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: "Marco Denicolai by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <Marco.Denicolai-at-tellabs.fi>

> I tried the values above and got the same values than you. Now I see what you
> mean: primary voltage rises to zero (from -5.6kV) and then starts becoming
> negative again. You have no polarity reversal THERE (-at- 4 us) but you have it
> BEFORE and AFTER this instant: I mean, Vc1 is oscillating all the time and
> getting negative and positive values.

Correct. The same occurs with the other special values of the coupling
coefficient. The currents cross zero, and at the same time the
primary voltage touches zero without a polarity reversal, while the
secondary voltage is maximum. What changes is the number of cycles
before this situation is reached. In the second series (modes, a,a+3),
there is first a "false notch" where the situation almost occurs, and
the complete transfer occurs only at the second notch. Modes a,a+5
would reach complete transfer only at the third notch, and so on.
 
> I see also that with k=0.6 it is very clear (after 1 primary cycle) the
instant
> when Il1=Il2=Vc2=0. Just as you said. The problem was I didn't realize your
> tabuled values were good only for f1=f2 (it was not mentioned there).

It's possible to show that the complete transfer only occurs with f1=f2.
 
> Makes sense to me that a better maximum gain is sqrt(C1/C2), as C1 is
actually
> the initial energy storage element. I tried now in several cases and,
yes, you
> are correct: you can get even a higher gain when f1=f2. Trying to optimize on
> sqrt(L2/L1) won't really give much insight.
> The Phung paper really tackles the problem from a wrong point of view: at
least
> the maths looks correct and interesting (at least to me).

I prefer to analyze these circuits from a different point of view. See
my paper on "multiple resonance networks" (2000 IEEE ISCAS):
ftp://coe.ufrj.br/pub/acmq/papers/is00mr.pdf

> So would this "optimizing" procedure be right?
> 
> 1. make f1=f2 by tuning/measuring the primary and secondary circuits
> (uncoupled,
> as much as you can)
> 2. increase k as much as your assembly, spark gap, etc, allows to
> 3. aim to the next lower k value from your table, to get a perfect (?) total
> energy transfer
> 
> Of course, practical issues, losses, uncertainty, etc. will makes an actual
> tuning different from the above mentioned :)

The procedure looks ok. A problem is that streamer loading changes the
tuning a bit from the low-power value, but if you adjust the tuning
and adjust the coupling alternately while looking at the primary
voltage waveform (or simply looking at the output sparks) you probably 
can reach an optimum situation quickly. 
  
> >The paper is readable. Do you have at hand the reference [5]?
> Sadly not. If you are able to get it, please, let me have a copy.

By next week I take a look at a library that has that periodical.
 
> Thanks for the educational discussion.

Isn't interesting how a so simple and linear circuit (two coupled LC
tanks) can exhibit a so complex behavior?

Antonio Carlos M. de Queiroz