From what I've read so far, the impedance of the transmission line used to wind the balun should be the geometric mean between the input and output impedances. For a 1:1 balun, no problem, all impedances are the same. For a 4:1 balun going from 50Z to 200Z the transmission line impedance is 100Z, again no problem, with proper spacing of the conductors, 100Z is achievable.
But when going from 50Z to 12.5Z, the geometric mean is now 25Z. Still a 4:1 transformation but the high Z balun winding is now connected to the 50Z input and the low Z balun winding is now connected to the 12.5Z load. Getting below a transmission line impedance of about 30Z looks to be a problem. It seems that the formula used to calculate transmission line impedance cannot handle two conductors separated by the varnish insulation on the wire.
Second question is about twisting the transmission line wire used to wind the balun. This perhaps will maintain wire spacing but will reduce capacitive coupling in the windings. Is this something that is done with fine wire and not so much with larger AWG wire?
All of this is the result of trying to match the input impedance of a WW2 aircraft radio which is said to be 5 ohms to a 50 ohm coax.
Hope all were dry this 4th of July, it got a bit damp here in Arkansas,
Jim
Logic: Method used to arrive at the wrong conclusion, with confidence. Murphy