I got myself a TV "Rabbit Ears" module originally for a TV. It came with a small length of coax, permanently attached to the antenna foot, and a Belling-Lee connector on the other end.
My idea was to use an RG-58 coax with an SMA plug with this antenna, because it is easy to make a handle for it, and it's easy to store.
Inside the mounting point for the two telescopic antennas, there is a ferrite core, with a couple loops around it, going off to the two telescopic antennas:
In the schematic, (a) is four turns, (c) and (d) are two turns, each. As I said it's a dual-ferrite core, so two holes in one block of ferrite (ignore the center tap on the (a) side, I couldn't find a transformer symbol with one inductor on one side, and two disjunct inductors on the other, with a core).
I also made a couple of pictures:
They are rather shoddily soldered together, and while handling the center core wire broke off from the solder point:
As you can see in the pictures above, then it's one ferrite block with two holes in it. A wire running from core to shield of the coax goes through both holes, looping four times. Then, each from the core and the shield a wire loops through either hole, twice and then connects to either of the two telescopic antennas, which I have removed, so handling is a bit easier.
Since this is a TV UHF antenna, this has to be 75 Ω, but I'm wondering how I should now modify the balun, such that the impedance is 50 Ω.
My first approach was to remove the balun altogether, and directly solder a length of 50 Ω RG-58 to either of the antenna solder points and that'll be it. But I'm not entirely sure that would be a good approach, since I believe the balun is here for a reason...
Instead of coming up with just a number of turns, it would be nice, if someone could provide a formula how to calculate these, or a place where I can find further information.
UPDATE: I think I've found the device that was wired up in my antenna in blog post Make a wideband antenna matching transformer.
So, it's a 4:1 balun, with 75 Ω on the coax-side. This means the antenna has an impedance of 300 Ω. 300 Ω for a dipole? It sounds strange to me, but I don't know.
Assuming this is a 300 Ω antenna, I'd need a 6:1 transformer / balun to match it up with 50 Ω. The closest I can practically wire up is a 2 and 5 turns transformer, resulting in a 6.25:1 transformer. I'm not sure that would be even usable. The closest match without going into crazy figures is 49 and 20 turns, resulting in 6.0025:1, which I think would be close enough.
I don't think I have a way of finding out the exact impedance of my rabbit ears antenna, so I guess I just have to assume it's 300Ω going by the fact how the balun / transformer was wired up, etc.