Using an Adafruit Trinket 3.3v with a TIP120?
The TIP120 is a Darlington transistor pair, which consists of two transistors with the Emitter of the first one connected to the Base of the second one. This provides very high current gain, but doubles the required Base bias voltage and increases the Collector saturation voltage.



10mA Base current is plenty enough to 'fully switch' the TIP120, but it has a minimum Collector-Emitter saturation voltage of about 0.75V (rising to 1V at 2A). You will never get the full voltage out of your battery using this transistor.

If you are switching the positive battery lead with an NPN transistor then it has to be wired in Emitter Follower configuration, and the output voltage will be less than the control voltage (3.3V in your case). To get full output voltage you must use a PNP transistor or a P-channel MOSFET, with level shifting to ensure that it is correctly biased. A MOSFET has the advantages of negligible bias current and lower saturation voltage than a typical bipolar transistor.

The level shifting circuit below uses a general purpose NPN transistor to drive either a PNP power transistor or a P-Channel MOSFET. With R1 at 150&ohm; it delivers ~20mA bias current to the PNP transistor. The MOSFET requires no bias current, but its Gate threshold voltage must be 1V or less to fully turn on with 3.7V.







simulate this circuit &ndash; Schematic created using CircuitLab