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Is it acceptable to have LT3033 constantly running in drop-out mode?


I'm interested in using LT3033 in a circuit I am designing, but my use case is a little unique, so I want to make sure I'm not misusing this part or exceeding any limits.

I have a circuit that can accept voltage between 4.0 and 5.5V (consumes max 1A), and I have a power supply that will output 4.5 - 7V. If I put the LT3033 between the power supply and load circuit, and set Vout to be 5V, is that acceptable? What if the power supply output voltage was always 4.5V? In that case, the LT3033's Vin would be 4.5V, and it would try (and fail) to regulate the output to 5V; it would be around 4.35V instead. That's fine for my voltage, but is it okay to use LT3033 like this in the long-term? 

Bonus question: in the situation above, where LT3033 is set to output 5V and Vin is 4.5V, what happens if there is some reverse current that causes LT3033's Vout to rise to 4.8V (i.e. higher than the input voltage but lower than Vout's set voltage of 5V)?

Thanks in advance for any help.

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