Thanks for your reply, I was thinking of using one of these:
POWER SONIC Scantronic 9448 Alarm Panel Battery - New Replacement - 12V 2.1AH
https://www.amazon.co.uk/dp/B071S3J2PX/ref=cm_sw_r_cp_apa_VEaDAb9TFZCJT
The problem with lead-acid batteries is that their output is very poorly controlled. They can easily reach 18V, which will certainly damage your DAC, and you need a special lead-acid charger for them.
Instead, I'd recommend something like this:
https://www.amazon.co.uk/dp/B075QZQSS1
Rather than a single lead-acid cell, this uses 3 lithium-ion batteries. Unfortunately I can't figure out who manufacturers these specific cells, and quality can vary a lot between manufacturers. Blue is not the color for any major manufacturer in 2600 mAh capacity (which these must be given the 78000 mAh spec for the whole unit).
Regardless of the cells, the big issue with this power bank is going to be that it uses a boost converter (a kind of switching power supply) to generate the 12 V output. These are electrically noisy and wouldn't be my first choice for an audio application. Unfortunately that's the only practical way to do what you need to do and from the picture they have of the PCB it seems that their output filtering is decent at least. If the efficiency regulations in the UK are anything like they are in the US, the wall wart that came with the DAC is almost certainly a buck regulator, another (albeit less noisy) type of switching converter. Since it's a DAC and not just an amplifier, I wouldn't expect power supply noise to couple too strongly into the output signal, so hopefully it doesn't cause any audible distortion.
The only thing I would be cautious of with this unit and the DAC is that you don't know if the barrel jack is center positive or center negative. 99% of barrel jack-powered things are center-positive, but check for a symbol like this on the wall wart that came with your DAC:
https://i.stack.imgur.com/zsp7C.png (feel free to send me a picture if you're not sure)
Unfortunately, the output barrel jack on the battery also doesn't show the polarity on the case, so I would check the manual when you receive it for a symbol like that. Alternatively you could pick up a cheap multimeter and check the output on the battery. Something like this would work, it's a piece of junk but you'd only need to use it once:
https://www.amazon.co.uk/ULTRICS®-Digital-Multimeter-Voltmeter-Ammeter/dp/B00TM0W8ZY
This has the advantage of letting you check the output voltage as well as the polarity to ensure you won't damage the DAC. If you decide to do that, shoot me a PM or reply to this thread and I can explain how to take the measurement.
To answer your earlier question, the supply (battery) needs to be able to deliver at least the amount of current (amps) as the load (DAC). If the supply is capable of supplying internal current that's totally fine, it will not be able to "overpower" the load or anything like that. The load self-limits the current being drawn as long as the supply voltage is correct (hence why the lead-acid battery is an issue).
Just so you know, you could expect to get about 1.25 hours out of this battery. I didn't see any mAh spec for the 12V supply, so here is some quick math: 2600 mAh / cell @ 3.6 V / cell (nominal) --> 28 Wh total energy --> 2.34 Ah @ 12 V output --> 1.56 hours @ 1.5 A load --> 1.25 hours @ 80% efficiency
This is approximate, and your lifetime will be greater if the DAC doesn't draw 1.5 A all the time (most likely draws less) and if the conversion efficiency in the battery boost converter is greater than 80% (it may be as high as 85%-90%).
Good luck and let me know how it goes!
