Determine an 8-SOIC MOSFET for boosting current capability
Looking at the board pictured and assuming those are dual n-channel chips, it likely works something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

At least, I think this is how it would work? It doesn't really seem suitable for 3A to me...

R1 and R2 form a voltage divider on M1s Gate. R3 is feed back.

The only formula you need for any of this is Ohms Law. The only specs that super matter for your components are obviously voltage, current and power dissipation being within your operating requirements.

There is no reason to copy that design though. It has some drawbacks, like being dependent on the input voltage. If your input voltage changes then so does the current, in fact a small voltage change will result in a large current change. I expect it also gets quite hot.