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4:1 lambda/2 coaxial balun. What happens if length not exactly lambda/2 ?

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drkirkby

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I'm trying to match a folded dipole to 50 Ohms using a 4:1 balun. The problem is a folded dipole is not exactly 200 Ohms, so a 4:1 balun does not result in a very good return loss.

I believe there may be some trick that can be played by having the length of the balun a bit less than lambda/2, to compensate for the fact the antenna is not 200 Ohms. But I'm not sure.

Does anyone know of how to derive the impedance of the usual 4:1 balun from transmission line if the length is not exactly lambda/2? I assume if I can find an equation, it may be possible to make the antenna and balun impedance more suitable. Ideally I'd like to get one to be the complex conjugate of the other, but I doubt that will be possible.

Some designs I have seen appear to have both the balun and the dipole shorter than I would expect. (I'm well aware of fact a half-wave dipole is not resonate, and cables have a velocity factor. Even taking the velocity factor of the cable into account, I've seen some baluns shorter than the theoretical figure. I'm interested in how this might work.
 
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