Re: More Coupling...

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

Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>" <paul-at-abelian.demon.co.uk>

Concerning calculation of mutual inductance,

Ed Phillips <evp-at-pacbell-dot-net> wrote:

> I suppose one could do it by computing M for each of the turns and
> then summing it,

Indeed. That's how my little acmi [3] program works. It's quite
accurate for a closewound coil of many turns, ie a secondary.
Primaries built from thick wire or pipe are likely to be less well
modeled by the current filament approximation used in the program.

> but that sounds like a lot of work and have never tried it.

Not really all that much effort for me, largely due to the efforts
of a chap called Grover who went to the trouble of making up a set
of tables [1] for inductance between concentric current filaments.
acmi is just table lookup and summing.

> I see a lot of fellows using flat primaries, and wonder how much
> coupling they actually get.

Me too. I welcome info on measurements of M (made at low frequency)
to help get a feel for the accuracy of acmi. At tesla operating
frequencies, inter-winding capacitance rears its head to complicate
matters. I don't have a good handle on that one yet [2], so getting
the right overall coupling is still a matter of trial and error as
far as I'm concerned.

Just for fun, I used the (recently fixed) acmi to produce a graph of
k factor against separation for a pair of flat coils [4]. The coupling
at close range seems asymptotic to about 0.68 for this choice of turns
and radii. A larger outer radius gives a higher maximum coupling. If
this trend is real and not an artifact of the program, then some quite
small separations are needed to achieve the k factors required for a
magnifier secondary. Some real measurements to confirm this picture
would be very nice.

Please note that k calculations of the type done by acmi, which assume
a uniform current in each winding, are only approximately valid for
tesla secondaries due to the non-uniform current prevailing at high
frequencies [2]. Hence the need to measure M at frequencies well below
the self-resonances of the windings involved.

[1] F.W. Grover, 'Inductance Calculations', 1946;
    Reprinted by Dover, 1962.

[2] tssp will be addressing these issues in the near future.
    http://www.abelian.demon.co.uk/tssp/

[3] http://www.abelian.demon.co.uk/acmi/

[4] http://www.abelian.demon.co.uk/tmp/n10x40x100.gif

Regards,
--
Paul Nicholson,
Manchester, UK.
--