I have a schottky diode in a sot23 package that is composed by 2 schottky diodes with a common catode connection. I need to use one of them.
Should I let the second floating with unconnected pin or should I connect it to ground?
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If the common is connected to a low-impedance node you can leave it floating. If not, I'd short it out lest it act as an accidental antenna/detector.
I'd also suggest using the single out of the pair that would be present if you bought the one-diode version of the 3-pin package (if possible), just for future compatibility. IOW if you're using the BAT54C or BAT54S, use pins 1 and 3 and either leave 2 open or short it to 3. If you're using the BAT54A you can't do this.
Yes, you can leave the anode of the second diode unconnected.
But, why use a dual diode package in the first place? There are plenty of single Shottky diodes available in small packages. Unless you are using the dual diodes elsewhere in the same design, just use the right part.