Four questions about (Super) capacitors in series - Page 1
Forum section: electronics / beginners

author: havewattwilltravel
author_rank: Contributor
timestamp: August 23, 2018, 06:26:56 pm
content: I'm trying to wrap my head around capacitors in series to see if I really understand them.1. Suppose I were to put 10 perfectly matched 1F capacitors in series and charge the series to 10V. Would each capacitor actually have the same charge/voltage, or would they vary slightly (and consistently) by position, with the outermost capacitors charged slightly more than the inner ones? (I'm thinking even if the ESR were the same for each cap, there's still a time delay as they charge that would leave them imbalanced.)2. Suppose I charged each capacitor to exactly 1V and left them for 10 days. If the leakage current was the same for each cap, would the charge/voltage be the same, or would they again vary (consistently) by position? (Would some of the leakage current effectively charge the outer caps rather than just heating them all evenly?)3. If that same string were partially discharged, would the resultant voltage on the outer capacitors be slightly less than those on the inner capacitors? (Because of ESR, wouldn't the outer caps be discharging into slightly lower resistance than the inner ones?)4. Assume I were to use real capacitors and compensate for the individual differences in capacitance and leakage by putting additional capacitors and resistors in parallel with each capacitor in the string to make them equal. Would they remain balanced over time, or do the parameters for each capacitor vary individually so much over time that they'd always get out of balance?

author: David Hess
author_rank: Super Contributor
timestamp: August 23, 2018, 07:09:01 pm
content: The series position will have no effect except through electrostatic and magnetic coupling at very high frequencies and through mechanical layout which could result in different temperatures of operation. In practical purposes, these can be ignored except for temperature effects in high ripple current applications.

author: helius
author_rank: Super Contributor
timestamp: August 23, 2018, 07:24:35 pm
content: Quote from: havewattwilltravel on August 23, 2018, 06:26:56 pmThe charge on each capacitor in series is the same because charge is conserved. The total charge put onto one plate of a capacitor is equal to the charge out of the other plate, and this is transitive across all of the series capacitors. The voltage on each capacitor will be according to V = C/Q; so if they all have the same capacitance, they will all have the same voltage.QuoteESR doesn't matter here, and there is no time delay. Each capacitor is charged simultaneously—obviously not in a bare instant, but the current through the series string charges them at the same rate.QuoteLeakage is modeled by a parallel resistance, not a current; but you specified that the leakage currents were equal. Well, okay: if you integrate a current over a period of time, the result is a certain change in charge. This has nothing to do with capacitors.QuoteBy the same reasons as (1), they discharge equally. ESR is a series resistance, and several resistors in series are equivalent to one. Different ESR does not effect them differently, they all see the same series resistance.QuoteYou didn't specify what "make them equal" means. As noted above, variations in capacitance and ESR have no effect whatsoever on the state of charge; the voltage will depend on the capacitance of each one according to the capacitor equation. The only reason to balance capacitors in series is leakage, since it acts as a parallel resistor that discharges each cap separately. If the caps have different leakage, some will discharge more than others—this can cause problems when the series is charged again, and the caps with lower leakage start from a higher state of charge, which could make them exceed their voltage specification. The way to deal with this is to place a high-value resistor in parallel with each individual capacitor, in effect overwhelming the unknown leakage with a predictable discharge.

