Electronic – transistor loop to limit the current

Your basic NPN transistor switch circuit is an inverter, if you put a pull-up resistor (maybe 10k?) between the collector and 5V. (i.e. the resistor replaces the relay in your linked diagram) When you switch on the base of the transistor (put it to 5V), the voltage at the collector goes to ~0V, and when you switch off the base (0V), the voltage at the collector goes to 5V.

So you could stick such a transistor inverter in between the DS2406 and the transistor driving the relay.

I still think you should be able to use the DS2406 with only one transistor though. Perhaps if you had a pull-up resistor (10k) going from the transistor's base to 5V. This keeps the transistor turned on, unless the DS2406 pulls the base down. Also, don't forget to put the current limiting resistor at the front of the base. If you don't have this, the transistor will "get hot and smelly" as you say. ;)

One, that switch does not directly control the motor. It's most likely a few mA at best, as it signals a microcontroller inside the cdrom to open/close the tray.

Two, what you are looking for is simple ohms law. Resistor = (Source Voltage - The Transistor Base/Emitter Drop) / Current Required in Amps. Since the hFE or current multiplication ability of the TIP120 is 1000, so roughly it will allow 1000 times the base current at the collector, any amount of current should be good at the base. Let's just use 5mA. The Base/Emitter drop is 1.25V minimum, as there are two transistor diodes.

Resistor = (5v - 1.25V) / 0.005A or 3.75V / 0.005A = 750Ω or close.

Update To further answer the question, you calculate the base resistor within the safe range of your source (Arduino, 40mA per pin, 200mA total at any given time). The unknown collector current in this case would be minimal for a button. For actual loads like a motor, you could simply max out the transistor by saturating it, giving the base transistor as much current as possible. In this case, you would have to have multiple arduino pins in parallel since the TIP120 base limit is 120mA and the Arduino is 40mA per pin. This is not ideal because you don't know the current at C-E or the amount of voltage it will drop.

The best answer is that you DONT. A proper design will find out how much current will be at the collector. Use a ammeter or multimeter in current mode to find out.