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MAX40200 Production
The MAX40200 is an ideal diode current-switch that drops so little voltage that it approaches an order of magnitude better than Schottky diodes. When...
Datasheet
MAX40200 on Analog.com

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Article Will the MAX40200 output be stable with an output capacitance greater than 100uF?

Yes, the MAX40200 will be stable with an output capacitance greater than 100uF.  The output does need at least 0.33uF, but there is no upper limit on the output capacitance. The datasheet lists the spec from 0.33uF to 100uF.  The reason 100uF is listed as the maximum is because of inrush current.  With a large output capacitance, inrush current through the MAX40200 will also increase.  Too much instantaneous current can damage the part.  So, the datasheet spec caps it at 100uF to be safe.