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Litz wire resistance

Discussion in 'Electronic Design' started by amdx, Mar 9, 2005.

  1. amdx

    amdx Guest

    I'm looking for a formula that I can use to find the a.c. resistance of litz
    wire at a frequency.
    Also the a.c. resistance of a solid wire.

    Specifically 12/36 litz
    and #22 solid.

    If possible please give me an example of it in use.
    I have a book (Terman) that has two different formulas and I get the wrong
    answer with both. (Ignorance on my part not the formula)

    Mike
     
  2. amdx wrote...
    If the skin depth is more than the litz-wire constituent diameter,
    the argument is that Rac = Rdc. I have found this postulate true
    much of the time, but not all of the time. As for ac resistance
    of ordinary (fat) wire, you have the skin-depth formulas. But in
    real-world situations, with multiple-layer windings, the proximity
    effect can increase the ac loss by up to 20x over simple skin-depth
    calculations. See Snelling for a good discussion.
     
  3. Terry Given

    Terry Given Guest

    Fr = 1 + ((5*p^2-1)/45)*DELTA^4

    p = no of effective layers

    DELTA = layer thickness/skin depth = d/delta

    d = copper wire OD*sqrt(pi/4) ie thickness of equivalent rectangular
    conductor

    This is only true at one frequency (ie that at which delta is
    calculated). For arbitrary waveforms, you can do a Fourier transform to
    get the coefficients of all the harmonics, and do lots of calculations.

    Hurley et al published a cute way to extend this to any arbitrary
    periodic waveform without knowledge of the fourier coefficients of the
    waveform - "optimising the AX resistance of multilayer transformer
    windings" IEEE trans. Power Electronics vol. 15 no. 2 March 2000, pp369-376.

    multiply Dowells Fr (above) by:

    [I'rms/(2*pi*Fo*Irms)]^2

    Fo = fundamental frequency

    Irms = rms value of I(t)

    I'rms = rms value of dI(t)/dt


    its pretty clear that for I(t) = Ipk*sin(2*pi*Fo*t) this scalar = 1

    Cheers
    Terry
     
  4. The Phantom

    The Phantom Guest

    Charles Sullivan at Dartmouth and his students have done quite a bit
    of work on this topic. Go have a look at their publications at:
    http://engineering.dartmouth.edu/other/inductor/papers.shtml
    The case of an isolated, solid, cylindrical wire is one of the few for
    which an exact analytical solution exists. This result was known to
    Maxwell.

    Given: c, the conductivity of copper at room temp = 1/1724
    f, the frequency in Hz
    d, the diameter of the wire in inches
    j, Sqrt(-1)
    x, an auxiliary variable = 2.54 * Pi * Sqrt(2*j*f*c)

    Then the ratio of the resistance of the wire at frequency f to the DC
    resistance is given by:

    Fr = Rac/Rdc = Re(x/2*(J0(x)/J1(x))

    Re() means Real Part, and J0() is the Bessel function of the first
    kind of order 0, J1() is the Bessel function of the first kind of
    order 1.

    For some reference points:
    .1 inch dia wire @ 50 kHz, Rac/Rdc = 2.42058
    .05 inch dia wire @ 50 kHz, Rac/Rdc = 1.33069
    22 Ga wire @ 20 kHz, Rac/Rdc = 1.00467
    22 Ga wire @ 50 kHz, Rac/Rdc = 1.02865
    22 Ga wire @ 100 kHz, Rac/Rdc = 1.10733
    22 Ga wire @ 300 kHz, Rac/Rdc = 1.59314

    But, beware. As Win mentions, when you wind wire into a coil, the
    proximity effect can make Rac/Rdc for the coil much larger than the
    value for an isolated wire.
     
  5. Fred Bartoli

    Fred Bartoli Guest

    Hi Win,

    Do you remember in which instances this have been false? (maybe not true
    litz wire but rather simply bundled wires)

    I have a low noise preamp (2R equiv noise resistance, and next 0.2R/0.3R)
    that have 1MHz BW. I'm planing to do the interconnect to the DUT with
    specially made cable based on litz wire, but your comment worries me a
    little.

    Any thought?

    BTW, did you receive the file I sent you a week ago?
     
