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

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

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  1. Guy Macon

    Guy Macon Guest

    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 Brown

    David Brown Guest

    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 Bruhns

    Tom Bruhns Guest

    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 Brown

    David Brown Guest

    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
    during a trade show.

    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 BC

    D from BC Guest

    Speaker wire ..phhhftpp :p
    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. 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. 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
    up. The optic link can be analog in nature, so no crying allowed by the
    "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
    links altogether.

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

    Jamie Guest

    Is that up there around the area of 99.99% oxygen free Monster speaker wire?
    :)
     
  10. Guy Macon

    Guy Macon Guest

    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...
     
  11. Tom Bruhns

    Tom Bruhns Guest


    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
     
  12. Tim Williams

    Tim Williams Guest

    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. 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 Thompson

    Jim Thompson Guest

    The lead also stops rodents and insects. I had to add plasticized
    lead sheathing to my pool control lines... otherwise replace every six
    months :-(

    ...Jim Thompson
     
  15. Tom Bruhns

    Tom Bruhns Guest

    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. Except that they get utilized in PARALLEL, not series.
     

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

  18. 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. "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 Macon

    Guy Macon Guest

    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
     
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