Re: conical secondaries

[paul-at-abelian.demon.co.uk (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

"acmnovak" <acmnovak-at-email.msn-dot-com> wrote:
> > What might the advantages of having a conical secondary be?
> > I'll be building a small coil with a conical coil,
> > but I'm not sure what to expect.
> > Does it give better voltage gradient or what?

"Malcolm Watts" <M.J.Watts-at-massey.ac.nz> replied:

> I don't know about operating advantages but it might make an
> interesting case-study for modellers. I imagine it would
> feature a voltage gradient profile different to a cylindrical
> coil due to the tapering L/height. Sounds like one Paul might
> apply his computer cluster to.

Yup, might be very interesting - could do it too, I think, if
I had either a formula for the bulk inductance of a conical
solenoid, or a measurement of the finished article.

May I guess?

The regular cylinder solenoid gives a nice, almost linear
rise in voltage along the length, approx uniform EMF per
turn. The current drops along the length more like a 
cosine, as current diverts into charging up the self
capacitance.

For example, see
http://www.abelian.demon.co.uk/tssp-data/tfltr45.vi97360.gif

(Guess mode on) The inductance per turn, therefore EMF
per turn, will reduce with height on the cone, so V will rise
steeply near the bottom, becoming almost constant towards the
top. Self capacitance is roughly proportional to the radius
of the coil, so will reduce with height in the cone faster than
with the solenoid, so you might get a much more linear
current profile. Neither of these sound very useful.

Now for some wild guessing: turn the cone upside down, 
balanced on its point, so to speak. Now the V rise is modest
per turn near the bottom, and with the high inductance turns
nearer the top I think the voltage would rise more rapidly
in the top part of the coil. The current would find more
self cap per turn higher up and would fall off more rapidly
than in the cylinder coil. This may turn out to be quite
helpful, shifting the high voltages towards the top,
and shifting the high currents towards the bottom turns where
the radius, therefore the resistance per turn, is least.

(Guess mode off)

I look forward to hearing more about your funnel shaped
upside down cone coil!!

Regards,
--
Paul Nicholson,
Manchester, UK.
Modelling project http://www.abelian.demon.co.uk/tssp/
--