Combining capacitors in series and parallel

[joshdfrazier]

So, I need a 600v cap. I've got plenty of nice 47uf/450v caps sitting around that I thought I might be able to use. Here is the idea, take four 47/450 caps.
Wire each pair in parallel, giving me two 94/450 caps. Then, wire those pairs in series, providing me with one 47/900 cap.

It sounds like a great idea in theory, but I feel like I could be overlooking something here. Is this safe practice?

[rock_mumbles]

That's fine just a lot of caps ... use load balancing resistors on the series caps

[Invertiguy]

As long as you use balancing resistors across the series capacitor banks to split the voltage evenly between the caps, you should be fine. I did the same thing when I built a 750V power supply for a monster sweep tube amp I had in the works before time and budget constraints got in the way... I'll get around to finishing the rest of it someday

[tubeswell]

The balancing resistors will act as a bleeder network, so I suggest you use 100k 1W resistors (1 x 100k in parallel with each set of parallel caps) to get the optimum amount of 'bleed' at about 200k for the whole lot. (not too much, not too little). 1W rating for each 100k resistor should cope okay with current surge at startup (but 2W would be even better)

[joshdfrazier]

Thanks for the lesson there, tubeswell. All of my resistors are Vishay 3watt, for peace of mind. I don't understand how the cap/circuit isn't affected by having a 100k resistor in parallel. Guess I have some reading to do!

[tubeswell]

You need about 200k between B+ and ground for there not be too much of a load on the HT winding. That's 100k in parallel with each filter cap (that you have put in series in order to double the filter cap's voltage rating). 200k also happens to be a good value for a bleeder network to discharge the filter caps. You could make each resistor 220k or 270k or 470k, but it takes longer to discharge and also the more resistance you have, the poorer the voltage regulation (and the whole reason you're putting a resistor in parallel with each cap is voltage regulation. i.e.: you want to keep the voltages seen across each cap within the voltage tolerance of the cap, and you do that by regulating the voltages seen across each cap with the parallel resistor network). Having said that, 220k or 270k in parallel with each cap will work just as well.

[angelodp]

good info, just at that stage on a current build. Ok for parallel caps same idea, just parallel the R - I have 150k's on hand 3w should work out.

[potatofarmer]

I've wondered about the ideal value for the ballast resistors, and the best info I can find is a link I got from ax84.com:

SERIES-CONNECTED CAPACITORS: Insufficient voltage ratings can be a problem, and series-connection may be the only way to obtain electrolytics with a high enough voltage rating. I know of only a very few modern-style electrolytics with voltage ratings above 450V, including LCRs (500v) and Sprague Atoms (600V). Series-connection requires addition of so-called "bleeder" or voltage balancing resistors, one across each capacitor, conducting a current that keeps the voltage across the series capacitors balanced. Some of this is covered in the manufacturer's application notes; sources here are the Nichicon and Rifa application notes in particular.

Even brand-new high quality electrolytic capacitors conduct to some degree. This leakage current depends on the quality of the electrolyte, temperature and condition of the capacitor, and can be represented by a resistance in parallel with the capacitor. In the figure, series-connected capacitors C1 and C2 have some leakage resistance RL1 and RL2. Because of the wide tolerances of electrolytics, this leakage current varies from sample to sample, and by Ohm's law, effects the voltage balance between electrolytic capacitors connected in series. Note that we consider only brand new, identical capacitors connected in series - no mixing of ratings, types or brands, please.

Balance resistors RB1 and RB2 keep the voltage balance between the series capacitors within tolerance by including another larger current in parallel with the leakage current. The balancing current is chosen large enough to overwhelm any leakage imbalance and thereby to guarantee safe operation. To calculate the value of the balancing resistors, first determine the approximate maximum leakage of the series-connected capacitors. The leakage current in uA ranges from 1/5 sqrt(CV) to 1/2 sqrt(CV) according to Nichicon, with C in uF, V in volts and current in uA. You can also get leakage specifications from your capacitor's data sheet. One common rule-of-thumb for the balancing current is 10x the leakage current - thus for two 100uF/350V capacitors connected in series to form a 50uF capacitor, maximum leakage of 1/2 sqrt(100*350) = 94uA, times 10 is about 1 mA. Let's say we want our applied voltage to be 650V, then RB1 and RB2 = 325K ohms. Power dissipation of I*V = 0.325W, so a minimum 1W resistor would give an adequate safety margin. Be sure to check the voltage rating of any balancing resistors too.

You'd think that two 350V electrolytics connected in series would have a voltage rating of 700V, but the loose tolerances of electrolytics again interferes. As pointed out in the Evox Rifa electrolytic capacitor application note, series capacitors act as a capacitive voltage divider, and N electrolytics connected in series with a capacitance tolerance range of Cmin to Cmax have a maximum divided voltage (at the junction of the two capacitors) Vdiv = (Vapplied * Cmax) / (Cmax + (N - 1) * Cmin). Ok, so in our example, with a +/- 20% capacitance tolerance, Cmax = 1.2*100 and Cmin = 0.8*100, with Vdiv = (650*120)/(120 + (2-1)*80) = 390V. This exceeds the voltage rating of the electrolytics by 40 vots; with some algebra we can see that 350+350 gives a 583V maximum when the capacitive tolerance is 20%. For our applied voltage of 650V, the minimum voltage rating for each capacitor would need to be 400V.

