Re: Acmi k x turns

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

Original poster: "Godfrey Loudner by way of Terry Fritz <twftesla-at-qwest-dot-net>" <ggreen-at-gwtc-dot-net>

Let Lp and Ls denote the self inductance of the primary and secondary
respectively, and M be the mutual inductance between the primary and
secondary. I first note that even the formula for Ls involving two complete
elliptic integrals is an approximation in that the coil is modeled as a
stack of current rings, but this formula is more accurate than Wheeler's
formula. By the way, the two complete elliptic integrals can be calculated
to at least six decimal places using an inexpensive hand calculator like the
TI-30Xa. This is accomplished using the AGM (arithmetic-geometric mean
iteration). The various methods for calculating inductance using the Neumann
integral seem to view conductors as idealized current filaments. Perhaps
further assumptions are made such as segments of conductors modeled as
current rings. Thus all the formulas are approximations to the rigorous
Neumann integral. Let m and n be the number of turns of the primary and
secondary respectively. The approximation formulas appear to take the shape
Lp = mmA, Ls = nnB, and M = mnC, where A, B, and C depend only upon the
geometry of the coil (shape factor) and the the number of turns. Then

k = M/Sq[LpSp] = mnC/Sq[mmAnnB] = C/Sq[AB] which is independent of the
numbers of turns.

I don't believe that k is independent of the number of turns if the rigorous
Neumann integrals are employed, but the effect of the numbers of turns must
be very small for the typical tesla coil. The rigorous Neumann integrals
present grave mathematical difficulties.

Godfrey Loudner

> > The observation that only the dimensions of the two coils, and not
> > their number of turns, affect k is very interesting, and I have
> > not seen this mentioned before.
>
> No? I've forgotten the number of times I've said this. The proof is
> in some of my posts in the archives. The results of many measurements
> brought me to this conclusion. It was later confirmed when Dr
> Rszesotarksi's MandK program based on Neumann Integrals (I think)
> correctly confirmed the measurements.
>
>  A simple formula
> > for k based on the geometry of the coils alone must then exist.
> Regards,
> malcolm