[SOLVED] Inductance and resistance of solid wire vs Litz wire

Hello everybody,

I have found a formula given by Wheeler which gives the inductance of a flat -single layer- spiral coil assuming the coil is made up of solid wire.
I also have a formula for the AC resistance of a solid wire derived in the book Electromagnetic compatibility Handbook by Kaiser and is very simply derived as follows:


However, my application needs the use of Litz wire in order to reduce as much as possible the AC resistance of the coil due to skin and proximity effect (very high Q of coil is needed).

My question is: Is still accurate to calculate the inductance of the coil using Litz wire with the formula above mentioned which assumes a solid wire is used? If so, I would use the equivalent diameter of the Litz wire as the "solid wire" diameter.

Asking with other words the same question: If one builds an inductor with solid wire, and then builds the same inductor, same geometry, same equivalent diameter and same everything but with the only change that Litz wire is used instead, will the inductance vary ?

As a rough estimation for the resistance, I would assume that the strands are in parallel which makes the AC Resistance of the Litz wire = AC Resistance of 1 of the little wire that makes the boundle/number of strands
But then... why not assume the same for the inductance ? i.e. Inductance with litz wire = Inductance of 1 of the little wire/ number of strands assuming the inductances in parallel because now I can neglect the proximity effect.

Any comment is much appreciated !

My question is: Is still accurate to calculate the inductance of the coil using Litz wire with the formula above mentioned which assumes a solid wire is used? If so, I would use the equivalent diameter of the Litz wire as the "solid wire" diameter.

Click to expand...

Yes inductance is same as long as the litz wire is like in the same "envelope" of space as was the solid wire.........as the diameter of the coil gets bigger, then this is less important.

Asking with other words the same question: If one builds an inductor with solid wire, and then builds the same inductor, same geometry, same equivalent diameter and same everything but with the only change that Litz wire is used instead, will the inductance vary ?

Click to expand...

yes, L will be the same

Inductance with litz wire = Inductance of 1 of the little wire/ number of strands assuming the inductances in parallel

Click to expand...

..no, the inductors in parallel equation is for when those inductors are totally separate entities, ie, not coupled into the same core.......i speak even if the "core" is air

- - - Updated - - -

proximity effect still applies to litz..unfortunately

Yup.
Treez has nailed it.

Wheeler and similar formulas are empirically derived. The fact that they don't specify a frequency dependency can be understand as ignorance of skin effect. In so far, using litz wire will extend the formula's validity to higher frequencies.

Empirical measurements of air inductors show a slightly decreasing inductance with increasing (skin effect) ESR.

proximity effect still applies to litz..unfortunately

Click to expand...

It doesn't, except for a small residual, due to the sophisticated twisting scheme.

FvM said:

The fact that they don't specify a frequency dependency can be understand as ignorance of skin effect. In so far, using litz wire will extend the formula's validity to higher frequencies.

Click to expand...

Wheeler himself states the same thing in his article.

----------------

Thank you everyone for solving the inductance question.

However, is it accurate to assume the AC resistance of the bundle of Litz wire ≈ DC resistance of the Litz wire since the Litz wire is there to reduce skin effect ? (working frequency is around 20 kHz (did not decide it yet ) )

However, is it accurate to assume the AC resistance of the bundle of Litz wire ≈ DC resistance of the Litz wire

Click to expand...

Yes, as a good estimation.

Litz is nice, but it can be difficult to terminate well. Every individual strand needs to be stripped and tinned. If not carried out with fanatical care the results can be disappointing. This can be a real problem if you are planning to produce large numbers on an assembly line.

It may be worth evaluating some of the very thin insulated copper foils that are available. These can sometimes be more space efficient than round litz wire, and much easier to both obtain and use. It may not be suitable for your particular application, but its worth a mention.