Is LTC4413-1/LTC4413-2 Can detect the Input Power Source automatically

SR,

You might consider the LTC4419 PowerPath Prioritizer for your application. It is designed specifically to validate and select power between two supplies. The LTC4419's internal P-channel MOSFETs are 2ohms. You will need to check the acceptable power dissipation for your application. If the power dissipation of the LTC4419's 2ohm MOSFETs is too high, you might consider the LTC4418 PowerPath controller that will control external P-channel MOSFETs. 

Alternatively, if you think the LTC4413-1 is appropriate for your application, refer to Table 2 of the datasheet. By observing that state of the STAT pin while changing the ENA and ENB pins, you may be able to determine the state of your input supplies, but it is more complicated than using an LTC4418 or LTC4419. 

SR,

You might consider the LTC4419 PowerPath Prioritizer for your application. It is designed specifically to validate and select power between two supplies. The LTC4419's internal P-channel MOSFETs are 2ohms. You will need to check the acceptable power dissipation for your application. If the power dissipation of the LTC4419's 2ohm MOSFETs is too high, you might consider the LTC4418 PowerPath controller that will control external P-channel MOSFETs. 

Alternatively, if you think the LTC4413-1 is appropriate for your application, refer to Table 2 of the datasheet. By observing that state of the STAT pin while changing the ENA and ENB pins, you may be able to determine the state of your input supplies, but it is more complicated than using an LTC4418 or LTC4419.