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I am wondering what is the frequency ty value of a capacitor is given for.

For example if you look at the datasheet of the GRM32ER60J107ME20L if you look at the caracteristic on page 2 figure 1 you have Z = 0.2Ohm for f = 120kHz.

Then you have: Z = 1/(2 * PI * F * C)

=> C = 1 / ((2 * PI * F * Z) = 63µF.

The problem is this capacitor is a 100µF capacitor. I understand the value changes with the frequency but what is the frequency for which the value 100µF is right? Is it always the same frequency?

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You assume that the capacitor is "only" a capacitor, unfortunately it is not :-(

Any physical capacitor (one that you can touch) also has series resistance and inductance. So the formula you use for Z is incomplete, Z consists of the sum of 3 impedances: Z = Zc + Zl + Zr

The capacitor value does not change, it is still 100 uF at 120 kHz BUT since the impedance of the capacitor is so low at 120 kHz, the parasitic components namely the series inductor and the series resistor also come into play. These make the impedance at 120 kHz appear higher than you would expect (from an ideal capacitor).

For a quick indication how "good" a capacitor is I look at the green |Z| curve, you see that at low frequencies it goes down in a straight line. This means it behaves like a capacitor at these frequencies. At around 0.1 MHz it starts to deviate from that straight line. Indicating that this particular capacitor is "good" up to around 0.1 MHz.

Up to what frequency a capacitor is "good" depends on many things, it's value, the way it is constructed. What type of capacitor it is. Find a datasheet for a 10 pF capacitor and you will notice that it will still be "good" at a much higher frequency.

Also see this article for an explanation.

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  • \$\begingroup\$ I understand there are parasitic impedances but I already saw in some datasheet that at 120kHz the capacitor is "derated" to be 62µF and not anymore 100µF at 120kHz. I guess if I need to do calculation I need to use 62µF and not 100µF anymore. Then the real value is really 62µF even if it from parasitic inductor and resistor isn't it? \$\endgroup\$ – damien Oct 20 '15 at 14:20
  • \$\begingroup\$ I think it depends on your application if you can safely derate a cap in such a way. If the impedance at 120 kHz is the only thing important then you could probably calculate like this indeed. But if the impedance at other frequencies also matter (for example, in a filter) then I would calculate with the complete impedance or use a better cap so that I would not have to derate it. I would not say that the value IS 62µF at 120 kHz, the cap only has an impedance corresponding to the impedance of a 62µF cap at 120 kHz. \$\endgroup\$ – Bimpelrekkie Oct 20 '15 at 14:29
  • \$\begingroup\$ It was for a compensation loop for a buck DC/DC converter. Then it is only relevant at 120KHz. Thank you for your answer. \$\endgroup\$ – damien Oct 20 '15 at 14:32
  • \$\begingroup\$ My pleasure :-) for DCDC converters the ESR (equivalent series resistance) is very important for loop stability. Indeed this is probably a case where you can indeed derate the cap safely. \$\endgroup\$ – Bimpelrekkie Oct 20 '15 at 14:35
  • \$\begingroup\$ I don't think this is a case of 120 kHz being so high that other parasitics start to affect the value. If you look at the curve at 10 kHz or 1 kHz, where ESL should surely be insignificant, the overall |Z| value is also consistent with about 60 uF capacitance. And the frequency-dependent ESR value is more than a decade below |Z|, so that too is not affecting |Z| much. \$\endgroup\$ – The Photon Oct 20 '15 at 16:36

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