Re: Coupling coeff. vs Voltage gain (was Re: Who needs a quenching gap ?)

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-uswest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
> 
> Original poster: "Ed Phillips by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <evp-at-pacbell-dot-net>

>         Don't think Antonio has stated this explicitly, but at this
moment ALL
> of the energy which was stored in the primary capacitor has been
> transferred to the secondary. For this condition the "voltage rise"
> should be very close to sqrt(Cp/Cs) as, for almost any imaginable
> circuit Q, there has been no appreciable energy dissipated.

This is the idea.

> > Isn't interesting how a so simple and linear circuit (two coupled LC
> > tanks) can exhibit a so complex behavior?
> 
>         Indeed!  Can't remember if you have stated this explicitly, but the
> circuits are, in effect, oscillating at two frequencies simultaneously;
> the higher the k the more separated they are until, at k=1, one is zero
> and the other is infinity.

Yes. The circuit oscillates simultaneously at two frequencies. But for
k=1 one frequency goes to infinity but the other remains finite
(see the post by Bert).
If the circuit operates in the mode (a,b), k=(b^2-a^2)/(b^2+a^2), and
the two oscillation frequencies are a*w0 and b*w0 rads/s, where
w0=sqrt((a^2+b^2)/(2*a^2*b*2*L1*C1)). (This assumes L1*C1=L2*C2.)
If a=1 and b>>a, k=~1 and w0=~1/sqrt(2*L1*C1). One frequency stays at
w0 (a*w0), and the other goes to infinity (b*w0).

>         I think you have published the solution for the infinite Q case
> (lossless inductor and capacitor), but have you worked it out for the
> lossy case, and particularly the case where primary and secondary Q's
> are different?  I've always been too lazy to go that far.

I have the solution for the general case implemented in the program
Teslasim (ftp://coe.ufrj.br/pub/acmq/teslasim.zip). The program can
compute the expressions, list them, and plot the voltage and current
curves. It can also help in the design of the Tesla coil system.

Antonio Carlos M. de Queiroz