BlueSails:
What if I can only fit 4 LEDs? Are my calculations correct if I use a 62Ohm resistor then? The online calculator says "power dissipated by resistor=600mW" Is this a lot?
What is Active current limiting and why is it necessary? I'm not sure I'm finding what you mean when searching for it.
Most "normal" trough hole resistors are 1/4 watt (250 mW), and you can even found smaller 1/8 Watt, so you'll need 1 W resistors. They are larger (of course) and a bit more expensive but they are not difficult to get by.
If you can't get the 1 W resistors you can allways use 4 1/4 W in parallel, use an online calculator to calculate the value for each resistor (4 x 270 ohm will do).
You need to limit the current when supplying LEDs or they'll "heat and burn" as they heat they'll let more current trough, as you can guess this will not end well and the leds will burn, so a resistor (or a constant current power supply) is used to make sure that the current supplied is not more than a set limit, wich will be less than the max the LEDs can take.
I would not be very happy wasting 1 W in heat, I'm sure you can find a better topology.
Much can be said about wiring leds in parallel vs series, read a bit about it.
Would it be better to just set this at 6V and then supply both the Arduino and the 4 LEDs in series? I guess no resistors are needed then. The specs say it can handle 3A
Buzzzz, wrong answer. Without current limiting of some kind the LEDs, transistor or the power supply will fail. LEDs look like a near dead short once the Vf is exceeded. That is, the voltage (Vf) stays nearly the same but current shoots up until something gives. Check out the Vf versus If graph in the data sheet.
Would it be better to just set this at 6V and then supply both the Arduino and the 4 LEDs in series? I guess no resistors are needed then. The specs say it can handle 3A
If you can use 6V instead of 12V that would mean less volts to dissipate, so less heat.
But the DC-DC converter (buck converter or step down converter) that you have does not do CC (constant current), so it might not be the best option to power leds, as the same thermal run away can occur. Being able to supply 3 A means that it might hit your LEDs with 3A, that will not be good.
The only way I am aware of lowering a DC voltage is dissipate it as heat, as the resistor and a linear regulator (like the 7805) will do. This wastes the energy that is converted to heat.
There are clever ways of obtaining a lower voltage, the buck converter is one of them, you feed it DC at a higher voltage, it then generates an AC of a lower voltage that is then rectified into a DC of the correct voltage (this is an oversimplification, see Note-1). Not much heat is generated here, and efficiencies can be over 90%. But this does nothing to the current, additional circuitry is needed, that's why a bench power supply is a good idea.
It's best use small resistors close to each LED in order to control the current, look at any PCB you want, near almost any LED there will be a resistor. It is not WRONG to do it by other methods, but the resistor is the easy way.
When having to "shave volts" for powering LEDS, sometimes is best to wire the LEDs in series, as they will drop the voltage (as any diode will do) while supplying light.