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In general, what is the best practice (mathematically) to choose an output capacitor for a boost or a buck converter?

In other words, could someone walk me through the design/decision making process for the output cap? I understand you have to consider output voltage ripple, but I'm not sure where everything fits in.

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Choosing the output capacitor for a switch mode converter is not as simple as it may seem.

First, find the amount of capacitance for an acceptable amount of ripple voltage, as this is a key parameter of a system.

The output capacitor is also part of the loop response for all these topologies, though.

Historically, the ESR of the output capacitor was high enough to produce a Zero at the 0dB crossing of the loop gain, adding phase boost, which aids in stability of the control loop in many cases, although in some topologies (boost and buck-boost) it can add a right half plane zero, which can be undesirable, to say the least.

With the advent of really low ESR capacitors (such as ceramic devices), this zero is beyond the loop bandwidth and the designer has to go to some lengths to ensure loop stability if that zero was necessary.

A common way of doing this is to add a capacitor across one of the feedback resistors:

Feedback resistor zero

So - the answer is that provided you realise that the ESR of the output capacitor may require more work in compensating the supply, then you can choose the capacitance you need for ripple performance.

On a related note, some older LDO voltage regulators require a minimum ESR at the output.

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