Re: Tesla Coil K Factor (was: I've lost my k. Can someone help me find it?)

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

John Couture wrote:

> The results of the  test I show below are for the "two resonant
> mode" (two humps) test and not the open/short test.

Ok, that's clear now.  

> The two "Two mode" test equations
>  JHC    K = (F2-F1)/Fr
>  Paul   x = F2/F1    K = (x^2-1)/(x^2+1)

Yours is incorrect, the one I give is the correct formula. 

> These JHC and Paul equations gave results with about
> 0.7 percent difference.

Pure luck.  It's easy to find a case that demonstrates the failure,
Take Fres = 100kHz, and k = 0.6, thus

 F2 = Fres/sqrt(1-k) = 100kHz / sqrt(0.4) = 158kHz
 F1 = Fres/sqrt(1+k) = 100kHz / sqrt(1.6) =  79kHz

With these values for Fres, F1, and F2, John's formula gives

 K = (F2-F1)/Fres = 79/100 = 0.79

as opposed to 0.6.   

John's formula becomes less wrong at small k, because we can make
the following two approximations:

  Fr ~= (F1+F2)/2     (the arithmetic mean of the two modes)

and

  Fr ~= sqrt(F1*F2)   (the geometric mean of the two modes)

If you put these two approximations into the exact formula

  K = (x^2-1)/(x^2+1) 

then you get an approximate formula

  K ~= (F2-F1)/Fr

Hope that clarifies things.  If anyone's not clear on how the
correct formula is derived, I'll be happy to go through it in
detail.
--
Paul Nicholson
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