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Re: Re: [TCML] Magnifier topics

Paul Nicholson wrote:

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
Terry tried to make a similar system, with a MMC fot C2. It had insulation problems in the driver, if I remember correctly. 

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
Very interesting. If you allow, I would like to add these simulations to my site. 

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.

I have this figured out. The program MultiRes, available at:
http://www.coe.ufrj.br/~acmq/programs
can design high-order LC ladder systems that are higher-order
generalizations of the magnifier. The program does not consider
transformers, but at least one can be made to appear by suitable circuit
transformations.
Series capacitances are also allowed, in the design method implemented
in the program MresHp.
I tried to do something about losses, but so far I can only optimize a
designed ideal system to minimize the effect of losses. The programs
Optesla and Optmag try to do this.


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;
Tuning the system at low power is quite easy. I apply a low-impedance low-frequency square wave signal across the spark gap and look at the transients at the square wave transitions, that are identical to the ones that appear when the gap conducts. Starting from a carefully designed system, I tune (in my system I adjust C3, the topload capacitance) the system to produce primary beats with the required number of cycles. The effect of C2 is small there. Then I adjust C2 to produce the correct waveform over it. I have to add to C2 the input capacitance of the oscilloscope used in the measurement. After a few adjsutments of C2 and C3 the system is tuned. C3 can be set to a somewhat smaller value to account for streamer 
loading.



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?

Above.


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.

One of the possible problems is that after quenching the voltage over C2
can reach higher values than during the forward energy transfer.


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.

Makes sense.

Another great possibility - the wave shape of the 3-coil is
just better for developing a good breakout.
The RMS value of the output voltage is smaller than in a 2-coils system. This, at first sight, appears to be bad, but may also be good, avoiding excessive losses during the energy transfer. In a 2-coils system, the envelope of the ideal output voltage is a sinusoid. In a magnifier with the mode defined by three successive integers, it is something as a squared sine, that applies less voltage to the load (streamers) at the first part of the energy transfer. The input current also decays faster in a magnifier, reducing the losses in the spark gap, when comparing with a 2-coils system with energy transfer in the same number of cycles. Below is a comparison between a 2-coils system in mode 5:6 and a magnifier in mode 5:6:7. Both with the same final resonator (L=28.2 mH, C=15 pF) and the same primary capacitance (10 nF), with the same initial voltage (10 kV). The simulations are from the programs Mrn4 and Mrn6. Look at the output voltages 
(V2 and V3) and the primary currents (I1).
2-coils: http://www.coe.ufrj.br/~acmq/tesla/xm56.gif
3_coils: http://www.coe.ufrj.br/~acmq/tesla/xm567.gif
The simulations are lossless, but a simulation with losses (I tried primary resistance) shows that the magnifier 
wastes less energy.

Antonio Carlos M. de Queiroz




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