Coupling Questions & coil measurements

I have a few questions about coupling.  I have measured the resonant
freq of the primary and secondary according to the technique described
in Malcolm's Electronics World (*) paper.  I checked the coupling using
the technique where you run 5-10A of 120VAC through the primary and
measure the voltage across the secondary (**).

In my reading, I have found several references that discuss "Magic K"
values.  Brent's  book explanation says that Magic Ks relate to even
integers (multiples) of "RF cycles". That makes no sense to me because
"RF cycles" are different for each coil and it's unique Fsec.

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?

On a similar topic, I'm not sure that I understand the "double hump"
response.  Can someone please describe how the resonant freq of the
primary/secondary system is different from the resonant freq of either
circuit measured independently and how this relates to coupling?

Once I get more of this figured out, I hope to devote a web page to
proper Tesla Coil measurement techniques and interpretation.  I intend
to discuss it in layman's terms and then spend a little time describing
the differential equations and showing how a few things are derived (for
us engineer/math types).  If anyone already has a page like this, please
let me know.  Also, any references to this type of information is

(*) Electronics World + Wireless World, March 1995

(**) I will drop this on my page at

Making arcs in SoCal,
Ross Overstreet
Huntington Beach, CA
ICQ 20762411