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TPS2116: Three possible power supplies

Part Number: TPS2116

Hi,

we need to supply our product from three possible power sources:
- Lead acid battery with solar charging (the output voltage can reach maximally 4.7V when charged).
- Lithium Thionyl Chloride (Li-SOCl2) primary cell (the output voltage is maximally 3.6V).
- 5V from USB if the product is connected to a computer via USB cable.

The intended connection of the two battery types is either/or not both connected at the same time.

The TPS2116 is used in OR-ing mode (MODE pin = External Bias ≤ 0.35V, bottom three rows of the 7.3.1. truth table in the datasheet).

After connecting the USB cable, the V_UNREG should rise to 5V and according to "7.3.4 Reverse Current Blocking", the
TPS2116 should prevent the current flow from VOUT to the connected battery to either VIN1 or VIN2, after tRCB=2us.
During tRCB the current flowing back can be TYP 1.4A, MAX 4A. I am quite sure this current would not harm the lead acid
battery, but not so sure about the Li-SOCl2 primary cell. For this reason I added the D3 diode to pull up the PR1 pin,
which should also put the VOUT pin to Hi-Z. It is only senseful if this mechanism acts faster than the "7.3.4 Reverse Current Blocking".

QUESTION 1: Would the TPS2116 chip function in this above described way?

QUESTION 2: Would the TPS2116 chip block the current flowing into VOUT from the USB when both VIN1 and VIN2 were open circuit?

Thank you in advance.
Peter