At Transmission line loss under mismatch explanations I wrote that there is a lot of woolly thinking amongst hams about transmission line loss under mismatch and worked a simple example that could be done ‘by hand' to show that formulas that some authors have produced as implementations of their explanations don't stack up.
I also gave a solution to the Zo*3 scenario using TWLLC, but not the Zo/3 scenario which a few eagle hounds have pounced on as evidence that the solution would not support the article.
Not at all, the Zo/3 TWLLC solution was not given so as to keep the article short and within the attention span of modern hams though it was eventually a quite long article, and for that reason I will address it separately, here.
To refresh your memory, the original basic linear circuit theory solution was:
We can use a simple series circuit of the total line resistance and load resistance, and since the same current flows through both, the loss is Rtotal/Rload=(119.7+0.015876)/119.7=1.0001327, or in dB, 10*log(1.0001327)=0.000576dB.
And here is the TWLLC solution:
Above, TWLLC 0.000587dB loss against 0.000576dB by the simple linear circuit model. The difference is well within expectation and TWLLC will be more accurate than the simpler basic linear circuit model (it does true transmission line analysis and there is less rounding error than in the ‘hand' calcs).
Remember that formulas given by (Maxwell 2001) and (Straw 2007) both gave 0.00032dB loss, 55% of the TWLLC value, and that suggests their explanation which gave rise to their formulas is wrong at least for the example scenario.
- Duffy, O. 2001. RF Two Wire Transmission Line Loss Calculator (TWLLC). VK1OD.net (offline).
- Maxwell, Walter M. 2001. Reflections II. Sacramento: Worldradio books.
- Straw, Dean ed. 2007. The ARRL Antenna Book. 21st ed. Newington: ARRL. p24-10.