Owen Duffy wrote:
. . .
Even the low frequency model of such a balun reveals this. If the balun
is analysed using the techniques common used for a 50Hz or 60Hz
transformer, the magnetising current (the current that flows into the
transformer with no load attached) is design point. If the core is a low
loss core, one could choose a relatively high mangetising current yet
still have low H+E losses because the Power Factor of that magnetising
current is quite low... or in the case of the RF transformer, one could
use a relatively lossy material (high magnetising current Power Factor),
but the higher µ of the lossier core means lower magnetising current, and
the losses are acceptable.
. . .

As you say, though, there are always tradeoffs. A higher magnetizing
current means a lower winding impedance. In a winding connected across a
transmission line, this means adding a relatively low shunt impedance
across the line. In a series connected winding, as in a current balun,
it means less effective choking of common mode current. Maximizing
winding impedance, which also minimizes magnetizing current, is always
beneficial. But as we've both pointed out, sometimes we're forced to
choose a material that gives us less impedance in order to lower the
loss to a level that won't cause a problem at high power levels. The
price is a smaller shunt winding impedance or less effective common mode
choke, and also typically a narrower operating bandwidth.

Roy Lewallen, W7EL