Original poster: "Gerry Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
Hi Bart,
I'm not sure what is being said about it giving 37 ohms for my coil,
but if Rac is defined as the effective resistance when runing AC
current thru it, the AC resistance can never be less than the DC
resistance. Skin depth is defined (for the benefit of others) as
the depth of the conductor from which if you throw away the interior
conductor and keep the exterior conductor and calculate the DC
resistance from the resulting area, you will have the Rac of the
wire for the frequency of the AC current (no proximity effects
included yet). In other words:
Rac/Rdc = wire_cross_sectional_area / (wire_cross_sectional_area -
area_internal_to_the_skin_depth)
So, for skin depth (sd) greater or equal to the radius (r) of the
wire, Rac = Rdc. For sd less than r:
Rac/Rdc = pi*r^2 / (pi*r^2 - pi*[r-sd]^2) which reduces to:
Rac/Rdc = r^2 / (r^2 - [r-sd]^2)
For proximitry effects for a close wound coil, divide the wire into
quadrants like below:
...(X)(X)(X)...
If you assume that the proximitry of left and right adjacent wires
forces the AC current out of the left and right quadrants and into
the upper and lower quadrants, then the effective area is further
cut in half and Rac_with_proximitry will be twice the Rac as
calculated from above. Note this is just a estimate but could be
compared to the tabular data in that reference book for radio
engineers that I can't remember the name of.
Also calculated Q values based on Rac_with_proximitry using the
following formula:
Q = sqrt (L/C) / R
could be compared to measured Q to determine the accuracy of the
estimate. Preferably, this should be done with coils having
different fo's and wire diameters. I will measure the Q of my coil
when I get a chance.
Gerry R.
(see comments below)
Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>
I've searched high and low for the reference to the equation, but I
can't find it. It is something I picked up from Googling and didn't
save the document (dummy me). You are correct, Rdc added to Rac
makes no sense. I'm sure I wrote it down as it was shown. I suspect
this may have come out of a text book, but I think it's use was not
interpreted as intended. I'm certain this was a skin effect approximation.
I've found another approximation calculator (excel throw-together)
for Rac and skin depth in cylindrical conductors. It gave 37 ohms
on your coil. If you remember, I showed 98 after adding the 61 Rdc
(per the equation), which is a difference of 37 ohms! It appears
the equation was using Rdc as part of it's approximation, but Rdc
should have been removed to identify Rac, such as:
Rac = Rdc(1+(r/(2sD))-Rdc
this equation reduces to Rac/Rdc = r/2sD and I dont believe it
unless Rac is defined as the incremental increase of resistance above Rdc.
Also the equation doesn't seem to take conduction areas into account.
where:
Rdc = DC resistance of winding
r = radius of wire diameter in inches
sD = skin depth in inches
For reference, another Rac approximation I found from Michael
Mirmak of Intel Corp (was for pcb traces originally using trace
heights and widths) I modified for a round conductor: It follows
the excel calculator for high and low frequency's.
Rac = L(((3.318*10^-7)*F^0.5)/(4*d))
(should be ready for excel - just insert the values)
where:
L = Length of winding in inches
F = Frequency in Hz
d = wire diameter in inches
I think in all these equations, it is important to understand how
they define Rac as it seems there isn't always consistency.
BTW, here's the excel file mentioned:
http://home.swipnet.se/2ingandlin/Skin_depth_calc.xls
Of course, we don't know how well any of these approximations work
for our coils. It would be interesting to measure and find the
proximity losses. Empirically, we could likely come up with
something similar, which of course gets better with time. So far,
no one is doing this. When I get my coils set back up, I'll have to
perform some Q measurements.