Re: self-C comments

Tesla List wrote:
> >From richard.craven-at-mkbbs.co.ukTue Aug 27 22:58:08 1996
> Date: Tue, 27 Aug 96 19:31 +0000
> From: richard.craven-at-mkbbs.co.uk
> To: TESLA-at-pupman-dot-com
> Subject: 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.

Many coilers are now using significantly larger toroids to get higher
discharge currents and "hotter" performance. I've found, through
indirect measurements/calculations, that the self capacitance of my 10"
x 31" secondary seems to be about 16pF, and the "effective" toroid
capacitance (8" x 32") seems to be about 26pF. The estimated "free
space" toriod capacitance would be about 35pF. 

> 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.

The smaller diameter at the top may create problems with corona breakout
at the upper portion of the coil. The conical shape will also tend to
lower the overall inductance of the coil for a given height, reducing
its energy storage capacity. "Top loading" with a relatively high
capacitance toroid (which would probably be essential to shield the top
of the winding from destructive breakout) will also tend to "swamp out"
the reduction in coil self capacitance. The only conical coils I've ever
seen were for very small, low performance, demonstration coils like
those from Edmund Scientific. Anyone seen/built a high-power conical
coil system??

> 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).
Good point! However Malcolm has shown that lossier coil form dielectric
materials DO have significant impact on reducing the measured "Q" of the
secondary coil (with no secondary discharge). It's not exactly clear why
this should be if we use your argument above... However, the losses due
to output discharges have a MUCH greater impact on lowering effective Q. 

> 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.
Right! There is a slight decrease in the characteristic impedance of the
coil. The protective benefits of a coating usually make this worthwhile,
particularly for 2-coil systems.
> 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.


Hmmm... I'm not sure I understand this. The effective coupling
capacitance and the electrostatic field between the secondary and the
primary should be largely unaffected by whether the gap is firing or
not. The "floating" voltage on the primary coil when the gap is
extinguished will be a limited by the HV transformer's output
capacitance to ground, presence of any bypass capacitors in the safety
circuit to ground, and other stray capacitance in the primary circuit.
Since a 2-bushing pig secondary is not grounded like the center tap on a
neon, you might see a somewhat greater voltage excursion capacitively
coupled from the secondary discharge terminal to the TC primary in a
pig-driven system. However, in all cases, this excursion should not be
greater than the breakdown voltage of the safety gap to RF ground (say
15 - 25 KV). Since this is normally MUCH less than the voltage across
the secondary:primary coupling capacitance, the primary should look
pretty much like "ground" to the secondary irrespective of the whether
the gap is firing or not. 
> 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.


Excellent points! A toroid mounted fairly close to the secondary will
lose a significant portion of its effective capacitance due to the
shielding effects of the secondary. On my system, the sheilding effect
drops the effective capacitance to about 26 pF. The C/d ratio, however,
is about 0.81... virtually right on! The 4:1 major:minor ratio might be
viewed as the LOWER limit for design of high performance coils. The
"acid test" is always final tuning or "smoke tesing"...

> 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.

This sounds feasible! It would also be interesting to compare breakout
currents (streamers to air) verus hot discharges to ground. I suspect
that the maximum discharge currents coming off the secondary could be
quite large. At the maximum voltage point, virtually all of the system
energy is in the large electrostatic field surrounding the toroid and
secondary coil. If we now discharge this fully charged capacitor to
ground, we've removed all of the energy in a very short time as opposed
to the relatively long "ring down" time associated with only streamer
discharges. They certainly look more evil!

Anyone care to estimate what the magnitude of these current peaks might
be??  10A?  100A??  More???   :^)

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

Me too. I think I'll go into a dark room and fire up the coil! :^)
> Richard Craven
> ---

Safe coilin' to ya!

-- Bert --