Re: Skin Effect in Solid/Stranded/Litzendraht Wire -Guy Macon

On Oct 11, 4:49 am, Guy Macon <http://www.guymacon.com/> wrote:
David Brown wrote:

Guy Macon wrote:

Consider three stranded wires of equal cross section. To simplify
the thought experiment, assume square/triangular/hexagonal strands
so that there is no space between them.

Wire "Litz" has infinite resistance between strands.
Wire "Stranded" has finite resistance between strands.
Wire "Solid" has zero resistance between strands.

The basic physics of electromagnetism is such that strands at the
center of the bundle experience a greater magnetic flux than strands
on the outside. This increases the self-induction-caused back EMF
for the center strands, which causes the current to want to jump
strands to concentrate at the outer, lower Z strands. "Solid" has
no resistance to hinder this, and thus has maximum skin effect.

This is just thinking aloud - it might be nonsense...

So to minimise the skin effect (not that it is significant for home
audio systems in the first place), what you really want is a cable made
from individually insulated strands, with the signal on half the strands
and the return on the other half, with the strands intermixed. That way
each strand is surrounded by strands generating an equal and opposite
flux, and thus the flux at any point inside (or outside) the cable will
be tiny. This would give you minimal inductance, minimal skin effect,
and maximal rejection of common mode interference - in effect, you have
an exaggerated twisted pair with many pairs twisted together. I suspect
you'd have a high capacitance, however.

Just as a thought experiment, one could, in theory, reduce the
capacitance to zero by wrapping each strand inside a driven
shield. Not at all practical, but cheaper than some of the stuff
I have seen for the Golden Ears audio market... :)

The audio snake oil sellers cause real problems in AC power.
An non-power engineer who knows that skin effect is too small
to make a difference in a speaker cable at 20-20K Hz. will
sometimes assume that skin effect is too small to make a
difference in a high-current bussbar at 60Hz.

There are other advantages to keeping the return close to the
supply as well. A few months back we had a customer who was
running two 1000A+ siggle phase 400Hz lines through two holes
in a shipboard bulkhead. He had made an error and routed both
hots though one hole in the bulkhead and both neutrals through
the other. His efficiency took a hit and the bulkhead got hot...

--
Guy Macon
<http://www.guymacon.com/>


Why would one WANT to reduce the effective capacitance to zero?
What's wrong with making an 8 ohm transmission line, assuming you want
to drive an 8 ohm load? (That is, what's wrong with the concept; in
practice at audio it's pretty tough if you don't use superconducting
wires.) I put the particulars of a 24 conductor, 26AWG ribbon cable
into a transmission line calculator; assumed Er for the dielectric of
4.5. The calculator tells me the RF impedance is about 6.8 ohms; but
because of the series resistance of the copper, at 20kHz, the
impedance would be about 11.1-j8.8 ohms, and at 1kHz it's about 44-j44
ohms. That's all pretty irrelevant for running a few meters of wire
across your floor, of course. But the point is that, because of the
distributed inductance, the distributed capacitance is NOT a
detriment.

About cables through bulkheads: the US National Electric Code forbids
running unpaired AC conductors through holes in steel (e.g. through
conduits) for the reason you mention -- it can also be a safety hazard
for people working on the wiring, too, since it's very hard to know
where the circuit goes if the wires aren't paired (or bundled in the
case of multi-phase).

Yes, at 60Hz, skin effect is significant even in long distance power
transmission lines, whose conductors may be a couple inches in
diameter. In copper at 20C, skin depth is only about a third of an
inch. If the conductor is a bundle of seven strands (each of which
may comprise a multitude of smaller strands, of course), it seems
reasonable to make the center strand steel, for strength, since it's
not conducting much current. Is that done? Or is the corrosion from
dissimilar metals reason to not do it?

Cheers,
Tom

.

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