[TCML] Magnifiers and transients

[Paul Nicholson <tcml88@xxxxxxxxxxx>]

Here is a 2-coil TC, conventional flat spiral primary placed
just below the secondary, k=0.12,

Waveforms and animation,

 http://abelian.org/tssp/tmp/c1.wave.gif
 http://abelian.netcom.co.uk/tssp/tmp/c1.anim.gif

And the voltage gradients along the secondary,

 http://abelian.netcom.co.uk/tssp/tmp/c1.grad.gif

Not much excitement there.   The two 1/4 wave modes share
almost equally 99.8% of the firing energy.  The tiny remainder
ends up in the HF transient that you can see most clearly in
the gradient animation travelling up and down the secondary.

The voltage gradient due to this transient alone is easier to
see if I remove the two operational resonances,

 http://abelian.netcom.co.uk/tssp/tmp/c1.trans.gif

In this example it kicks up to about 6 to 8 kV, worse near the
ends of the secondary.   Even though the energy involved is quite
small, it is concentrated spatially and in time.

Raising the primary to just above the base of the secondary,
we obtain k=0.16 and the transient gradient is now

 http://abelian.netcom.co.uk/tssp/tmp/c2.trans.gif

The transient makes a round trip of the secondary in about 3uS,
after which it decays due to losses and dispersion.

Raising the primary further still increases the coupling to
0.2 and with this setting (primary about 10% of the way up the
secondary), we have 0.64% of the firing energy in the transient.

 http://abelian.netcom.co.uk/tssp/tmp/c3.trans.gif

But the transient voltage gradient is no longer so high.  Even
though there is more energy in the transient, its frequency
components don't go so high - it is less concentrated.

There seems to be a worst case for this transient voltage
gradient, I'm not sure just where but it probably occurs when
the primary is level with or just above the secondary base.

Experimenters with adjustable primary height, base current
CT and digital scope should be able to confirm this effect by
analysing the HF ripples present in the base current waveform.

Now at this point I turn the secondary coil into a 'magnifier'
system by cutting the coil at 25% height.   I wrote a quick
program to use Antonio's design equations and found that
a tuning mode of 2:3:4 is within reach of these two coils.
This mode required a coupling of 0.46 so I had to switch to a
helical primary, but I kept the firing voltage and primary cap,
and hence the firing energy, the same as with the 2-coil.

The design program suggested a particular C2 and with that
installed the resonant frequencies, when modelled in the
simulator, came out within 2% or so of expected.   I wrote
another simple program to help me tune the thing:  I measure
the three frequencies and put these into the program and it
tells me which way to adjust k and C2, up or down, to bring the
system closer to correct tuning.  This worked very well and the
simulator produces frequencies with the correct ratio to within
0.01% (would be interesting to try this with a real system).

Waveforms and animation of the magnifier,

 http://abelian.org/tssp/tmp/c5.wave.gif

 http://abelian.netcom.co.uk/tssp/tmp/c5.anim.gif

Voltage gradients along the secondary,

 http://abelian.netcom.co.uk/tssp/tmp/c5.grad.gif

By turning the coil into a magnifier, the transfer time has
reduced from around 20uS to 6.4uS and the peak voltage has
gone up slightly.   The voltage gradient along the secondary
is much higher though - we now have a couple of hundred kV
across it!

The firing energy is divided amongst the three operational
resonances with ratios of about 28.5%, 28.5%, and 43%.  Less
than 0.015% of firing energy is going into the HF transient -
this is less than 1/10th of the transient energy seen in the
original k=0.12 2-coil system.

If I subtract out the three operational resonances, the voltage
gradient due to the transient alone is now

 http://abelian.netcom.co.uk/tssp/tmp/c5.trans.gif

The only part of the system where the transient has any
significant voltage gradient is at the base of the tertiary.

Well, to the extent that models can be relied upon, this
particular 3-coil system has much smaller HF transient voltage
gradients than when the same firing energy is put into the
same winding as a 2-coil.

Hopefully we will soon see these effects confirmed and measured
in a couple of magnifier systems.
--
Paul Nicholson
--

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