I wanted to light an LED without affecting the input impedance of the device I was measuring without buying a FET. Having the Darlington pair creates the digital-like steep ramp you see below in the simulation results by achieving the product of the current gains (beta) of each of the NPN transistors. The base resistor decreases the base current to a minimum to prevent affecting the load of V2. The green line shows the I-V relationship of voltage source V2 and its current output. You can see a slight change in slope (Ohms) at the output end, but it is negligible considering the purpose.
