Replacing Electrolytic Caps - Putting Two Caps in Series?

[Ten Over]

You cannot use series capacitors at their rated voltage. If you did, any imbalance in leakage current would put one of them over their rated voltage. The balancing resistors necessary to prevent over-voltage would have to be zero Ohms because anything greater than that would allow one of the units to exceed their rated voltage in the event of unequal leakage currents. Zero Ohm resistors cause huge problems in most circuits.

[Ten Over]

If you're going to use Vishay's balancing resistor formula, then you might as well use their spec for leakage current. I like it because it addresses temperature which has a huge effect on leakage current. Most of the time leakage current is quoted at +20 deg C. It gives good numbers for that manufacturer, but essentially useless numbers for circuit designers.

Vishay Leakage Current.png

[R.G.]

You cannot use series capacitors at their rated voltage. If you did, any imbalance in leakage current would put one of them over their rated voltage. The balancing resistors necessary to prevent over-voltage would have to be zero Ohms because anything greater than that would allow one of the units to exceed their rated voltage in the event of unequal leakage currents. Zero Ohm resistors cause huge problems in most circuits.

I think I'd soften that a bit. Obviously, you >can< use series caps at their rated voltage. How good or bad this idea is depends on a lot of things.
Leakage currents go up with voltage. The "rated voltage" on the data sheet is determined by the manufacturer to be the voltage where the vast majority of units shipped will not develop leakage hot spots and short or lose too much of their electrolyte to evaporation and go low capacitance, etc. within the manufacturer's specified lifetime hours. That is, rated voltage is as much an economic/warranty rating as it is an instant-failure rating. Rated voltage is not a razor-edge failure point. It's more of a guideline and a warning. Electro caps in particular have funny behavior with the interactions of leakage current, withstand voltage, re-forming, and evaporation of electrolyte.

Conservative design is to not design right up to the edge of the rating unless you have no other options. I would use a 450V rated cap in a 450V circuit for a short time until I could get something more reliable, I would use two 250V rated caps in a 500V supply for short term testing and prototyping, but not for long term use. My best intuition is that both of these would work for a while, long enough to figure something else out. Then I'd replace them with parts having a higher reserve rating.
How much to derate a cap (or any other part!) for a given lifetime is the artistic part of design.

[Ten Over]

I think I'd soften that a bit. Obviously, you >can< use series caps at their rated voltage.

I wouldn't soften it at all. The post goes on to clarify why you cannot use series capacitors at their rated voltages. With the criterion that the maximum rated voltage cannot be exceeded, you cannot use series capacitors at their rated voltage. This is immediately obvious to anybody that has analyzed series capacitors with balancing resistors.

Published maxima can almost always be exceeded to some degree. However, you need to draw a line somewhere and a published maximum is a darn good place to draw it. First, it gives you a concrete number to work with instead of some gut feeling number. Second, it makes you look as though you don't know what you're doing when you design things that exceed a published maximum. That second one is to be avoided at all costs if there is any chance that someone else might see what you have done.

[Ten Over]

Conservative design is to not design right up to the edge of the rating unless you have no other options. I would use a 450V rated cap in a 450V circuit for a short time until I could get something more reliable, I would use two 250V rated caps in a 500V supply for short term testing and prototyping, but not for long term use. My best intuition is that both of these would work for a while, long enough to figure something else out. Then I'd replace them with parts having a higher reserve rating.

Well, there you have another reason not to exceed maximum ratings. However, my reason is a mathematical one.

[R.G.]

Well, there you have another reason not to exceed maximum ratings. However, my reason is a mathematical one.

