Re: 8 kHz Tesla Coil

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Malcolm Watts" <m.j.watts@xxxxxxxxxxxx>

Hi Gerry,

On 25 Sep 2005, at 22:07, Tesla list wrote:

> Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
>
> Hi Malcolm,
>
> I found a set of formulas on the web for skin depth (SD) of round
> solid conductors that are said to be conservative and overpredict the
> AC effect (with no proximity effect).  The author compared the results
> to measured Rac to verify his claim.  The following equations were
> given:
>
> for SD < r ;
> SD = 2837 / sqrt(f)      (Skin Depth - mils)
>
> Rac = Rdc * (r^2) / (r^2 - (r-S)^2)  [based on effective area
> reduction due to SD]
>
>
> My coil uses 1440 turns of 23awg where Rdc is 61 ohms.  At 82KHz, the
> skin depth is 9.9mils.  The copper diameter is 22.6mils (~2 SD's) so
> Rac is 2% higher than Rdc (or 62 ohms).  Seems like the resistance is
> hardly affected by skin effect for this case.  The Q for a series RLC
> circuit is:
>
> Q = sqrt(L/C) / R
>
> R = 62 ohms
> L = 83mH  (Les)
> C = 46pf    (Ces)
>
> Q = 685

Is the Q and Rac measured or calculated? BTW, the wire diameter is
about 2.5 sd by my calc. I agree that proximity effect is probably
the biggest headache in the high Q stakes. My measurements suggest
that your Q is actually going to be considerably lower than what you
get taking skindepth alone into consideration. A measurement would be
nice (if the figure you give is indeed by calculation?).

By way of comparison, here are the _measured_ figures for a resonator
with the following specs:

Ls about 42mH
Ctot about 26pF
Rdc = 53 Ohms
Measured Q on a dry day = 320
Rac (calculated from measured Q) = 126 Ohms

The coil is spacewound 1:1 with 0.56mm dia wire (about the same as
yours!) on a 9.8" dia former with a winding length of about 46" or so.

> I just got my 8x36 coil with the larger toroid (8x32) working, tuned,
> and optimized for spark length.  The wall power is 2100 watts. My
> longest power arc currently is 86 inches.  Granted, proximity effects
> have not been included, but this coil, using wire that is only 2 SD's
> thick, performs with a Freau factor of 1.9
>
> I think by using this formula, one could easily make a table for a
> given coil size and plot the Q and L as a function of AWG.
>
> Gerry R.

I can't argue with results like that ;)  In the end, anything to
reduce primary losses (such as a high inductance secondary forcing a
high primary inductance) has got to be beneficial.

     I may be in a position to wind several coils for Q comparisons.
I have litz wire, plenty of solid section wire of various gauges and
some aluminium wire on hand (for an interesting side comparison).
I'll do a bit of measuring this evening to see whether I have the
materials necessary wind three coils with the same pitch and same x-
sectional area copper on three identical formers for Q measurements.

Malcolm
<snip>