In its application note, Nichicon presents a more precise calculation of the balancing current than the 10x-leakage rule given above. Let Vdif = (Vmax - Vmin) be the difference in operating voltage resulting from leakage imbalance for the two electrolytics in series and Idif = (Imax - Imin) is the maximum difference in leakage current between the two capacitors, then RB1 = RB2 = Vdif / Idif (see the application note, although it's fairly easy to derive this result). Using the current range given above, Idif = 0.3*sqrt(CV)*Tc*F, where Tc is a temperature coefficient and F is a fudge factor. Electrolytics conduct more as the temperature increases, with Tc at 20C of 1, increasing to 2 at about 60C and 5 at about 85C. Again, you can find this characteristic in your capacitor's data sheet. The fudge factor is an arbitrary safety factor of an extra 40%, thus for our example at 60C: 0.3*sqrt(100*400)*2*1.4 = 168uA. Nichicon picks an arbitrary Vdif of 10% of the capacitor rating, but by knowing the intended application we can make a better worst-case estimate.

Consider that the worst-case voltage imbalance due to leakage current between the series capacitors increases with decreasing balance resistor current. Thus the larger an imbalance we can tolerate, the smaller our balance current can be. If we do not ignore the capacitive tolerance, we must add the capacitive and leakage effects to get a valid worst-case estimate of the voltage imbalance. Using the 2 at 400V/100uF series connection operating at 650V, the worst-case voltage imbalance due to the capacitive tolerance of 20% is 390 - 260 = 130V. This imbalance can increase due to leakage at most by 20V to 400 - 250 = 150V, and Vdif/Idif = 20V/168uA = 120K ohms or 2.7mA. This is 0.9W per balance resistor... requiring two 2W or larger power resistors. A better solution would be to increase the voltage rating to 450V, resulting in a small increase in leakage current difference (10uA) with an increase in voltage imbalance tolerance by 100V. Then Vdif/Idif = 120V/178uA = 675K ohms or 480uA at 0.16W. It may also be worthwhile to match devices to minimize capacitive imbalance, although some tolerance should remain to accomodate possible changes in the characteristics of ageing capacitors.

Since 450V is the highest readily available electrolytic voltage rating, for voltages much over 650V we should increase the number of series-connected capacitors. With 3 450V series-connected capacitors and 20% capacitive tolerance, the maximum operating voltage is 450*(120 + 2*80)/120 = 1050V. Choosing an operating voltage of 900V, with a nominal 300V across each capacitor, if two capacitors operate at their lowest voltage and one at its highest, then Vmax = 1.2*900/(1.2 + 0.8 + 0. = 346V. Here Vdif = 2*(450-346) and Idif is still 178uA, thus Vdif/Idif = 1.2M ohms or 250uA.

Boiling this down to math-free conclusions, for multiple identical series-connected electrolytic capacitors:

The sum of the voltage ratings should be 30-40% higher than the applied voltage.
A voltage-balancing resistor network is required, and the balance current need be no more than about 1 mA.

The 10x-leakage rule makes no assumptions about the voltages of the capacitors in use, providing a conservative requirement, although not considering the voltage imbalance due to capacitance and leakage current tolerances. For the amateur builder/repairman, using a bit more balance current than the minimum, as recommended by the 10x-leakage rule, won't matter. A more thorough analysis will guarantee that the voltage ratings of the series-connected capacitors are safely within worst-case limits. The manufacturer's recommendations point out the factors that effect the capacitor balance - temperature, range of leakage current, capacitive tolerance, voltage range - and these factors should be considered in selection and installation.

http://www.nmr.mgh.harvard.edu/~reese/electrolytics/

Is this guy's analysis valid?

[DonMoose]

good info, just at that stage on a current build. Ok for parallel caps same idea, just parallel the R - I have 150k's on hand 3w should work out.

For parallel caps, you only need one bleeder.

The phrasing 'one resistor in parallel with each cap' is a little loose - it's one bleeder per each [1 or more caps in parallel] in a series stack. But that's unwieldy.

[Leo_Gnardo]

Just had a first look at this thread. Lots of good advice and the article from AX84 looks spot on to me.

Balancing resistors: note Marshall often use 56K 2W, Fender 220K 1W, and I've used up to 330K, all seem to work fine. So use what you have on hand and no worries.

