AC resistance and DC resistance for a layered coil?

[zenerbjt]

Hi,
There is an equation relating R(AC) to R(DC) for a coil of multiple layers.
This is on page 18 of AN-53 as follows

AN-53
https://ac-dc.power.com/sites/default/files/product-docs/an53.pdf?download=1

“m” is said to be the layer number, but surely the resistance is more in the middle layers, and less at the outer layers, and the equation doesn’t account for this?
Also, it says “h” is the layer thickness. Does that mean the diameter of the wire?

 

[zenerbjt]

The equation on page 18 of AN-53 is not giving a good answer. (as attached excel shows). I am getting RAC/RDC for a 0.29mm copper inductor at 100khz as 0.5, and this isnt correct. Also, varying “m” has no effect, and it should do.

Does anybody have a good RAC/RDC equation? There are millions on the internet and they are all different and give widely varying answers

--- Updated Dec 14, 2020 ---

The attached excel spreadsheet called "skin effect calc Rac_Rdc" shows that for a 1mm round wire at 100khz, the Rac/Rdc ratio is 2.73.
This sounds way too low to me....but i would imagine a formula which gives Rac/Rdc truthfully is very hard to find, because the proximity effect is also in there... and proximity effect is basically as restrictive as skin effect for a tight coil of turns like you get on an offline ferrite transformer.
Do you have any formulae?

 

[Easy peasy]

h is the layer thickness, i.e. from wire centre to wire centre on the next adjacent layer

the delta symbol is the skin depth at the freq of interest ...

usually all numbers should be in SI units, i.e. meters, not cm

--- Updated Dec 15, 2020 ---

Skin depth = 0.0656 / ( SQRT MHz ) so for 100kHz, = 0.2 mm, i.e. the current density falls to 37% as you go 0.2mm into the wire.

thus having a conductor that is 0.2 - 0.35 mm dia will work very well for 100kHz as the Rac will be about twice the Rdc

0.1mm even better

excepting proximity loss effects ...