Yep, I saw that.
What I was trying to say, subtly, was that it's not that simple.
Yes, you can mathematically prove that you'd have to use zero ohm resistors to keep different-leakage caps from going over their datasheet ratings. But real-world caps do not live or die by whether they go over their rated voltage.
The datasheet rating is a manufacturer's advertising/promise/semi-contract that their caps will not fail when used at the rated voltage. Over that, they will not guaranteed their parts to function, and moreover, they will disallow warranty claims for such use.
It does not say that the parts are good below the rating, and die above it. There are some very high powered statistics at work behind a manufacturer's datasheet to let the makers know that if they put a number (like, say, 400V) on a cap's voltage rating, then over their production run they will have to refund less that the amount they have set aside ahead of time for warranty claims for that part, and suffer less than an intangible amount of customer reputation gain/loss.
As a bit of a thought experiment, imagine that you have a 100V rated electrolytic capacitor. You put 100V across it and measure the DC leakage current at a given temperature. If the leakage is more than the specified number on the datasheet for those conditions, you have a valid claim against the maker for refund or replacement.
Will it die? Almost certainly not. Modern parts makers are in general very good at what they do, and bad new-out-of-the-box parts are very rare. In general six-sigma rare, but that's another story.
Turn up the voltage to 100.1V. Will it die? I bet not. In fact I'd bet a large sum of money on that one.
Turn up the voltage to 101? Dead? No? Turn it up to 110. Do these watching the leakage currents. It's really, really unlikely that the cap will even exhibit high leakage until near its surge voltage rating. Over the surge voltage rating, the cap can be forgiven for getting hot and going to higher leakages. If you limit the voltage so the leakage current doesn't go over the oxide forming current density, especially on a new cap, you might see the leakage start to slowly decrease as the leakage current forms the oxide layer to a modestly higher voltage.

Yes, one can prove mathematically that zero-ohm resistors are needed to keep capacitors from exceeding their voltage rating in the hard-numbers sense. Yes, there was an aeronautical analysis that proved mathematically that bumble bees can not fly. That bumble bee analysis was based on the starting assumption that they were fixed-wing aircraft, not moving-wing devices. It's really important in a hard-numbers analysis to take into account all of the relevant factors, not just the numbers.

Good on you for having the insight that there are hard-numbers limits lurking around. I've seen cases where those kinds of things were lurking under some wishful technical thinking.

[Ten Over]

Yep, I saw that.
What I was trying to say, subtly, was that it's not that simple.
Yes, you can mathematically prove that you'd have to use zero ohm resistors to keep different-leakage caps from going over their datasheet ratings. But real-world caps do not live or die by whether they go over their rated voltage.
The datasheet rating is a manufacturer's advertising/promise/semi-contract that their caps will not fail when used at the rated voltage. Over that, they will not guaranteed their parts to function, and moreover, they will disallow warranty claims for such use.
It does not say that the parts are good below the rating, and die above it. There are some very high powered statistics at work behind a manufacturer's datasheet to let the makers know that if they put a number (like, say, 400V) on a cap's voltage rating, then over their production run they will have to refund less that the amount they have set aside ahead of time for warranty claims for that part, and suffer less than an intangible amount of customer reputation gain/loss.
As a bit of a thought experiment, imagine that you have a 100V rated electrolytic capacitor. You put 100V across it and measure the DC leakage current at a given temperature. If the leakage is more than the specified number on the datasheet for those conditions, you have a valid claim against the maker for refund or replacement.
Will it die? Almost certainly not. Modern parts makers are in general very good at what they do, and bad new-out-of-the-box parts are very rare. In general six-sigma rare, but that's another story.
Turn up the voltage to 100.1V. Will it die? I bet not. In fact I'd bet a large sum of money on that one.
Turn up the voltage to 101? Dead? No? Turn it up to 110. Do these watching the leakage currents. It's really, really unlikely that the cap will even exhibit high leakage until near its surge voltage rating. Over the surge voltage rating, the cap can be forgiven for getting hot and going to higher leakages. If you limit the voltage so the leakage current doesn't go over the oxide forming current density, especially on a new cap, you might see the leakage start to slowly decrease as the leakage current forms the oxide layer to a modestly higher voltage.

Yes, one can prove mathematically that zero-ohm resistors are needed to keep capacitors from exceeding their voltage rating in the hard-numbers sense. Yes, there was an aeronautical analysis that proved mathematically that bumble bees can not fly. That bumble bee analysis was based on the starting assumption that they were fixed-wing aircraft, not moving-wing devices. It's really important in a hard-numbers analysis to take into account all of the relevant factors, not just the numbers.

Good on you for having the insight that there are hard-numbers limits lurking around. I've seen cases where those kinds of things were lurking under some wishful technical thinking.

I have no idea why you keep quoting me and then go on and on about something that has nothing to do with what I said. It's like you're trying to use apples to argue with my orange. Or maybe you're arguing with someone else but you keep quoting me by mistake.

I have expressed no opinion whatsoever regarding the strict adherence to published limits, other than the tendency to make you look ignorant when you exceed them. Even then I'm not commenting on whether other folk's perception of you is accurate. All I said was that the maximum voltage cannot be exceeded in order for my other statements to be true. I did not say, nor did I imply, that the limits cannot be exceeded in actual practice.

