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When using a balanced antenna such as a half wave dipole, with an unbalanced feed line such as coax, an RF choke can be used to block RF current emitted by the transmitter from splitting up at the antenna feed point and traveling along the antenna and also down the outside of the coax. Without the choke, the outer shield of the coax becomes a radiating part of the antenna, which is usually not desirable.

Why do amateur radio operators refer to the RF choke in this instance as a balun?

To me it seems that the RF choke isn't a balun and doesn't convert an unbalanced transmission line to a balanced system at all, but rather just removes one of the effects of connecting an unbalanced transmission line to a balanced antenna, that being the unwanted current traveling on the outside of the shield of the coax, by blocking it.

Isn't a real balun for example a ferrite ring with wires arranged such that common mode current is cancelled out in the same way that a transmission line operates while at the same time allowing differential mode current to pass?

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"Balun" is a portmanteau of "balanced" and "unbalanced". Anything made to interconnect a balanced and unbalanced load can be called a balun.

A common-mode choke (like a length of coax wound over a ferrite ring) works as a balun because it inserts a high impedance in the common-mode without affecting the differential-mode. By action similar to a voltage divider, most of the current will then favor the differential-mode.

Typically the common-mode impedance will be something like 75 ohms, that of a resonant dipole. A decent choke can provide a common-mode impedance of 4000 ohms. Because the differential-mode impedance is so much higher, the common-mode current will be very low, practically negligible.

A common-mode choke like this accomplishes the objective of converting between a balanced and unbalanced load. It's easy to manufacture, has low loss, high power handling, can be effective over a wide band, is inexpensive, and works even if the "balanced" load isn't quite perfectly balanced.

This is by no means the only way to make a balun, but for HF and lower this particular design has a lot of advantages, making it very popular. It is very much a proper balun, and with an appropriate design and application is can be a superb solution.

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