Skin Effect in Solid/Stranded/Litzendraht Wire -Guy Macon
- From: Guy Macon <http://www.guymacon.com/>
- Date: Wed, 10 Oct 2007 14:38:30 +0000
John Larkin wrote:
David Brown wrote:
According to:
http://www.audioholics.com/education/cables/skin-effect-relevance-in-speaker-cables/
stranded wire *does* help reduce skin effect. I think the idea is that
although the strands are not insulated from each other directly, there
is still a significant resistance between the strands (due to poor
contact, air gaps, corrosion, migration of chemicals from the outer
insulation, etc.). Thus stranded wire ends up somewhere between solid
core and Litz wire regarding skin effect.
Opinions seem about equally divided on this. Anybody know for sure?
See _Stranded Wire With Uninsulated Strands as a Low-Cost
Alternative to Litz Wire_ in the References below.
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.
Many people are under the false impression that simply insulating
the strands will create something that they call "Litz wire" that
will avoid the current concentrating on the outside of the bundle.
A moment's thought will reveal that this cannot be true. Nothing
about insulating the strands changes the fact that the center
strands have a higher impedance, or that in a parallel circuit the
lower-impedance path has more current going through it. They are
confusing insulated-strand wire with Litzendraht wire -- the word
"Litzendraht" meaning "Woven." In Litzendraht wire, the strands
are insulated and then woven so that they take turns being on the
outside. There are also related effects that complicate things
such as proximity effect and AC current jumping between insulated
strands through capacitive coupling.
Now consider wire "Stranded." The resistance between the strands
is not infinite (maximum voltage, zero current, zero power
dissipated) like wire "Litz" nor is it zero (maximum current,
zero voltage, zero power dissipated) like wire "Solid." Instead
it has a resistance that reflects the copper oxide layer and the
series of point contacts. This keeps some of the current from
jumping strands and makes the wire act like something between
the "Solid" and "Litz" cases -- and this resistance varies over
time, temperature, cable flexing, and perhaps phase of the moon.
It also dissipates power, but this appears to be something the
RF fellows worry about, not us AC power folks.
That being said, when dealing with 60 Hz. AC power and high
current (thick) conductors, you can pretty much ignore all of
that and assume that the stranded wire will not have enough skin
effect to reduce the capacity of the wire. And, of course, in
speaker wire applications the wires are not thick enough to have
any noticeable effect -- especially considering the response curves
of all available tweeters.
Another helpful hint is that wire with a few large strands tends
to keep the same strand in the center, while wire with many fine
strands tends to weave them in and out. Consider a long run where
partway down the run the current has mostly migrated to the outside.
if that outside conductor dives into the center, it will take the
current with it, and the current has to migrate all over again.
References:
_Stranded Wire With Uninsulated Strands as a Low-Cost
Alternative to Litz Wire_
http://thayer.dartmouth.edu/inductor/papers/stranded.pdf
_Litz wire Applications_
[ http://www.litz-wire.com/applications.html ]
_Optimal Choice for Number of Strands in a Litz-Wire
Transformer Winding_
[ http://thayer.dartmouth.edu/other/inductor/papers/litzj.pdf ]
_Cost-Constrained Selection of Strand Wire and Number
in a Litz-Wire Transformer Winding_
[ http://thayer.dartmouth.edu/other/inductor/papers/litzcj.pdf ]
_Computationally Efficient Winding Loss Calculation with
Multiple Windings, Arbitrary Waveforms, and Two- or Three-
Dimensional Field Geometry_
[ http://thayer.dartmouth.edu/other/inductor/papers/sfdj.pdf ]
_Scots Guide: Skin Effect and cable impedance_
http://www.st-andrews.ac.uk/~jcgl/Scots_Guide/audio/skineffect/page1.html ]
[ http://www.st-andrews.ac.uk/~jcgl/Scots_Guide/audio/Analog.html ]
_Dartmouth Magnetic Component and Power Electronics Research
Transformers and Inductors for Electronics Applications_
http://engineering.dartmouth.edu/inductor/papers.shtml
--
Guy Macon
<http://www.guymacon.com/>
.
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