From time to time I see online discussion about determining matched line loss (MLL) from Return Loss.
Something like 150 years ago a self educated genius thought about the problem of ‘smearing’ of telegraph signals in submarine cables and developed a model for the behavior of transmission lines that remains a very good model today. (The guy’s day job was as a telegraphist.)
He needed to develop new mathematics and new concepts like reactance, and he did this in the face of recognised engineers of the day dismissing the ideas.
The smearing problem was different propagation speed of the fundamental and harmonic components of the telegraphy waveform, he referred to it as distortion and in terms of his RLGC transmission line model he defined the requirements for a “Distortionless Line”. Zo for a Distortionless line is a purely real number, and a Lossless Line is a special case of a Distortionless Line.
Today, most transmission line theory and most field measurement and analysis assumes Distortionless Line, much of it depends on Lossless Line assumptions.
To the matter of MLL measurement, the practical cables being measured have Zo that is not purely real and that alone may result in observable different Return Loss measurements with S/C and O/C sections when the measurement instrument is calibrated at some other impedance (eg 50+j0 ohms).
I first tweaked to this when I bought a Bird43 when I started work (~1970), albeit on a pretty meager wage… but such is the thirst for knowledge. I set about justifying to myself why the Bird cost so much by measuring O/C and S/C terminations on the instrument and through some short lengths of coax and found they did not reconcile.
Bird had the answer they thought, they explained in the manual that O/C terminations were not reliable, only use S/C. Whilst Bird sold transmission line measuring equipment, evidently the author of the manual did not understand transmission lines. The imperfection of an O/C termination (perhaps some tens of fF of fringing capacitance as a first approximation) was insignificant at low HF where the observations were made, there was another explanation to be found in the Telegraphers Equation.
Oh, who was the largely forgotten self educated genius that gave us this understanding of transmission lines? Oliver Heaviside.