Inductor wire CSA?

Looking for air core inductors, the XO circuit shown by XRK971 calls for a 4mH at 0.44ohm and the other XO calls for a 4mH at 1.26ohm.

Is there an ideal wire gauge (CSA) for these?

The one coil supplier I tried so far can't get a 4mH down to 0.44ohm, I guess this would require much thicker gauge wire. Most of his coils are wound with 18 gauge.
 
Worth bearing in mind especially with air-cored inductors is the proximity effect. That makes AC losses increasingly higher than the DCR the thicker the gauge of wire used. Multiple smaller strands (ala 'litz') is the way to go if AC losses need to be low.
 
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I guess it depends how thick you make the wire, and what significantly means - a factor of 2 might be viewed as significant by one and irrelevant by another, especially if the total resistance is << 8 ohms... The speaker cable has the same issue with skin effect and people use thick wire all the time for that. The bottom line is how much change to the frequency response you are willing to tolerate: 1dB? 0.5dB?

And the HF roll off for an inductor already exists, these effects just steepen the slope a little.
 
As you referred to 'the same issue with skin effect' above and lumped skin effect together with proximity effect in your earlier post, I wonder if you were aware of this (pasted from the link in my post) :

Proximity effect can be several orders of magnitude greater than skin effect, and it grows exponentially with the number of layers of wire in the winding.
 
Ah, yes that's interesting - multi-layer coils are the thing to avoid if possible, and edge-on tape-wound is the best way with single conductor. Multi-filar construction is possible too, Litz wire isn't really needed if skin-effect isn't the major problem, and you pay a space penalty for braided construction you don't with parallel multi-filar.