I have a Raspberry Pi model B+ and I've been trying to design a solution so that I can switch power supply without having to shutdown.
The idea is this: I have 2 li-ion 18650 batteries with protection board(DW01+) which disconnects the batteries when they reach a lower threshold of 2.4V and an upper threshold of 4.3V. I want to connect those in parallel to a step-up power converter (mt3608) which will give a steady output of 5V to power the Raspberry Pi.
I also have a charger circuit TP4056 which can supply up to a maximum of 1 Amp that I want to connect to the battery pack. The Pi requires around 0.56 A and 5V with a few peripherals connected but I want to supply extra power for whenever it might need it.
When I have access to an electric outlet I want the battery pack to be disconnected and the Pi powered with a 5V 2.1 Amp DC adapter. I want it to power the Pi and at the same time charge the battery pack and if I disconnect the DC adapter it should switch back to running of the battery pack again without the need to shutdown first. The reason for this is that I want to use the full capacity of the charging circuit to charge the batteries and because I haven't found a suitable charger that can supply a higher current than 1 Amp.
Is it possible to do this with mosfet transistors to switch on and off the inputs? I thought of using a relay to switch between the power supplies but that's too slow and would require a big capacitor as I understand it. Every solution I can think of seems to require a diode but that would lower the voltage below the threshold for what the Raspberry Pi accepts. I should also add that my knowledge of electronics is a bit limited.
Edit: This schematic is far from pretty but maybe it helps to show how I want to connect things. I put two transistors in the schematic but part of the problem is that I don't know where I should connect the gates.
Edit 2: Added clarification about the batteries, the power converter and about my goal.