self-C comments

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 

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 

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