# Re: Coupling Questions & coil measurements

```"The paper "Tesla Transformers" by Von Werner Heise also describes
"values of K to strive for".  One of the magic K values is 1.33.  I have
helped measure K on 3 well performing coils in the last week and all had
a K value of almost exactly 1.33!?!  The coils varied in size from 3 ft
long secondaries to secondaries as tall as me.  I may be
misunderstanding Mr Heise, but it seems that his argument is based on
first notch quenching.

Can someone explain why some of these K values are supposedly better.
Has anyone seen evidence of superior performance after moving from a sub
optimal K to a "magic" K?  In other words, is it an artifact of the math
or does it really matter?"

k over 1????  That doesn't sound right at all, at least with the usual
definition of coupling coefficient, which can never be greater than 1.
As for the "magic k" values, it goes something like this:

Assuming the primary and secondary circuits are tuned to the same
frequency, when the spark gap fires there will be waveforms at two
simultaneous frequencies in both the primary and the secondary.  The
ratio of these frequencies is a function of the coupling coefficient k.
With the magic k's, at some time after the gap closes the voltage and
current across/in the primary will be both be zero at the same time that
the current in the secondary is zero and the voltage is at a maximum.
The significance of this is that, at this instant, ALL of the energy
originally stored in the primary capacitor will have been transferred to
the secondary.  If the gap "opens" (quenches) then, the secondary
voltage will be at the maximum possible value.  There is an infinite
series of k's which will allow this condition, but the important ones
are the larger ones, which minimize the number of cycles (and hence
power loss) before this time is reached.  The magic k's are valid even
for quite low values of primary and secondary Q.

Note that, as k approaches zero, the two frequencies will approach each
other closely, and the cycles to the magic time will be very large.  As
k approaches 1 the separation between the frequencies increase until, at
k = 1, one is at infinity and the other at zero.

Ed

```