  6. Fred Bartoli wrote...
    No, I generally use many-stranded litz wire from one of my custom-
    made rolls. The cases I have seen where Rac for litz exceeds Rdc
    are generally situations where the magnetic flux becomes highly
    concentrated in one portion of the windings. E.g., in a toroid,
    or in a many-layered coil situation where there would be a high
    Rac proximity effect increase for ordinary thick wire.
    I think you'll be OK. But don't know if litz is necessary, because
    in a bridge, etc., fixture and wiring Rac can be nulled out.
    Yes, now, where did I put that?
     
  7. Fred Bartoli

    Fred Bartoli Guest

    Oh, that makes sense now. I guess you probably were in a situation where the
    length of the "high concentration zone" was lower than the litz
    "interwowing" step length (sorry I miss the word for this). This would
    prevent the litz wire to do its work on that portion. Now, it you had
    several layers, or several passages in the same zone, I think that would
    have mitigated the effects on the average, unless you had a cumulative
    effect due to bad luck (litz interwowing length about the wire length
    between 2 passages).

    Now that I understand why, I think too it'll be OK.
    And yes, I'll need this kind of link. The preamp is not for a bridge but for
    qualifying very low noise levels out of a low noise supply and after an RC
    LPF (200nVrms over 1MHz BW).

    I can send it again along with a pretty girl pic to make sure you'll
    remember this time :)
     
  8. I read in sci.electronics.design that Winfield Hill <[email protected]_rowland-
    Is it still in the cake? (;-)
     
  9. Genome

    Genome Guest

    There is this nice librarian at the Central Application, Philips Product
    Division Electronic Components and Materials. Eindhoven, The
    Netherlands.....

    Who, if you can find an appropriate e-mail and make the request will snail
    mail you a copy of E.A.B No.3 parts 1 and 2.

    That's Electronic Applications Bulletin. Vol 35, No.3 May 1978.

    It's by J.Jongsma.

    Bugger it..... I shall scan the bastard and post it in ABSE.... that'll be


    I'll leave you know when it's up.

    If you don't have access to the above and want me to e-mail the thing then
    my e-mail addy as shown is valid.

    DNA
     
  10. amdx

    amdx Guest

    "Fred Bartoli"
    Sounds like I'd like that file also!
    Mike
     
  11. amdx

    amdx Guest

    I'll be looking for it.
    Thanks, Mike
     
  12. Genome

    Genome Guest

    Posted, you'll have to fiddle the page order. It's 18 jpgs.

    DNA
     
  13. The Phantom

    The Phantom Guest

    The Jongsma paper is good, but somewhat dated. He uses the Dowell method (see his
    references) with modifications by Snelling.

    Be aware that recent research:
    http://thayer.dartmouth.edu/other/inductor/papers/newcalc.pdf
    has shown that the Dowell method and Ferreira's method can have substantial errors.

    Sullivan has published a further simplified treatment in the very recent paper:
    "Simplified High-Accuracy Calculation of Eddy-Current Loss in Round-Wire Windings", IEEE
    2004 PESC (Power Electronics Specialists Conference), Page 873.
     
  14. legg

    legg Guest

    I've been trying to get a look at this article by Jongsma, since '82.

    Did they, perhaps, also copy you Publication#207 from '86?

    RL
     
  15. Genome

    Genome Guest

    Unfortunately not, I didn't request it.

    I've scanned the other one and posted it to the binaries newsgroup.

    Like I said I e-mailed someone, it might have been the webmaster at Philips
    website. He passed the request on and the librarian offered to snail mail me
    photocopies.

    You might try your luck.

    DNA
     
  16. Genome wrote...
    You put up pages 162 and 163, and page 211. What about the rest of it?
     
  17. Genome

    Genome Guest

    Like it's my fucking problem that e-mail and newsgroup postings are shite.

    You're the old bloke, why haven't you sorted it out?

    http://genome.dna.tripod.com/jongsma/jongsma.html

    DNA
     
  18. Genome wrote...
    Hey, good job, DNA!!! I combined the .gifs into two .pdf files,
    and placed them on s.e.d. for everyone's downloading convenience.
     
  19. Genome

    Genome Guest

    Wonderful!

    DNA
     
  20. Terry Given

    Terry Given Guest

    Hi Win,

    thanks for that. Just one question - what do I do with the pile of ASCII
    stuff I see in SED?

    Cheers
    Terry
     
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