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Re: [TCML] Spark models, revisited
Hi,
I made the tests, mentioned in my posting below. The capacitance, added by
attaching a thin wire (0.4mm) to the topload, works out to around 6pF/m,
resp. 1.8pF/foot. That's in fair agreement with Udo's calculation from the
wikipedia formulas, and with Terry Fritz's 1.5 pF/foot, of his proven simple
leader model ...but in not so good agreement with Antonio's elegant
calculation (11pF/m). Perhaps the 1uH/m inductance of the transmissionline
in the model could be a bit different? From the experiments, the Fres
detuning of the secondary system, by adding a thin wire, is quite
remarkable. I "think", only the low overall Q of a sparking TC (~10), is
making it feasible, to tune to zero detuning, and observing acceptable
sparks anyway. Primary detuning to lower Fres seems indicated, indeed, while
not possible excessively, in order not to hinder breakout. - Well: thin
wires are not yet real sparks!
Following, the original results of my tests. Hope the tables appear not
scrambled. They are written with Font "calibri 12", and copied from my
Excel, which I can mail you, if desired (including 2 graphs). Pic's of the
experiment setup also exsist.
Regards, Kurt
Here the results:
Thin Wire model of Leader capacitance Experiments
of Oct. 27th/28th 2012
Instruments used:
1.) LCR Meter ELC-131D von ESCORT Instruments Ltd. (Taiwan)
2.) Siemens W2087 Pegelsender 200Hz-1620kHz, with 6-Digit f-counter
3.) Hewlett Packard HP5216A 7-Digit f-counter
4.) Tektronix TDS 2024B Oscilloscope / 200 MHz
5.) Low Z Amp with LM12 Power-OpAmp, max. ~500kHz, after Terry Fritz
TC used for Tests: UBTT
for details: http://home.datacomm.ch/m.schraner/UBTT-Betrieb.pdf
Coil-Inductance Wire used in Experiment:
Ldc=66.6[mH] Magnetwire 0.4mm Diameter
double insulated (Thermex,
Isola)
Symbols:
Ldc = Inductance of secondary coil
Fres = Resonant frequency of secondary system, including wire / measured
Lwire = Length of magnetwire attached to topload /measured
Csec = Capacitance, needed for Fres, Csec = 10e9*[1/(2*Pi*Fres)^2/Ldc]
dC/dLwire = deltaCsec/deltaLwire --- Capacitance per meter of wire
Test 1: Bare Secondary Coil, without Toroid
Fres Lwire Csec dC/dLwire
[kHz] [m] [pF] calc. [pF/m]
194.625 0 10.041 -
171.335 0.657 12.956 4.437
132.29 2.13 21.733 5.958
118.1 3.02 27.269 6.220
100.302 4.36 37.805 7.863
Test 2: Secondary Coil, with 50 cm / 12.5 cm Toroid
Fres Lwire Csec dC/dLwire Remarks
[kHz] [m] [pF] calc. [pF/m]
122.039 0 25.537 - coil with toroid only
121.91 0 25.591 - coil with toroid +
brakeout point
116.753 0.657 27.902 3.517 "
101.784 2.13 36.712 5.981 "
95.052 3.03 42.096 5.983 "
85.021 4.56 52.615 6.875 "
-----Ursprüngliche Nachricht-----
From: Kurt Schraner
Sent: Wednesday, October 24, 2012 5:46 PM
To: Tesla Coil Mailing List
Subject: Re: [TCML] Re: Re: Spark models, revisited
This thread is really interesting. Would be nice, to have a formula for
spark capacitance, relevant for TC's. Antonio's appoach seems very
convincing, because it only relies on basic physics law's and the model of
a transmission line. May be, the transmission-line model can be questioned
for this case. On the other hand, the formulas given in Wikipedia
http://en.wikipedia.org/wiki/Capacitance seem well established. I see kind
of a dilemma.
On the other hand, in trying to measure secondary resonance frequencies,
including toroid & sparks, thin wires, attached to the toroid were used,
simulating the sparks. If I'm not wrong, none of these experiments were
shown on this list. In my experiance the influence of a thin wire on a
toroid-tpoload seems quite strong, but didn't yet collect quantitative data.
I would perhaps like to do some fairly controlled experiments with different
wire-lengths, in order to have an raw estimate of spark capacitance. Perhaps
others, having already done these measurements might add their comments.
Kurt
-----Ursprüngliche Nachricht-----
From: Udo Lenz
Sent: Monday, October 22, 2012 3:51 PM
To: Tesla Coil Mailing List
Subject: [TCML] Re: Re: Spark models, revisited
If I apply the equations for a wire of 0.2 mm diameter 1 m
above a conducting plane from
http://en.wikipedia.org/wiki/Capacitance
I get 5.6 pF/m. For 11.1 pF/m I would need wire diameter of 2.7 cm.
Antonio Carlos M. de Queiroz wrote:That formula doesn't work if the distance
of the plane is large (gives zero capacitance). A better approach is to
consider the capacitance of a thin toroid in free space, that can be
calculated exactly (discussions in the archives of the list, years ago) and
divide the capacitance by the toroid circunference.
A neat trick and you are right about beingcareful which formula should be
used. The wiki pagegives at its end an equation for infinitely
distantplanes. For my 70cm arc at 0.2mm diameter it works outto 6.5pF/m,
which is more than the value I gave abovebut not really enough to get the
currents and powerdissipation in the arc at the voltage I run on.Udo
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