Re: horizontal half wave (double ended) coil

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Lee Kohlman wrote:

> I have modified my design...
> J A V A T C v.10 - CONSOLIDATED OUTPUT
> Wednesday, March 23, 2005 8:18:56 PM

Hi Lee,

This is looking better in terms of resonant frequencies and
coupling.  You also have more breakdown tolerance and room
to manoeuvre with the primary tuning.

I think others will agree, this is a better design, and you've
obviously made good use of the list feedback.

Gerry made a point:

> ...the only difference between 1/4 and 1/2 wave operation would
> be that haft of the primary energy would find its way into the
> top load of one of the 1/4 wave coils.  If this is correct, than
> it seems like the topload voltage predicted by JAVATC would be
> 41% too high.

Quite so.  The JavaTC output assumes all the bang energy (the initial
stored energy in the primary cap) is eventually transferred to the
single topload.  But in the bipolar, that energy is shared between
two identical coils (effectively), so all the secondary voltages and
currents are reduced from the single secondary predictions by around
a factor 1/sqrt(2).

The firing energy in this case is 6.2 Joules, and the equivalent
energy storage capacitance of each half-secondary is 55pF.  Making
use of energy = 0.5 * C * V^2, we would get a peak top voltage of
sqrt( 6.2 / (0.5 * 55 * 10^-12)) = 470kV.   But the energy storage
capacitance of the whole coil will be 110pF, giving 335kV at
each end, ie a difference of 670kV since the end voltages are
of opposite polarity at any instant.   So the end-end voltage is
actually now sqrt(2) times higher than the prediction by JavaTC for
the full energy into a half-coil.

Will the system allow break out from the toroids, or will a breakout
point be necessary (maybe an advantage)?   I don't know.  In this
application it's the differential voltage which counts, and there
seems to be plenty of it.

Another difference between the real half-wave and two times a
modelled quarter wave lies in the coupling coefficient.   The
coupling from the primary to a half secondary is k=0.136.  If I
run the calculation for the full secondary (using acmi), the result
is k=0.187,  and the total secondary inductance becomes 47.5mH,
which is 6% larger than two times the 22.26mH of each secondary,
due to mutual coupling between the two coils, so making the secondary
frequency 3% lower than 141kHz.  This has already absorbed all the
percentage detuning of the proposed primary, so that may need some
refinement.

To summarise some remaining weaknesses,
a) The coupling is perhaps still a little high?  And there's
no opportunity to reduce it by moving the primary.
b) The primary may not tune low enough - there is no allowance
for secondary detuning due to spark loading and un-modelled
end capacitance.

I wonder, is this bipolar primary tuning and coupling adjustment
problem a good candidate for 'off-axis' inductance in the primary
circuit?  Putting another inductor into the primary circuit, one
which isn't coupled to the secondary, will reduce the primary
frequency, reduce the coupling, and offer greater tuning range.

Some explanation of the coupling issue...

We base our prediction of peak top volts on the assumption that
all the energy ends up in the secondary, but we know that when
streamers are formed, some of the energy must be dissipated, and
also the streamers themselves draw charge away from the topload.
These effects reduce E and increase C in the energy equation
E = 0.5 * C * V^2, and so the secondary voltage will, with good
breakout, be limited by that breakout, hopefully to a level at
which the only breakout is the wanted breakout!

The snag is, we think it takes quite a while for the streamers to
form, which they do in small, rapid steps, but with fairly long
pauses in between.  We think it can take several RF cycles, or
even several bangs, to form enough breakout to begin to limit
(and effectively regulate) the output voltage.    During this
time, the secondary may be exposed to voltages approaching the
full predicted values.   It is desirable therefore to slow down
the primary to secondary energy transfer, to perhaps several
RF cycles instead of just 2 or 3, to allow time for long streamers
to develop sufficiently to restrain the voltages.

This is where low coupling coefficients become desirable.  The
time taken for transfer of the bang energy into the secondary is
given by 1/(2 * F * (1/sqrt(1-k) - 1/sqrt(1+k)).   This comes
out to 26uS for k=0.136, and 18uS for k=0.187.  The energy transfer
time in the bipolar coil is reduced by 30% from the value predicted
for the single half-coil.

It is well known that too much coupling tends to cause breakout
in unwanted places, such as along the coil.  The speculative
explanation above may be wrong or only part of the story, but the
adverse consequences of high k are well established by coilers, as
is the cure: reduce k.  The non-split bipolar doesn't offer much
opportunity for k reduction without changing the primary dimensions,
so maybe some off-axis inductance is the answer.
--
Paul Nicholson
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