A device usually described as a 1-to-1 choke balun is amongst the most
simple of all radio components.

Actually, 1-to-1 has nothing to do with impedance-matching or
transformation, or anything else.

The choke simply allows a balanced circuit, of no particular impedance, to
be connected to an unbalanced circuit, of another no particular impedance,
without any significant interaction between them.

It is just a very short length of balanced-twin transmission line, like
speaker cable, of no particular impedance, wound on a ferrite ring to behave
as a bifilar-wound RF choke.

Loss is negligible. There's only copper loss. The ferrite plays no part in
transmission along the short line, only in the longitudinal choking action.

If there are any ferrite losses they only occur due to the very small
longitudinal current - which is what the choke is doing its best to get rid
of anyway.

When used at the end of an antenna feedline a choke balun is just a short
continuation of that line, albeit of a different impedance. Which is of no
consequence.

At the junction of the balanced-to-unbalanced lines, such as coax to
open-wire, there's going to be a large mismatch anyhow. But that's what the
tuner is for.

The balun does indeed have an impedance transforming property as does any
other short length of line. But in the case of multiband antenna systems it
merely transforms one set of random-value impedances to another random set.
Which, in effect, leaves things as they were.

The average impedance of speaker type cable is about 140 ohms which, for
perfectionists, fits very nicely between 50-ohm coax and 450-ohm ladder
line. But it hardly matters.

The length of line wound on a balun should not exceed 1/8 wavelength at the
highest frequency of interest, at the lines own velocity. Choke action at
the lowest frequency of interest depends on number of turns and permeabilty
of the ferrite.

For multi-band operation a choke balun should be used. It is far better than
fixed-ratio 4:1 and 9:1 baluns which involve wishful thinking and are best
used over relatively narrow bands.

Choke baluns also make balanced tuners redundent. Who wants to crank two
roller-coasters when one will do.
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Reg, G4FGQ