Capacitors in series - pitfalls?

[Herald1360]

I don't think those dishwasher caps are electrolytic, so even better. They'll probably be a better fit size wise too!

[brymac]

They are smoothing caps in the Mullard High Speed Valve Tester - given that there is some seriosu EHT voltages flying around, I want to go for the traditional large can electrolytics - anyone want to answer the question about motor caps?? Bryan

[trickie_dickie]

Over 50 years in electronics and I've never put 2 caps in series.

[brymac]

Well I think with a mere 48 years in electronics I'll give it a go!

Bryan

[dinkydi]

I think that connecting capacitors in series is not such an issue as it may seem, certainly for electrolytics.

If we assume equal capacitors for simplicity, the leakage current through each capacitor is always identical (they are in series). It should not be assumed that the leakage current is a linear function of the voltage across the capacitor. The voltage across the "leakier" capacitor will be less than if it had half the total voltage across it and, due to this, its leakage current will always be well within specification, assuming good capacitors. Voltage balance is not important in a simple series configuration.

In fact, in a series configuration the leakage current goes up for the less leaky capacitor and down for the more leaky capacitor, as the voltage distributes itself between the capacitors, but the crux of the matter is that the leakage current is always well within spec by this process. Even when the voltage rating of one capacitor is exceeded, the leakage current is kept within spec by the other capacitor. If the leakage of an over-voltage capacitor does start to increase, let us say, the voltage across it will reduce and this brings down that leakage - there is a stabilising mechanism in the system.

As has been pointed out, most SMPS use electrolytics in series. In these circuits the voltage across the series electrolytics must be balanced due to the requirements of the following circuitry. The balancing is implemented by resistors (they must be good quality and have adequate power rating) across each of the capacitors. This serves to swamp the leakage. If one of these fails the voltage balance is destroyed and the following circuitry malfunctions. This is a rare fault and in my experience even this does not result in capacitor failure despite the use of resistors potentially causing an out-of-specification leakage current under resistor failure.

Personally I favour the use of resistors in parallel with the capacitors - you can understand what is happening, how the voltage divides - they make the designer feel good and in control. However, the reality is that they are generally redundant unless the following circuit requires balance - series capacitors look after themselves without help, provided the sum of their voltage ratings is adequate.

Peter

[GMB]

It should not be assumed that the leakage current is a linear function of the voltage across the capacitor.

I was just about to make this point too...

I have found that paper capacitor leakage is more like exponential than linear.
Electrolytics behave a bit like zener diodes.

I think this explains why people get away series connection, but it does mean that one of the components will be stressed out somewhat while things balance up, so resistors are still a good idea in my opinion.

[Craig Sawyers]

Here's an analysis on calculation of balancing resistors for series connected electrolytics

Craig

[dinkydi]

Hi, Thanks for the responses.

GMB: I don't think "people get away [with] series connection" at all. I suggest that the capacitor that has the greatest stress is the one with the highest leakage independent of the applied voltage. The series connection gives the LOWEST maximum stress of the 2 capacitors (sorry, but this may require rereading). This is because the leakage of the leaky cap reduces and the leakage of the less-leaky cap increases until both leakages are equal. The use of resistors maintains the unbalance of the leakages, that is, one capacitor is always stressed more than the other (unless the capacitors are perfectly matched in the first place). That is, the use of resistors gives HIGHER maximum stress.

Craig: Thanks for the analysis reference. This analysis starts with the assumption that the capacitor voltages should be kept equal. No one has justified this assumption. It might seem reasonable at first, but I believe it is wrong. The lowest leakage occurs when the capacitor voltages are NOT balanced (in general). The reference honestly criticises its own methodology "does lead to higher, and possibly unnecessary dissipation levels in the resistors". The reference also states "the change of leakage current vs voltage follows an exponential curve" and in the end concludes that "This [voltage unbalance] leads to a self balancing situation whereby any voltage offset will reduce the leakage current difference,which in turn reduces the voltage offset." As I have said, without resistors "there is a stabilising mechanism in the system" - resistors are simply not needed and lead to higher and unbalanced capacitor leakage current.

Peter

[GMB]

I suggest that the capacitor that has the greatest stress is the one with the highest leakage independent of the applied voltage.

