which amp to use?

Yeah, for 5W, you need a bit more voltage. Nominally, it would be P = V^2/R, so 4.5V. However, accounting for a maximum modulation index of say, 85%, you need more like 5.3 volts.

If 5W is not the peak power, but rather the average or "rms" power of the driver, than the 5.3V voltage should be multiplied by 1.414, to allow for some headroom in the transients, so about 7.5 volts.

Two Li-ion cells can deliver more than 7.4V so should be fine in both cases. Of course, a bit more voltage headroom is always to account for some small voltage drops here and there. You can see why a lot use two or three cells. However, this does not mean that the driver will sound good at that level.

If you want to remain with one cell, you can look at including a small boost module between the battery and the amp. Remember to use some kind of BMS on the cell!

Regarding the amp, the TDA7297 can be good, but it seems to be of class AB. I would not go with class AB for portable use to increase battery life.

I've had good success with TPA3118 boards. It might be a bit overkill but will work great. Some even come with a bluetooth receiver on the board:
30W+30W TPA3118 Bluetooth Receiver Stereo Digital Power Amplifier Car CA | eBay

Something as simple as a TPA3110 could be sufficient here:
TPA3110 2x15W Digital Audio Stereo Amplifier Module Board DC12-24vM0*es | eBay
 
Also it's a fairly compact little amp.


Rob43
 

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The TPA series is really good, but I've heard some good things for the PAM too.

You should think about including a BMS of some sort. What you mentioned is a charging board (good to have! with thermal protection!), but not a protection system. If the cheap XL6009 board craps out or some loose wire falls in the wrong spot, the cell will be shorted. If you don't have a high quality cell, it may explode or catch fire... Similarly, nothing prevents the battery to overdischarge. This happens easily in this context and then the cell is dead. A one cell mini BMS board is cheap and can be had on amazon, ebay, etc.

If you use a class d board with minimal output filter, like the TPA3110. Try to place the amp as close to the drivers as you can with short twisted wires to reduce differential mode EMI. This is to prevent the RF switching noise from interfering with other things, such as your bluetooth module.
 
They seem to be really close, with discharge curves that are similar under 1-2 amps. This means that, in series there should be no problem. You could verify your battery pack after a few months to check that it is not out of balance. As they are used, I would match their capacity first. So as to not overdischarge/overcharge them.


In parallel, they might work ok with small loads, but then keep in mind that, depending on the point in the discharge curve, they will not share the load equally. Equalize the voltage before connecting!
 
how to check the balance and capacity(in mah or volts)?


Balance is when all cells are at the same voltage. To evaluate capacity, you need to do a charge or discharge test. Either by monitoring by hand or with a smart charger.



A good reference website is batter university. In particular, see:
BU-803a: Cell Matching and Balancing – Battery University


See also,
Serial and Parallel Battery Configurations and Information


In fact, I'd read a few pages on that website if I were you.