How do I choose a transistor to operate in active/linear mode?
This isn't an answer yet, but it was too long to put it in the comments, so here we go.

If you want a linear current sink, use Bimpelrekkie's schematic. This needs tuning, it can be a BJT or a FET, but you get the idea.

Your DAC outputs a voltage that the opamp mirrors on the current sense resistor Rs, which creates a constant current sink.

Since your issue is smooth current control over a very wide range of currents, and especially at the low end, the problem you will run into is:


You want a low value sense resistor, as the voltage on it results in wasted heat.
However, the opamp's and DAC's offset voltage (total Vo) are not zero.


With your 12V supply and 11.8V LED, this leaves only 0.2V for the transistor and sense resistor.

With 100mV on the sense resistor, at your current of 4.8A, Rs will be 20 mOhms.

Therefore, 10µV offset in the DAC/AOP chain will result in 500µA current.

I'm sure your LEDs will produce visible light at this current. If the offset is positive, even when setting the DAC at zero, you won't be able to turn the LEDs off.

Also if your supply is 12V +/- 5% then the -5% end of the range is 11.4V so the LEDs won't reach full brightness.

Additionally your RGB LEDs have low Vf, so if you drive them from 12V with a linear (non-switching) current source there will be lots of dissipation (efficiency will be 3.8/12 = 31%, so 69% of the power will be wasted as heat in Rs and the transistor).

So, this needs rethinking &amp; planning, more info about the LEDs, how to arrange them in series/parallel to get the best Vf which gives enough headroom for the transistor+Rs without too much waste.

Also you need to decide between a linear and a switching solution.