I don't understand why that would be the case.

The big issue is not the leakage itself, but rather that with very low leakages the actual leakage values may be wildly different (but both still minute).
So if one capacitor has an ohmic resistance of 100Gohm and the other was only 10Gohm then the voltage ratio will be 11:1 and that is bad news if the ratings are both roughly half the applied voltage! (And note that it would take a very long time before you would notice).

What I am saying is that the actuality is not like that at all because the leakages are not at all ohmic, so it works better than one might fear.

[Norman Wells]

Dear me ! 'When ignorance is bliss 'tis folly to be wise' After 70 Years in this game I should be alarmed at what little I know !!

[dinkydi]

Hi GMB, My point is that leakage is the direct result of voltage stress on a capacitor, not only that but leakage is the exact measure of the stress. A capacitor with a lot of volts across it but very low leakage is a happy fellow. One with a lower voltage but higher leakage is not faring so well. However, the stress on a capacitor can only be inferred in a rough general way by comparing its voltage with the rating on the cap body and yet this is the common approach.

I am indeed saying that the big issue is the leakage itself and it could well be the case that the leakages are substantially different (when the caps are apart) as you point out. You are also correct in pointing out that the voltages may distribute themselves in an unbalanced fashion, not in accordance with the voltage ratings of the caps. You suggest that this may be bad news, but what exactly is this bad news? I argue that it is actually good news because the actual leakage is being minimised - this is the fundamental issue, not the voltage rating written on the body of the cap. This minimisation does not occur if you add resistors.

It is indeed bad news if you believe that the voltages should be balanced, but my argument is that this is an artificial constraint that we are placing on the design - this constraint is not a necessary condition for best design. We have all been taught and accepted the wisdom that voltage ratings on components are sacrosanct, it takes a lot of consideration, perhaps, to accept that this is not necessarily true and this approach in this case leads to a better, more robust, simpler design.

The series connection of capacitors minimises the leakage of the "leakier" cap. When balancing resistors are added that cap leakage current increases, so the design with resistors is by default an inferior design.

We don't need to worry about cap voltage ratings because leakage current is the measure of how well the cap is faring under voltage stress and the design without resistors minimises this. Of course we must ensure that the total voltage ratings of the caps are adequate otherwise neither cap may be operating within specification (I don't recommend this!), even if it is operating in the best manner in the circumstances.

Peter

[dinkydi]

Hi Norman, Great to have you in this crucial discussion about whether or not to use a resistor or 2! We should all be alarmed at what little we know.

Peter

[kalee20]

I've been following this and although I agree with the self-equalising of voltage in some types (due to internal leakage rising rapidly with voltage, a bit like a soggy zener diode, as has been mentioned), I wouldn't rely on it.

If capacitors are indeed mismatched (such as 100GΩ and 10GΩ) the the voltage will, in the absence of balance resistors, be distributed in the ratio 10:1.

If you add balance resistors, then far more leakage current will flow, because the 10GΩ capacitor will now have half the supply voltage across it so will leak more current. One could argue that it is being more stressed, current-wise. But, as long as it is still within its voltage rating, it will be designed to cope with it. However, the voltage across the other capacitor will be reduced from 91% of the supply to only 50%. And this reduction of voltage stress could be far more preferable.

Some capacitors, when overstressed voltage-wise, don't start progressively leaking more - they just fail (film/foil types particularly, but also solid tantalum). The internal stored energy causes thermal damage at the site of the breakdown - and if the capacitor is charged to a higher-than-rated voltage, the energy is a lot more than normal (energy being proportional to volts squared).

It's also worth bearing in mind that without balancing resistors, even perfectly matched capacitors could share voltage badly, due to external contamination, condensation, etc, precipitating a failure.

[GMB]

We have all been taught and accepted the wisdom that voltage ratings on components are sacrosanct,

I suggest that they are to a large extent, because you don't know what headroom they have.

The voltage on them is the stress they must endure. The leakage that flows is just an indication of their condition and not a "stress" as such, although it is true that the leakage current leads to potential degradation of the dielectric so is undesirable, but when we talk of new components these currents are seriously small.

