# Skin Effect in Solid/Stranded/Litzendraht Wire -Guy Macon

Discussion in 'Electronic Design' started by Guy Macon, Oct 10, 2007.

1. ### Guy MaconGuest

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

2. ### David BrownGuest

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.

3. ### Tom BruhnsGuest

So, go do some research on RF transmission lines. Capacitance per se
is not bad; it is an integral part of what makes the line have a
particular impedance. Series inductance and shunt capacitance,
primarily, determine the impedance at RF frequencies. At audio, the
series resistance has a profound effect on the impedance, but it also
doesn't make much sense to worry about it as a transmission line
unless it's pretty long. A line from one end to the other of any
house I've ever seen probably wouldn't qualify as "long" at 20kHz,
where the wavelength in a typical cable is roughly five miles
(assuming a velocity factor of 0.5).

I recall reading some reasonably objective evaluations of various
speaker wires. One of the best (with respect to measured transmission
of transients, and instrumented frequency response of cable-output
versus cable-input, over the audio range) was many-conductor ribbon
cable, with alternate strands conducting opposite directions. That's
very easy to do using the typical insulation-displacement ribbon cable
connector, as alternate strands connect to opposite sides of the two-
row connector. But there's a lot of question in my mind just how much
difference this all makes anyway, given the high resistance of the
wire in the drivers in the speaker system, at least for runs of modest
distance. Also, as Guy notes, the transducers aren't inherently
"flat" enough to warrant putting a lot of effort into it. If you
really think it makes a difference, why not just put the amplifier at
the speaker, and run low-level or fiber to the amp?

For sure, Litz wire is useful for certain applications. I've been
playing a lot with RF filters in the 1MHz region lately, and get far
higher (like, a few times higher, not just tens of percent) Qu in
coils wound with the proper Litz wire, as compared with coils the same
size wound with single-strand copper wire. But I was somewhat
astounded when I priced Litz wire at how expensive it is! That was
from commercial wire houses, not from audio-phool sources. Good thing
I found some assorted sizes kicking around here.

Skin depth in copper at room temperature is about 2.6 mils at 1MHz,
and goes as 1/sqrt(freq); at 10kHz it's 26 mils, so unless you're
working with pretty big conductors, there's not a lot to be gained
from Litz at audio. In coils, I believe things are rather different
because of the addition of proximity effects.

Cheers,
Tom

4. ### David BrownGuest

That all fits in with what I understood from before (but it's always
nice to get confirmation).
I don't think it makes a *significant* difference, but some people
certainly do! I'm just trying to think about how to improve the flat
frequency response of the cable (over audio frequencies) from merely
insignificant skin effect down to virtually non-existent skin effect.

The best idea I heard of for speaker cable is heavy extension cables
(the kind used for electric lawnmowers) - you have thick cables and
therefore low resistance, and excellent value for money. Apparently
Quad (who make very expensive speakers, among other things) used them

As for ribbon cables, it certainly sounds like a convenient way to make
the cables I thought of. Perhaps using the 80-pin IDE cables would be
even easier, and some even come rolled up in advance. The would not be
long enough off the shelf, but I'm sure rolls are easily available.
I'm aware that the skin effect is somewhere between negligible and
non-existent for audio frequencies and reasonable sized speaker cables,
but since snake oil salesmen get hefty mark-ups on their cables by
reducing the skin effect, I was wondering about ways to get even less.

mvh.,

David

5. ### D from BCGuest

Speaker wire ..phhhftpp
Fiber optic link to active speakers. Now that's a soaker..
It'll be so expensive I'll make "special wire" look like a deal..

D from BC

6. ### ChairmanOfTheBoredGuest

Nope. You use thick Teflon insulated SPC wire, not mag wire strands.
This keeps the individual strands far enough from each other so as to not
create to high a capacitive effect over then span of the wire, and they
are not individual twisted pairs, but interwoven braid. It's like
macrame with no knots, of course, however.

You end up with an equivalent of like #10 gauge wire. Kick ass speaker
cables that are flexible, mostly flat (physically and electrically), and
quite durable.

7. ### ChairmanOfTheBoredGuest

This is actually the way the true audiophiles do it now.

