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Re: Rotary Spark Gap Design
Skip,
I have done a lot of thinking about this over the last day or
so to the extent of re-reading the Corum's notes again (80 pages
or so for about the 6th time). You wrote...
> You are attempting to deal with lumped constants when you try to
> say that the secondary capacitance is c self + c term. I do not
> necessarily agree with the voltage as specified but what if you
> deal with the secondary as a wave guide or transmission line
> instead. It seems to me that the capacitance in the secondary may
> be extremely small when referred to the primary and the cv=cv
> equation will yield much higher voltages in the secondary. This may
> also help to explain why higher Q secondaries yield longer
> discharges. I'm not into the math on this but it seems to me that
> I remember from college that the capacitance looking into a
> transmission line or wave guide is not the sum total of all of the
> capacitance of the line or guide.
I agree with what you say in sentence one. I have yet to find a case
where that doesn't work, but I'll certainly accept my error if one
is presented. Secondly, whatever one sees looking into the line is a
transformed value, not what is actually hung on the end (Y-N)?
Here is my argument :
Ecp = 0.5xCpxVp^2 = 0.5xCs(tot)xVs^2 (assuming all energy is
transferred). This is easily manipulated into the form I gave.
Using the figures Rod gave and some I derived from the data, I
came up with Cself for the coil of about 40pF and about the same for
the terminal. A number of scenarios spring from this plus the
uncertainty about the value of Cp.
Looking at the best possible scenario (assume that Cp=0.2uF and
is charged to 20000V x SQRT2, and all energy ends up in the terminal
capacitance alone), you get Vs = 2MV peak. But this takes no account
of energy being distributed along the line. Also, if Vterminal = 2MV
the implication is that V at the top of the secondary is zero which
implies an infinite current in the wire between the top of the coil
and the terminal, so I think that is unrealistic. Also, it doesn't
square up with formula given by Hoffman et al. using inductances.
(I have ignored both gap losses and secondary discharge losses)
If there is an error in my reasoning, please tell me where it
is - I want to know.
Interestingly, the Corums give an example at the end of their
tutorial (p72) which appears to treat Ls as an accurate lumped value
to derive Cs(total) from fr for a two coil system secondary (they
still analyse it from a Tx line point of view on the next page). They
also state at the top of that page "During the spark dwell time, the
magnetic flux produced by the primary links the entire secondary.
Consequently the primary/secondary interplay of energy may be treated
by lumped circuit analysis". It's important to note that once the
transmission line model comes into play (pri. gap ceases to conduct),
no further energy transfer can occur between the two coils. From then
on, the secondary can only ring down as it loses energy, rather
rapidly if it's sparking. My point is, that in a capacitor discharge
system, there is only a finite amount of energy to start with for
each primary gap fire and energy conservation must be observed.
I have agonized for months over discrepancies between my thinking
and what they say and am still agonizing to the extent of calling on
some outside expert help in this. In the final event, I may be moved
to contact the Corums themselves and try and resolve this. I just
don't think you can escape the fact that there is a real lumped
capacitor hung on the end of the line.
If anybody out there can help to resolve this, please end my
agony.
Lastly, for everyone's interest, I derived a couple of figures
for Rod's coil that weren't in the specs : Ls = 50mH and Lp = 80uH.
As always, I stand to be corrected on anything I've said. I count
any criticism of what I say with the highest regard.
Many Regards,
Malcolm