(How) does this balun work? (Tonna / F9FT balun for Yagis)

This article proposes an explanation of how the balun used on some Tonna Yagis works.

It appears Tonna no longer manufactures these antennas, I do not know if this design is novel. I do not recall seeing them used by other manufacturers, they may be protected by patent.

Above is a pic of the balun structure on a 2m antenna.

Above, the manual shows that the black sleeve on the balun sleeve would be slid up over the coax connector, making a neat finish. There are slightly different versions for 70cm antennas.

Above is a diagram of the structure. The key elements are the boom (pink), the coaxial feed line (blue) and the balun sleeve (green).

The balun sleeve is located over the coaxial feed line but insulated from it, and the right hand end is just short of the connections to the driven element, and not in electrical contact. The balun sleeve is bonded to the antenna boom at the left hand end.

The balun sleeve and antenna boom form a short circuit transmission line stub, and the impedance looking into the pair from the right hand end is approximately infinite. So, the stub presents an extreme impedance to current that might try to flow on the outer surface of the sleeve tube, current I1≅0 at the left hand end.

By virtue of well developed skin effect which effectively isolates the outer and inner surfaces of the balun sleeve, we can say that the current flowing leftwards on the inner surface is equal to the current flowing rightwards on the outer surface, so I1 flows leftwards on the inner surface and I1≅0 at the left hand end.

A coaxial transmission line is formed between the inner surface of the balun sleeve and the outer surface of the coaxial feed line shield, and it operates in TEM mode. By virtue of TEM mode, we can say that at any point along the line, the current on the outer surface of its inner conductor (the outer surface of the coaxial line shield in this case) is accompanied by an equal current in the opposite direction on the inner surface of the outer conductor (the inner surface of the balun sleeve in this case), and since this current is approximately zero at the left hand end, common mode current on the shield of the coaxial line is approximately zero.

So, in summary it is a balun that relies on a tuned length of transmission line (the sleeve and boom combination) to force a common mode current minimum near the right hand end of the sleeve and is narrowband, though it may work successfully on harmonics. In most implementations, the dielectric for this transmission line stub will be mainly air, and so its velocity factor will be close to unity.

The construction is simple, and could easily be made tuneable with the spring clip mounting used by Tonna, but I would be inclined to an electrically more permanently weatherproof connection.