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How do I wire the 4 pin to the Arduino correctly?
I think that those drivers are I2C ¿? -
What kind of 5v power do I need to run the logic?
Do you mean to get the arduino working? Just USB power would be ok, or any stabilized 5 V PSU would work. You do not need much power (amps) -
If I get this working I'll be extending it to 20m. What would my current usage look like then?
-That would depend on how many LEDs / drivers you have, and how much current they need to work, but it will be quite a bit. -
Do I need to worry about running too many amps through the 5v? (I'm imagining if one of the strips gets disconnected
through the 5v¿? Nope, you have to worry about the 12 Volts instead, that is where the LEDs/Drivers will get feed. 5 Volts is only for the arduino. Look out, since you are using just 12 volts over a long strip you will get voltaje drops, maybe you want to feed it not from an end, but from some places. -
Do I need a common ground? I'm guessing yes.
Of course, ALWAYS!! Even if you do not need it, always put all the grounds together. -
Do you know the original manufacturer? I'd love to contact them directly and get a sample Arduino app to extend for my use.
Not me.