# Re: Couples Therapy

```Tesla List wrote:

> Original Poster: Parpp807-at-aol-dot-com

> << k=(b^2-a^2)/(b^2+a^2),
>  where a and b are integers with (b-a) odd >>

> Would you please explain how this equation is derived.
> Do a and b have dimensions?
> Can you give refereces for the texts you refer to?

(Sending again this message. The last one returned with a
routing error (??!!))

This relation can be derived "down" from the relations for the
magnifier. See:
http://www.coe.ufrj.br/~acmq/tesla/magnifier.html
I have added some extra material there today, including
the simplification leading to that relation.
There I use "k" and "l" as the integers, instead of a and b.

k and l are adimensional factors that multiply a base frequency w,
so the oscillatory modes of the complete system are at
the frequencies k*w and l*w. This integer relation,
added to the condition that the initial currents in
the coils are null when the gap fires, result in periodical
simultaneous nulls in the currents of both coils.
In the case of a Tesla coil, this, and the
tuning of the separate primary and secondary circuits to the
same frequency, are enough for complete energy transfer
at the "l"th semicycle of the secondary voltage.
The value for k comes from the analysis of the coupled
system that results in those natural frequencies.

Antonio Carlos M. de Queiroz

```