Re: Improved Model for a Primary Charging CKT

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Robert Jones" <alwynj48-at-earthlink-dot-net> 

Hi,

Comments in the text
----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Friday, January 23, 2004 7:07 AM
Subject: Re: Improved Model for a Primary Charging CKT


 > Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
 >
 > Tesla list wrote:
 >  >
 >  > Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net>
 >
 >  >>  > Cp at 120 BPS if chosen correctly  (see Terry Fritz's derivation).
 >
 >  > Please comment (especially ANTONIO),
 >
 > Your derivation is essentially correct, unless for the errors pointed.
 > Some problems are:
 > R would have little effect in a practical transformer, but it's not a
 > big problem to include it in the calculations.
 > The presence of a spark gap complicates the analysis substantially.
 > The circuit would never reach the steady state assumed in the
 > calculation
 > between "bangs".
 >
 > A more precise analysis must consider a transient response caused by
 > the AC source Vs and the current in the transformer inductance at
 > the end of the last gap firing. This solution would include the forced
 > response due to Vs as calculated above, added to a decaying oscillatory
 > waveform caused by both IL and Vs. The obtained solution would be valid
 > until the next gap firing, where the capacitor voltage would return to
 > zero (if you don't complicate considering the fast energy transfer
 > transient to the secondary circuit too) instantaneously, and the
 > process would repeat. The gap firings can be (almost) periodical in
 > a rotary spark gap, that can be syncronous with the power line or
 > not, or can be determined by Vc in a static gap.
 > In the general case, the obtained output voltage Vc(t) would be not
 > periodical, and very difficult to predict exactly without a simulation.
 > It's not difficult, however, to write a specific simulator for this
 > problem. (If you are interested in details, contact-me directly.)
 >
 > Antonio Carlos M. de Queiroz
 >

I believe Antonio comments are correct in the general case.

However just inspection of  the equations provides considerable insight in
to the apparently chaotic behavior.
i.e. none integer ratios of the LC to supply frequency.  Where as simple
integer ratios much like the magic k values may result in simple time
traces.

For particular cases the problem may not be so intractable.
For example if you assume the sg fires at peak voltage, zero supply voltage
and zero cap current this may effectively make it a half cycle solution.
Which is applicable if deQ diodes are used and or a sync rotary gap/
triggered gap.

In any case values like peak cap voltages and rms charging currents should
be derivable.
I have the fundamental equations in s and to as a mathcad file if any one
would like them.
They can be read with a free web plug in from mathsoft.

Writing this it has just occurred to me that one approach to the general
problem may be to use power spectrums. Although it will not give you any
specific time traces it will produce rms values and even peak values with
probabilities in some cases.

Yes circuit simulation is very usfull but you can spend a lot of time
exploring the parameter space. Maths can tell you were its best to look.

Bob