I agree with the comments from Kalee20 in that you can get serious and permanent damage to non-electrolytic capacitors when they are taken to their breakdown voltage. Also, that the external leakage must not be ignored (at these tiny levels).

Electrolytics are a bit different in that the effect of low-current leakage is to continuously increase their working voltage (that's rather how it got there in the first place) but at the expense of their capacity of course.

[Craig Sawyers]

Originally Posted by dinkydi

Craig: Thanks for the analysis reference. This analysis starts with the assumption that the capacitor voltages should be kept equal. No one has justified this assumption. It might seem reasonable at first, but I believe it is wrong. Peter

Well no - it sets a "mid point" voltage Vm, which is not necessarily half way, V/2. The trick is to ensure that the balancing resistors are chosen so that with typical leakage current mismatches the maximum voltage of either capacitor is not exceeded.

The difficulty is estimating what the leakage current mismatch is.

Craig

[murphyv310]

Hi.
Personally I wouldn't think of not using balancing resistors. Anyone that has worked with smoothing circuits that handle thousands of volts will tell of catastrophic failures without the balancing resistors!

[McMurdo]

And you must factor in not only how they behave when new but how they behave when they're 5 years old. It is too much to expect 2 identical electrolytics to age at exactly the same rate to the same degree and in the same attributes.

[dinkydi]

Hi Kalee20, Thanks for your thoughts.

Your reasoning for the use of balancing resistors is very clearly put. However, the model you use is linear, that is, the resistors (100GΩ and 10GΩ) are fixed in size. In reality, the leakage current of an electrolytic capacitor increases, not linearly as with a fixed resistor, but instead, at an ever-rising rate as the capacitor voltage increases. This means that you do not end up with the extreme 10:1 ratio that your linear model predicts. Instead, the ratio becomes close, in line with the capabilities of the actual capacitors employed.

The non-linear relationship between the voltage and leakage current of an electrolytic capacitor means that the magnitude of the current is a strong measure of the voltage stress of the capacitor. That is, if one considers the leakage current, voltage and current stress are not separate issues.

I take your point regarding the sudden failure of film/foil capacitors (the situation with tantalums is more complex and off topic) but my argument only concerns electrolytic capacitors (see post #25, para 1).

As far as contamination and condensation are concerned, these issues should be addressed separately. The effect of such problems can be quite varied, based on a linear model (imbalance may well be corrected!). Non-linear reality is more sanguine. All electronic circuits require special protection from external influences such as contamination and condensation, if these are relevant concerns. Failure to provide this protection, when a circuit needs it, may have serious consequences.

Peter

[dinkydi]

Hi GMB, I completely agree with your comment about voltage ratings, and my post also accords.

However, you highlight a problem with voltage ratings: voltage ratings are general ratings for a particular type of cap - the actual voltage that a particular cap will work to is higher (due to headroom) and we don't know what it is. This is why the behaviour of the leakage current is important - it reveals the true voltage capacity of the cap - it tells us the headroom.

I don't think that the leakage current of a new electrolytic can be described as "seriously small", especially in the region of interest: near maximum voltage.

I have addressed Kalee20's comments, above.

Peter

[GMB]

OK, I think we have some confusion. I was commenting on capacitors in general and my remark about seriously small leakage was directed at non-electrolytic types.

As I went on to say, electrolytics are different in that they self repair (so long as things don't get out of hand).

The maximum voltage of a non-electrolytic is the point where catastrophic failure will occur so you don't want to go near that!

The maximum working voltage of an electrolytic capacitor is only what it says on the side when brand new. Once in service it will very gradually end up being whatever voltage the capacitor is subjected to because they do rely on the electrolytic process to maintain the dielectric but this can only be up to the actual voltage applied. So it's a moving target and thus unlike non-electrolytic types - something to be aware of if you recycle one to a circuit applying higher voltage (i.e. it will need reforming).

So electrolytic capacitors can fair better than expected without resistors - something that you could guess if you stop to consider how "non polarised" electrolytics are constructed. But they do need to be well matched, so things can still start to drift badly because although they self-repair it isn't as good as when they were made originally and depends on the exact conditions (they use a different electrolyte to form the dielectric during manufacture to get a more uniform thickness).