author: ArthurDent
author_rank: Super Contributor
timestamp: August 23, 2018, 10:37:07 pm
content: I had bought one of the 6 supercap units on Ebay to check out and see if I could use it to power a low current (35Ma) circuit during power outages. It consisted of six 500F 2.7VDC supercaps in series for about 80F @ 16.2VDC max with equalization circuits across each cap for protection.What I found was that 2 of the caps had high leakage so if I charged the bank up to 2.7VDC per cap and let them set, the 2 worst caps would discharge below 1 VDC quite fast. I bought 2 replacement caps from another vendor and the replacements worked better. One of the remaining original caps would discharge much more rapidly under load than the rest indicating it had less capacity (1/2?) than the rest so to get full benefit from the bank I would have to replace that cap as well. I found that to keep them charged (or ‘float’) needed about 25Ma current to compensate for the leakage.The equalization circuit consisted of a MOSFET switch and a comparator on each cap that would place a resistor load across each individual cap if the voltage reached 2.7VDC because going above that rating could be very bad. You also have to be very careful not to short the caps because they are capable of many amps of current output. Some of the larger banks of supercaps have been used to replace car batteries and start the car which requires massive current.So to answer your question from my experience I would say that although while the caps position in the series will not matter, that this may not work as well as you hope. I do believe that where your caps have much less capacity than mine and you probably won’t experience problems to the extent I did with mine, which were cheap Chinese caps, they may not work as well as you think they should. The smaller values around 1F are used for memory back-up in some electronics so your plan might work but you might want to do some testing like I did before you wire them into your device.

author: havewattwilltravel
author_rank: Contributor
timestamp: August 23, 2018, 11:00:39 pm
content: My intuition isn't agreeing with physics, but which one of these two is wrong?With three capacitors in series, with the leads connected end-to-end and a battery to the other ends, the resistance between the middle capacitor and the other two is (at least) twice the resistance between the end capacitors and the battery. If the battery briefly charged them, and was disconnected, why wouldn't the middle capacitor have less charge than the ends?

author: oPossum
author_rank: Super Contributor
timestamp: August 23, 2018, 11:04:21 pm
content: The current flow through all the caps is the same, so the stored charge will be the same if they all have the same capacitance.

author: IanB
author_rank: Super Contributor
timestamp: August 23, 2018, 11:05:01 pm
content: Quote from: havewattwilltravel on August 23, 2018, 11:00:39 pmIf the capacitors are connected in series, then by definition the current though all the capacitors is equal at all times. If the current through each capacitor is equal to the current through each other capacitor, then by definition the charge in each capacitor must change equally. Resistance does not affect this calculation.

author: IanB
author_rank: Super Contributor
timestamp: August 23, 2018, 11:07:07 pm
content: Quote from: oPossum on August 23, 2018, 11:04:21 pmAnd even if they don't.

author: oPossum
author_rank: Super Contributor
timestamp: August 23, 2018, 11:14:56 pm
content: If you have additional constraints such as none reach their rated voltage.

author: havewattwilltravel
author_rank: Contributor
timestamp: August 23, 2018, 11:19:32 pm
content: IRL I'm using a bank of surplus Maxwell 2600F caps, which have very little leakage. I also don't charge them to more than 80% of their rating because I don't want them to ever fail. They're very handy when I feel the need to arc-weld during a power outage. Ever seen 16ga wire vaporize before?My experience with other super-caps on Ebay is that they're defective rejects that are being dumped. Like Ebay batteries, which may or may not be filled with sand, you can't trust them. You might be better off putting the good ones in parallel and using a DC-DC converter.

author: IanB
author_rank: Super Contributor
timestamp: August 23, 2018, 11:20:13 pm
content: Quote from: havewattwilltravel on August 23, 2018, 11:00:39 pmIntuition is a very bad substitute for science. It is best not to have intuition until you have many years of experience becoming an expert in a field. Until then intuition will just give you wrong answers.

author: havewattwilltravel
author_rank: Contributor
timestamp: August 23, 2018, 11:33:56 pm
content: Is the resistance in the middle is impeding the current flow in the outer capacitors as much as it is impeding the flow in the middle one then? For an electrostatic potential to form, the electrons have to move (assuming a shift in probabilistic charge distribution is movement), so anything that impedes their movement will impede the potential from forming anywhere in the circuit equally?I wish I just take an equation and use it. But my brain doesn't work that way. Arithmetic never made sense until I took set theory. If they'd started with that, my academic life would have been much easier.

author: ArthurDent
author_rank: Super Contributor
timestamp: August 24, 2018, 12:14:09 am
content: Many years ago an instructor told me something very profound: "Things that are in series are in series with each other."

