# Re: Coupling Questions & coil measurements

```Hi Ross,

> Original Poster: Ross <ross-o-at-mindspring-dot-com>
>
> Hey,
> 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.

Brent is correct. At values other than the magic k values, the
primary does not go completely quiet when the secondary has rung up -
i.e. energy doesn't transfer to the secondary in its entirety.
However, the popular magic k values are for lossless circuits and a
practical TC is far from lossless, particularly due to the primary
gap. As a consequence, energy disappears from the primary faster than
in a lossless system and the magic k values have to be adjusted
upwards for a real coil. So 0.12 would become 0.13 *for a particular
system*.
I find it doesn't matter a great deal at low k's as these values
start getting pretty crowded but it certainly matters as k goes up
in value.

> 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.

Not possible. K is always less than 1. Most coils will fall somewhere
in the 0.1 to 0.2 range.

> 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?

The math is used to derive these values. It is not a mere artifact.
However, the operational differences become insignificant below 0.2 or
so.

> 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?

With the secondary coil in place,  bridge your gap and feed the signal
generator in series with a resistor (say 10k) across the primary coil
or cap (same difference) then tune either side of the resonant
frequency (Fo) of the secondary (or primary as they should be
individually tuned to the same frequency), you will notice that there
is a null where Fo should be. This is a consequence of the degree
of coupling between the two tuned circuits.
If you monitor the electric field coming off the secondary with
your system operating normally using a scope and aerial probe (at a
good safe distance), you will see a waveform which looks like a
double-sideband modulation envelope. You will see the system ringing
at Fo with an amplitude variation which corresponds to the energy
transfers. It is important that your scope aerial is far enough away
from the coil to avoid picking up the waveforms coming from the
primary circuit. You will see Fo going up then down in a sinusoidal
looking envelope. If you multiply the envelope sinusoid with Fo, you
get a result which shows two quite different frequencies being
present. These two frequencies are those that you measured while
doing the frequency sweep with the signal generator. It is not quite
as simple as that either since the amplitude of the envelope is
dropping as the system loses energy but for a quick picture, it is OK.
One should note that whatever frequencies one appears to end up
with, the scope (time domain) shows the secondary ringing at its
natural frequency with an amplitude variation. At any instant, the
amplitude of the waveform is indicative of the voltage present at the
top of the coil.
I did a simplified math derivation of this once to illustrate how
the side frequencies come about. It should be in the archives from a
couple of years ago. It is not exact but designed to give an
intuitive feel for what is happening and why. The fourth order
differential equations that are published in most papers on the
subject give exact solutions, unfortunately mostly for an ideal
lossless coil which is never the case :(

Malcolm

> 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
> appreciated.
>
> (*) Electronics World + Wireless World, March 1995
>
> (**) I will drop this on my page at
> http://www.geocities-dot-com/CapeCanaveral/Cockpit/3377/tesla/measure.htm
>
> Making arcs in SoCal,
> --
> Ross Overstreet
> Huntington Beach, CA
> ICQ 20762411

```