These mixed-mode scattering parameters can be mathematically obtained from single-ended parameters, which can, for example, be measured with a four-port vector network analyzer. There has been recent efforts to develop extended or modified versions of mixed-mode scattering parameters, especially for tightly-coupled lines. This can be a point of confusion in interpreting the behavior of differential lines. In this paper, we introduce the mixed-port scattering and hybrid parameters, which do not suffer from any such ambiguous definitions. Mixed-port hybrid parameters are the most natural way to represent any four-port differential circuit, as they are based on intuitive differential and common-port excitations of the network. They also enable extraction of the current division factor experimentally, which is a critical parameter for electromagnetic interference analysis of differential lines. Mixed-port scattering parameters are also defined based on common and differential port excitations, allowing a simpler interpretation than their mixed-mode counterparts, without the need for defining even, odd, common, or differential-mode impedances. As such, mixed-port scattering and hybrid parameters can be used to analyze the performance of a general differential network, certainly including coupled or asymmetrical lines, without any ambiguity.