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This might be a simple one to answer.

I am using a controller IC (MCP73871) whose load output is connected to an LDO (lm1117Mp3.3). Now according to the datasheet of the MCP73871, I should be adding a capacitor of 4.7uF at the output, while according to lm1117Mp3.3, I need a 10uF capacitor at its input. So is it ok to use both capacitors or just use the one with higher capacity, or it doesn't really matter. Many thanks in advance.

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according to the datasheet of the MCP73871, I should be adding a capacitor of 4.7uF at the output

If you read the data sheet for the MCP73871 on page 17 it says this: -

Bypass to VSS with a minimum of 4.7 μF is recommended.

This means you can add more and more usually is the safer option in most circuits.

I would probably use a 10 uF for the output and another 10 uF for the LM1117's input.

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