Controlling the power supply of a bluetooth module via GPIO and a transistor
the problem there is that when using a npn bipolar transistor or a N channel mosfet you need to keep the gate or base voltage above the emitter or source voltage, in the case of BJTs, you must also consider that these are current driven devices.

so lets consider the situation at hand, i'll be assuming the bluetooth module input voltage is 3.3, i can't know the voltage drop on R2 since you haven't specified the current the module draws, i will make the assumption that in active mode it draws about 30 mA, and in idle it draws less than 1,

in the active mode case the situation would be as follows

Vbt = 3.7-R2*iR2-VQ1

Vbt = 3.7-36*0.03-0.7

Vbt = 1.92V

so approximately you would get that voltage if the transistor is in the saturation region, most likely it wouldn't be able to drive the module at all

in the case module is idle, i will assume the current is in the order of tens of micro amps, hence the voltage drop across R2 would be negligible, and the voltage on the input pin of the BT module would be around 3v, since the voltage drop of the transistor would still be there, so if my assumptions are correct, the device may work until it starts doing something

a proper solution would be as follows







simulate this circuit &ndash; Schematic created using CircuitLab

this replaces the NPN bjt by a P channel mosfet which doesn't draw current to turn on, in the case of p channel mosfets, they are on when the gate voltage is lower than the drain voltage, hence this arrangement would be active low having the pull up to ensure it's off at boot up