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TPS562200: Excessive output capacitance

Part Number: TPS562200

We currently use this part to step down a nominal 12V to 5V.

I want to use the same part to step down 12V to 3.9V @ 1A. This is to supply a 4G Wireless modem which peaks at 2A during transmission bursts.

The recommendations from the 4G modem manufacturer is to use lots of bulk capacitance close to the modem to prevent voltage drops.

This means that the TPS562200 will in effect have a lot of capacitance on its output, and I see from the datasheet that this may upset its control loop and affect stability.

Can you advise if this will work, or will it cause a problem? Is there a way around it?

 The 470uF capacitors will be tantalum, TAJD477K006RNJ. They have an ESR of 0.4 Ohm.