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Re: AC Resistance of wires - was 8 kHz Tesla Coil

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote: 
Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>
At 12:13 PM 10/2/2005, Tesla list wrote:

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote:

Original poster: "Gerry Reynolds" <gerryreynolds@xxxxxxxxxxxxx>


The work that Dr Gary Johnson did for AC resistance seems to solve the Rac/Rdc problem for round wires (no proximitry effects). 

>...
The following table shows

this for wr/sd up to 8.
wr/sd      Rac/Rdc
------------------
  1            1.020
  2            1.263
  3            1.763
  4            2.261
  5            2.743
  6            3.221
  7            3.693
  8            4.154



A simpler calculation, assuming that all the current is concentrated in
a ring with thickness equal to the skin depth and external radius equal
to the wire radius, results in:
Rac/Rdc = (wr/sd)^2/(2wr/sd-1)
The table above becomes:
wr/sd    Rac/Rdc  difference
1        1.000    -2.0%
2        1.333    +5.5%
3        1.800    +2.1%
4        2.286    +1.1%
5        2.778    +1.3%
6        3.273    +1.6%
7        3.769    +2.1%
8        4.267    +2.7%
The error is negligible in comparison with the more exact formula. So,
the basic skin depth formula can be used with round conductors quite
well.

Exactly why you sort of need to start with a statement of what accuracy is "good enough". The maximum error (and it changes sign quickly) is at the radius/sd = 2 area, which is an area of some interest for coilers (esp for big low frequency coils).
Is 5% "good enough" (gut feel.. you betch it is) 

5% is difficult to even see in an oscilloscope, and the precise value
for wr/sd=2 looks a bit "out of the curve". Possibly wrong.
Consider also that for Tesla coils, at least in secondary coils, the
proximity effect is very significant. And also, the operation is
not at sinusoidal steady state, and so the use of a fixed value
for skin depth is an approximation only.

Antonio Carlos M. de Queiroz