Switching regulator input/output capacitor equations

I recently read an article on Digikey’s website titled ‘Use Low-EMI Switching Regulators to Optimize High-Efficiency Power Designs’.
https://www.digikey.com/en/articles/use-low-emi-switching-regulators-high-efficiency-power-designs

In the article are several equations for determining capacitor values, etc. I was wondering if anyone could point out reference sources for these equations? I am interesting in seeing how these equations are derived and would like to read further into the topic.

Thanks

Greetings,

I’m not sure what sources the contributing author might have referenced, but those equations would ultimately derive from the basic ohm’s law and capacitor equations (V=I*R and Q=C *V) in conjunction with whatever circuit is being referenced.

The general idea is that real capacitors possess some finite amount of ESR, and that current flow through that resistance is additive with whatever voltage is present across the device’s capacitance; this is one source of ripple in switch mode converters, the other discussed in the article being the change in voltage across a capacitance that occurs as a result of applying or withdrawing charge from it.

A third ripple/noise source which does not appear to be mentioned in that piece is series inductance or ESL; change the current flow through an inductance and a voltage appears across it. Such inductance is present as a hidden parasitic component arising from the fact that a capacitor’s leads and the conductors connecting it to a circuit form a loop enclosing some finite area. Because that area is dependent on one’s circuit layout, it’s much tougher to estimate up front.

In terms of study resources, the application sections of many switching regulator datasheets can be a good source of information; they quite naturally address the specific context of a part’s intended use, and as such can avoid confusion that sometimes occurs when a more generalized discussion doesn’t spell out the particular path it took to its destination or mention simplifications or generalizations that it assumes.