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I want to determine the output droop in a transient load step for a buck converter I am designing.

The output capacitor will supply current during this load step, and there will be a drop associated with the ESR of the cap. Since the ESR of the capacitors is very frequency dependent, what frequency would I assume for this load step? Am I thinking about this correctly, or is there a simpler ESR number I can use?

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    \$\begingroup\$ Choose a decent supplier and they'll specify all you want to know on their website and data sheets. \$\endgroup\$
    – Andy aka
    Commented Mar 28, 2023 at 18:32
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    \$\begingroup\$ How fast is the load step? Therein lies your answer. \$\endgroup\$
    – Tim Williams
    Commented Mar 28, 2023 at 23:24
  • \$\begingroup\$ @TimWilliams Can you elaborate? As an example say the load step is fast, on the order of 1A/nsec \$\endgroup\$
    – MaxwellEE
    Commented Apr 3, 2023 at 19:16
  • \$\begingroup\$ Then you are unfortunately asking an incorrect question: the bandwidth of that step (assuming a quick rise to modest surge currents say 100A peak, as might be expected from mechanical contacts switching a load from a nearby capacitor) exceeds that of the C + ESR model alone. You must include not only ESL but probably higher order elements as well. The present answer gives some hint as to what this means, though the equivalents are fairly low order, not general; in general, consider that any of the R, L or C elements in the series equivalent (D) might have (A) equivalent models, and so on. \$\endgroup\$
    – Tim Williams
    Commented Apr 3, 2023 at 19:22
  • \$\begingroup\$ But, most likely the 1st order (R+L+C) equivalent will still give you close enough to what you want (say, within 20%?), and the parameters will be measured around the series resonant frequency (ESR = Z(Fs), C = left asymptote, L = right asymptote). \$\endgroup\$
    – Tim Williams
    Commented Apr 3, 2023 at 19:23

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Some capacitor manufacturers will give detailed information about their capacitors. However, I have found information from some manufacturers to differ quite a bit from measurements I have performed.

Measuring the characteristics of the capacitor on a swept impedance or network analyzer would be the way to go. Some analyzers can calculate values for various equivalent circuits.

enter image description here
Equivalent circuit selection menu from the HP4194A impedance analyzer manual. The HP4195A also has the same functionality.

Topology D is used for modeling capacitors. With this model, you can use a SPICE simulator and model what happens when you perform a step load change. The frequency of the test signal depends on how fast things calm down. Start with 100 Hz and play around to see what happens.

If the controller has a suitable model, you can model the whole power supply and adjust the compensation components when applying a step load before committing to a PCB. Be sure to examine what happens when there is an increase and decrease in current.

There is no substitute for building up a circuit and measuring what happens.

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