Re: 3rd harmonic trap. Apology

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Steve Ward wrote:

> Thanks for clarifying that its actually a 3/4 wave resonance!

> SSTCs have a particularly hard time with this upper resonance
> coming into action during ground strikes.

Actually, it may not be a 3/4 wave resonance.  During ground
strikes,  both ends of the secondary are more or less grounded,
which is a substantial change in boundary conditions, changing
the whole pattern of resonant modes to 1/2 wave, 1 wave, and so
on.   The half wave could well be at say 2 to 4 times the normal
operating frequency.

But presumably this is just a temporary state of affairs and as
soon as the ground strike ends, the mode spectrum returns to
normal, and the driver moves to a new frequency, either the
correct one or the 3/4 wave.  You can see how the thing might
run normally until a brief ground strike makes it switch to
the 3/4 wave by means of a double jump.

I wrote:
> Has anyone deliberately tuned their coil's first overtone to
> the drive 3rd harmonic, just to see what happens?

Terry wrote:
> Is it a mater of miss tuning the system to hit some magic
> resonant point?

No, the system remains in tune, but with both primary and secondary
at new frequencies.  As an example, let me start with the coil
described in

 http://drsstc.com/~terrell/notes/DRSSTCspecifications.pdf

(appreciating that you've since lowered the frequency with a larger
topload).  As it stands the model predicts 122kHz for the
secondary, which is a little higher than measured, but reasonable
without putting in details of the test setup.  The 3/4 wave mode
is up at 403kHz, a ratio of 3.3.  If we replace the topload with
another of only about 8pF, we obtain new secondary frequencies of
141kHz and 425kHz, a ratio now close to 3.0, and the primary would
have to be adjusted to 141kHz to bring the system back into tune.

This is a rather big tuning alteration, especially for the primary,
and the system would probably not work too well with the small
topload.

It might be better, therefore, to try for an alignment of a higher
mode with one of the drive harmonics.  The first few resonant modes
are 122kHz, 403kHz, 624kHz, 822kHz, 1043Khz, 1244kHz, ...
and the first few drive signal components
are 122kHz, 366kHz, 610kHz, 854kHz, 1098Khz, 1342kHz, ...

As you can see, there are some potential collision opportunities
there, up at the 5th and 7th harmonics with 2nd and 3rd overtones.

Adjustment of the harmonics with respect to overtones is possible
because topload alterations change the fundamental by a larger
factor than the overtones [*].

If you can update the specs, we can have a look at the frequencies
in the latest setup.  Chances are we can find a harmonic and an
overtone that can be brought together without requiring a major
retune.

The best place to measure the overtone excitation is to monitor
the secondary base current, because there, the overtones have the
highest amplitude compared to the fundamental - a fact which no
doubt encourages self oscillating drivers to jump modes in the way
that Steve describes when taking feedback from the secondary base
current.

The questions to be answered are:
* Is there any significant overtone current as a result?
* If so, is it a problem for the driver to handle?
* Is there any performance benefit/loss?
* Should forced response coilers seek/avoid/ignore
  overtone-harmonic collisions?

I've often wondered if a bit of high frequency excitation might
be good for the streamers, by way of a heating effect.

To answer these questions it would be necessary to monitor base
current and primary current on the scope so that we can analyse
the mode content, and perhaps to compare streamers too.  Comparison
runs with the system in some harmonic alignment tested against a
tuning either side would be required.

For a traditional coil resonating freely from an initial primary
cap charge, we can calculate the initial overtone amplitudes
quite accurately because they only depend on the geometry of the
system.   But with the forced response, the steady state harmonic
currents are hard to calculate because they also depend on the system
loss factors which are difficult at the moment to predict.  Hence
this matter is something which will have to be tested in hardware!

Harmonic currents are never going to be very high, because the
coupling coefficient is smaller at the overtones.  The reason for this
is that at the overtones, parts of the secondary have currents of
opposite phase to other parts, thereby cancelling some of the mutual
induction with the primary.  This cancelling effect is reduced as the
primary coupling is more concentrated onto a limited section of the
secondary.  This relates to the reason why we see stronger overtone
content in more tightly coupled systems.  It's not the high coupling
itself, but the fact that the primary coupling tends to be more
concentrated on the bottom end of the secondary.

[*] Another way would be to fit something like a strike ring around
the secondary, at 1/4 height or thereabouts, and adjust it to tune
the first overtone down to match the drive 3rd harmonic.  This can be
modelled quite accurately to see if it's feasible.  This application
of extra capacitance part way along the coil corresponds to adjusting
the C2 of a triple LC lumped model.
--
Paul Nicholson
Manchester, UK.
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