Litz Limitations

Question

Litz wire is very old, perhaps 100 years. It was used and still is used on Medium Wave ferrite rod antenna coils. The thinner the wire is the better things are at higher frequencies but more strands are needed and packing factor is reduced. If the wire gets too thin then there will be supply problems due to fabrication difficulties. Understandably the optimum strand diameter will fall with increasing frequency; there are tables on the internet for this. From bench results 100 kHz 0.1 mm strand is good. Early pre-internet texts say that litz loses efficiency at about 2 MHz.
My question is why?
Is it the self capacitance? Is it that the strands would need to be too thin? Is it because the twists per inch would need to be too great? Would thick enamel help at high frequencies?

Answer 1

For Litz wire to do its job, the strands need to be thin enough that skin effect has little effect on their resistance. This means that as frequency goes up, the strands must get thinner.

As wire diameter decreases, it becomes more difficult and expensive to make. Very thin wire breaks easily. Very thin insulation is difficult to apply and to make stick. IIRC it's the insulation thickness that hits an economic lower limit first. Any further reduction in the copper diameter results in a much lower proportion of copper to insulator, precisely the effect of the skin effect you're trying to avoid.

The upper frequency limit for effectiveness of Litz wire is not precise, it has to do with the economics of handling very thin wire, so the military and space might still use it where commercial users have just gone to larger components wound with solid wire.

I read a very interesting paper a while ago on using uninsulated stranded wire as a cheap alternative to Litz wire. The essence is that the contact resistance between strands is much higher than the copper resistance along the strands. It was reported that stranded wire could achieve much of the improvement of Litz wire over solid, but the improvement was sensitive to the structure of the wire.

I did muse over the possibility of insulating the thin wire by chemically forming a very thin layer of insulator on the copper, the oxide or the sulphide perhaps. But then you have to remove the layer for terminating the wire, which would need another chemical process.

Answer 2

In addition to Neil's answer, there are extenuating factors in play when you go to really thin strands and lots of 'em.

This is a very hand-wavey explanation, to an effect that isn't very well defined anyway (i.e., several material characteristics and geometric parameters are missing), but suffice it to say, the effect applies at some point, where those characteristics come to dominate.

Consider the voltage around any given strand, and also around the cable itself, overall.

First of all: transverse magnetic fields around a wire, create a voltage around it, inducing eddy currents (in a winding, we call this proximity effect). This current, subject to skin effect, plus the normal (axial) current flow (again subject to skin effect), describes the loss in a wire/strand.

I mention transverse fields, because they are inevitable: in a simple say solenoidal (helix) winding, the field from adjacent turns induces such a component. More generally, field nonuniformity induces such current. Nonuniformity arises from the general inverse dependence of field strength vs. distance, both from center of the coil itself, or distance from a wire due to the leakage field around that wire.

Furthermore, when we move to litz cable, we have strands constantly diving up to the surface and back down into the bulk of the cable; the very construction itself is inherently inhomogeneous. This does a good job in pursuit of one goal (uniform current density), but it also means the transverse field inducing eddy currents between strands is greatly emphasized by the construction itself.

So we already have a strong pressure to keep strand diameter low, not just to avoid skin effect, but there is a synergistic effect from all those eddy currents making it even worse, and so we need to keep strand diameter even lower still. Which is why, when you look at a curve of losses vs. strand count, the range of say 5-50 is generally worse, due to eddy losses dominating. Strands have to be made much smaller to reduce their eddy current cross-section far enough to be worthwhile.

Now, consider a transverse field inducing a voltage across the whole cable, or in a loop around (near) the surface. We have myriad voltage drops, across insulation between strands, and even across the strands themselves. A displacement current thus flows through the insulation, which includes some power dissipation, depending on loss tangent. The copper loss even has some effect, small though the resistance may be (i.e. "thick-wise", across the diameter of a strand). The phase shift inherent in any loss mechanism, gives the same attenuation vs. depth effect for which skin effect arises. Thus, even though we have this hybrid air-plastic-copper matrix that seems a good (transverse) electrical insulator, EM waves will eventually be stopped by it, at some depth, thus shielding the inner strands, and dropping more voltage across them (lengthwise), and thus losses increase. (Note that voltage drop lengthwise along a strand includes the leakage inductance of that strand to its surroundings; this doesn't need to be a lossy effect, the capacitive loss effect will suffice to explain that -- but there is copper resistance here too, so there is additional contribution.)

There are some solutions to this. More distance can be maintained between strands, reducing the displacement current somewhat; higher-Q coatings might be used; and rather than a solid build, a hollow cable can be made -- so that the span, in terms of distance from the center of the cable, that any given strand travels, is fairly modest, and thus strands stay near the surface of the build, within this bulk-equivalent skin depth.

I don't know that such constructions are used very much; they appear in manufacturers' catalogs, but they might not see much use outside of powerful MW applications (transmitters and industrial). In any case, when they do, it's by arranging sub-builds of litz around an insulating (e.g. fiber or polypropylene rope) core.

On the upside, as frequency rises into the 10s of MHz, despite the thin surface layer that's carrying current, reactance has increased faster, and high Q factors are a lot easier to reach just with ordinary solid wire.