Also consider film caps. Solen makes some excellent ones, very affordable when you consider one replaces two electrolytics plus their balance R's plus your time wiring the whole mess. I've used 22 uF 630V Solens in B-15 and similar amps to replace the 20 uF 600V "dynamite stick". The DS's are often made of series connected El's and NO balance R's. Many are 40 to 50 years old and ripe for breakdown. OTOH the Solen is a good deal wider and may take some creativity to mount. Antique/CE has a selection of Solens. Now Panasonic has some rectangular film caps available at hi voltage, certainly worth a look. Meant for PC board mounting I guess, these also may make for a challenge mounting in old or even new guitar amps but they're an option that's worthy of consideration. Mouser has 'em and I think DigiKey too. The film caps likely will last near forever compared to electrolytics. Carr has been using Solens if I'm not mistook for some years now. Whether you like Carr's or not, it's doubtful any tech will need to rebuild their power supplies in this lifetime.

[rp]

I've used 22 uF 630V Solens in B-15 and similar amps to replace the 20 uF 600V "dynamite stick"

So while we got you here, what'd you notice/think of the sound and feel, if anything? Clients notice any difference other than the new cap perkiness?

[potatofarmer]

Also consider film caps. Solen makes some excellent ones, very affordable when you consider one replaces two electrolytics plus their balance R's plus your time wiring the whole mess.

Any thoughts on motor run caps as suggested by RG years ago in the Immortal Amp Mods articles? I bought a couple of 'em cheap for a rotary speaker crossover but I also have an amp where I'm going to have to recap it with totem-pole'd caps at every node and it seems like this might make more sense.

[gingertube]

Just a few notes from personal experience:

The balance resistors should be sized to conduct about 3 times the leakage current - going to x10 the leakage current is just wasting power and it demands higher power resistors. The EPCOS Electrolytic capacitor Application Notes actually say this ( X3 not X10).

If you do the calcs for leakage current using the values from the capacitor datasheets it quickly becomes apparent that 95% of commercial Guitar Amp designs which use series connected caps in the main B+ filter have inadequate current through the voltage share (voltage balancing) resistors. The resistors used are just too high in value - See my suggested values below.

Important for newbies:
For equal voltage sharing in series connected capacitors then you MUST use equal capacitor values - this is actually easy to understand, the same charge current runs through the caps. They charge up to a voltage determined by that current and the capacitance value ( a 100uF cap would charge to twice the voltage as a 200uF cap) - so don't mix capacitor values, the balancing resistors will do very little to correct this.

I would encourage you to do the calcs yourself but from calcs I have done for various projects I offer the following "BALLPARK" maximum resistor values (designed to give 3 x the leakage current in the balancing resistors):
2 x 470uF in series - use 47K across each cap, you will probably want to use 5W resistors
2 x 220uF in series - use 100K 3 or 5 Watt
2 x 100uF in series - use 220K 2W
2 x 47uF in series - use 390K (470K MAY be OK) 2W
2 x 22uF in series - use 470K 1W would be OK IF the resistor voltage rating is sufficient, else use 2W

These maximum values are, in general, about 1/2 or 1/3 the typical values that I've seen used in Commercial Guitar Amps.

Other Hint for home builds: The currents in the share resistors are such that they are around what a High Sensitivity LED wants. Put a RED LED in series with the bottom resistor (on the 0V side). When you turn off, the caps will bleed down, and when it gets to a low enough voltage for you to be able to work on the amp, then the LED will have gone OUT. RED LED ON - wait a bit longer, RED LED OFF - safe to work on.

Even if you do not use series connected caps you should install a bleed resistor and it is a good idea to put a RED "Hey I still have voltage here" LED in series with it.

Cheers,
Ian

[rp]

^ this should be in the reference files or a sticky.

[Leo_Gnardo]

Also consider film caps. Solen makes some excellent ones, very affordable when you consider one replaces two electrolytics plus their balance R's plus your time wiring the whole mess.

Any thoughts on motor run caps as suggested by RG years ago in the Immortal Amp Mods articles? I bought a couple of 'em cheap for a rotary speaker crossover but I also have an amp where I'm going to have to recap it with totem-pole'd caps at every node and it seems like this might make more sense.

Can't say I've ever used motor runs or seen them used in a guitar amp build. The hi fi guys again - some of the Audio Asylum chaps - seem to favor them. Now they're easily available at Mouser and some other spots, don't seem too expensive, full of vegetable oil not PCB, and not excessively expensive, gets a green light from me to go ahead & try 'em for those that want to experiment. I'm sure they'd work a treat.

rp, I didn't hear any tone or "feel" changes in amps where I used Solen film filter caps to replace main or secondary B+ filters. Customers were just delighted they got their amps fixed. There's a claim for a more "immediate" sound whatever that means. At AA last week one of the comments was "they punch over their weight as power supply filters" compared to El's. Well a microfarad is a microfarad so they say. Those with a better ear than mine may hear some difference.

Electrolytics top out at 500V, but you need more sometimes, even if it's for a little safety margin. So I keep a few 630V Solen films on hand for repairs. Sometime I'd like to try a build from scratch with them. The "real" test would be build 2 or 3 simple amps otherwise identical, electrolytics in one, film in another and why not motor runs in the third. ABC test to your heart's delight and maybe then get an answer as to which is best, or at least what characteristics to expect in the sound & feel.