Hi,
If your collector current is 1.1A then your minimum base current, assuming a gain of 1000 will be for saturation of the TIP120.
Base Current = Collector Current / Gain.
Base Current = 1.1 / 1000 = 0.0011 Amps
or 1.1mA to saturate or fully turn ON the TIP120.
To make sure the TIP120 is fully saturated, and you have the current capacity of the output of the opto to do it( up to 50mA ), use 10 times the Base Current needed.
So opto output current = 1.1mA * 10 = 11mA.
The volt drops we have in the opto and TIP120 circuit are,
0.5V across the opto when it is ON
2.5V Vbe on the TIP120.
So the volt drop across the base series resistor will be
12 - 0.5 - 2.5 = 9V
So the base resistor has 9V across it and 11mA flowing through it.
R = V / I = 9 / 0.011 = 818 Ohms.
So 820 Ohms will do the trick.
680 Ohms will also be fine.
I would go with the 680 Ohms as the DC gain (1000) is not etched in stone for all TIP120.
I hope I got that right.
Tom... 