I have a 3V3 rail and want to run an LED with a Vf=3.1V at 10mA with a constant current source. I'm used to circuits like the one below but the problem is that I only have 200mV of overhead and discrete circuits I am familiar with count on the 0.7V Vbe, which would brown out the LED.
Can anyone provide a constant current circuit using cheap discrete parts that can provide 10mA with less than 200mV of overhead? I am familiar with specific LED drivers or circuits that use op amps but they seem like engineering overkill to turn on an LED.