Capacitor Ripple Current and ESR Calculator
Capacitor Ripple Current and ESR Calculator
What ripple current does to an electrolytic: the power its ESR dissipates, the core temperature that produces, the three parts of the ripple voltage and which of them dominates at your frequency, and the expected life that follows from the Arrhenius ten-degree rule. This is why a capacitor that meets the voltage spec still fails in two years.
Ripple heating, ripple voltage and the life that follows
2.0 A rms of 100 kHz ripple in a 1,000 µF 35 V part with 27 mΩ of ESR, rated 2.23 A and 7,000 h at 105 °C, sitting in 85 °C
Heat on one side, volts on the other
Rth = ΔTrated ÷ (Irated² · ESR)
life = liferated · 2(Trated − Tcore) ÷ 10
|Z| = √( ESR² + (2πfL − 1/(2πfC))² ) Vripple = I · |Z|
f0 = 1 ÷ (2π√(L·C)) and above it the capacitor is an inductor
- ESR
- equivalent series resistance AT YOUR FREQUENCY. It falls with frequency and with temperature, so the figure matters as much as the number
- Rth
- thermal resistance from the element to ambient. A ripple rating is a disguised statement of it: the rated current is the one that produces the rated rise
- ten degrees
- the Arrhenius rule of thumb. Ten degrees cooler, twice the life; ten degrees hotter, half
- ESL
- series inductance. It does nothing at 120 Hz and it is the dominant term above about 50 kHz for a large can
Worked example
2.0 A rms of 100 kHz ripple in a 1,000 µF 35 V part with 27 mΩ of ESR, rated 2.23 A and 7,000 h at 105 °C, sitting in 85 °C
The ESR dissipates 2.0² × 27 mΩ = 108 mW — which sounds like nothing until you see where it has to go
The rating itself gives the thermal resistance: 2.23 A produces a 5 °C rise, so Rth = 5 ÷ (2.23² × 27 mΩ) = 37.2 °C/W
So the core rises 4.02 °C above the 85 °C ambient, to 89.0 °C — 16.0 °C below the rating
Each ten degrees doubles the life, so 7,000 × 2^(16.0 ÷ 10) = 21,188 h, about 2.4 years of continuous running. Drop the ambient to 65 °C and it becomes 84,752 h — the ambient, not the ripple, is what is killing it
The same current makes ripple VOLTAGE three ways: 54 mV across the ESR, 3.183 mV across the capacitance and 18.85 mV across the ESL. They combine in quadrature to 56.23 mV, and the ESR is plainly in charge — this capacitor self-resonates at 41.09 kHz, so at 100 kHz it is already past being a capacitor
Nichicon UHE frequency coefficients for the rated ripple current
| Capacitance | 120 Hz | 1 kHz | 10 kHz | 100 kHz and above |
|---|---|---|---|---|
| 27–330 µF | 0.60 | 0.85 | 0.95 | 1.00 |
| 390–1,000 µF | 0.65 | 0.90 | 0.98 | 1.00 |
| 1,200–18,000 µF | 0.75 | 0.95 | 1.00 | 1.00 |
Where the ripple voltage comes from, for this capacitor
| Frequency | ESR | 1 ÷ 2πfC | 2πfL | Dominant term |
|---|---|---|---|---|
| 120 Hz | 27 mΩ | 1,326.29 mΩ | 0.011 mΩ | capacitance |
| 1 kHz | 27 mΩ | 159.15 mΩ | 0.094 mΩ | capacitance |
| 10 kHz | 27 mΩ | 15.92 mΩ | 0.942 mΩ | ESR |
| 100 kHz | 27 mΩ | 1.59 mΩ | 9.425 mΩ | ESR |
| 1 MHz | 27 mΩ | 0.16 mΩ | 94.248 mΩ | inductance |
The capacitor that met every spec and died anyway
An aluminium electrolytic capacitor is a rolled sandwich of etched foil, paper and a wet electrolyte. Everything good about it — the enormous capacitance per unit volume — comes from that electrolyte, and so does everything that eventually goes wrong. It dries out. The rate at which it dries out is governed by a chemical reaction, so it follows Arrhenius: roughly a doubling of rate for every ten degrees, which is the same thing as a halving of life. A part rated 7,000 hours at 105 °C is rated for 7,000 hours at 105 °C; run it at 65 °C and it will last sixteen times as long, and run it at 95 °C and it will last twice as long. Nothing about the voltage rating enters into this at all, which is why a capacitor that comfortably meets the voltage spec can still be the part that fails first.
Ripple current is how the circuit heats the capacitor from the inside. The ripple flows through the ESR and I²R comes out as heat in the winding, where the electrolyte is. The datasheet’s ripple rating is really a thermal statement: it is the current that produces a defined core temperature rise, usually about 5 °C, at the rated temperature. That makes it useful in a way most people miss — the rating and the rise together give you the thermal resistance, and from there you can compute the rise at whatever ripple you actually have. This page does that by default.
