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# self-C comments

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Hello Group,

My measurements and calculations show that for most TCs the value of
capacitance of the secondary terminal itself lies between Cself/2 and
Cself of the secondary coil in isolation. By this I mean that for a coil
with a calculated self-C of say 30pF the toroid will typically be 15-
30pF in size.

The secondary coil capacitance is dominated by its area per turn (i.e.
larger diameter coils have higher self-C). Some TCs were built which
have conical secondaries: typically the perpendicular is 1.5 times the
base diameter. These constructions would have a large inductance per
unit height at the bottom of the coil which would provide good coupling
(because the flux linkages per unit turn would be high). The top of the
secondary would have a lower self-capacitance because the area of the
turns is smaller.

Bearing in mind erudite comments from Richard Hull (basically all the
strays due to buildings floors and the like), has anyone any comments on
conical constructions? I am not planning on building one, but it is an
area of some interest.

Some may wonder why the capacitance of a secondary is unaffected by the
dielectric coil form upon which the coil is wound. If we remember that
the electric field of a TC extends outwards from the coil towards
ground, it can be seen that the dielectric in which this field exists is
air. If we put polyethylene inside the coil form, the electric field to
ground is hardly modified. If we coat the wire we are using with a high
permittivity dielectric, the percentage volume occupied compared with
the air is also tiny so again the self-C is virtually unaffected ( I
would guess we are looking at changes of a fraction of 1% and anyway
these are swamped by extraneous C effects).

The capacitance between turns may be affected by the addition of a
dielectric coating on our wire, but if you consider that we might have,
say, 500 turns in series, we then end up with 500 tiny capacitances in
series which still adds up to a tiny total interturn capacitance. Even
if we fill the gap between turns with a high dielectric, the total
effect is still very small compared with the capacitance to ground.

All of the expressions for capacitance of coils (from Terman, Langford
Smith, Radiotron ITT reference books) express the capacitance to ground
in terms of the coil height and radius (or diameter or area). The
expressions are identical to those for isolated cylinders to ground
(Terman).

Again, as Richard Hull mentioned when this subject came up before, the
self-C of a coil can be obtained in isolation but this won't have much
relevance to actual operating conditions. Malcolm Watts found that even
the Q of his coils shifted when he measured in different rooms; Robert
Golka's big coil got pulled by the effects of a new environment when it
was moved to a different building.

All of this ignores the electric field coupling that exists between
primary and secondary; when the gap is non-conducting the electric field
to ground will be high and will be largely symmetrical about the plane
of the spiral . This infers that the secondary must experience a field
due to the primary and I wonder what pulling this might exhibit on the
secondary.

Why are toroids preferred compared with spheres?  The low profile, flat
shape of the toroid gives good voltage grading and thus corona shielding
performance.  A sphere whose diameter was similar to the major diameter
of a toroid would give similar grading but the loading on the secondary
would be much higher; toroids give something in the region of 45% lower
load C than a sphere of comparable size (but a toroid needs to have a
major diameter of around twice that of a sphere in order to achieve the
same corona inception voltage).

The major diameter of a toroid is the main controller of capacitance: C
is proportional to the major diameter and very roughly speaking I have
seen that every inch of major diameter gives a pF of capacitance ( a 30"
toroid would be in the region of 30pF). I again acknowledge Richard
Hull's comments about rules-of thumb: these are rough guides and can be
easily disproved for a given set of circumstances.

Suffice it to say that for data on 11 toroids, C/d =0.79. This was based
on calcs from textbooks, quoted data from manufacturers and averaged
calcs from my own derivations that were within 10% of other sources.
Most toroids that I have looked at have had a major/minor ratio of 4.

If you build a toroid, measure its big diameter in inches. This is the
sort of capacitance it will have in operation. When added to the self-C
of the secondary,it will ring with the self-L of the secondary at around
the right frequency. You then need to tune for maximum output in situ.

On another note, re the time-domain vs frequency domain argument (
VSWR/Q, Tx line/LC coupled ccts with arbitrary amounts of wire): has
anyone looked at putting a VSWR bridge in the grounded end of a
resonator/toroid and driving it from an appropriate RF source? Using any
of the typical L or Z match ATUs it should be possible to match into the
base of the resonator. (You could even go in via a balun to get away
from a coaxial setup, or even connect the balun to the base and the top
end via a simulated spark channel). You could then use an easily
constructed directional coupler to at least look at the magnitudes of
forward and reverse currents as a function of drive frequency.

Another point that I discussed with Malcolm Watts the other day
concerned a modification of Dr Gary Johnson's idea of an isolated E
field probe (1992 Tesla Symposium available from ITS, ISBN 0-9620394-4-
6). My plagiarism was to look at the currents sourced from the toroid
when it breaks. You could insulate the toroid and use a short conductor
as a discharge termial, or use Richard Hulls' preferred method of the
foil bump. A simple ferrite core around the discharge element could be
made that would not saturate, and any number of instrumentation op-amps
would be wideband enough. The electronics could go inside a diecast box
inside the toroid and would run easily off a battery supply, including
the fibreoptic link.

I have to go and lie down in a dark room now; my head's hurting

Richard Craven
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CMPQwk #1.42 UNREGISTERED EVALUATION COPY
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