[Ten Over]

For those that are new to series capacitors, the upshot from my original statement is that the sum of the rated voltages for two identical capacitors needs to be larger than the DC voltage applied across the series combination. The balancing resistors will limit the voltage imbalance between the two units, but you still need some voltage rating cushion for the unit that has the greater voltage drop across it. That greater voltage drop is going to be larger than one-half of the total DC voltage.

[roberto]

I have no idea why you keep quoting me

Hi Ten Over, the reason why R.G. (who is a well know, highly respected and very experienced technical person) is keep on quoting you, is because he wants people to think on things as every designer must (not should!) do, without pedantically applying formulas.

You have shown the Vishay formula: Rmax = (2*Umax - U)/Ileak– 5min
https://www.vishay.com/docs/48296/_did- ... 5-1709.pdf

and based on that formula you say you can mathematically demonstrate that the leak resistor tends to zero as U approaches Umax.
Based on that formula the leak resistor won't be zero, but Umax/Ileak– 5min. Mathematically.

I have to say that I've never used that formula to calculate balancing resistors, but I always calculated them to have around 2 to 3 times the leakage current, working with 10 to 20% margin on the voltage.

What R.G. is saying is that in real life capacitors are rated at a lower voltage then their real maximum, and that is obvious on a production point of view.
So if you exceed by 1... 2... 10% the rated voltage for a short time, nothing happens.
If you exceed by a large percentage the rated voltage for a short time, something (bad) happens.
If you exceed by a small percentage the rated voltage for a long time, something (bad) happens.

Would anyone put two 250V in series on a 500V supply? Actually yes, I've seen 450V caps in series produced amps with 470V B+, but it's really rare and I would never do it.
Would anyone put two 250V in series on a 450V supply? Yes, taking care of the balancing resistors.
Would anyone put two 250V in series on a 400V supply? Yes, safely, but I'd use one rated at 450V.

[Ten Over]

Maybe if I re-worded my original assertion:

The maximum voltage rating will be exceeded if you attempt to operate series capacitors at their maximum rated voltage.

No two capacitors are exactly the same, so the voltage drop across each one is going to be different to some degree. In the case at hand, if you put 100V across the two 22uF/50V in series, then one of them would have something less than 50V across it and the other would have something more than 50V across it. It may be a minuscule amount, but the maximum voltage rating is exceeded nonetheless.

Note that the re-worded assertion makes no comment on the practical, legal, or moral ramifications of exceeding the maximum voltage rating. The original also made no comment on said ramifications.

I direct your attention to section 2-1-1 (6) 2 in the Nichicon dissertation.

[Ten Over]

You have shown the Vishay formula: Rmax = (2*Umax - U)/Ileak– 5min
https://www.vishay.com/docs/48296/_did- ... 5-1709.pdf

and based on that formula you say you can mathematically demonstrate that the leak resistor tends to zero as U approaches Umax.
Based on that formula the leak resistor won't be zero, but Umax/Ileak– 5min. Mathematically.

I didn't show that formula, martin manning did.
I didn't base anything on that formula.
I have already explained why the leak(sic) resistor would have to be zero. If that formula doesn't give zero, then that formula is invalid. You have proven that it is invalid, so discard it.


I'll tell you what. I've never been accused of so many things since they had me down at the station with a bright light in my face.

[R.G.]

Maybe if I re-worded my original assertion:

The maximum voltage rating will be exceeded if you attempt to operate series capacitors at their maximum rated voltage.

No two capacitors are exactly the same, so the voltage drop across each one is going to be different to some degree. In the case at hand, if you put 100V across the two 22uF/50V in series, then one of them would have something less than 50V across it and the other would have something more than 50V across it. It may be a minuscule amount, but the maximum voltage rating is exceeded nonetheless.

I agree with that re-formatting. Two caps, even of identical brand, type, and even manufacturing run, are never identical, hence one will be more, one will be less. The question is then: how much are they imbalanced?

Re-wording my replies: Doing that ( two nominally identical caps in series, at exactly twice their individual rated voltage, with reasonable and non-zero balancing resistors) is (1) not likely to result in immediate failures of either cap (2) possibly sustainable for a modest time, given the vagaries of surge voltages and forming action and (3) a bad idea for long term reliability and keeping one's engineering job.