How it works
An aluminum electrolytic capacitor ages mainly by losing electrolyte, and the rate roughly doubles for every 10 °C. The temperature that matters is the core's: ambient plus the self-heating from ripple current. Life estimates therefore start from the ripple current, convert it into a core temperature rise, and apply the 10-degree rule.
Ripple usually arrives at several frequencies, for example 100 Hz from the line and the switching frequency from a PFC or converter. ESR falls with frequency, so the same current heats the capacitor less at high frequency. Datasheets express this as frequency multipliers F, and Nippon Chemi-Con's technical note converts each component to the reference frequency as I/F and adds them as a root sum of squares.
The core rise can be taken from the rated values, ΔT = (I/I_o)²·ΔT_o, where ΔT_o is the rise at rated ripple for that series, or computed from ESR and the can's surface as ΔT = I²R/(βA). The first is usually more reliable because ΔT_o comes from the manufacturer; the second needs a radiation constant that depends on mounting and airflow.
Chemi-Con gives two life formulas for radial and SMD types: one for series rated at DC voltage only, L_o·2^((T_o − T_x)/10)·2^(−ΔT/5), and one for series rated with ripple superimposed, L_r·2^((T_o − T_x)/10)·2^((ΔT_o − ΔT)/5). Ambients below 40 °C are evaluated at 40 °C, and results over 15 years are treated as 15 years. Film capacitors are simpler: the hot spot is ambient plus R_th·I²·ESR, and voltage is derated above a stated temperature.
Design procedure
- 1Split the capacitor current into its frequency components: line-related ripple and switching ripple. Simulation or the converter calculators on this site give the RMS values.
- 2Enter the frequency multipliers from the series datasheet and the number of capacitors sharing the current.
- 3Enter the rated ripple, ΔT_o, the rated life and the upper category temperature. Check whether the series is rated with ripple superimposed or at DC voltage only.
- 4Set the ambient temperature next to the capacitor, not the room or enclosure average.
- 5Check ΔT against the limit, the core temperature and the life. If the life is short, add capacitors, pick a higher-temperature series or reduce the ambient.
- 6Confirm with the manufacturer's calculator for the exact part, and measure the case temperature in the finished unit.
Formulas
- Ripple at the reference frequency
- I_fo = √Σ (I_fn / F_fn)² (per capacitor, I_fn = I_bank,fn / N)
- Core temperature rise
- ΔT = (I_fo / I_o)²·ΔT_o or ΔT = I_fo²·R / (β·A), A = π·D·(D + 4L)/4, R = tan δ / (2π·f·C)
- Radiation constant (Rubycon approximation)
- β ≈ 2.3·10⁻³·S^(−0.2) W/(°C·cm²), S in cm²
- Life, endurance at rated voltage
- L_x = L_o·2^((T_o − T_x)/10)·2^(−ΔT/5)
- Life, endurance with rated ripple
- L_x = L_r·2^((T_o − T_x)/10)·2^((ΔT_o − ΔT)/5), T_x below 40 °C taken as 40 °C
- Film capacitor hot spot and voltage
- T_hs = T_amb + R_th·I_rms²·ESR, V_allowed linear between (T₁, V₁) and (T₂, V₂)
Worked example
The defaults take the output capacitor of the CCM boost PFC calculator's default design: 5.54 A rms at 90 V, 1 kW and 400 V. Of this, the 100 Hz part is I_o/√2 = 1.77 A (the boost diode delivers power pulsating at twice line frequency), and the remaining 5.25 A is at the 65 kHz switching frequency. The bank is four identical 105 °C radial capacitors with assumed example ratings: 0.9 A rated ripple at 120 Hz, ΔT_o = 5 °C, 10,000 h with rated ripple, and a multiplier of 1.4 at 65 kHz. Each capacitor carries 0.443 A at 100 Hz and 1.31 A at 65 kHz, which is 1.037 A at the reference frequency, 115 % of rating. The core rise is 6.6 °C, within the 15 °C limit at 65 °C ambient, and the life comes out at about 127,600 h, or 14.6 years. At 55 °C the formula gives about 255,000 h, which is capped at 15 years. With only two capacitors, ΔT would be 26.5 °C, well over the limit. In film mode the defaults reproduce KEMET's example: 46 A through 2.4 mΩ with R_th = 5.8 K/W at 40 °C gives a 69.5 °C hot spot. The defaults not listed above are a 100 Hz multiplier of 1.0 against the 120 Hz reference and, for the rated-voltage endurance option, L_o = 10,000 h; the two endurance options keep separate values.
Common mistakes
- Adding RMS currents at different frequencies directly. The heating depends on each frequency's ESR, so the components must be converted with the multipliers first.
- Using the room temperature as T_x. Capacitors next to heatsinks and magnetics run much hotter than the enclosure average.
- Assuming paralleled capacitors share equally. Layout and ESR tolerance make the closest capacitor carry more high-frequency current.
- Quoting formula results beyond 15 years. The seal and other mechanisms limit life regardless of the temperature calculation.
- Applying the radial-type formula to snap-in or screw-terminal capacitors. Their life formula uses different, series-specific factors.
Frequently asked questions
Why convert the ripple to one frequency instead of adding the currents?
Heating depends on I²·ESR, and ESR differs at each frequency. Dividing each component by its multiplier converts it to the current that would cause the same heating at the reference frequency, and the root sum of squares then adds the heating correctly. Adding RMS currents directly would overstate or understate the heat depending on the frequencies.
Which ΔT method should I use?
The rated-ripple method whenever you know ΔT_o for the series, because it is the manufacturer's measured figure. The ESR method is useful when ΔT_o is not published, but the radiation constant depends on mounting, airflow and nearby parts, and the Rubycon approximation refers to the case surface, so the core is hotter than it shows.
Does a lifetime of 30 years mean the capacitor will last 30 years?
No. The Arrhenius-type rule describes electrolyte loss only. The seal ages independently, so Chemi-Con and others treat about 15 years as a practical maximum. The calculator shows the formula result and caps the headline figure at 15 years.
Is there a voltage derating term for electrolytic capacitors?
For radial and SMD types, Chemi-Con's formulas have none: life depends on temperature and ripple. Its formula for snap-in and screw-terminal types includes a voltage factor and other series-specific factors that the manufacturer supplies on request, so it is not included here. Film capacitors are different, and their rated voltage falls with temperature, which the film mode handles.
How were the formulas checked?
With a script: the film hot-spot formula reproduces KEMET's example (69.45 °C against 69.5 °C), and the linear voltage derating reproduces Vishay's example (637.6 V at 91.2 °C against 638 V). For the electrolytic formulas, the ripple-rated form returns exactly L_r at T_o with ΔT = ΔT_o, and the ESR method returns the same ΔT as the ratio method when the ESR is chosen to match ΔT_o.
Results are engineering estimates. Verify your design with datasheets, simulation and measurement.