# Re: Couples Therapy

```Tesla List wrote:
>
> Original Poster: "Ruud de Graaf" <rdegraaf-at-daxis.nl>

> Sorry, but I don't understand your formula (and I can imagine there are more

The complete derivation is a rather long story. I will make it available
in the web soon by a new method that I have found. That formula is what
results from a magnifier design if you remove the secondary capacitor
and consider the resulting circuit as a Tesla coil.
(see http://www.coe.ufrj.br/~acmq/tesla/magnifier.html)

A "perfect" lossless Tesla coil can be designed with the primary and
secondary circuits tuned for the same frequency and with a coupling
coefficient given by that formula:
k=(b^2-a^2)/(b^2+a^2),
where a and b are integers with (b-a) odd. ("^2" is a square.)
These values of k are sometimes called "magic values". They make
the secondary voltage reach a maximum when there is no energy in the
primary circuit. The usual formula seen in several texts consider
b=a+1, but this is not necessary, and overlooks other possibilities.
If you have a simulator, try and see the waveforms.

> Overcoupling is the moment that an inductive loose coupled bandpass filter
> stops to decrease the weakening of the signal transfer and the bandpass is
> widened to form two peaks in the dB/f graph. This is on a distinct point in
> the graph. k<k-critical -> 1 freq-peak (fo),
> k > k-critical -> two freq. peaks period. What exactly do YOU mean with
> overcoupling.

This condition would require explicit resistances in the circuit, and
result in an extremely lossy Tesla coil.
Tesla transformers are designed to operate as essentially lossless
circuits during the energy transfer. In this sense, they are always
extremely "overcoupled", using that definition. I don't see any
relation between the theory of coupled bandpass filters and Tesla
transformers. The circuits are similar, but the function is different.
The most usual reference to "overcoupling" that I see in this list
is in the sense that the transformer has its windings excessively
close. This can only create arcing. There is no limit in the coupling
coefficient of an efficient resonant transformer, other than 1,
and no relation to the meaning of the term "overcoupling" in filters.
As Malcolm said, sparking coil (induction, or Ruhmkorff coils) operate
with tight coupling coefficients and work well too.

Antonio Carlos M. de Queiroz

```