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Arc Impedance Study - Computer Models



Hi All,

	I ran a bunch of Spice models today using an arc load of 220k ohms and
5pF.  This is the estimated arc load value I found from measurements on my
coil.  I tested the ability of the coil to deliver power to the 220k
resistor while I varied the coupling, Lp, the ratio of Ls and Ct, and Fo.

The numbers my computer model used are as follows:

Primary Capacitor Voltage	20000
Primary Capacitance		17.05uF
Primary Resistance		3 ohms
Primary Inductance		120.6uH
Fo					111.0kHz
Secondary Inductance		75.4mH
Secondary Total Resistance	270 ohms
Secondary Capacitance		27.26pF
Secondary Load			220k ohms + 5pF


	First the coupling tests.  I tried a number of coupling coefficients and
found the following:

K		Peak Current	Burst Time	Relative Power
0.05 		336mA			120uS		2.98
0.105		597			80		6.27
0.123		653			70		6.56
0.145		719			63		7.17
0.172		783			55		7.42
0.201		846			45		7.08
0.250		909			35		6.36
0.300		966			31		6.36

Relative power is calculated by taking 220000 ohms multiplied by the peak
current squared and then multiplying by the burst Time.  This gives an
estimate of how much relative power is being dissipated in the 220k ohm
resistance.  this should be an indicator of the power being delivered to
the arc.

It appears that a coupling of 0.172 is best for my coil.  This corresponds
to my secondary being 1 inch above my primary.  This has consistently been
the best point for my coil and now these calculations show this also.



The Primary Inductance may have to be somewhat greater than the calculated
value due to the added terminal capacitance from the streamer.  Richard
Hull and others tune their coils with about 5% greater primary inductance
to account for this.  My results are as follows:

Inductance	Peak Current	Burst Time	Relative Power
-20%		588			40		3.04
-15%		635			45		3.99
-10%		667			52		5.09
-5%		698			56		6.00
0%		719			63		7.17
+5%		737			65		7.77
+10%		739			65		7.81
+15%		734			69		8.17
+20%		718			66		7.48

The primary inductor appears to have to be 15% greater than the calculated
value for my coil.  This allows for the added 5pF from the streamers.  The
range of +5% to +15% seems to be relatively constant and supports my coil's
insensitivity to exact primary tuning.  These results support what many
have reported.


Ls to Ct ratio.  There has been much discussion on what effect the ratio of
secondary inductance to capacitance my have on coil performance.  In effect
this is sort of a measure of the output impedance for a coil.  
	For this test the frequency is held constant.  The secondary inductance is
varied and the secondary terminal capacitance is adjusted to keep the
frequency consistent.

Inductance %	Peak Current	Burst Time	Relative Power
200%			747			57		6.99
150			741			60		7.25
100			719			63		7.17
66.7			664			65		6.30
50			608			65		5.29	

The burst time is very hard to see in the first two tests which make the
results rather hard to use.  However it appears that a somewhat larger
secondary inductance would provide more power to the arc.  It appears,
however, that the Ls to Ct ratio is not having all that great of an effect
on the output arcs.



Fo.  In this test, I proportionally scaled all the primary and secondary
capacitances and inductances to see what difference changing Fo would have:

Fo		Peak Current	Burst Time	Relative Power
27.75kHz	321			245		5.55
55.5		533			124		7.75
111		719			63		7.17
222		777			35		4.65
444		741			20		2.42

When I vary the primary capacitance, the primary energy changes so I need
to account for this by dividing the Relative Power by the relative primary
cap size: 

Fo			New Relative Power
27.75kHz		1.39
55.5			3.86
111			7.17
222			9.3
444			9.68

So this indicates for a given primary energy, higher frequencies are more
efficient.  These last results may be affected by the size of the arcs such
coils would produce and the resulting different loads those arcs would
have.  Apparently this is due to the fact that higher frequencies produce
lower reactance in the 5pF load capacitance and thus allow more current to
flow.  Of course, high frequency coils don't have nearly as much primary
energy as large coils so larger coils, that have proportionally more
primary energy, do somewhat better.

So what does all this mean?  For my coil I should set the coupling up to
0.172 and tap the primary 15% higher.  Perhaps running the experiment over
trying high secondary terminal capacitance would also show some interesting
results.  This would lower the system frequency without hurting any other
factors.

----
I just went back and did this with the following results:

Ct,Lp Ratio		Peak Current	Burst Time	Relative Power
x4			316			125		2.75
x2			512			88		5.07
x1			719			63		7.17
/2			872			45		7.53
/4			926			35		6.60

This would indicate lowing the secondary terminal capacitance would improve
power to the arc.
----


	In general this spice computer test shows that the results from the
computer model match the scope results well.  The scope photos and the
spice models are the same.  Best yet, the spice models appear to be
accurate enough to test coil designs on the computer and have those results
match real world observations.  In short.. It all works :-)
	There is still some refining to do but the use of 220k ohms plus 1pF of
capacitance as a value for arc impedance seems to be holding up so far.

	Terry Fritz