Re: How much does aspect ratio of secondary really matter

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Jared wrote:

> We use the definition of inductance:  L = N phi/ i

> Since phi equals  ( u N A i /  length )

Those equations only apply to an infinitely long solenoid or
toroidal coil in which all the flux is trapped (by symmetry)
within the core.

For real solenoids, it is necessary to include the Nagaoka factor
as a coefficient, which takes account of the limited coupling
between turns caused by escaping flux.  The calculation of
inductance becomes

 L = K(length/diameter) * u * area * N^2 / length

where K(h/d) is the Nagaoka function of h/d ratio.

K varies from about 0.75 to 0.9 for the range of h/d used in TC
secondaries.   Without this factor, the formula for L is too naive
for either design use or as a foundation for theoretical statements.

K can be calculated accurately with a double intergral over some
elliptic functions, but there are some good and simple approximations
such as Wheeler or Lundin.
--
Paul Nicholson
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