Re: Equivalent lumped inductance and toroidal coils

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

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

Antonio wrote:

 > The calculation of the low-frequency inductance is no great
 > problem with the decomposition of the coil in rings, specially
 > considering the many symmetries.

Agreed.  This case is attractive due to the symmetry and
uniformity of the coils.   I'm hard pushed to suggest any
reason why either the voltage or current amplitude
distributions should depart from a sinusoidal function
of position.

 >> Does Antonio have this case covered?

 > No, I don't.

Well I'll code something to do the low frequency inductance.

And if the amplitude distributions really are sinusoidal, then
we also get the HF inductance quite easily.

 > The consideration of the distributed capacitance looks
 > complicated, because the charge distribution would be not
 > uniform along a turn.

Yes, we cannot use our usual solution in terms of charge
rings.  But I wonder perhaps if the symmetry and lack of
end effects might just lead to a closed formula for the
elements of the capacitance matrix, with respect to some
natural surface tiling of the toroid, rather than ring
by ring.
--
Paul Nicholson
--