Re: Capacitance of Tesla secondary coi

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Partha Sarkar wrote:

> I want to calculate the inter-turn capacitance of the
> secondary windings, or the capacitance between any two
> turn on the secondary.

For the capacitance between neighbouring turns, the Palermo
formula is an approximation,

C = 2 * pi^2 * epsilon * coil_radius / (ln(a) + sqrt(a^2 - 1))

where a = 1/spacing_factor = winding_pitch/wire_diameter

and ln() is natural log.  See A.J. Palermo, 'Distributed
Capacity of Single-Layer Coils', Proc IRE 1934, Vol 22,
p897; I can probably email you a scan of this article if
you need it.

Palermo's experimental measurements are dubious, but the
above formula has a straightforward derivation.

However, this direct turn-to-turn capacitance only becomes
a significant determining factor of the propagation
characteristics at high frequencies - well above the quarter
wave fundamental axial mode resonance used by Tesla coils.
For the resonant modes involved in coiling, the longer range
internal capacitance is much more significant - this is the
combined effect of the large number of small capacitances
between the pairs of well-separated turns.

Bart Anderson's JavaTC program will calculate the
quarter wave resonance of conical coils,

 http://www.classictesla.com/java/javatc.html

To see the secondary C calculations that go into this,
visit

 http://www.abelian.demon.co.uk/tssp/geotc/

Also, Antonio Carlos M. de Queiroz has some excellent
physical L and C calculators at

 http://www.coe.ufrj.br/~acmq/

None of the above formulas/programs take account of E-flux
passing through the coil former dielectric.  They assume
'air cored' coils, ie thin walled tubes.

Hope that helps,
--
Paul Nicholson
--