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TPS54331: Risk Assessment: TPS54331 output connected to 3.9V while no voltage input

Part Number: TPS54331

Hi Team,

My customer has a TPS54331 design, it is used to get an output of 3.9V from the input 15V. 

But there is a backup power from the battery, which is also 3.9V, directly connected together to the output of TPS54331. 

In this case, if there's no 15V input to the TPS54331, The battery will provide 3.9V to the loading, as well as the output PIN of the TPS54331. 

Then in this test, they found that the input PIN of the TPS54331 is ~3.5V. 

So here comes the problem:

1. Risk assessment: is it all right to directly give the TPS54331 output PIN with 3.9V while no input voltage? 

2. why there would be 3.5V in the VIN of the TPS54331 when output has 3.9V. The voltage of the input PIN seems coming from the chip internal sourcing from the output 3.9V.