Re: Lower secondary cself => better performance?

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

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

Marco wrote:

> If I recall correctly, in the past it has been suggested to build a
> secondary coil with a certain H/D ratio (also) in order to minimize
> its self-capacitance.

The coil's effective capacitance does show a minimum in the region
of unity h/d, as suggested in Medhurst's figure 9. This is easy to
understand in terms of the separate contributions of internal and
external capacitance. As the diameter is reduced, both Cint and
Cext are reduced. As the length is reduced, Cext is again reduced
but Cint increases (since points on the coil with a large PD between
them are brought closer together). Thus there will be a minimum
capacitance, at a certain h/d, below which, Cint dominates and above
which, Cext dominates. The modest h/d at which this minimum occurs is
probably less than ideal for impulsed TC applications due to voltage
breakdown considerations.

> Was therefore believed that a lower self-capacitance results in
> better performance?

Based on energy conservation, the output voltage of the secondary
for a given bang size net of primary losses is inversely proportional
to sqrt( Cee) where Cee is the equivalent energy storage capacitance
of the resonator.

Thus, selecting the optimum h/d ratio and using the smallest possible
coil length, along with the smallest possible topload, is the advice
I would give to achieve the maximum output voltage for a given input
energy.

However, the experienced coilers on this list all seem to advocate
using the largest possible topload, reporting that performance
improves as the toroid size is increased.

Why should this be?  There must be some other factor(s) which in
practice are more important than energy storage considerations.

The conditions for obtaining efficient primary circuit operation and
an optimum coupling to the secondary may demand a larger topload.
The effective inductance Les of the secondary coil does increase as
topload is applied, and it could be that an over-sized (from the point
of view of energy storage) toroid is of benefit by enabling use of a
higher primary L/C ratio and a lower f1, both of which may lead to
greater primary efficiency. Also there is the matter of obtaining an
optimum power-transferring impedance match between the toroid and the
breakout loading, and it may be the case that a large toroid provides
the appropriate shunt matching - the optimisation is then for power
transfer rather than top voltage.

Anyway, for what it's worth, those are my speculations on the subject.

Cheers,
--
Paul Nicholson,
Manchester, UK.
--