But how good is the efficiency when the balun/transformer is working
between completely the wrong impedances (which will be most of the
time)? My understanding (and limited experience) is that most of your
power simply heats up the ferrite.
Ian.
==============================
Ian, both your understanding and experience of how a balun works are
limited. But don't be disheartened - you are in good company! ;o)

They are not simple transformers. The windings are in fact transmission
lines consisting of a pair of wires running in parallel, either coaxial or
balanced-twin - it doesn't matter which although balanced-twin is slightly
more efficient and physically more easy to construct.

Their full name is "Transmission Line Transformers".

They have a wider bandwidth and a higher HF response than ordinary
primary-and-secondary HF transformers. This is because the normal
capacitance between turns and between windings is incorporated in the
transmission lines instead of being directly in shunt with winding
inductance.

They are inherently very low loss devices because there's only short lengths
of high-conductivity copper involved.

In theory, there is no loss in the ferrite core because the currents in the
transmission line wires flow, adjacent to each other, in oposite directions
and the flux cancels out in the core. But cancellation is never completely
perfect and HF-quality ferrite core material should be used. However, LF
grade materials found in the junk box often work quite satisfactorily.

Cancellation is better with coaxial lines than with balanced twin but this
is hardly a matter of importance. Ferrite rods require more turns to achieve
the same inductance than rings at the low frequency end.

The ordinary inductance of the windings considered as single wires, in
conjunction with the nominated terminating resistances, sets the low
frequency response of a balun transformer in the usual way.

The high frequency end of the range is limited by the physical length of the
line winding. Line length should be small in relation to the wavelength
along the line. Upper frequency response and ratio begin to fall off when
line length exceeds about 1/8 or 1/10 of a wavelength at its own velocity.
Not free space velocity. This allows a frequency range of 1.8 to 30 MHz on a
core of ordinary proportions with permeability in the range 200 to 400.

------------------------

The performance and behaviour of an X-to-Y ohm balun, as with ordinary
transformers, goes haywire if it is not operated between its designed-for
resistances. Or at least resistances in the right ball-park.

Hence the futility at HF of using one between a multi-band antenna and any
sort of transmission line or tuner. The range of impedances to be covered
is even greater than those listed by our good friend Cecil.

A choke balun, a single short length of transmission line wound on a ring or
rod, is a different kettle of fish. Its range of impedances is unlimited.
----
Reg, G4FGQ