# Electrolytic capacitor ESR, ripple current and frequency

Electrolytic capacitor ESR and ripple current ratings vary with frequency and temperature.  In this post I’ll start looking at the effect of frequency. Often, a datasheet will specify the ripple current at a certain frequency (120Hz is common) but you may want to use the part at a different frequency (e.g. the 120Hz part in an SMPS) so you need to know how the ESR and ripple current scale.  I have a hunch that the frequency the capacitor’s datasheet gives for the ripple current is intended to be a clue as to the frequency the component’s designers expect the part to be used at, but I’d like to confirm this.

Cornell Dubilier (CDE) have some excellent documentation, and their Application Guide, Aluminum Electrolytic Capacitors [2] defines ESR as “The equivalent series resistance (ESR) is a single resistance representing all of the ohmic losses of the capacitor and connected in series with the capacitance.” The ripple current is related to the ESR because the power dissipated within the capacitor is the ripple current squared multiplied by the ESR.  The same document gives a short description of the ESR’s relationship with frequency, where $DF_{lf}$ is the low-frequency dissipation factor in percent, and $ESR_{hf}$ is the high-frequency ESR in Ω:

“Like DF, the ESR varies with frequency. Rewriting the DF equation … ESR can be modeled [sic] as below:

$ESR=\dfrac{10000DF_{lf}}{2\pi fC}+ESR_{hf}$

Expressing the ideas in ESR terms, at low frequencies the ESR declines steadily with increasing frequency and crosses over to constant ESR at a frequency inversely proportional to capacitance. This crossover is typically below 10kHz. The ESR of high-capacitance capacitors changes little with increasing frequency because high-capacitance causes them to have low crossover frequencies. The $ESR_{hf}$ ranges from 0.002 for large, screw-terminal capacitors to 10 for miniature devices.”

This statement reflects what CDE publish in their datasheets.  For the Type 350 high frequency capacitors the ripple current is specified at 20kHz, and the following ripple current frequency multipliers are:

 Ripple multipliers at Rated WVDC 60Hz 120Hz 360Hz 1kHz 5kHz 10kHz+ 6.3-20 0.53 0.65 0.73 0.90 0.95 1.0 25 to 35 0.45 0.55 0.65 0.85 0.92 1.0 50 to 75 0.36 0.50 0.60 0.80 0.90 1.0 100 0.29 0.40 0.52 0.75 0.87 1.0

On the other hand, the CDE Type 400C capacitors have their ripple currents specified at 120Hz, with the following ripple current frequency multipliers:

 Ripple multipliers at Rated WVDC 50Hz 60Hz 120Hz 360Hz 1kHz 5kHz+ 100-160 0.80 0.85 1.00 1.05 1.08 1.08 200-350 0.8 0.83 1.00 1.15 1.20 1.20 400-500 0.78 0.80 1.00 1.30 1.40 1.40

CDE give the following warning [2]:

“Rated ripple current can be adjusted for operation at frequencies other than 120 Hz. Multipliers are shown in the specifications. Generally the multipliers are derived based on expected ESR change with frequency; however, … ESR is a complex function of temperature, capacitance and rated voltage as well as frequency. So it is difficult to create ripple-frequency multiplier tables that accurately model the frequency dependence. For high-ripple current applications verify ESR at frequencies of interest and calculate total power dissipated.”

A few other manufacturer’s datasheets were checked to confirm if the CDE multipliers are similar to those given for other brands.

### Duracap

Duracap publish [1] the following ripple current frequency multipliers for their “Extreme Application” range of capacitors:

 Ripple multipliers at Rated WVDC 60Hz 120Hz 400Hz 1kHz 2.5Hz 3 to 50 0.8 1.0 1.05 1.10 1.14 50 to 150 0.8 1.0 1.08 1.13 1.16 150 and up 0.8 1.0 1.15 1.21 1.25

### Panasonic

Here are a few tables from Panasonic, all of which have their ripple current specified at 120Hz:

 Ripple multipliers at Series 50,60Hz 120Hz 1kHz 10kHz+ M Type A 0.7 1.0 1.30 1.70 S Type V 0.7 1.0 1.30 1.70 KS Type A 0.7 1.0 1.30 1.70

The Series M Type A caps are available in voltages from 6.3V to 450V, the Series S Type V caps are available in 4V to 100V and the Series KS Type A caps range from 4V to 50V, but the same multiplies are given. Panasonic don’t break the multiplies into different voltage ranges the way Duracap and CDE do.

### Nichicon

Nichicon are slightly different again.  Here are the multipliers from the HE series datasheet, which are specified for 100kHz.  Again, the HE series was selected at random.

 Ripple multipliers at Capacitance (uF) 50Hz 120Hz 300Hz 1kHz 10kHz+ 0.47 to 33 0.45 0.55 0.7 0.9 1.0 39 to 330 0.6 0.7 0.85 0.95 1.0 390 to 1000 0.65 0.75 0.90 0.98 1.0 1200 to 18000 0.75 0.80 0.95 1.0 1.0

The consensus is that the ESR falls with increasing frequency, resulting in a corresponding increase in maximum ripple current.  The ripple current multipliers vary between manufacturers and between component series, but interestingly the variation of multipliers with rated voltage isn’t consistent, e.g. the multipliers increase with increasing voltage for the CDE types given, by decrease with increasing voltage for the Nichicon HE series.  This deserves a little more investigation.  I haven’t yet found precisely why it is that the ESR falls with increasing frequency; I’ve sent an email to CDE asking for help.

The dissipation factor will be discussed in a future post.