RE: Lower secondary cself => better performance?

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

Original poster: "Lau, Gary by way of Terry Fritz <twftesla-at-uswest-dot-net>" <Gary.Lau-at-compaq-dot-com>

Hi Paul:

Concerning why large toploads appear to give superior performance, as
opposed to using a small one designed to maximize topload voltage - what
follows is the reasoning I have heard and understood.  You no doubt have
studied these issues in far greater depth than I have, so I would enjoy
hearing your take on this.

The total secondary capacitance Csec occurs in two components - the Ctop
from the toroid, and Cself, the distributed capacitance of the secondary
windings.  When a streamer breaks out, the charge from Ctop is there with
just the metal in the toroid between the Ctop charge reservoir and the
streamer where it wants to go.  But the charge in Csec is distributed along
the length of the secondary.  There are many mH of inductance between most
of this charge and the streamer that wants to drain it.  The streamer is a
very high frequency, short-lived event, so the intervening inductance just
won't allow it to be useful in terms of feeding the streamer.  So it is
desirable to have as large a portion of Csec in the form of Ctop and as
little as possible in the form of Cself.  I think this is why space wound
secondaries are sometimes favored, as it minimizes Cself (in addition to
lowering Rac and raising the Q) of the secondary, though I've heard of no
direct experimental performance comparisons.  Adding a larger topload to an
existing secondary serves to raise the ratio of Ctop/Cself.  

When streamers occur may be one (important!) instance where the lumped model
of the secondary may not accurately describe what happens should charge be
drained from Ctop to a streamer, but "stranded" in Cself.

I'm not sure that maximizing the theoretical peak pre-breakout secondary
voltage is useful in maximizing streamer length.  Maximizing the efficiency
of getting the total energy stored in the secondary to the streamer is.
Easier said than done, for sure.

Comments MOST welcome!

Gary Lau
Waltham, MA USA



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.
--