author: IanB
author_rank: Super Contributor
timestamp: August 24, 2018, 12:17:50 am
content: Quote from: havewattwilltravel on August 23, 2018, 11:33:56 pmBroadly speaking, your brain works the same as any other brain. All brains share the same biological design.Everything can be learned, if you apply yourself to learning it.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 24, 2018, 12:20:31 am
content: Equalization isn't a big priority (well, unless you get truly awful caps like Dent's example!), because leakage goes up exponentially above 2.2V or so.Note that dielectric absorption is extreme on these types: it's not so much a long time constant, as it is a diffusion characteristic (which makes sense, given what these things are). If you apply 2.5V to a supercap for 10 seconds, then watch it settle out, it'll drop to, probably about half, over the next couple days. The settling curve has a 1/sqrt(t) form, corresponding to the diffusion property.Tim

author: havewattwilltravel
author_rank: Contributor
timestamp: August 24, 2018, 01:39:16 am
content: Actually, that's demonstrably not true on both a cognitive and neuro-biological basis. Take Autism and Alzheimers, for example; both show divergence in cognitive function and neural anatomy.People really do think differently, and the people who think differently have brains that arephysicallydifferent. There are also intrinsic limitations in learning because of this.I have to apply myselfdifferentlyto learn something than you might. Both the method I use to learn, and how I learn to use what I've learned are different. This comes up in math education, for example, where there are at least five different ways to do division. All of them yield the correct answer. But not everyone grasps each different version equally easily or can do them equally well. Some people get stumped if they're taught one way and assume "I'm no good at math" until someone shows them a different way.I knew someone who was about to fail out of school before I went around the room with her measuring things and moving fingers left or right. After that she was able to do arithmetic; negative numbers suddenly made sense! She went on to become a teacher. I also knew someone who was a slacker art major until a professor challenged him to learn calculus. So he spent one month stoned the whole time doing nothing else but learning calculus. When I last saw him, he was doing six body gravitation problems.People arereallyweird, but really wonderful when their weirdness gets channeled in productive directions.I'm finding that learning components individually does me no good. I have to think about an entire circuit, and all the aspects of it (capacitance, inductance, resistance, vibration, and temperature) simultaneously to make sense of it.

author: havewattwilltravel
author_rank: Contributor
timestamp: August 24, 2018, 01:47:16 am
content: Interesting: I've always kept my caps at 2.2V or below.I've also noticed that if I apply a pulse to them that it starts a wave of voltage changes (where the wave is the rate of change and direction). The wave has ripples, and it looks like a standing wave in some ways. I assume there are multiple effects going on simultaneously, and I'm guessing that different caps would have different frequency responses and Q's in response to a pulse too.Not the ideal way to start learning about capacitors when they behave so differently from a textbook!

author: IanB
author_rank: Super Contributor
timestamp: August 24, 2018, 01:48:57 am
content: Quote from: havewattwilltravel on August 24, 2018, 01:39:16 amThose are disorders. Obviously disorders do not count in the categorization of normally functioning brains.QuoteI'm sorry, but unless you wish to claim you have a brain or learning disorder, I'm not buying it.QuoteBut this is wrong. When we learn math we do not learn ways to do division, we learn what division is. Once we understand what division is, we see that all ways to do division are somewhat equivalent, and we become able to invent our own ways of doing division.

author: havewattwilltravel
author_rank: Contributor
timestamp: August 24, 2018, 02:11:28 am
content: If you wish a different perspective, search on "fmri learning". For example :http://drexel.edu/now/archive/2018/May/New-parts-of-the-brain-become-active-after-students-learn-physics/Even "ordinary" people exhibit highly divergent neural pathways.Consider this too:https://www.scientificamerican.com/article/scientists-surprised-to-find-no-two-neurons-are-genetically-alike/Another example, for which I can't find my bookmark: After years of performing hundreds of human dissections, a anatomist noted that he had never seen a single body with the textbook number and location of lobes in the lungs. Textbooks present an average, but like the average family with 2.5 children, it doesn't exist in real life.Quote

author: IanB
author_rank: Super Contributor
timestamp: August 24, 2018, 02:26:25 am
content: Quote from: havewattwilltravel on August 23, 2018, 11:33:56 pmFor example, here you have strung a lot of complicated words together in a jumbled way that conveys almost no meaning. It's like you have got some words out of the dictionary and put them in a blender. This makes your question impossible to answer because it isn't a question.It seems you have not yet formed an understanding of the most basic ideas of electricity, yet if that is the case where did you come across such complicated words?

