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Measuring marx bank characteristics (R and L)

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PanosB_GR

Sat Jun 26 2010, 02:58PM

Registered Member #1680 Joined: Fri Sept 05 2008, 04:19PM
Location: Greece
Posts: 43

In case anyone is interested:

I guess this method is quite accurate:

I short circuited all the spark gaps in my marx design and i attached a variable frequency voltage source and an oscilloscope to the terminals of my marx bank (one to the "ground" and the other to the last stage).

I drove the circuit with a 20V sine wave from the voltage source (source is 50Ohm) and measured the amplitude of the sine wave with the oscilloscope, for a lot of frequencies (up to 3MHz). The circuit is a series RLC with a good approximation (neglecting all parasitic capacitances to the ground). I came up with a good RLC characteristic.
By the way, setting my capacitance to what the equivalent of the series connection is (~14nF), i get a 2Ohm series resistance and a ~4Î¼Î— inductance.

I guess the deviation to the higher frequencies is due to the capacitive parasitics and nonlinear inductance phenomena. Better fit to the upper frequencies would be obtained with a lower capacitance and a higher inductance.

Proud Mary

Sat Jun 26 2010, 03:38PM

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

Very interesting and very worthwhile -

- but you can't simply ignore the stray capacitances to ground, as these are essential for wave erection (rather than the sequential firing of the snail pace Marx)) and must be designed into the generator if really fast rise times are to result.

see:

SUB-NANOSECOND JITTER OPERATION OF MARX GENERATORS
J. R. Mayes, W. J. Carey, W. C. Nunnally, L. Altgilbers

which also contains useful ideas for Marx trigger strategies.

As you know, resistors - especially carbon ones - can exhibit resistance variation with applied potential, but how much this will affect your model I do not know.

klugesmith

Sat Jun 26 2010, 03:49PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Excellent work; thank you for sharing it. The classic way to fit RLC values to a real circuit!

It would be educational to see your chart with a couple of modifications:
1) Translate the vertical data from volts to ohms (20V would be infinite ohms)
2) use logarithmic scales for both axes. Then the RLC model has two straight-line asymptotes, as in this chart borrowed from

Step 1 is easy when the impedance magnitude is much smaller than your 50 ohm source impedance. That seems to be the case for your Marx bank around its resonant frequency.
When the magnitude of measured voltage approaches the source voltage, there are measurement sensitivity and phase issues. That could be mitigated by taking another data set with a high-value, non-inductive resistor between source and the element under test.

Other perturbations to beware of, for critical measurements: How much do your source voltage and source impedance vary with frequency? Can get an idea by repeating the frequency sweep with an appropriate, good resistor as the element under test.

radiotech

Sun Jun 27 2010, 05:04AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

The reactive elements at resonance are 17 ohms each. By the series equivalent from the generator , ie 50 ohms, in parallel
with the network, the scope can only see the loading drop in voltage
of a series lc network that is highly damped. The 14 uHy , I assume is due to the geometry of the generator wiring and therefor not measurable directly so the thing to try is measure the current through network at you sweep it, by using a low value resistor between source and network, perhaps, 50 ohms, so maximum power from the signal generator would occur, at maximum drive.
You would have to use a lower scope cMv setting.

I agree with Klugesmith in using a much higher value series resistor to display a truer series resonance curve, but that would reduce the drive current through the capacitors to a level where hidden effects (dielectric absorption) might skew results.

PanosB_GR

Wed Jun 30 2010, 04:38PM

Registered Member #1680 Joined: Fri Sept 05 2008, 04:19PM
Location: Greece
Posts: 43

Hello all.

Regarding the parasitics, they are quite a problem to actually measure, and I am not quite familiar yet with how they work on the wave erection and the general behaviour of the marx bank.

I am curious how a resistive element would help in measuring a series RLC characteristic. Placing a resistor inbetween, would only make the resonant frequency minimum not clear enough.

The idea is to measure the voltage division product of a 50Ohm resistor and a complex impedance element, i.e
Vosc=Z/(Z+50),

where Z(f)=Rseries+j*2pi*f*L+1/j*2pi*f*C

In the resonant frequency (700kHz in my case) the voltage readout should be
Vosc=Rseries/(Rseries+50)

Therefore a higher value Resistor would only make the voltage drop insignificant.

Note: the deviation to the higher frequencies from the linear RLC model should actually be nonlinear inductance and capacitance issues. In fact i did some simulation of something like the life-size model of this marx bank. I noticed increase in the inductance of the circuit.

Regards

PanosB_GR

Wed Jun 30 2010, 04:44PM

Registered Member #1680 Joined: Fri Sept 05 2008, 04:19PM
Location: Greece
Posts: 43

This is the simulation i was talking to you about.

The two graphs are the models of the "old" (high-L) configuration and the "new" (low-L) configuration.

Model is as close as i could get it to be within reasonable efforts to my actual setup.

In fact i was actually surprised to find out the insane 4uH match of inductance value of my marx bank.

1277915981 1680 FT91458 Marx Inductances

Dependence of the inductance on frequency can clearly be seen

and the truth lies somewhere in there...

radiotech

Thu Jul 01 2010, 04:29PM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

"I am curious how a resistive element would help in measuring a series RLC characteristic."

If you could measure the voltage across each of the elements directly you would need no additional resistances. But you mentioned ground in connection with the oscilloscope. Had you used a scope with a differential input, (two floating inputs, no ground back to the scope), the current or voltage method of looking at the voltages at resonance based upon voltage drops across the measurement resistor would not be needed. Even better would be a 2 channel scope (four input terminals) to show phase relations between the elements.

Of course , that is the nice thing about simulators, they have vector voltmeters that show E<theta with two isolated terminals. But that is just virtual.

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