Re: Dr. Antonio's Papers - Questions regarding mode of operation in Tesla Coils

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: Rob Maas <robm-at-nikhef.nl>

 > Some aspects regarding these 'modes' is puzzling me. I first summarize
 > a particular case according to your method, as outlined in your ICES 2001
 > paper:
 > take a=7, and b=8, then k_12=(b^2-a^2)/(b^2+a^2)=0.1327
 > then the two frequencies are given by
 > w1 = a.w0, and w2 = b.w0, so the ratio w1/w2 = a/b = 7/8 = 0.875
 >
 > The frequnecy w0 is defined as w0 = (1/a.b).SQRT((a^2+b^2)/(2.L_2.C_2))
 > If I now define w_res = 1/SQRT(L.C), then we have
 >
 > w0 = (1/a.b).SQRT((a^2+b^2)/2).w_res = (1/56).SQRT(113/2).w_res = 
0.1342.w_res

Ok.

 > So far so good. Now I go to the paper of Kenneth D. Skeldon et al. "A high
 > potential Tesla coil impulse generator for lecture demonstrations and
 > science exhibitions", Am. J. Phys. 65 (8),744-754, 1997.
 >
 > In this paper there are also two frequencies (here called w_l and w_u, l 
and u
 > refer to 'lower' and 'upper' respectively), which depend on the coupling k
 > according to
 >
 > w_l = w_res / SQRT(1+k^2), and w_u = w_res / SQRT(1-k^2), where the coupling
 > constant k is being defined in the usual way via the mutual inductance M
 > and the two inductances L_1 and L_2 via
 >...

Something wrong here. It's just "k", not "k^2". The equations agree
after the correction.

 > Now the questions:
 >
 > 1) do w_l and w_u have the same meaning as 'your' w1 and w2 ?

Yes.

 > 2) is Skeldon's coupling coeff. 'k' identical to your k_12

Shound be. I didn't find the paper here, but in your equations k_12=k^2.

 > 3) what is the PHYSICAL meaning of 'your' w0

The energy transfer time is Pi/w0, or 1/(2*f0), or half period of
w0. w0 is the frequency of the beats in the waveforms.

 > In Skeldon's approach the picture is rather straighforward:
 > the Tesla system comprises two circuits, both tuned to the same
 > frequency w_res = 1/SQRT(L1.C1) = 1/SQRT(L2.C2)
 >
 > When the system becomes excited, there is a shift from the original
 > frequncy w_res into two frequncies w_l and w_u which are VERY CLOSE
 > (in the given example w_l and w_u are less than 2% apart), and the
 > beat between these two frequncies determines the energy transfer
 > between primary and secundary circuit.

With the correct k, the separtion is the same by both approaches.

Antonio Carlos M. de Queiroz