author: helius
author_rank: Super Contributor
timestamp: August 24, 2018, 02:28:30 am
content: There's considerable risk getting your science from university press releases (or from Scientific American, a respectable journal for 100 years, but more and more a Popular Science clone). fMRI is a field with huge methodological problems; a study using common (for fMRI) statistical methods identified "neural pathways" activated in a dead salmon.

author: havewattwilltravel
author_rank: Contributor
timestamp: August 24, 2018, 04:01:57 am
content: It doesn't matter if the resistance is between the middle capacitor and the others, or all in one place, because it's the total change in the electrostatic potential of the entire circuit that evokes the effects, right?And my point: this is how I learn, I have to rediscover. In my case, it's been more than 40 years since I looked at any of this. Apologies if it strains your patience.

author: IanB
author_rank: Super Contributor
timestamp: August 24, 2018, 04:04:59 am
content: You are still using strange, complicated terms to create a word salad. This is what strains my patience. Why not use simple words like voltage and current?

author: JS
author_rank: Frequent Contributor
timestamp: August 24, 2018, 04:14:18 am
content: I would mention something that's not exactly on topic but I think it should be mentioned here...For a reliability point of view, is usually safer to put several caps in parallel than several caps in series, also, as with series caps you need balancing resistors the leakage is a problem, through the resistors this is, in parallel caps you don't need that.Now, you need several caps to fit in some space X amount of capacitance for X voltage, so in the same package you can get higher voltage lower capacitance and end with a similar result, with all the caps rated for the desired voltage and get to the desired capacitance.I do know it could be easier or cheaper to get one or the other, let's go for 1F 5V and 10mF 50V caps, let's go to mouser, cheapest ones, for 10, $2.85 for the 10mF 50V, $3.55 1F 5V... YMMV depending on the ratings. I also didn't compared sizes, this 10mF 50V ones are likely bigger than the 1F 5VJS

author: havewattwilltravel
author_rank: Contributor
timestamp: August 24, 2018, 04:26:19 am
content: You'd expect that with fMRI since the only thing it shows is where the oxygen is.Are you suggesting learning is possible without physical changes in the brain? Or that brain development is uniform and not environmentally directed on a neuron basis?

author: havewattwilltravel
author_rank: Contributor
timestamp: August 24, 2018, 04:52:18 am
content: Because using those does not enable me to understand what's going on!Clearly, we're failing to communicate (ironically illustrating my point).Thank you for your help.

author: Brumby
author_rank: Unknown
timestamp: August 24, 2018, 05:09:19 am
content: People learn differently, so further discussion on this is a pointless tangent. Let's not continue down that path any more. Please.

author: Brumby
author_rank: Unknown
timestamp: August 24, 2018, 05:13:18 am
content: Without regurgitating much the same in my own words, this gets my vote as a good answer...Quote from: helius on August 23, 2018, 07:24:35 pm

author: helius
author_rank: Super Contributor
timestamp: August 24, 2018, 07:13:07 am
content: Quote from: JS on August 24, 2018, 04:14:18 amI considered mentioning those practical aspects, but from the way the question was phrased I guessed it was just a theoretical problem.Series capacitors are rarely used unless the working voltage of the available components is too low for the application. So a long series string of capacitors usually means very high voltages, as in a Marx Bank. The other case is when working voltages are super low, like the 2.7V of EDLCs/ultracaps. In either case, attention must be paid to the effects of different leakages making the caps unbalanced, because the caps are already being charged to their working voltage limit (or you wouldn't need a series string of them).