Capacitors @ very low frequency ripple current; deriving RMS from transient

[kellogs]

One of the transients I need to withstand takes the shape of an ~200 us spike every 0.5 s. How should I treat this ripple equivalent in my caps ?

1. Treat it like some sort of 5 kHz ripple and somehow account for the rest of these 0.5 s being devoid of any current

2. Calculate an RMS value the usual way and treat it like a 2 Hz ripple current.

3. ?

Second way is quite hard as the sort of MLCC caps I am looking into have their ESR specced at frequencies upwards of 1 kHz. I did derive an ESR value for 2 Hz and it was not good at all with respect to temperature rise.
Naturally I went for film caps - these being ESR-specced from 100 Hz and upwards. They are generally suitable for the kind of current RMS ripple that I need, but they are soooo huge! And a bit expensive. Also there is something bothering me about this approach...

Help please!

 

[crutschow]

Need to know the current capability of the spike, i.e. what is the source impedance of the spike?.
Without that you can't calculate the ripple of the spike in a capacitor.

 

[kellogs]

Source impedance is 10 ohm, but i have added 100 ohm externally. Ran a simulation, done some shape approximations and came up with

\[ sqr(I_{rms}) = 0.000865 \]

Extrapolated an ESR value from the curve at https://ksim3.kemet.com/capacitor-simulation for the R46KN4100JHP1M cap like so:

\[ a = ln(y_2/y_1) /{ ln (x_2/x_1) } = ln (100/400) / ln(700 / 107) ~= -0.74 \]

For 2 Hz:

\[ ESR = 100 mOhm / [(700 Hz/ 350 Hz)^{-0.74}] ~= 7.63 ohm \]

And thus:

\[ P_{rms} = 6.6 mW \]

Which gives a small temperature rise on that polypropylene cap. Does it look about right ?

The MLCC's ESR, extrapolating its curve given by its manufacturer, is just huge at 2Hz - in the kOhm range