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How to calculate peaking capacitor for Marx?

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ahahn

Fri Nov 23 2012, 09:24AM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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Hi all,
How do I calculate the peaking capacitor value for a small Marx bank? I'm building an N2 laser and the cheap HV caps I have won't get anywhere near the necessary risetime without one.

Shrad

Fri Nov 23 2012, 12:17PM

Registered Member #3215 Joined: Sun Sept 19 2010, 08:42PM
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with N2 lasers you are aiming at least inductance possible

could you post a picture of your marx?

ahahn

Fri Nov 23 2012, 01:21PM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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Yeah, but there's only so much I can do to get rid of inductance in the Marx bank. Do I have to figure out the Marx bank's inductance? And how does that change the peaking cap's value?

I'll see what I can do on the picture front, will have to dig out the camera when I get home.

ahahn

Sat Nov 24 2012, 07:20AM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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My camera flash seems to be stuck on "nuclear," so no photos until I get it fixed (or just buy a new one).

Fortunately, it's pretty boring -- just imagine one of these:

Only with a lot fewer stages and 10kV ceramics. And 10K 3W wirewound resistors for interstage charging resistors.

On the subject of inductance, when you say least inductance possible, you mean inductance /along the path of the erect Marx/. I've found some references that replacing the charging resistors with inductors actually improves risetime and makes for a faster discharge. Presumably this is because the inductors enable proper wave erection better than a bit of stray capacitance would have... as a test I replaced two of the resistors (for the second stage) with inductors, and -- lo and behold! -- the Marx was now capable of "dry" firing (i.e without an output spark gap). I'd previously spent a good half hour trying to figure out why the thing wouldn't erect, until I added a spark gap to ground on the output, then it worked... d'oh!

Tests with a peaking capacitor made out of FR4 with edges insulated with hot glue suggests that a peaking cap also aids wave erection, but the single FR4 board would still arc at the edges when I ran the Marx at any decent voltage.

ahahn

Sat Nov 24 2012, 07:42AM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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I just found this page, in a readable mix of French and English:

(the formulas are taken from Aguet M. , Ianoz M. - Generateurs de hautes tensions transitoires -in Traite d'Electricite,Volume XXII, Presses polytechniques et universitaires romandes, 1990,Lausanne)

Seems invaluable for designing fast-risetime Marxes... or just Marxes in general. It seems the parallel resistor goes a long way to determining wave shape, and therefore risetime.

It took me a bit but Cg seems to be the stage capacitance and Cc the peaking / output capacitance. The formulas all assume you know the erect series resistance, and depending on how well you can model it they get more complex.

As alpha goes up so does the ratio of fall time to rise time, as well as the ratio of fall time to Q.

Q as the overall time constant is proportional to rise time, the lower Q, the faster the rise time.

For all Marx layouts it seems that Q is approximately sqrt (Cg * Cc * Rseries * Rparallel) .

h is the efficiency, the degree to which the erect voltage approaches Vcharging * Nstages. For the simplest case (where the series resistance is assumed to be directly after the spark gap, before the parallel resistance) it's 1 + Cc / Cg + Rseries / Rparallel if I understand right... which is kind of crazy, since it's saying that maximum efficiency is reached when the peaking capacitor is equal to or larger than the stage capacitance, and/or the series resistance is equal to or larger than the parallel resistance.

alpha is then figured as 1/2 * Rparallel * Cstage * h / Q ... in other words, the output takes longer to descent to zero and gets to Vmax faster as Rparallel goes up, Cstage goes up, efficiency goes up, and Q goes down.

It also provides formulas for impedance as well as finding Rseries and Rparallel from given impedance, alpha, Q, and Cstage/Cpeaking values.l

ahahn

Sat Nov 24 2012, 09:37AM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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Since Rseries seems to be quite important... The page does cite an interesting article that provides the means for calculating the series resistance of a spark gap:
Heilbronner, F.W.; , "Firing and Voltage Shape of Multistage Impulse Generators," Power Apparatus and Systems, IEEE Transactions on , vol.PAS-90, no.5, pp.2233-2238, Sept. 1971
doi: 10.1109/TPAS.1971.293069
URL:

(IEEE subscription required)

The (somewhat simplified) way to look at the instantaneous resistance of a spark gap is
R(t) proportional to ( Toepler's constant * gap spacing ) / ( transported charge through the gap during the previous time step + ( gap current * length of time step ). In other words, the resistance of a spark gap goes down as gap spacing goes down and/or gap current goes up.

Also floating about on the Internet is Pai's "Introduction to High Power Pulse Technology," which has all sorts of interesting things on the design of Marxes.

ahahn

Sat Nov 24 2012, 09:47AM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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Hmm, according to Pai (p.18) if the load impedance isn't properly matched to the peaking capacitor, the peaking capacitor-load current loop becomes oscillatory and the risetime increases (becomes longer) dramatically.

Proud Mary

Sat Nov 24 2012, 11:13AM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

If you are not intending to use the popular amateur Blumlein configuration, then you may need to couple your MG to a PFN combining pulse sharpening spark gaps (and/or perhaps saturable reactors) and transmission lines to form a fast pulse suitable for N2 lasing at atmospheric pressure.

ahahn

Sat Nov 24 2012, 05:10PM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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I wasn't (very) aware of pulse sharpening gaps or saturable reactors for Marx use, though I've seen both in textbooks. Do you have any references?

ahahn

Sat Nov 24 2012, 05:51PM

Registered Member #6075 Joined: Wed Aug 08 2012, 11:48PM
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Okay, so as I read Pai, it seems that the risetime of a Marx with peaking capacitor is wholly independent of the Marx itself -- it all depends on the peaking cap. In other words, if I have a suitably fast and low inductive peaker, I ought to be able to pump the laser with the sloppiest Marx in the world and still have it work.

I guess the main characteristic that still matters is the Marx being able to charge the peaking cap fast enough.

So what good would additional pulse-sharpening gaps or saturable reactors do?

[added]
Hmm, I'm starting to wonder if the inductors (used in place of charging resistance) might boost the Marx's risetime, or even final voltage. Since the inductor tries to keep current flowing, once Marx erects then the inductors will keep dumping current into the capacitors -- contributing to the current that's arriving from the capacitors earlier on.

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