Re: Breakdown voltages of toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:

 > Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk>

 > I see you've been pretty busy putting out some very useful
 > software.  Wish I could run the stuff but no windows here...

I am trying to do a port to Linux using Kylix, after finally making
Linux work in my computer (apparently...). But too many
problems are appearing.

 > I agree, the thing with the self potential calculations can
 > get a bit messy.  There are whole books devoted to this problem,
 > so we should be relieved that the methods we're using work as
 > well as they do - it could have been a lot worse!

Yes. 0.1% of precision is easy.

 > For bulk C values, the distortion of the charge distribution is
 > negligible, and only really becomes a problem when we want accurate
 > values for surface field.  Even then, other factors make this
 > problem relatively minor, I think.

I have the exact expression (series) for the potential around a toroid
coded now. A little more messy than the series for capacitance. Now
I will see if I can find the electric field too.

 >  > I will eventually code a simulator like yours, since I have how
 >  > to calculate inductances and capacitances from coils.
 >
 > Yes, I think you have done the hardest parts already.  Now you just
 > have to model a suitably detailed equivalent network.  When doing
 > this, to get reasonable accuracy and to reproduce all the
 > qualitative features of the V/I distributions, you have to include
 > the effect of C between each pair of N secondary coil rings, ie
 > N*(N-1)/2 capacitances.

I can just use the complete capacitance matrix that comes from the
inversion of the potential matrix. It's directly a nodal matrix.
Inductances and resistances can then be added without great problems
(maybe a matrix inversion for the inductances). A small problem is
that with the ring formulation the terminals of the capacitances are
the entire rings, and the inductors are entire rings too. I have
to decide on where are the terminals of the elements. For inductors,
the terminals are naturally two per ring, at the same location.
For capacitors, I have to split the capacitances between the two
terminals of each ring, or to shift them to just one side (difficult
to explain this without a drawing).

 > This is what I call the 'internal'
 > capacitance in my notes.  Other coil models that I've seen fail to
 > do this, or only include capacitances for immediate neighbour rings.
 > Then their authors wave hands rapidly to explain why the results are
 > a few percent out at the fundamental, and proportionally more error
 > at the higher modes.

There is no great cost in using all the capacitances.

 > For the higher order resonances to work out
 > right, the internal C must be reasonably well approximated.  I also
 > include C terms for distributed capacitance between topload and
 > secondary, which is another kind of 'internal' capacitance.  All
 > this requires meticulous book keeping of the many internal C terms
 > involved, but is well worth the extra effort.

I am thinking about considering conductors as topload, ground, etc.
as just coils with all the turns in parallel. The capacitances
continue to be treated in the same way, with only the treatment
of inductances (and resistances) being different.

The ideal would be to formulate the system with a variable degree
of distribution, by grouping sets of rings, and so obtaining models
with higher or lower degree.

Antonio Carlos M. de Queiroz