Conclusion

Single wire wave propagation in screened single pair is not possible due to existing coupling between both wires. Energy is hence continuously transferred from one wire to the other.

This can be interpreted in terms of common/differential modes (which represent the eigenmodes) excitation and propagation. Modeling this behavior perfectly reflects the measured curves.

Intra-pair skew as defined in the standards is hence not a relevant parameter. It is moreover obvious that the measured signals will strongly depend on the position of the measurement i.e. the length of the cable. Perturbing effects like mode coupling must then rather be looked at using differential to common mode conversion parameters.

Annex

Modified Mixed Mode Representation of Intra-Pair Skew

Another description of intra-Pair skew has been proposed using modified mixed mode S-parameters.¹

In this representation, intra-pair skew is defined as the difference in the propagation time (phase difference) of a differential signal sent at differential Port 1 and received respectively at single wire ports 2 (S_2d1) and 4 (S_4d1).

One can show that: 

S_{2d1 = (}1/√2) (S_21 − S₂₃)              (1)

S_4d1 = (1/√2) (S_41 − S₄₃)             (2)

Figure A1. Connection scheme with port numbering.

Where d1 stands for “differential mode at logical port 1 in. (see Figure A1 ).

One can however also show (using mixed mode parameters description) that: 

S_2d1= (1/√2) (S_dd21 + S_cd21)        (3)

S_4d1= (1/√2) (−S_dd21 + S_cd21)      (4)

Considering for ease of interpretation that: 

S_dd21 ≫ S_cd21                              (5)

(which is the case for the measured cable), the phase difference between these 2 new S parameters will be π (minus sign of S_dd21) plus some oscillations which amplitude is related to the ratio between  Transverse Conversion Transfer Loss (TCL) (TCTL=S_cd21) and differential Insertion Loss (IL=S_dd21) and phase related to the difference in propagation speed of both differential and common modes.

Exchanging the sign of S4d1 as suggested¹ to take into account the 180° phase difference between both “signals” of the differential mode will only move the curve by π down to around 0 (see Figure A2).

Figure A2. Graphical representation of S_2d1 and S_4d1 calculated from S_dd21 and S_cd21.

This is what is observed in the measurement (see Figure A3 and Figure A4).

Figure A3. Sdd21 and Scd21.

This is then obviously not related to some propagation speed difference between both wires, but the envelope of the curve reflects the relative importance of TCL as compared to IL.

Figure A4. Phase difference between S_2d1 and ±S_4d1.

REFERENCES

1. S. Baek, E. Lee and B. Sung, "Computation of Intra-pair Skew for Imbalance Differential Line using Modified Mixed-mode S-parameter," 2007 IEEE Electrical Performance of Electronic Packaging, 2007, pp. 179-182, doi: 10.1109/EPEP.2007.4387154.
2. Ron Olisar , HDMI, DVI and DisplayPort jitter from unbalanced twisted pair and differential cables, EDN October 31, 2008, https://www.edn.com/hdmi-dvi-and-displayport-jitter-from-unbalanced-twisted-pair-and-differential-cables/
3. E. Mayevskiy, J. Huffaker, Limitations of intra-pairs skew measurements in Gigabit range interconnects, DesignCon 2016, TE Connectivity
4. J. Poltz, J. Beckett, M. Josefson, Measurement and simulation of differential skew in twisted pair cables, Proceedings of 55th International Wire & Cable Symposium