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I am making a four layer PCB. The top and bottom layers are signals and the internal layers are power and ground layers.

L1 --- Signal
L2 --- Power
L3 --- Ground
L4 --- Signal

I am using Li-ion battery and then using LDO to convert it to 3V. 3V is then powering the whole circuit. Should layer L2 should be connected to the 3V LDO output or Li-ion battery positive output? Both are a positive supply source, so I am unable to decide whether I should connect LDO 3V output or Li-ion output to the L2 power plane.

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I would drop the Li-ion battery onto the board right next to the LDO and then have the LDO output connected to the power plane. This gives the battery power the least ability to interfere with what's happening on your board.

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Since the vast majority of the board’s components are powered by the 3V output of of the LDO, the 3V should be your power plane. If you put the battery voltage on the power plane, you’d need some other way to connect the output of the LDO.

On the other hand, if you had multiple POL (point of load) regulators spread out over the board, then you could use the power plane to connect the inputs to those regulators.

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