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AC coil resistance equation
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