I haven’t captured an IR of a synth but the general physics are similar between physical systems, hardware devices, and software chains.
There are 3 main ways to make IRs - which is better depends on the scenario.
- True Impulse - mainly for software, or hardware devices with audio line inputs - Create an audio file with the first sample at maximum value and everything else silent. Play this through your system and record the output. The output file is your IR.
- Realistic impulse - mainly for acoustic spaces or hardware - Make any sort of quick, loud, sound that fills the frequency spectrum as evenly as possible, and recording the resulting echos. Options include noise bursts, starter pistols, hand claps, etc… just be aware that your choice of impulse sound WILL color the output.
- Sine Sweep - mainly for acoustic spaces but it works everywhere - demonstrated here. it’s one of the most clean methods because it avoids most of the physical limitations of your sound source’s ability to produce every frequency at one instant in time.
- bonus: you can do the same deconvolution process with other sources than a sine sweep! However, the sine sweep is still one of the most reliable sources.
If you are going for cleanliness, always lean towards the Sine Sweep - record the dry sweep, then record the sweep through your system, then deconvolve using software. If a fully accurate IR isn’t that important to you, then play around with different techniques and keep the IRs you like. It’s a creative process, after all!
final note - if the feedback loop in question involves some sort of distortion, compression, saturation, or other non-linear process, convolution won’t faithfully recreate the behavior of the system. That doesn’t mean you won’t get an interesting result though!