Lets say there is a 60uF cap charged to 600V. The energy in that caps
E = CV^2 which is ~ 22 joules
If the cap has 3 ohms of ESR and the output was shorted across a .1 ohm resistor. How much of the neergy would be dissipated in teh cap vs. in the resistor?
Would it be as simple as 0.1/3.1 = ~ 3% of the total energyin the resistor? I cna get my hands on some resistors rated for 3-5 joules that will fit in the confines of space and wondering if they could be destroyed by the capacitor spark test (less than 5 times).
Actually, there is a divide by two in that formula, also, so only half that.
Instantaneous power dumped into a resistor is related to the current by P=I^2*R, so since the current through both series connected resistors is similar at all times, the total energy dumped into the series resistors must be proportional to their individual resistance.
** The ratio of resistances is gonna be close to the mark.
** Low ohm resistors may not like high pulse voltages as the gap in the spiralling may arc over at the moment of applying a 600 volt charged cap.
If I understand your question, there is insufficient information to provide an answer.
ESR is not simply the capacitor's series resistance. If it were, then the simple analysis would work. In fact, ESR is measured at some (unspecified) frequency. ESR, or whatever you might choose to call it, of a capacitor discharged as you describe is likely to be different.
You could assume ESR is invariant wrt energy (likely true) and perform a simple test on the capacitor at much lower voltage levels.
Chuck
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My point was only that because ESR is frequency-dependent and the frequency at which 3 ohms was measured is unstated, 3 ohms may not be valid for the analysis.
It is still not clear to me how we know the ESR is not less than 3 for the OP's time constant. None of the posts seemed to address this. If I understand your analysis, you have taken 3 ohms as the actual ESR at the frequency of interest, just as the 0.1 ohm resistor and the 90 uF capacitor values were taken as actual.
I'm open to "recalibration".
Chuck
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OK, I'll explain. This is what we see if we measure and analyze many electrolytic caps. ** First, if you examine datasheets, you'll see esr is usually specified at 100kHz. In fact, there's a broad region where the ESR changes very little, e.g., from 0.48 to 0.40 ohms from 1kHz to 200kHz, for a 68uF 350V electrolytic I measured this afternoon. From 5kHz and up, the nearly-constant ESR is well below 1/Xc, and this shows a that single value at 100kHz is a genuinely-useful parameter. (I apologize for not posting a graph to show this better - we'll do that in AoE 3rd-ed.)
I can tell you, a 1-to-200kHz relatively-flat esr frequency range is what we generally what we see when measuring small electrolytics. We have to take the OP's 3 ohms for his part.
** Second, as we go down in frequency, where does Xc take over from esr? f = 1 / 2pi C Resr = 1 / 2pi 63uF 0.44-ohms = 5.7kHz for the "68uF" 350V capacitor I measured. Now, to get into the dielectric series-resistance loss region, shown in the QuadTech document you referenced, we have to go down another factor of 50 to 100 in frequency from there, e.g., to below 60Hz. In fact, my "68uF" cap has a loss resistance of 1/69 Xc at 60Hz, and I have to go all the way down to 5Hz to reach the 1/100 dielectric loss that we expect to see for an electrolytic. So, clearly there are dramatically-different regions for electrolytic capacitors, and we can generalize about them, and most of the time the dielectric losses are really not much of an issue, being at very low frequencies.
** For example, consider my 68uF cap at 120Hz, the operating frequency for a bridge-rectifier storage cap. Here the esr measures about 0.7 ohms, not a whole lot higher than its 0.45 ohms in the 5 to 20kHz region. But consider, in a rectifier storage capacitor situation, with a short charging-conduction time, say 1/5 of a cycle's peak, we're really talking about 5*120 = 600Hz. Here I measured an esr of about 0.5 ohms, or nearly as low as a datasheet-frequency 100kHz esr = 0.4-ohms.
In conclusion, we can safely rely on a single reported value for capacitor esr, and not worry about whatever dielectric losses might be at frequencies far below f = 1 / 2pi C Resr.
Here are some specifics on the capacitor. The 60uF capacitor is actually a module consisting of 60 indvidual capacitors. These are the capacitors used in the module
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The one we used is the 100uF
125VDC @25C in the T case.
The capacitor module is 6 parallel strings of 10 series connected capacitors to make a module that is 1250V @ 25c and 750C @ 200C capacitor bank that is
60uF total.
This application will see 200C temperature so that severely limits the type of capacitor used to this large monstrosity. :)
thanks for the input and if you have any more insight I'm all ears...well eyes.
My 68uF 350V cap has an esr of about 0.44 ohms at 5kHz, which is its internal time-constant frequency. If we assume a simple series R+C circuit, charged to say 324V, an instantaneous 0.1-ohm load would create a 600A peak discharge current, and initially 264 volts would appear across the internal series resistance. Shall I try it? I have some IGBTs that can handle the 600A switching.
The internal construction can, at least, be assumed to be distributed evenly throughout the body of the part, by distinctive layer. This is ideal for power surge absorption.
Arcing? Under what influence?
What I've observed, is physical movement, as the inductance is forced to attempt to reduce dI/dT. A 'jumping' of the electrolytic element within the case. It's no easy matter to get anywhere near an ideal innitial instantaneous current peak, nor for that matter, to measure it.
I think that you're asking for trouble using tantalum caps in pulsed power circuits. I'm not sure what options there are at 200C. Placing the capacitive energy storage in the hostile environment, if there are alternatives, could be asking for trouble.
You don't mention bleeder equalization parts, or other frequency compensating components that I would expect to see in a series-parallel connected module of this sort. This argues against predictable pulse performance.
Well, PottyMouth Humorboy suggested that "low ohm resistors ... may arc over" with a 600V pulse applied. Perhaps, but I'd rather expect that (1) with the effective series R and L involved, the resistor would never see close to 600V, and (2) resistors that can handle that much energy are likely not constructed in a way that would have a problem with a 600V impulse (though the latter should of course be confirmed and not blindly assumed).
Well, if it's easy. I was thinking I could use a little SCR to do something similar; long ago (well before power mosfets) I used them to generate reasonably fast rise pulses -- basically a pulse-forming network switch, as used in pulsed magnetron radars.
The short circuiting is a infrequent but possible fault condition. Im not concerned about the capacitor being damaged. I'm more concerned if this capacitor discharged into .1ohms what peak energy rating on the resistor is required to withstand this without blowing open. If that .1ohm resistor opens up, there will be hell to pay. I have as big of a resistor I can comfortably fit there now, I just need to know if it is up to the task without actually doing an arch test. I will do one eventially but not right away.
Your 60uF 600V capacitor bank stores 11J of energy. Most small power resistors I've looked at have a transient-power maximum spec of 5x their rated power for 5 seconds. That means, for example, a 1-watt power resistor would be able to safely absorb 25J into its thermal mass over 5 seconds. Presumably this energy could be absorbed into the thermal mass much faster than 5 seconds. A de-rating can be used, to take into account that very rapid events, say faster than 10 to 50us, might be absorbed entirely into the resistance wire, which has less thermal mass than the entire resistor with its leads.
If your capacitor bank has the 3 ohms = maximum esr, then a 3.1-ohm discharge will have a 186us time constant. But if in fact it's much lower, say 0.5 ohms, then the 0.6-ohm discharge time constant will be 36us. And more of the bank's energy will go into the 0.1-ohm resistor. However, it still looks good, even with a small 1-watt power resistor.
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