Litz wire resistance

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

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:

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.

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?

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?

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 :-)

I read in sci.electronics.design that Winfield Hill wrote (in ) about 'Litz wire resistance', on Wed, 9 Mar 2005:

Is it still in the cake? (;-)

-- Regards, John Woodgate, OOO - Own Opinions Only. The good news is that nothing is compulsory. The bad news is that everything is prohibited.

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:

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

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Sounds like I'd like that file also! Mike