Capacitors in Series – Voltage Drop Due to Leakage Current

capacitancecapacitorelectrolytic-capacitorleakage-currentvoltage

Capacitor's in series

When capacitors are connected in series in a DC circuit, the voltage drop across individual capacitors at and immediately after the initial charging period is inversely proportional to the individual capacitance of each capacitor. But afterwards, this begins to change due to leakage current.

  1. How does this affect individual voltages across each capacitor?
  2. Will this process eventually result in the capacitor with the lowest leakage current gaining a voltage drop nearly equal to the voltage drop across all of the capacitors in series?
  3. Or will this situation eventually lead to voltages across each capacitor being entirely dependent upon the leakage currents (assuming each cap has a similar external load/or no load whichever is suitable for this assumption?) and whatever the capacitance of each cap does not affect the final voltages?

Best Answer

A simple model for a leaking capacitor is to consider an ideal capacitor in parallel with a leakage resistor, as bellow :

schematic

simulate this circuit – Schematic created using CircuitLab

Based on this assumption, in steady state (ie DC), the ideal capacitors behave like open circuits, and we just have a voltage divider based on R1 and R2, and therefore Vout = Vin * R1/(R1+R2)

So the final voltage depends only on the leakage resistors of each capacitor.

So to answer your questions :

  1. Yes, leakage current (or resistance) will afect the final voltage seen by each capacitor (U_C1 = Vin * R1/(R1+R2) ; U_C2 = Vin * R2/(R1+R2) )
  2. No, you will not have one capacitor with nearly all the voltage, excepted if they have a completely different leakage resistance. Expect a relative difference in the same order of magnitude than the relative difference in leakage resistance (which might be tightly specified, loosely specified, or not specified at all)
  3. Indeed, the capacitance of each capacitor will not mater for the final voltage (but will during transients). It might have some indirect influence : for a given manufacturing process, the leakage resistance will vary with the capacity, usually in inverse proportion (higher capacitance = bigger area or thinner insulation layer).

If you care about keeping the same voltage on each capacitor (for example because otherwise you exceed the maximal voltage ratings), then just add yourself resistors in parallel to the capacitors (with smaller values than the leakage), so it is your voltage divider that will fix the voltage on each capacitor in steady state (nb : it will increase the global leakage, so make sure to use low leakage capacitors, so you can use resistors with high resistivity)