Re: Acmi k x turns

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

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

Antonio wrote:

> A simple formula for k based on the geometry of the coils alone
> must then exist.  This also adds some simple constraints on the
> geometry of the coils, if the design is to be aimed at a
> particular value of k.

Yes, I agree.

My approach would be to compute numerous cases and then fit a 
curve to the data.  Perhaps someone with the necessary math
skills could take a more analytical approach, but I'm sure it
can be done, therefore probably has been done, somewhere. There
would be four input parameters to the function, these being
ratios of the overall coil dimensions, since the answer is both
turns invariant and scale invariant.

Godfrey wrote:

> I don't believe that k is independent of the number of turns
> if the rigorous Neumann integrals are employed,

I've only ever seen the Neumann integral defined for the case of
a filamentary current.  As soon as you move to a non-zero conductor
radius, the radial current distribution becomes significant, and
you are forced into the solution of a differential equation for
the current distribution and the induced EMF across the coil(s).

Within acmi/tssp, etc, which both approximate windings by filaments,
I have some leeway over the placement of the filament within the
conductor, ie centrally, the inside edge, the outside, etc.  I use
this to estimate the overall intrinsic error of L calculations by
finding the extremes, but this ignores an additional frequency
dependent bit of physics involving circulating currents within
the conductors. 
--
Paul Nicholson
--