Capacitor Ripple Current - Frequency coefficient

Question

I am designing a motor controller with a 11A max start load and 3A max continuous load. Looking for capacitors I found in this datasheet a "Frequency coefficient for ripple current", what is that and how am I supposed to use this in calculations.

Answer 1

The ESR of an aluminium capacitor is frequency dependent so there needs to be a way of compensating for this in terms of ripple current.

Assuming the temperature rise at different frequencies are the same if R0 is the resistance at f0 (low frequency) and R1 is the resistance at f1 (higher frequency) then

$$ I_0^2 \cdot R_0 = I_1^2 \cdot R_1 $$

$$ I_1 = \sqrt{\frac{R_0}{R_1}} \cdot I_0 $$

the factor

$$ \sqrt{\frac{R_0}{R_1}} $$

is the frequency coefficient for ripple current. In other words it is the factor you would apply to the allowable ripple current (which would heat up the capacitor) over a range of frequencies.