Please let me know if someone I've misinterpreted the datasheet in any way.
Yes, It's like Keith said.
The input voltage has to be greater than the output voltage + the dropout voltage. So if Vout = 3.3V and Vdropout = 1.3V, then the minimum input voltage is 3.3 + 1.3 = 4.6V.
I think the confusion comes from the term "MAXIMUM dropout voltage". Dropout voltage is a property of the chip. If there's less than that amount of voltage between input and output, the chip won't work properly.
So if the maximum dropout voltage is 1.3V, then it's possible that some chips will have a dropout voltage of say 1.1V.
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In other words:
"Maximum dropout voltage" is
not the maximum voltage allowed between input and output.
It's the maximum possible value of the chip's dropout voltage, where the dropout voltage is the
minimum voltage it needs between input and output.
- - - Updated - - -
I have to admit the way it's specified in the datasheet is a bit misleading, but consider this:
If you look at the top of page 5 of the datasheet (page 6 of the PDF), the current limits are specified with Vin - Vout = 5.5V.
Also, the "typical application circuit" at the top of page 1 shows Vin >= 4.75V for Vout = 3.3V.
At the top of page 4 it says "Maximum Input to Output Voltage
(VIN to GND) = 13V". -10 points to whoever wrote that, since it's self contradictory, but you get the idea.