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Is it correct that when selecting an inductor for a buck converter I should be choosing an inductor with the saturation current higher than the converter's peak current?

How much of a margin should it have?

E.g. is it fine to use an inductor with the saturation current of 1.2A for a buck converter IC with the peak inductor current limit of 800mA?

I'm looking at using this buck IC.

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That's right, saturation current should be equal or higher than peak current. Margin depends on the core material. When it saturates, the inductance might drop slowly or rapidly. And at the saturation current, the inductance has already dropped somewhat. If you want to be super conservative, you could select the inductor so that the rated RMS current equals the peak current.

It does sound OK to use inductor with 1.2A saturation current with 800mA peak current.

Having an inductor with larger current ratings usually have smaller resistance, which improves efficiency.

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Select your buck inductor well .The switching regime of the chip gives a peak inductor current of twice the average current .I have switched like this at higher currents and voltages with discrete components and see great EMC benefits compared to fixed frequency hard switch current mode chips that crowd the internet .The switching scheme will give a lower inductance value than the orthodox approach which implies smaller size .Remember that by orthodox I mean inductor current switching off at 133% of DC output current and switching on at 66% of DC load current .This means that your core will run hotter due to ferrite losses.From experience I find the semiconducters are cold and the coil is hot .So use good ferrite from reputable manufacturer and your coil will be cool and your efficiency will be very good.

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