How can this cap have low ESR yet large Dissipation Factor?

[humidbeing]

I'm looking at this Wurth cap part number: 870055673001
It's 10uF, 35V, Aluminum Organic Polymer
ESR is 40 mOhms, DF is 12.

According to Digikey, we calculate ESR from DF using this formula:
ESR = DF / (2 * PI * Test Freq in HZ * Capacitance)

Using that formula, with a 120Hz test Freq, I get 1.6K ohms for the ESR, but the datasheet lists it 40 mOhms. How can that be?

[Kleinstein]

The formular is not telling the whole story. The DF is usually frequency dependent and the ESR only applies to the higher frequency case.
The ESR form is used to decribe the rather high frequency case when the capacitor behaves essentially like a resistor with little effect of the frequency.
The DF is mainly used for the range when the capacitor still acts like a capacitor, but with losses. The ESR calculated from the formular would be frequency dependent.

Usually the DF is << 1 ,  so 12 would be more like 1/DF or maybe 12% as more typical values for electrolytic capacitors.

[bdunham7]

DF = 12 is wrong, it is 12%, so DF = 0.12 and your calculated ESR at 120Hz is ~16R.  The 40mR is at a different test frequency of 100kHz. 

[humidbeing]

DF = 12 is wrong, it is 12%, so DF = 0.12 and your calculated ESR at 120Hz is ~16R.  The 40mR is at a different test frequency of 100kHz.

Whoops. Mouser listed the DF as 12 not as 12%, now that I inspect the full datasheet I see that it's in percentage. Thanks for pointing that out, gang.

So, to check my understanding: A lower DF @ 120Hz means the cap will perform better for low freq ripple?

[Kleinstein]

The DF in the datasheet is about the losses at relatively low frequency, where the capacitor is still behaving like a capacitor. For the capacitor here this could be 120 Hz and maybe 1 kHz.
The usual ESR number is for a high frequency where the capacitor is more or less reduced to the parasitic resistance, like 100 kHz for this size capacitor.

A lower DF would mainly cause less heating of the capacitor. The ripply voltage would still be about the same, just a little phase shift.

The equation to link DF and ESR is questionable - it is a different kind of series resistance the formular uses.