Hi all,
I want to build a battery powered device with an Uno, a LiIon battery, a charging regulator (TP4056) and a step up converter (MT3608). I want to use the USB connector of the Uno for charging the unit and sometimes for data transmission.
Since you can use the Vin pin and the USB connection at the same time, I have drawn the enclosed schematics: switch in lower position: the battery is charged, using the uno's USB jack for connecting a 5V wall wart. ( I will solder two connection wires to the USB connector).
Switch in upper position: The battery powers the device via the step up converter. I have to set the converter to 6.6 V for getting the Vin to work.
Do you think that I have a fallacy in my thoughts? This link will show my circuit:
https://drive.google.com/file/d/1LKsiaqkpo5FBYJa0Kx1fLOGyespowBvC/view?usp=sharing
Bad idea from the start. A UNO is a particularly inconvenient form factor. A Nano is far more sensible. But.
A 3.7 V LiIon battery is not particularly suitable for a 16 MHZ Arduino such as a UNO or Nano. Boosting it to 5 V with a boost converter is not the best of ideas; you would be better to use an 8 MHz Pro Mini and connect a USB adapter when you need to interface to a PC.
Point is that having the USB interface on the battery powered system wastes power. You probably want to put it to sleep to conserve power when nothing is happening.
Just use the proper "5V" pin if you must do it that way. Disconnect it when using USB to connect to a PC.
Even more ridiculous and confused. 
Don't use "Vin"! 
Maybe it will, but if you want people to see it, post it on the forum here.
Maybe read the instructions? 
Take a look at the Adafruit Feather boards. They are designed to run off Li-Ion batteries and already have the connector. You can either purchase one or look at their schematics and copy it. It's OSHW after all.
I set it up with a Nano, but the TFT display did not work with it. I assume the Nano delivers not enough power. The Uno can deliver up to 150 mA on its 3.3 V pin to the TFT.
The device should be "unexperienced student proof". Plugging and de-plugging an USB converter if needed/not needed ist not desired. And I think the pro mini will fail, too, because of lack of current.
The last point is worth thinking
Same reason as above. There should be nothing to connect/disconnect in different situations. A power switch, a connector for the probe and one USB port for charging or for reading data when used indoors, nothing more.
Why not? I cannot power the microcontroller over USB and +5 at the same time (so it's often told), but I can power it up over USB and Vin at the same time, the Arduino "chooses" the appropriate source. So the idea of using the Vin parallel to the USB as power source. But the voltage regulator of the Arduino needs 6.6 V minimum, therefore the idea of setting the step up converter to 6.6 V.
I would have done that, but the editor of the forum does not show any possibility to attach a file (or I did not find it...).
OK, I did it. Dragging a picture into the text is a little unusual in forum softwares (so far I know). I did so now:
Thank you for the detailed answer!
Ladeschaltung.pdf (10.1 KB)
May be the case. First we have heard of the TFT! 
The Nano does not have an actual 3.3 V regulator as the UNO has, but uses a sort of reference output from whatever USB chip happens to be fitted to a particular clone.
Now you are really asking for the ridiculous! 
Particularly using LiIon batteries.
The Pro Mini has an extreme lack of supply current at 3.3 V. 
Frequently muddled understanding of the consequences of the UNO design. It has nothing to do with powering the UNO or a risk to the UNO itself. There is a notional danger of connecting to a PC or laptop via USB if a capable 5 V power supply is connected to the "5V" pin which may if slightly higher than the USB supply, feed back to it and cause the PC USB subsystem to malfunction. As powered USB hubs routinely connect the external 5 V supply the the USB input it surprises me that this is not a reported problem outside the Arduino environment.
So the TFT displays used 3.3 V or I presume 3.7 direct from the LiPo? And require level converters if connected to 5 V systems. In which case an 8 MHz Pro Mini would be the proper device operating at 3.7 V.
Please understand that a PDF is not a picture and cannot be embedded in a Web page. Use an image format.
So far, it seems your design is entirely backwards. If you are operating a TFT, and it can be driven adequately by a UNO, then the appropriate way do do this is to use an 8 MHz Pro Mini with everything directly connected to the LiPo.
Of course, if there are actually other things you have so far failed to mention, then we are just going to be going round and round in circles.
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