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BQ51050B: System supply while charging battery

Part Number: BQ51050B
Other Parts Discussed in Thread: TPS2112A, , TPS63051, BQ51013B

Dear Ti support,

I am currently building a small portable device around an microcontroller and a 1S 500mAh LiPo battery that needs to be wirelessly charged and I have chosen the BQ51050B for this purpose. My implementation is largely based on the application example in the datasheet, however I would like to also be able to supply power (~10 to 100mA) to the system while charging. In previous implementations with simple charging through USB I used a dedicated charge controller and a TPS2112A power mux to automatically switch the system power supply to USB when present, in order to prevent the random system consumption from disturbing the charging algorithm (which would effectively prevent the charger from asserting the "charge done" signal).

My question is : is it possible/recommended to use the RECT pin of the BQ51050B (connected to the same power mux as described above) to supply power to the system while not disturbing the charging process on the VBAT pin?
I am aware of the varying voltage on the VRECT pin during charging, but this shouldn't be a problem for the TPS63051 buck/boost controller that regulates 3.3V for my system.

If not, my other options would be :
- either dropping the power mux, connect the system directly to the battery (VBAT), and setting an appropriately high termination current to take Isys into account, but this sounds hacky
- or dropping the BQ51050 for a BQ51013B or similar, and keeping the power mux and dedicated LiPo charger chip that I'm used to, but this takes more space

Thank you in advance for your time,

Anthony