How to provide enough current for the GSM circuit, and still use a LiOn battery

The breakout board clearly has a voltage regulator on it which explains the different voltage requirements.

The module itself wants ~4V. This is designed for use with cellphone batteries which output 2.9V-4.2V depending on their state of charge. It should work fine with any reasonably sized Li battery (tiny ones under 500mAh may not work).

However, you'll need to measure its power consumption in the "on and able to recieve SMS" state. I suspect this will be in the 100mA range based on my experience with similar modules. You'll need to work out exactly which level of "standby" this is for that module.

Achieving 3 months will either require that it's off most of the time (e.g. power up every 3 hours to check for SMS) or a large pack of many Ah.

Edit: look at the BOB schematic. First page has a spx29302 linear regulator from the power jack to regulated 3.8V. This is a convenience to let you power it off anything. The higher the input voltage the more will be wasted in the regulator.

This is all fairly rough but based on your numbers and some past experience:

• 40 mA for the GPS receiver is probably a good figure to use for a start, although for most GPS receivers the maximum current is running at the maximum update rate which looks like 5 Hz for that module. You can probably save some power by setting it for a slower update rate even though you might still want the update rate to be higher than the transmission rate to capture maximum speeds for example.

• You'll probably find the GSM module may spend about five seconds in transmit mode per minute or say 12% of it's time at 200 mA which would give an extra 24 mA on average. Maybe round that up and say the GSM module will take 50 mA. GSM modules are always a little trickier because it can also depend on how many retries are required and the transmit power needed to reach the basestation.

• One problem I see is that page you've linked says while running an Arduino Uno the current is 46.5 mA without a load, the I/O current limit 0f 40 mA isn't related to that so you need to add on that current required by the Arduino itself. But the Nano is simpler and after a quick look at the schematic 20 mA would probably be closer the mark.

So I'd estimate as 40 + 50 + 20 = 115 mA but don't forget to take into account any conversion losses if somewhere along the line you're using a switching converter for the power supply. It's probably better for a prototype to add in say a 50% extra margin and then do some actual testing on current draw. If you don't have much in the way of test equipment just using a battery of a fairly known capacity should give you a good idea.