# Re: k=0.6 (Was TC Optimum Coupling)

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

Tesla list wrote:
>
> Original poster: "Jason by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<jasonp-at-btinternet-dot-com>

> Sorry, I havent been following the thread - where does this 0.6 value come
> from? I would have thought that it would be best to get the K as close to
> one as possible...

K=0.6 comes from the following: When two LC parallel circuits tuned
for the same frequency are coupled magnetically (or in many other ways),
the resonance frequency of the combination splits in two frequencies,
one above and other below the original resonance. There is a set
of frequency pairs that lead to complete energy transfer from the
primary capacitor to the secondary capacitance, that is when the
ratio between the two frequencies is the ratio of two integers with
odd difference. The most practical relations happen when the ratio
is between two successive integers, as 5:6, 4:5, 3:4, 2:3, and 1:2.
With the two integers being a and b, it can be shown that the
corresponding coupling coefficient is given by k=(b^2-a^2)/(b^2+a^2).
The complete energy transfer is obtained after b/2 cycles of the
primary voltage.
With a=1 and b=2, the result is k=0.6. This is the fastest possible
mode with complete energy transfer (1 cycle). The next would be k=1
(0:1), but this is impossible to achieve.
Usual Tesla coils operate in slower modes, around 9:10 (k=0.1),
taking about 5 cycles for complete energy transfer.
To experiment with the waveforms, try my Teslasim program:
ftp://coe.ufrj.br/pub/acmq/teslasim.zip

Antonio Carlos M. de Queiroz

```