# Balancing Resistor Values for Series Capacitors

I just wanted to confirm my rough calculations are correct in selecting balancing resistors for 2 capacitors in series.

Here are the specs: 2x 10,000uF Capacitors with 500V rating in series.

I found this estimation equation online: R = 10 / C where R =Mohm and C = uF. Based on this, I got 1kohm resistors to use as balancing resistors for each capacitor.

I'm using this setup to filter out transient behavior from a power cycler supplying 900V. Are those resistor values correct (or in the ballpark)?

• Your calculation gives about 0.45 amps through the resistors. They would need to dissipate 202.5 watts each. You should probably use somewhat higher value resistors. – Peter Bennett Oct 28 '16 at 0:35
• wrong! he said RC=10MΩ*uF= 10 Second leakage decay time constant. Critical factors are temperature vs leakage and Tolerance error between parts. 10sec seems reasonable but depends on part number, and quality and Ripple current with temp rise. – Sunnyskyguy EE75 Oct 28 '16 at 1:55
• In this case, it might be worth consulting the capacitor manufacturer for advice. – Spehro Pefhany Oct 28 '16 at 3:27
• For new parts that are matched, A 10 second balance RC value seems reasonable for parts with > 1000 second T but dynamic balancing may be required like batteries which tend to be balanced <1% unlike capacitors which tend to have a large tolerance "unless" from same batch. – Sunnyskyguy EE75 Oct 28 '16 at 3:35

As I understand it, you want to make a 1 kV polarized capacitor from two polarized 500 V capacitors:

The bleeder resistors are intended to keep the voltages on the capacitors roughly balanced. OK so far, but this seems rather extreme.

The resistors will draw ½ A with 1 kV in! That's 500 W of power, and each resistor will dissipate 250 W. This might work if you're trying to make a small toaster, but then you wouldn't need the capacitors at all.

Another way to look at this is to see when the result looks mostly capacitive and when mostly resistive. The -3 dB point of 1 kΩ and 10 mF is 16 mHz. If all your frequencies will be substantially above 16 mHz, then you're actually OK from that point of view.

I would look carefully at the worst case this circuit will be subjected to and see if the resistors can't be made much larger.

Dissipating 500 W just to avoid more expensive high voltage caps seems like a poor tradeoff. Look at 1 kV caps, and also pop up a couple levels and re-examine why you think you need this in the first place.

interesting question.

• from these choices for 10kuF 500V price ranges from $137/ea to$341/ea (usd)

• 1st looking at the cheapest, UCC p.n. E37X501CPN103MFM9M

• summary indicates:

• Leakage current: 0.02CV(µA) or 5mA,whichever is smaller, >5 minutes @25'C
• Standard capacitance tolerance: +/-20%
• worst case is 5mA @500V = 100kΩ > 5 minutes thus RC= 1,000 seconds

The problem here is the caps like batteries have "double-layer effect" and a memory effect as well as an aging leakage that rises with age and requires burning off contaminants so that the leakage current drops below the rated limit in uA.

Pd in 100k= $V^2/R=500^2/100k=2.5W$

• THe uncertainty is the transient leakage after some unused period of time, which is why historically large e-caps were charged up with 100k series R until the voltage charged up fully then it could be put into service. thus it depends on how well matched the two caps for "Balancing".

A soft start is a safe plan or twin MOV/TVS's at rated voltage to balance fused Caps , but may be hard to find and not very precise.

simulate this circuit – Schematic created using CircuitLab

• Thanks for your informative answer Tony! I hadn't considered a lot of those factors before! – Cobi Yu Oct 28 '16 at 16:22
• We used to buy mainframe caps with 60V 100k uF caps in the late 60's . If you didn't heed the advice of the elders about burning off leakage resistance with a high series R, the big cap had explosive results. Now they have vents and may or may not or internal fusing. FWIW Tesla version 2 LiPo cells all have fuse wires now to prevent fires from faulty cells that fail with shorts instead of normal open circuit or high ESR and Tesla puts hundreds of matched cells ( like matched cap) in parallel then many series modules to have >4k?x 16850 LiPo cells. – Sunnyskyguy EE75 Oct 28 '16 at 16:58
• So, you see matching Ah and Voc or ESR, Rp & C is as important to LiPo as big HiV caps – Sunnyskyguy EE75 Oct 28 '16 at 17:02