What is the operating principle of this single-transistor constant current source?
Here is an equivalent circuit with parts values. Any general purpose transistors can be used. You cannot substitute diodes for the diode-connected transistors and have it behave quite the same way, because of the ideality factor in the Shockley equation. With diodes the current will be lower than typical for the IC with the stated 48K internal resistor. You could also use something like an LED rather than the transistors or diodes. 

Basically the voltage across the two diodes Q2/Q3 is relatively constant with current and is (ignoring the current difference) about one diode drop more than the Vbe drop of Q1 so that voltage appears across R1 (in parallel with an external resistor if desired) and so you get a collector current of about 0.7V/(R1 || Rext). 







simulate this circuit &ndash; Schematic created using CircuitLab

The catch? It's not a very constant current source. It's temperature sensitive (-0.15%/°C, including self-heating) and has relatively poor line regulation (changing the supply voltage from 12V to 24V changes the output current by about 6%. 

A discrete version could be made a bit more stable from self-heating by coupling,say Q2 thermally to Q1 and allowing Q3 to be independent, but it's hardly worth it.