The frequency multiplier trips people up in both directions. A general-purpose series is rated at 120 Hz, and because ESR falls with frequency, the part will take MORE ripple at 100 kHz — the multiplier is above 1. A low-impedance switching series is rated at 100 kHz already, and its multiplier at 120 Hz is BELOW 1. Applying the wrong one gets you a factor of about 1.5 in the wrong direction. Read which base frequency your part’s rating uses before you touch the table.
Ripple voltage is a separate calculation with the same inputs. The current sees three things in series: the ESR, the capacitance and the ESL. At mains ripple frequencies the capacitance dominates and the familiar I ÷ 2πfC is the whole story. Somewhere in the low kilohertz the ESR takes over, and from there more capacitance of the same type buys nothing — the ripple voltage is I × ESR and stays there. Above the part’s self-resonant frequency, which for a big can with 15 nH is only about 40 kHz, the ESL takes over and the capacitor is an inductor. The L·di/dt step at a hard switching edge is a fourth thing again, and it is what you see on a scope as a spike on every transition; no amount of electrolytic fixes it, and a small ceramic with a short loop does.
What this page leaves out: the ESR it uses is a single number, and a real part’s ESR varies with both frequency and temperature — typically halving between 20 °C and 105 °C, which makes the self-heating self-limiting to a degree that this model does not capture. The life prediction is a wear-out model under a steady stress and says nothing about overvoltage, reverse voltage, mechanical stress or a bad batch. And the end of life it predicts is a specification limit — usually a 20% loss of capacitance or a doubling of ESR — not a bang. For what the ripple current actually is in your converter see the buck converter designer and the flyback converter calculator; for the energy stored, the capacitor energy calculator; and for reactance at any frequency the reactance calculator.
Frequently asked questions
How long will an electrolytic capacitor last?
Take its rated life at its rated temperature and double it for every ten degrees the core runs below that rating. A 7,000-hour 105 °C part whose core sits at 65 °C is predicted to last about 112,000 hours — thirteen years. The same part at a 95 °C core lasts 14,000 hours, under two. The core temperature is the ambient plus the rise the ripple current causes.
How much does ripple current shorten a capacitor’s life?
Only through the heat it makes. Work out I²×ESR, multiply by the thermal resistance to get the rise, and add it to the ambient. In a well-ventilated spot that rise is often only two or three degrees and the ambient is doing almost all the damage; next to a heatsink with the ripple at the rating it can be five to ten degrees and both matter.
Why does adding more capacitance not reduce my output ripple?
Because above a few kilohertz the ripple voltage is set by the ESR, not the capacitance: V = I × ESR and C has dropped out. Paralleling identical parts does help, because it divides the ESR as well as the current — but doubling the capacitance of a single part usually does not halve its ESR.
What does the ripple current frequency multiplier mean?
Ripple ratings are quoted at one frequency, and the part will take a different current at another, because its ESR changes. The data sheet gives the multiplier. The trap is the base: general-purpose series are rated at 120 Hz and get a multiplier above 1 at high frequency, while low-impedance switching series are rated at 100 kHz and get one below 1 at low frequency.
Should I use the 120 Hz ESR or the 100 kHz ESR?
The one at the frequency your ripple is actually at. They differ by a factor of five or more: the same 1,000 µF part might be 160 mΩ at 120 Hz and 27 mΩ at 100 kHz. Using the 120 Hz figure for a switching supply overestimates the heating by that factor; using the 100 kHz figure for a mains rectifier underestimates it by the same.
Is the capacitor’s self-resonant frequency worth worrying about?
Yes, and it is lower than most people expect. A large radial can with 15 nH of ESL and 1,000 µF self-resonates around 40 kHz, so at a 100 kHz switching frequency it is already inductive. That is not a disaster — the ESR still dominates its impedance there — but it does mean the electrolytic is doing nothing at all about the fast edges, and something small and ceramic has to.
Related calculators
References
- Nichicon, UHE series catalogue. The default part’s figures: 35 V 1,000 µF in a 12.5 × 25 mm can, 2,230 mA rated ripple at 105 °C and 100 kHz, 27 mΩ impedance at 100 kHz and 20 °C, tan δ 0.12, and the frequency-coefficient table reproduced above (0.65 / 0.90 / 0.98 / 1.00 for 390–1,000 µF at 120 Hz, 1 kHz, 10 kHz and 100 kHz).
- Nichicon, Technical notes on aluminium electrolytic capacitors. The life formula Ln = L₀ · 2^((T₀−Tn)/10) · 2^((Δt₀−Δtn)/K), the statement that “the life doubles for each 10 °C drop in temperature”, and the convention that the core temperature rise at rated ripple is about 5 °C for a 105 °C snap-in part.
- Cornell Dubilier, Aluminum Electrolytic Capacitor Application Guide. ESL of 10–30 nH for radial-leaded parts, 20–50 nH for screw terminals and up to 200 nH for axial, with the note that the winding itself is usually under 2 nH; ΔT = I²·R_s·q_T for the ripple rise; and the recommendation to compute the core temperature as T_A + 1.5·ΔT rather than T_A + ΔT, which is the second option offered here.