Equalizing Resistors in context of electrolytics.

[Station X]

I need to replace the smoothing and reservoir capacitors in a PSU with an output of about 700V DC. At manufacture it was fitted with 2 X 32 uF 450V capacitors in series to give 16 uF 900V. No equalizing resistors were fitted.

Do I need to fit equalizing resistors with the new capacitors and if so what value should they be? I assume that the resistors are needed because the high tolerance of electrolytic capacitors means that when in series they could have different voltages across them possibly exceeding the rating of one capacitor?

I have googled this subject and it seems to have generated some heated discussion. There is talk of failure of an equalizing resistor destroying the capacitors and it is recommended that high power wirewound resistors be used. Is this necessary? I was planning to use 2W metal film types.

Graham.

[Norm_Leal]

Hi Graham

Electrolytic filter caps have some leakage. If they aren't equal the one with least leakage will have the most voltage.

The manufacturer may have decided his original caps were matched close enough where he didn't need equalizing resistors?

Best to add some resistance across your replacements even if 470K or 1 meg. These resistors will help divide voltage equally between caps.

Norm

[Station X]

Norm.

I expected to see a few replies on this, but yours is the only one. The question probably doesn't arise very often, as dometic receivers don't have 700V DC HT Rails.

I've changed the caps and fitted 470K 2W metal film resistors across each of them. I'm not able to test the arrangement yet, as I have more work to do before I dare apply HT.

Graham.

[Colin]

Hi Graham,

I've had to use series connected caps a number of times and found the article below covers the subject in as much detail as I ever needed. The interesting point is about taking into consideration the capacitance and leakage tolerance of the components used. If they're rated at 20% you may find you need 3 off 350v caps to safely cover your 700v applied voltage - not two.

It's worth a read.

In practice I've used new series connected caps of the same type without bleeder resistors and because the leakage across each is pretty much the same there's been no problem with the voltage across them falling comfortably within their maximum rating.

rgds
Colin

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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.

The attached graphic should be viewed here.

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 + 0.8) = 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.
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[Station X]

Hello Strech289.

Thanks for posting the article. I wish I'd read it before I did the job! I think that if I do the calculations I might worry myself needlessly. I'll wait until I'm in a position to apply power and then measure the voltage across each capacitor. If it's less than 450V I'll leave things as they are. Balancing current should be about 0.75 mA The resistors are well within their power ratings.

I've dug out the power supply diagrams of several old transmitters which use HT voltage in the 600V DC region. They all use electrolytics in series, but none of them have equalizing resistors. I find it hard to believe that electrolytics were better balanced 60 years ago than they are today.

I have also committed the cardinal sin of replacing one of a series pair of electrolytics in another old set with a modern type, whilst leaving the other in place. Nothing's blown up so far though. Perhaps it's a case of ignorance is bliss?

Graham.

[Paul Stenning]

Colin,

Can you state where that article came from (who has the copyright) if you know please? With that amount of information from a 3rd party, it's only fair to give due credit to the author.

[Sean Williams]

Just to add my thoughts here,

I build high power Valve RF amplifiers for my station here, and I use an HT varying from 1800 to 3500 volts at currents approaching an amp in some cases, in all of the power supplies used here I employ electrolytic caps.

Normally for a 2kv supply I use 6 390uf at 450v caps, each are equalised by 100k 2watt MF resistors - I have never had one of these fail on me, and they also provide a useful bleeder function.

There has been a discussion on the amps@contesting.com web forum about this idea, and the field is truly divided!

However, it is common practice, and given tolerance variations I would continue to do so! - these capacitors are flipping expensive at 7a ripple rating, so anything that helps keep them happy is worthwile (you know, soothing music, fresh flowers, and cool envioment, along with a bedtime story )

Cheers
Sean

[Colin]

Colin,

Can you state where that article came from (who has the copyright) if you know please? With that amount of information from a 3rd party, it's only fair to give due credit to the author.

Hi Paul,

Thanks for picking me up on this. I had the information on my PC as a document that I had printed off to use in the workshop so I simply cut & pasted it into the thread. It's an extract from a much longer document entitled -

'Strategies to Repair or Replace Old Electrolytic Capacitors'

It can be viewed here - http://www.nmr.mgh.harvard.edu/~reese/electrolytics/

The author is
Tim Reese
reese@nmr.mgh.harvard.edu
MGH NMR Center
Charlestown Navy Yard
13th Street, Bldg 149 (2301)
Boston MA 02129


RgdsColin

[Station X]

I've applied some power. As expected with equalizing resistors the voltages across the two capacitors are equal and well below 450v DC.

Thanks everyone.

Graham.