Re: Inductance calculations

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:

 > Original poster: "Paul Nicholson by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

 > I didn't recognise the recipe used by Moshier, but I would expect
 > Inca (great name!) to give better answers for very low turns than
 > fantc/acmi, because it uses a more direct method which doesn't
 > rely on circular filament approximations.

The calculation with elliptic functions assumes circular filaments,
and appears to work very well. See my other post.

 > As the wire becomes more stretched out, mutual inductance between
 > remote part of the coil gets smaller, so that the overall self
 > inductance drops, and the minimum is reached with a straight line.
 > Can Inca follow this trend all the way, I wonder?

It can, with numerical integration (that assumes true spirals), but
for a solenoid at some point the results will get weird, because the
present formulation calculates inductances as the mutual inductance
between two filaments places at a certain distance (Maxwell's g. m. d.),
vertically. The program keeps the wires at the correct distance for
solenoids and flat spirals, but not exactly (but well enough) for
conicals. It can calculate correctly the inductance of a flat spiral
with a fraction of turn, that is a wire as straight as we may want.

 > This whole matter of low inductance structures is quite challenging
 > both for calculation and measurement, and it remains to be seen just
 > how far these programs can go.  We can clearly see the limits of the
 > circular filament approximation, and I think that direct Neumann
 > integration of small linear elements ought to do much better here.
 > But there remains the thorny question of what to do about structures
 > made from fractional turns of wide sheets and thick tubes.

Maxwell's method can, in principle, be applied to wires of any shape,
provided that we know the current distribution in the wire.
The only approximation is that the cross section of the wire must be
much smaller than the radius of curvature of the turns, but it's
not clear for me yet how this affects the results, or how to take
the effect into account.

 > I'm still pondering k factors following Antonio's post of several
 > days ago.  Some of the math in pn1401 section 6 is wrong and I can't
 > extract the k just using determinants in the way proposed. I'm in
 > rewrite mode and rethink mode, but for now the only way I can
 > predict an operational k is to continue with just computing the two
 > mode frequencies and using these to calculate the k.  However I feel
 > that there ought to be a more direct method which doesn't involve
 > computing the modes first, only I haven't seen it yet.

And I didn't implement current profiles in my program yet. But this is
simple with Maxwell's method.

Antonio Carlos M. de Queiroz