Phil Hobbs said:

The skin effect explanation for Litz wire is wrong all through. If it

were correct, Litz would be lossier than solid, because in solid wire, at

least the current has a straight shot on the thin outside layer, whereas

with Litz, all of it spends a lot of time inside the bundle.

Lossier, per resistive length, factored by current-carrying cross sectional

area? (Making some sort of estimation of current density and resistivity in

the areas where current does flow...) Of course, it ends up better in the

end, because you can use much finer wire, which gives much more perimeter,

and thus more cross sectional area for current to flow in, even though it's

choked up much worse from being forced into to a constant average current

density.

Compared to single strands in free space, even of much larger diameter than

the individual strands, the stuff is lossier. If you look at Rac/Rdc for

decreasing strand diameters, the single free strand might level off at, I

forget, 28AWG or something, at say 100kHz, whereas in a big Litz cable (say,

a thousand strands), it keeps going until 36 or 38AWG, and even then, the

total resistance for equivalent area is larger (in addition to the increased

length due to the weave). It's like making copper a better resistor (or

alternately, a worse inductor).

The nice part is, you get to carry more total current, in an only slightly

larger volume, which is significantly smaller than the volume required of a

single massive strand. That is to say, at high frequencies, a large solid

conductor is O(N), while fine conductors are O(N^2). Litz has a smaller

constant multiplier on that Big-Oh than a single fine strand, but

appropriately chosen, it scales independently of frequency (as diameter

squared), something a solid conductor doesn't (it's perimeter limited). One

of those things that "shouldn't work" by certain physical principles, but

when considered holistically by the engineer, works great. ;-)

But anyway, in a seven-conductor construction, the always-central bundle is

completely surrounded by fields from the other six, and so has much more

eddy current losses, or higher Rac, or stronger proximity effect, or thinner

skin depth, or however one likes to say it (they're all aspects of the same

phenomenon, after all).

The skin effect argument is far from straightforward in the presence of

other conductors, and especially of ferrite cores. You can't just take

the 1-D isolated conductor result and wave it over the design like a dead

chicken.

Yes. Proximity effect is all over the stuff, which is why the strands have

to be so much finer than the free space skin depth would suggest. Even 10

strands of 28AWG will be noticeably higher in resistance than 1/10th of a

single strand. 100 or 1000 strands need strands finer and finer still. The

scaling between number of strands and required decrease in strand diameter

is of course "far from straightforward", for the same reason.

The actual benefit is due to reducing eddy current loss in the wire due to

dB/dt. Copper tape winding is about equally effective IIRC.

I haven't seen any analyses of tape, but I've seen it used here and there.

Trouble is, the field around a conductor 'wants' to be round, and forcing it

to wrap around a foil conductor is somewhat counterproductive. It

necessarily must penetrate the conductor, particularly along the edges. The

conductor must be thin enough to allow this; a thick conductor will shield

its self-induction, and you get standard skin effect along the edges (within

a constant factor).

The result is, eddy currents flow along the edges. This manifests as skin

effect. Except, because we're talking about a somewhat two-dimensional

conductor, it's really edge effect, and instead of bulk resistivity,

thickness can be factored into the area resistivity, which edge penetration

then takes as a factor. For a finite thickness, edge penetration is deeper

than the free space skin depth (which is the limit at infinite thickness,

i.e., an infinite slab), but I don't know by how much.

If depth is inverse with thickness (a crude but not unreasonable guess,

taking the area resistivity approximation as a suggestion), then one would

need a conductor of thickness t = d^2/w, for width w and skin depth d. (If

t = w, you have a square conductor of dimension d, which is in the right

order of magnitude.) Unfortunately, copper at 100kHz is already only a few

mils, so you need truely microscopic foils to actually achieve full

utilization across the width of an average bobbin. That stinks.

Proximity effect still applies, so while you're doing this, you can't just,

say, wrap ten turns of foil primary, a layer of tape, then ten turns of

secondary; the innermost facing turns will burn up from all the congestion.

Tape does at least suggest itself nicely for transmission line approaches:

if the turns are similar, just layer primary and secondary together, with

tape between, like the plates of a capacitor. Except with a core in the

middle. Isolation capacitance won't be great, but leakage inductance will

be teensy. The image currents from primary and secondary will tend to flow

along the faces as well as the edges, because it looks more like a parallel

plate transmission line than an isolated foil conductor; that helps

efficiency a lot.

You can of course apply the Litz trick to foil, but you don't have any free

lunch; the geometry reduction is still required whether putting together a

bunch of strips or strands. Ten strips woven together will have less

resistance than a single strip of the same width and thickness, but higher

than 1/10th of an isolated strip that size. I know of at least one company

that claims to have some sort of foil technology that reduces Rac like Litz,

presumably doing some kind of weave. Tempting to buy a bigass custom part

from them just to take it apart and look, see how they put the stuff

together. I can't imagine it's all that easy to make, considering there are

only two US companies making the round stuff as is.

Tim