Re: [TCML] Magnifier topics

[Paul Nicholson <tcml88@xxxxxxxxxxx>]

So far I think the only documented example of multiple resonant
tuning of a TC is Antonio's 3:4:5 system described here,

 http://www.coe.ufrj.br/~acmq/tesla/mag345.html

As a test of modelling software I set up a distributed model
of this system.   Plugging in the dimensions of all the coils,
the 62pF 'transmission line' capacitance, and a guess at some
of the topload dimensions, reproduces the behaviour quite well.
I had to add an extra 2pF of top capacitance and I actually
needed 70pF on the t-line compared with Antonio's 62pF, in
order to get a reasonable tuning.

Here is a comparison of lumped and distributed models, showing
the impedance response seen looking into the gap:-

 http://abelian.org/tssp/acmq345a.gif

The red curve is from a lumped model using the component
values given by Antonio, plus a bit of resistance to simulate
a plausible loss factor.   The green curve is the distributed
model, adjusted to match reasonably well by tweaking C2 and
C3 as mentioned above.

From Antonio's web page you can see that the lumped model
gives a very good account and in this case the distributed
model doesn't have anything much to add.

Here is an animation of the resonator voltages (800 kbyte,
200 frames):

 http://www.abelian.netcom.co.uk/tssp/acmq345.anim.gif

The 'resonator' in the top two graphs is the combined secondary
and tertiary, with the dividing line marked at position 29.

Output voltage reaches a peak at 6.6uS which is frame 132.
If you can freeze it at that point, you see that there's
only a little residual current in the secondary and hardly any
secondary or transmission line voltage at all.  Nor is there any
tertiary current - all the bang energy that survives the losses
is momentarily in the third coil's E-field.  This animation
has a 10kV firing voltage and the peak output is about 210kV
(the lossless lumped model predicts 227kV).

The step change in current between the top of the secondary
and base of the tertiary is due to the current diverted into
the added C2 - the 'transmission line' capacitance.

You'll see some HF components excited in the secondary at
the beginning of the bang.  These don't couple well into the
tertiary and are almost completely trapped in the secondary.

It's fascinating to watch how the secondary coil drives the
tertiary resonance, whipping it up to a peak.  Getting the
timing of that 'whiplash' correct is what multiple resonant
tuning is all about.  You can see from the animation that it
really 'looks' right, but is not quite perfect because my model
is still slightly out of tune.

If more overtones where brought in and tuned correctly,
it really would start to look like a whiplash at the peak,
with (momentarily) all the resonator voltage rise occurring at
the top end of the tertiary.  Extra overtones can be tuned
by hanging capacitance onto the resonator at key points,
and/or splitting the resonator into yet more coils, each with
suitable reactance.   What you end up with in the limit is a
pulse forming network involving stepped or graduated impedance
transformation.  This could be described as a 'wide band' or
'pulse' TC.  It wouldn't be of any practical use because it
would be lossy and the final segment of the resonator has
to withstand the entire peak output voltage.  However, the
principle probably crops up here and there in pulse forming
networks in power electronics.

Note that the current distribution in both coils is almost
uniform, especially so the secondary.  This means that the
effective inductance is very close to Ldc.   Consequently the
voltage distribution in each coil is almost a linear rise
and this makes the Medhurst C valid for the equivalent shunt
capacitance.  This enables Antonio's lumped model based on Ldc
and Medhurst to give such a good prediction of the resonant
frequencies.

Apart from those little HF ripples, the distributed model
doesn't have a lot to add here, although it gives a nice
picture of the resonator in action.

There are three resonant modes (almost correctly tuned) in
operation here.  Separate animations of each:-

1/4 wave, 227kHz (232kHz measured, -0.4% error):
 http://www.abelian.netcom.co.uk/tssp/acmq345-1.anim.gif

3/4 wave, 303kHz (307kHz measured, -1.3% error):
 http://www.abelian.netcom.co.uk/tssp/acmq345-2.anim.gif

3/4 wave 383kHz (385kHz measured, -0.5% error):
 http://www.abelian.netcom.co.uk/tssp/acmq345-3.anim.gif

and just for fun, the next higher resonance, which is not
being tuned here,

5/4 wave 873kHz:
 http://www.abelian.netcom.co.uk/tssp/acmq345-4.anim.gif

This overtone makes 500V available at the topload at 20k ohms
reactive impedance.

The errors of the distributed model (-0.4%, -1.3%, -0.5%)
could be improved if we took the trouble to measure all the
dimensions accurately and track down all the 'stray' wiring
capacitances, etc, but the lumped model with errors of (1.8%,
-1%, -1.3%) is already more than adequate for practical work.

This 3:4:5 system really is a very good demonstration of
multiple resonant tuning. The added C2 is large compared with
the secondary coil's own shunt capacitance, which means that
Ldc and Medhurst C are good to use.   The tertiary coil is not
quite so 'lumped' due to the relatively small topload but is
still very well described.  These conditions are likely to
be present in most magnifiers and the well thought out set
of design equations and programs that Antonio provides are
completely justified for practical work.

Hopefully the animations in this post will be helpful in
visualising what the multiple resonant tuning is aiming for.

The challenge for the coiler is as follows:   you build the
system according to the design equations and measure the three
resonant frequencies.  They will not initially be correct
because the reactances can't be designed and built perfectly.
They need to be adjusted to the desired ratios.

Once the coils are wound, the system has three tuning variables
to play with:  topload height, added C2, and the primary tap.
Or perhaps four if coupling can also be adjusted.

Actually I think it is quite a problem to know which to adjust
and by how much, in order to move the three frequencies into
a correct alignment.   Perhaps it is possible to define a
tuning procedure?   For example: C2 affects the 3rd frequency
more than the others;  coupling mostly affects the distance
between 1st and 2nd (or is that 1st and 3rd); C3 affects the
1st frequency more than the other two;

If one can allow that it is only the ratios of the frequencies
that matter so that there are only two degrees of freedom,
then in theory only two of the reactances need to be tunable.
From considerations like these, can a tuning procedure be
defined?

There is no quenching in these models, so after 6.6uS the
energy starts to transfer back to the primary.  If anyone
is interested, I can animate the response with quenching,
and also with simulated discharges to ground from the topload.

I'd like to post some more models of 3-coil systems, ones that
aren't so lumped.  There's some interesting physics to be found
by looking at how the overtone mix, excited by the bang, changes
when the secondary is split.  I hope to show that it is not
so much the higher k, but the extent to which the coupling is
concentrated onto a smaller fraction of the overall resonator,
that is responsible for higher overtone content.

Dex wrote:
> 1.Overall coupling in many magnifier systems
>   is in 0.2+ range.That means magnifier is
>   more efficient than a typical coil which
>   usually has problems when coupling is that
>   high.

That's surely the simplest explanation for magnifier
performance.  Simply a fast energy transfer being more
efficient.

> 2.Voltage shape of the outputs are not completely
>   same even with the same overall coupling
>   (perhaps some effect to spark is possible due to
>    that difference)

Another great possibility - the wave shape of the 3-coil is
just better for developing a good breakout.

I think 'accidental' multi-mode tuning must come further down
the list of possibilities, and HF overtone heating effects at
the bottom.  Having spent much time studying coil overtones,
I've still not found a use for them but I keep trying.

--
Paul Nicholson
--


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