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Arc Impedance Study



Hi All,
	
	With my forth generation fiber-optic probes and field antennas, I can now
measure all the voltages and currents on my coil with an accuracy of at
least 10%.  More importantly, I can also get accurate phase information to
determine the phase angles between the various signals.  All the old
saturation problems and such I was having have now been solved.  By
measuring the output terminal voltage and current delivered to the arc, I
may have found a rather simple and interesting property that could be used
in the design of coils to optimally drive arcs.  I describe this below.
Forgive that this is long and has heavy math.  Those of us that care will
know what it means :-))  If you are a "newbi" to coiling, run for you life
now!
 
	First, I considered the sphere20us.jpg scope photo from Greg Leyh's
Electrum coil (www.lod-dot-org/electrum/sphere20us.jpg).  With this scope photo
and the technical information Greg has on his coil, a large amount of
information can be found.  By knowing that the Electrum operates with 48
amps peak of secondary current at 38kHz with a secondary inductance of
0.13H one can calculate that the secondary voltage peaks at 1.5MV.  The
sphere to arc current is around 5 amps peak which implies an arc impedance
of 300K ohms.  However there is another very important bit of information
that can be found.  Assuming the terminal voltage is 90 degrees out of
phase with the terminal input current and with careful study of blown up
photos of the scope waveforms, it can be found that the current to the
arc's phase is delayed by about 3uS.  Since the total period of the signal
is 26.3 uS the delay is 41 degrees (note that one of the traces seems to be
180 degrees out of phase due to the way the current transducers were
wired).  Since the current precedes the voltage, the load is capacitive.
So we have a magnitude of the impedance and the phase angle.  Geometry will
show that the 300k ohm impedance is composed of 226k ohms of real
resistance and 197k ohms of capacitive reactance.  By knowing the frequency
we can find that the capacitance is 21.3pF.  So the arcs Greg's coil was
driving are similar to a 197K ohm resistor in series with a 21pF capacitor.
 Still more information can be found when one considers that the RMS
current is around 2 amps for 120uS (the full burst time) into 197k ohms...
the energy is I^2RT or 94.5 joules per burst.  That would hurt!!

	Now I do all the same with my relatively tiny coil.  The scope photo at
www.peakpeak-dot-com/~terryf/tesla/misc/c2ss2a.jpg shows the similar waveforms
but the bottom waveform is output voltage at 100kV/div and the top waveform
is sphere to arc current at 500mA/div (my polarity is correct).  The
frequency is 111kHz and the delay is 1.5uS with a cycle period of 9uS.  The
delay angle is 60 degrees with current leading voltage indicating a
capacitive load.  With the output voltage peak of 225kV and a current of
400mA the magnitude of the impedance is 563k ohms.  This implies an
impedance of 282k ohms resistive and 3pF capacitive.  The burst power works
out to 0.56 joules (out of 0.85 joules from the capacitor charge).  A
measly 1/170th of Greg's big coil.

	What I found very surprising, is that the real resistance of my small arcs
were very close to the real resistance of the Electrum's giant arcs at
around 200k to 280k ohms.  The capacitance seems roughly proportional to
1pF per foot of arc (my streamers were about a 1 to 1.5 feet in this test).
 So the impedance of an arc appears to be around perhaps 220k ohms of
resistance plus 1pF per foot of arc.  This seems true for my small arcs as
well as Greg's giant arcs.  Of course, now the spice models can easily run
iterations and such to optimize a given coil to drive this rather
simplified load.  Hopefully, this will eventually tie back to some of the
simplified impedance match equations I mentioned a few months ago.
However, those studies did not consider complex impedance loads.

	If one looks at Greg and I's sphere to arc currents, it appears that most
of the current waveform represents the current needed to drive the arc's
capacitance.  Both Greg's and my waveforms show roughness at the peaks of
the current waveforms which may represent the instability of the arc
"frying nitrogen".  

	Still more to study here but the implications of such research may impact
our future coil designs greatly.

	Terry Fritz  (who has done more than just read mail lately :-))