I am building a portable 3W Mono Bluetooth speaker

I am building a bluetooth speaker, this is my first audio project and I am not sure about some things, can you all help me out?
I want to know how is volume control implemented in an audio amplifier. In various datasheets I have seen that there are only 3-5 options for gain control but speakers usually have more volume levels.
Maye I am confusion volume control with gain control. How is volume control implemented ?
Can you suggest some good amplifier ICs?
 
Welcome to the forum!

The purpose of a gain control is to tune the amplifier's input stage to match the input signal level.

Too much gain leads to distortion while too little gain means the signal get lost in noise, so you should choose a gain setting somewhere between those two extremes.

The control of volume in use is normally the task of a potentiometer (volume pot) which is wired between the signal source and the amplifier.

Is that of any help? If not please come back with more information.
 

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Where are you located in India?
Just find out if medium size FM radio is available, those have Bluetooth.
Just convert to battery, 3 x 18650 cells.
Or find FM radio with 12V input...use battery.
Or use FM module, the remote will control line level.
Use a 12V chip amp like 4440 or similar for output, 5V is also possible, see seller sites for those boards.
Class D is also an option..
 
There is a lot of information on the internet (e.g. videos) and on this forum re building Bluetooth speakers, and I suggest you do some additional research.

Note that bluetooth modules are stereo and it is actually more convenient to build a two speaker stereo system than a mono one.

I would simply buy an all-in-one module similar to the one shown in the attachment. The question of which speakers and enclosure to use would be a personal choice, as would the voltage of the power source.
 

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If you need strictly 3-5Ws and nothing else, I'd suggest the PAM family of chip amps. They tend to be biscuit-sized (no kidding), so would be comfortable in the cramped space of a small BT speaker.
TPA3116 is a good choice, but judging by the power requirements it could be more difficult to implement (as you need greater input voltage).
Thin speakers: I'm sure there are plenty on Aliexpress (Sure Wondom has several models, comes already enclosed and ready to be used, T/S parameters included), or you can recycle speakers from dead/old TV sets.
DAC: Maybe a Qualcomm QCCxxxx board would do?