Good luck finding 300 ohm twin lead in this day and age. When I go to Lowe's and Home Depot or other stores that sold TV hardware, I don't see it any longer. There's plenty of RG-6 and OTA TV antenna hardware.
To measure the characteristics of balanced line I first find the freq where the line under test is a quarter wave long. I do this by connecting the line under test, with its far end shorted, across a 50 ohm load at the output of the balun (the terminals that were calibrated). I then sweep from the lowest frequency looking for the freq where the return loss is the highest. The return loss is often higher than 20 dB at this freq. The return loss is the highest at this freq because the shorted transmission line under test looks like a high impedance (parallel resonance) leaving the 50 ohm load hardly disturbed and having a pretty high RL. Next I remove the 50 ohm load from the test terminals and attach it to the far end of the transmission line under test. The impedance measured (Zin) by the Nano at the freq where the line is a quarter wave long should be resistive. Using the old Q section formula where Zo = (Zin x Zload)^0.5. Zload is the resistance placed at the far end of the transmission line under test.
For 300 ohm line, with Zload being a 50 ohm resistance, Zin should be a resistance of about 1800 ohms. Check: 300 = (50 x 1800)^0.5. Note that everything is a resistance which makes the math pretty easy not requiring complex algebra. ( on the Smith chart the resistances are 9 o'clock and 3 o'clock centered on Zo)
I have JSC twin lead myself. It is not the part number mentioned above. I think it is JSC 1018, spec'd to be 300 ohms. It looks like TV twin lead but it has 18 gauge stranded conductors. Years ago (like 15 to 18 yrs), using the above Q section formula the Z is not the nominal 300 ohms and came in at about 230 ohms. I wondered why this could be so I asked the mfr and never received a reply. I believe the usual TV 300 ohm line uses 22 gauge wire instead of 18 so the JSC 1018, made with the 18 didn't get its spacing adjusted wider to get Zo to be 300 ohms.
