Re: LC III

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Hi All,

Phil LaBudde wrote:

> I pointed a retired EE with no Tesla Coil experience at the
> Corums papers for his opinion. This was one of the discrepancies
> that he noticed right off the bat. His conclusion was that the
> Corums were very mistaken about many things - and their work was
> a lot of talk with no actual experimental data of their own to
> back up their claims.

That pretty well sums up my own feelings which were formed within
two minutes of first encountering an example of their work.

One obvious problem was that they didn't realise that Q and VSWR
amounted to the same thing.   Instead, they puffed up the imagined
difference into a general claim that 'lumped' and 'distributed'
were two different modes of operation of the coil, with voltage rise
in the former determined by Q and by VSWR in the latter.  They
went so far as to claim 'extraordinary' output if the mode of
operation was changed to 'distributed', justifying this with mystical
sounding statements based on 'coherence'.   It was all wrong and
pointless and fueled a debate that lasted for years.  It was still
going when I came to the list in 2000.   I tried to do something
about it with a thread called 'The great and silly transmission
line debate' (Aug 2000), but clearly the issue still isn't dead.

IMO, the only thing they got right that was relevant was to stress
that a distributed (ie transmission line) model was necessary in
order to fully understand the system.

I wrote:
> The LC values which give the correct Fres and Vtop/Ibase don't
> give the correct energy storage at Fres, ... the single LC model
> doesn't contain a storage element to represent energy stored in
> the coil's internal capacitance ...  way to treat this in a lumped
> model is to use three capacitors, one to ground from each end,
> plus a capacitance in parallel with the coil.

Phil wrote:
> The last part of the last sentence above confuses me.

The three-capacitor model looks like (fixed font)

     base o--+--[coil]---+---o top
             |           |
             +---[C3]----+
             |           |
            [C1]        [C2]
             |           |
       ------+-----------+----------  ground
       /////////////////////////////

You're right Phil, when the coil is operated as a secondary,
the base is grounded so C1 is bypassed and has no further
involvement.

But the result does not quite leave C3 in parallel with C2,
although that may appear to be the case at first sight.

Consider the case where the coil is set up for testing with
the base grounded via an RF ammeter because we want to test
the ratio between top volts and base current.  We can allow
the ammeter to be perfect, ie no voltage drop, so the
coil base is at earth potential and C1 has no effect.

Under these conditions the current through C2 is Vtop*2*pi*F*C2
and similarly Vtop*2*pi*F*C3 through C3.  However, only the
current through C2 is returning via the base terminal of the
coil and thus via the ammeter. The current through C3 is returning
into the coil itself, missing the ammeter.   Thus, not all of
the resonator's circulating current is registered by the ammeter.

Thus, to relate top volts to base current, we must use use
Vtop = Ibase/(2*pi*F*C2), whereas to describe the stored energy,
we must use 0.5 * (C2+C3) * V^2.  Hence the appearance to two
distinct equivalent capacitances, Ces for the equivalent shunt
capacitance (C2), and Cee for the equivalent energy storage
capacitance (C2+C3).   Hope that's a bit clearer.

The circulating current through the 'internal' capacitance C3
has some significant qualitative effects, one of which is to
raise the position of the current antinode from the base of
the coil, by around 5%-10% for a typical secondary h/d, and
tending towards 50% in very short coils where C3 becomes much
more significant.

The base capacitance C1 comes into play if the coil is base
driven, for example as the tertiary of a 3 coil system.  For
h/d ratios capable of withstanding high voltage, C3 is usually
small enough to neglect unless you are into precision coil
measurements, in which case it cannot be ignored below the
5%-10% accuracy level.

See section 7 of

 http://www.abelian.demon.co.uk/tssp/pn2511.html

for definitions of the various equivalent reactances of a coil,
and section 8 for some cool identities between them.
--
Paul Nicholson
Manchester, UK.
--