The amp is right next to the driver. Thumbs up there. There can
actually be an amp for each driver in a cabinet as well. Another thumbs
"valve tards".

Yep. That is the wave of the future. Next thing will, of course, be
to BlueTooth it over to the driver cabinets, and do away with the hard

I'll bet the valve tard boys couldn't even tell the difference in a
blindfolded side by side comparison test if it were engineered correctly.

Not one iota!

Ahhh... the wonders of QAM 256!

8. ### ChairmanOfTheBoredGuest

Only at 70k ft in a low level pressurized cabin.

9. ### JamieGuest

Is that up there around the area of 99.99% oxygen free Monster speaker wire?

10. ### Guy MaconGuest

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
hots though one hole in the bulkhead and both neutrals through
the other. His efficiency took a hit and the bulkhead got hot...

11. ### Tom BruhnsGuest

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.

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

12. ### Tim WilliamsGuest

In fact, they often use steel cored aluminum and copper wires. Excellent
strength. Supposedly, I've heard of running transmission through the
center as well (what kind of signals, electronic or fiber optic, I don't
know), which would work, but seems awfully hard to get at.

Tim

13. ### Winfield HillGuest

I have a one-foot-long cross-section of an ac 115kV HV
transmission cable, from when the 234MW power plant
across the street was installed. It's 4.2" thick with
a 2" dia copper interior. Although the very center of
the conductor carries no current, it's still made of
copper, like the rest. BTW, this is an underground HV
cable. They installed three sets of four cables for
the entire plant output, IIRC, one set being a spare.
The cable has a 1/8" outer plastic or rubber insulation
followed by a 1/6" thick inner lead sheath. I was told
the lead sheath was grounded, to act as a short-inducing
element in the event of a cable breach. The cable was
manufactured by Pirelli, the tire people. It's marked
115kV / 138kV.

14. ### Jim ThompsonGuest

lead sheathing to my pool control lines... otherwise replace every six
months :-(

...Jim Thompson

15. ### Tom BruhnsGuest

Hi Win,

Ah, back when copper was cheap... ;-)

Of course, that's an entirely different application than the one I was
thinking of, where the wire is strung between towers and generally is
not insulated -- and where strength matters. Tim W. says that yes,
cores are commonly steel. I tried a web search just now but didn't
turn up anything useful. Maybe I'll drop a note to our local PUD or
the like and see what they say. I suppose with the current price of
copper, Pirelli would consider making the core from some relatively
inexpensive and much lighter material. I wonder if the construction
of long distance transmission lines was covered in that old power
engineering book you got from me about three years ago. Might be
interesting to compare "then" and "now."

Cheers,
Tom

16. ### ChairmanOfTheBoredGuest

Except that they get utilized in PARALLEL, not series.

17. ### ChairmanOfTheBoredGuest

"unpaired AC conductors" refers to POWER transmission lines, not
goddamned low level signal lines.

18. ### ChairmanOfTheBoredGuest

You mean you don't KNOW how it is done?

HIGH TENSION refers to the steel carrier center "strand" cable!

The lines are steel cables shrouded in aluminum wires!

19. ### ChairmanOfTheBoredGuest

"Commonly" Try ALWAYS! Long spans between tie points ALWAYS require a
steel carrier strand.

Even long cable TV coax runs need a steel carrier strand to keep them
from damaging the coax at the tie points. Not talking about hard line
here, as that gets bundled to a STEEL carrier strand as well!

20. ### Guy MaconGuest

Fascinating! How many strands, and how thick is each one?

Any remote chance that this was a high voltage DC line?

I am curious about the four cables. Three phase is usually
configured as delta (no neutral), not wye at those voltage
and power levels. HVDC tends to use two condutors, and even
the fairly rare six phase and twelve phase systems don't use
four conductors. Any idea what was going on there?

References:
http://en.wikipedia.org/wiki/Electrical_pylon
http://en.wikipedia.org/wiki/Delta_pylon
http://en.wikipedia.org/wiki/Single-level_pylon
http://en.wikipedia.org/wiki/Two-level_pylon
http://en.wikipedia.org/wiki/Three_level_pylon