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TPS62810-Q1: Buck is not a proper shutdown when the input voltage is low.

Part Number: TPS62810-Q1

As an input source, I'm using a 4.2V/7800mAh battery and my output voltage is set to 3.3V. I have configured the Buck PFM/PWM mode by connecting MODE/SYNC to the ground through a pull-down R23 resistor.

Everything works fine. My output voltage is 3.3V perfectly, but when the input was below 3.4V (Discharged Battery is 3.4V) the buck was on because of its low input voltage range (Input voltage range: 2.75 V to 6 V), at that time the voltage and current are low. So unable to deliver proper current to the system or unable to shut down properly.

The battery fully charged voltage is 4.2V.
The battery fully discharged voltage is 3.4V.
The buck output voltage is 3.3V/3A.

Q1: How to fully shut down the buck converter at battery discharged voltage?

Could you please help me with this issue?

Here I'm sharing my schematic.

Thanks & Regards,
Smitesh Dhanani