Modeling the Dual-Slope Behavior of in-Quad EL-FEXT in Twisted Pair Quad Cables

It is well known that the ratio between received crosstalk and received signal in telephony cabling increases with the frequency until both levels become about equal. Transmission systems like VDSL and G.fast are designed to cope with that. But the awareness that the increase of EL-FEXT (equal level - far end cross talk) becomes much stronger above a certain frequency (increases with 40 dB instead of 20 dB per decade) was raised only recently in ITU and BBF standardization bodies for G.fast. This second order effect became known under the name “dual slope” effect, was initially not well understood, and resulted in a number of conjectured explanations. This paper demonstrates that this second order effect in far end crosstalk between opposite wire pairs in the same quad is deterministic in nature. It is caused by the interaction of the twist in a quad and its metallic surroundings (e.g., shield). The twist of these quads reduces this second order crosstalk effect significantly, but what remains causes a slope of 40 dB/decade. This paper shows via a model that this second order effect scales linearly with the cable length and twist length, and validates that via measurements. It quantifies how sensitive this effect is to cable design parameters like twist length and capacitance to shield. In addition, an extension is proposed to a commonly used simplified system model for describing the far end cross talk as a function of the frequency and cable length.