Sounds like you've found out you don't need to step up the voltage, but just in case anyone else is reading this with the idea of upping the voltage on their battery be extremely careful.
The reversible (reversible in a strictly thermodynamic sense) voltage of a battery is determined by the chemistry of the battery. That's why alkaline batteries are 1.5 V, lead-acid 2.2 V/cell x 6 cells/battery = 13.2 V, and Li-ion batteries 3.4 - 3.7 depending on the specific chemistry used in the cell.
When discharging a cell irreversibly - any real world application necessarily operates irreversibly - the cell voltage will drop as current increases (less power - P= I x V - is available due to parasitic losses like internal resistance and others). When charging a cell irreversibly, the cell voltage will rise (more power is needed to charge the cell faster).
Things get VERY dangerous if you charge or discharge too fast - that is to say at a higher current. If the cell voltage goes negative or too high other reations can occur. For instance, with lead-acid batteries, trying to charge the battery too quickly can cause the negative electrode to start evolving hydrogen gas which could ignite with a spark.
Li-ion batteries have 2 additional problems.
1) depending on the quality of the battery, charging at high currents can cause dendrites (like stalgtites or stalagmites) to grow. If these grow all the way across the cell to the other electrode, it will short the cell giving a giant current density with giant local heating leading to fires and explosions
2) although manufacturers have moved away from LiHClO4 (Li perchlorate) as the electrolyte since it is explosive, there are still problems with thermal runaway (ask Apple and Dell about their experiences)
Remember your high school chemistry demonstration with what happens when Li (or Na or K or Cs or Fr) reacts with air or water. Also, 3.7 V is a HUGE single-cell potential. Hydrogen and oxygen give only 1.2 V - so there's a bigger driving force for reaction with Li-ion batteries than hydrogen gas in air. They are that volatile. In fact the urban legend about static charges from cell phones causing fires at gas stations are much more likely to be due to fires from the cell-phone batteries. Not to mention meth labs that have burned down from Li fires.
That being said, there are many safety mechanisms built into the cell packs to make sure you can't get into too much trouble. Just don't by pass them unless you know exactly what you are doing.
You can step up AC voltage easily with a transformer (with a proportional loss of current). DC voltage can be stepped up with solid-state electronics, but needs a minimum input voltage to operate.
The danger here is that you try to step up the voltage and either draw too much current in order to match the load's current requirement or accidentally allow the higher voltage to drive current through the cell and overcharge the battery. Either situation could result in an explosion.
So be careful and have a dry chemical fire extinguisher handy!
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