That sounds nice, from an academic exercise point of view, but when you're actually trying to build something and a single part (the battery) is the most difficult and undocumented part to find and the most expensive, it makes more sense to start there. If i can find a well documented battery, of any size (within reason), I can make it work. If i design to a specific life with specific current usage, I believe that I will not find a battery suitable.
However, for argument's sake, I'll play ball.
Operational current: 50mA
Standby current: 2mA
Operational Duty Cycle: 20%
Required Life between Charges: 48hrs
Required circuitry voltage: 3-5V
Now that I have that, I can estimate the battery size (ignoring self-discharge and variations in draw at different voltages).
48hrs * (50mA * 20% + 2mA * 90%) = 556.8mAh, but I'm only discharging to 3V, so there will be 0.2V left, but as i understand it they drop off pretty fast after 3V, so say we lose 5% of the battery
556.8 /95% = 586mAh
So, who sells a well documented, self protected, off the shelf battery that is thin and small like a cell phone battery (please don't tell me to design the case and then pick a battery to fit in the arbitrary hole size I chose), and is not overspecified for 586mAh, and will work with my charger circuit?
If anyone can actually answer this question, I will ship you a case of beer. Otherwise, I would like some help finding a battery supplier to design my circuit around.