The idea of the braiding is to try to equalize the effective resistance
of all the strands by giving them all the same exposure to the outer
layer of the bundle. A nice inclusive democratic idea, but all bat's
wings and newt's eyes from the POV of electromagnetics--and even circuits.
Here's the circuits argument. Suppose you take two series strings of
resistors, each of which alternates 1k and 10k, like this:
*----1k---10k---1k---10k---1k---10k---*
| |
0--*---10k---1k---10k---1k---10k---1k----*--0
Total resistance: 1650 ohms (3.3k per string). Now suppose you put all
the 10k resistors in one string and all the 100 ohm resistors in the
other--like letting a couple of strands be the outside conductor the
whole way. Then you have this:
*---10k---10k--10k---10k--10k---10k---*
| |
0--*----1k---1k----1k---1k----1k---1k----*--0
Which is 6K // 600 ohms, or 545 ohms. Which is better?
The electromagnetic argument for Litz wire is also murky, because it
relies on that dopey single-straight-wire-in-free-space derivation we
all know and love. It's mathematically simple, but it has very little
to do with the actual physical environment inside a transformer, where
there's all that other copper running with similar dI/dt right nearby,
plus the huge collective effect of the other turns and the core.
We pretty well know what the dB/dt is inside the winding. For a single
conductor, the B field at the surface is transverse, and is all due to
the current in that one wire. That field configuration gives rise to
zero eddy current in the wire, just a radial gradient of the current
density, and it makes very little difference to the fields outside the wire.
In a winding, however, there is a huge component of B perpendicular to
the wire surface, due to the fields of all the other wires and the huge
effect of the core. That will drive circulating currents inside the
diameter of the wires (like turbulence in a pipe). There is thus the
opportunity for a lot of eddy current loss in the copper if it isn't
split up into very small transverse pieces (as in a laminated core).
The net effect is that parallel multifilar windings ought to be at least
as good as Litz wire in transformers.
I've never seen a proper derivation of the eddy current loss in a
transformer winding, but I'm sure it's been done. It sure doesn't have
much to do with classical skin effect, though.
Cheers
Phil Hobbs
