# Re: AC coil resistance equation

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From: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>

Hi Jim,

> From: "bmack" <bmack-at-frontiernet-dot-net>
>
> Hello all
>
> I haven't been very active on the list of late, so I thought now is as
> good time as any to participate.
>
> A few months ago I wanted to calculate the unloaded Q of my coils,
> but had no equation to find the AC resistance. The only thing I could
> readily find was a passage in the 1995 ARRL handbook that states
> that the starting frequency for skin effect has the relationship
> f = 124/d^2. Where f is frequency in MHZ, and d is the wire diameter in
> mills.
>  This in itself is pretty much useless, but then they state
> ( I paraphrase for clarity):" the ac resistance increases by about a factor
> of
> ten for every two orders of magnitude".  Or another way is to say each
> order of magnitude increases the over the dc resistance by a factor of
> sqrt(10) which is approx 3.2.
>
> Therefore AC resistance has the relation
>
> Rac=3.2*Rdc(log fo/fc).    fo is the operating  frequency, and fc is the
> skin
> effect frequency, both in MHZ.
>
> Now I substitute fc since fc=124/d^2
>
> resulting in Rac= 3.2*Rdc*(log (d^2 *fo)/124)
>
> d= wire diameter in  mills
> fo= operating frequency in MHZ
> Rdc= coil dc resistance
>
> At least this way the math is a single step affair and the logarithmn
> povides an accurate magnitude calculation.
> Did I help anyone or did I just reinvent the wheel?
>
> Jim McVey

I used the measured figure for Q of one of my coils (300),back
calculated to find Rac (136 Ohms) and then used that as a substitute
for 3.2*Rdc in your equation. I guessed that d^2*fo should be divided
by 124 before taking log base 10. I got an answer of 786 which is
about 2* what it should be. I think your 3.2*Rdc figure doesn't take
turn-turn proximity effect into account. I was impressed nonetheless.

Malcolm

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