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Re: [TCML] Measuring spark gap resistance



Hi Gary and all,

Had to dredge up some old notes to respond to this question... :^)

Lau, Gary wrote:
Hi Bert,

Re-reading and discussing my post from 2000 where I measured tank
circuit losses due to eddy currents induced in nearby things has
gotten me interested in comparing and measuring gap losses between my
sucker, vortex, RQ, and RSG's.  It should be relatively easy to
record the tank ringdown waveform without the secondary in place.
The ringdown envelope will be a linear decrement so it will be
largely independent of firing voltage, and easy to compare.  But to
put the results in a truly useful form, suitable for use in
simulation models, I would like to boil that down to a representative
equivalent resistance.

I understand that arc resistance is a very dynamic thing, dependant
on current.  In that post from 2000 I referenced a formula that I
attributed to you, to convert the linear ringdown time and inductance
into an equivalent resistance: R = 2L/t.

This relationship was originally derived by J. S. Stone in "The Resistance of the Spark and Its Effect on the Oscillations of Electrical Oscillators", Proc. of the IRE, Volume 2, Issue 4, Dec 1914, pages 307 - 324.

In the above referenced equation, R is actually defined as the gap resistance _at the first current peak of the discharge_. The loop current is found to decay linearly when the spark gap accounts for the dominant loss within the oscillating system. Stone also confirms that the dynamic resistance of an RF spark is inversely proportional to the amplitude of the loop current (similar to the behavior of electric arcs).

Interestingly, Stone also comments that using certain cooling techniques (air blast, magnetic, hydrogenous atmosphere being mentioned) may cause deviations from a linear decrement. However, neither compressed air nor vacuum seemed to cause significant deviations from linear ringdown during Gary's experiments.

It only now dawned on me
that this is probably misleading me.  Since the ringdown is linear,
if Vbang is reduced by a factor of two, the calculated resistance
will be increased by the same factor.  While this makes sense given
the dynamic nature of arcs, it doesn't help me arrive at a useful
simulation resistance.  It looks like the ringdown slope is the
indicator of losses, rather than the calculated R.

Stone also shows that gap resistance (as a function of time during linear ringdown) can also be estimated. The first current peak is assumed to be at time t=0. During linear current ringdown over total time (To), the dynamic gap resistance can be approximated as:

    R = 2*L/(To - t)

As time (t) approaches To, the gap resistance heads toward infinity. This is also consistent with gap resistance being an inverse function of gap current.


I don't really understand the significance of the 2L/t value and how
it might relate to an "average" resistance.  Can you suggest a way to
leverage the linear ringdown measurement into a fixed resistance that
can accurately model gap losses?  I fear the short answer is "No, it
can't be made that simple", but I thought I'd ask!  If not, the
ringdown times alone will give a clear and useful quantitative
comparison of losses.

The simplest way may be to assume that all of the system losses reside within the gap, and that all of the initial energy (residing in the tank cap) was expended within the gap during the ringdown time (To). We could then ask what "effective" (or "average"?) gap resistance (Reff) would be needed within a simple RLC circuit to discharge the tank capacitor within the same time as the spark gap circuit. Since we get an exponential decay for the RLC circuit, virtually all of the initial energy would be dissipated after 5 RC time constants (with less than 1% error). Thus:

   To = 5*Reff*C

Rewriting:

   Reff = To/(5*C)


Regards, Gary Lau MA, USA _______________________________________________ Tesla mailing list Tesla@xxxxxxxxxxxxxx http://www.pupman.com/mailman/listinfo/tesla


Not a perfect model, but best I can do for a closed form solution...  :^/

Bert
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