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I am looking at the datasheet for a relatively ordinary looking aluminum electrolytic capacitor.

I cannot find any place in this datasheet that specifies the ESR of the capacitor. Is it normal for a capacitor datasheet not to specify ESR? Or is there a way I can calculate it from the parameters that are given?

(Note: I understand that ESR is frequency and temperature dependent, so there may not be a single value, but I'm not seeing anything at all about ESR in this datasheet.)

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    \$\begingroup\$ In general, GP capacitors don't list ESR because it's abysmal. Some manufacturers are now listing this resistance as "ripple current at frequency" - clever way to obfuscate it. \$\endgroup\$
    – rdtsc
    Jan 12, 2023 at 18:00
  • \$\begingroup\$ As you can see from the answers there is a wide range of resistances proposed, from 50 Ω to 2 Ω depending on calculation or model. If you really have a requirement I'd recommend to look for other components with given ESR rating. On the other hand there is a good chance that Würth might give a helpful answer if you ask them. \$\endgroup\$
    – datenheim
    Jan 12, 2023 at 20:41

4 Answers 4

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The max dissipation factor is specified at 120Hz, so you can deduce the max ESR (at 120Hz) from that.

Neglecting ESL:

\$DF = \dfrac{ESR}{X_C}\$

At 120Hz:

\$0.18 = \dfrac{ESR}{\dfrac {1}{2 \pi \cdot 120Hz \cdot 4.7 \mu F}} \$

\$ESR = \dfrac{0.18}{2 \pi \cdot 120Hz \cdot 4.7 \mu F} = 638 \mu\Omega\$

Non-general-purpose capacitors often will specify ESR explicitly, since operation of those components tend to be in more electrically 'stressful' applications (high ripple, etc.). For general-purpose caps, you generally ought to be less concerned with ESR - the fact that you are concerned means you may want to rethink the capacitor type choice.

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  • \$\begingroup\$ Oh, Xc is 1/(2 pi F C). \$\endgroup\$ Jan 12, 2023 at 17:43
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    \$\begingroup\$ 0.18 * 2pi * 120 * 4.7u = 0.0006 ohm. not 50 ohms. the formula should be 0.18/(2pi * 120 *4.7u) \$\endgroup\$ Jan 12, 2023 at 20:46
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    \$\begingroup\$ I blame lack of coffee for the blunder. \$\endgroup\$ Jan 13, 2023 at 13:28
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is there a way I can calculate it from the parameters that are given?

I'd go to the Wurth page that this capacitor is on and download the PSpice file for it. If you open the data sheet and click on the bold part number in the bottom right hand corner it will take you to the Wurth web page for the 865090340001 part. Then hit the "7 file" download button and scroll down to the PSP file.

Open the file in a text editor and find the part: -

.subckt ASLU_865090340001_4R7uF 1 2
Rser 1 3 2.00437098761
Lser 2 4 8.90117854E-10
C1 3 4 0.0000047
Rpar 3 4 5333333.33333333
.ends ASLU_865090340001_4R7uF

AS you can see, it is a 0.0000047 farad capacitor with a series resistance of 2.00437098761 Ω, a series inductance of 8.90117854E-10 henries and, a parallel resistance (leakage) of 5333333.33333333 Ω: -

schematic

simulate this circuit – Schematic created using CircuitLab

Node numbers are taken from the PSpice model i.e. Rser 1 3 is between node 1 and node 3 as shown in the schematic.

If you try and use the dissipation factor it will be a series value that represents both losses (parallel and series resistors). I wish more electrolytic capacitor manufacturers provided PSpice facilities like this.

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  • \$\begingroup\$ Hopefully the model is accurate - some suppliers tend to put 'wishful thinking' into their model parameters... \$\endgroup\$ Jan 12, 2023 at 17:43
  • \$\begingroup\$ @AdamLawrence can you justify your comment in this particular case? \$\endgroup\$
    – Andy aka
    Jan 12, 2023 at 18:05
  • \$\begingroup\$ If you set up a SPICE fixture to measure the model's ESR, you'll probably find it underestimates it in the LF range where dielectric loss dominates. (Assuming an ESR plot can be found for comparison, of course.) \$\endgroup\$ Jan 12, 2023 at 18:15
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    \$\begingroup\$ I've been burned before, albeit more with MOSFET and gate drivers. Admittedly not so badly with caps, but enough that I do not explicitly trust a SPICE model parameter unless it correlates with a published figure on a datasheet. \$\endgroup\$ Jan 12, 2023 at 19:30
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As Adam Lawrence answered, you can convert between Dissipation Factor and ESR, but only for the frequency specified.

More and more manufacturers are creating interactive online simulation tools for their parts, Wurth included. If you go to the product page for this part (https://www.we-online.com/en/components/products/WCAP-ASLU#865090340001), and then click the button for this model under the "Simulation" column of the parts table, you will find exactly the information you were looking for, plus more:

enter image description here

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If you require an ESR figure at some frequency, keep shopping to find parts with that rating.

General purpose electrolytics are often rated by dissipation factor only (if that). They aren't a good choice for applications that need low or controlled ESR (and again, as you know, electrolytic ESR isn't very reliable to begin with).

Damping factor or "tan δ" is another way to give the Q factor,

\$D = \dfrac{R_{ESR}}{X_C} = \dfrac{1}{Q}\$

so,

\$R_{ESR} = \dfrac{D}{2 \pi F C}\$

Note that ESR varies with frequency:

ESR vs. Frequency for various types
(From: What are impedance/ ESR frequency characteristics in capacitors? - Murata)

The figure at 120 Hz will probably be near the LF asymptote, where ESR is decreasing with frequency; the minimum value will be much lower than this.

Other options:

Würth has some characteristics available on their REDEXPERT portal (but, they are rather hard to dig through and find actual characteristics, not in relation to some typical application they've pre-cooked data for).

SPICE models (where provided) may provide some clues -- but mind they are often generated for particular frequencies or ranges, so may not be as generally applicable as one would like. (Netlists are also rather hard to read until you have some experience with them..)

Or there's always, buy some and test yourself. But beware, this leaves you at the mercy of manufacturing variation and future updates, so such qualification testing is best employed on an ongoing basis in production. It's fine for one-offs of course.

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