Minimum Vin for TPS54394

It's a little complicated.  The hard limit is set by the minimum off time.  If the nominal switching frequency is around 650 kHz,  then the max duty cycle is 1 - f*toff = 84.6% and Vin min = 7.092V.  In actuality, the corner is somewhat soft.  As Vin decreases towards that minimum voltage the regulation starts to degrade, maybe 1 or 2 %.  Also, operating at near the maximum duty cycle results in worse transient response to load step changes.  We usually recommend max duty cycle of 65%, so 9.2 V is a good nominal minimum input voltage.  If you can tolerate some lessened regulation and transient response, you can operate at a somewhat lower input voltage.  I don't have actual data for that particular device, but it is generally true for all DCAP2 devices.