DC pulse and current limiter

[Darlington]

I am studying a constant current limiter so as to keep the current drawn by the LED constant.
Everything works fine with a constant voltage generator, but if I try to see the behavior of the circuit with a pulsed DC voltage the graph shows me positive and negative spikes.
I now assume that the spikes are due to the intervention of transistor Q2.
How can I get a current limiter that is also good for limiting current with a pulsed DC generator?

[Benta]

That circuit is potentially dangerous EMI-wise, it tends to oscillate in the +100 MHz region. There are several threads on this forum about the issue.
A suggestion is that you replace Q1 with two 1N4148s in series, then it will always be stable.
Also, increase R1 to 10 kohms or more.

The spikes may also be related to too small a timestep in the simulation.

This is the circuit I use myself. R2 is crucial, as it prevent the oscillations I mentioned above:

[D2236]

How can I get a current limiter that is also good for limiting current with a pulsed DC generator?

Be careful when doing your simulations. Quite often some of the default values for the pulse source is set to unrealistic values. For instance, look at the values for rise-fall times, and make sure it is not set to something silly like 1 ps. Take note that a good quality function generator used in university labs will have their fastest rise-fall times in the order of 10 ns. Try to evaluate your circuit with this in mind, and you should get better results.

[Darlington]

I tried your circuit and it seems to work well. I followed your suggestions and actually the rise time and fall time were set to 10ps, changed them to more real values like 10ns and they seem to be fine. I also found a constant current settable led driver the PSSI2021SAY by NXP Semiconductors. I tried it in the simulation and it seems to work well even with a pulsed DC generator. Is this simulation reliable?
What leaves me in doubt is that the on/off control and power supply are the same thing, while the datasheet suggests another configuration.
In my case, actually the power supply acts as a control, if no current flows the generator will not work.
What do you guys think?