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INA169: Any concerns having output saturated at 0V for long periods at a time

Part Number: INA169

Hi currently using the INA169 for current monitoring of our system which as after a relay
we are in works of a new version of the board and I want to add a second one before the relay to measure the current flow of a charger to the battery during charging. I will ensure the positive terminal of the INA is connected to the charger positive rail and  negative terminal of the INA to the positive rail of the battery

I am wondering if there is any concerns with doing this as the currents will be switching directions here and there and saturating the output of the INA at 0V for long periods at a time. 

There is no need for bidirectional sensing at this moment as we want to have the separate INA for measuring current to a specific load after the relay