I would like to ask you if I can indirectly predict the phase margin (or the op-amp stability) of the op-amp by using sinusoidal signal and running DSP functions like FFT or etc.
I am curious to know the other methods, while recently I use the common two methods from AC analyses or from step response.
AC analysis is (of course I am simplifying) is like writing the circuit equations in frequency domain and solving them to find their frequency response.
You can do a transient analysis with inputs at different frequencies and take the FFT of the output to reconstruct your frequency response. (Make sure to give time for the output to settle). Also don't make your inputs too large as then you will start seeing non-linear effects.
Step or impulse response can give you any "readable" result only.
If you look on Fourier transform of sinusoidal signal transferred through opamp transmittance, you get linear combination of sinusoids, so I doubt that such results would be useful.
Here is paper which overviews known stability Simulation methods:
Ten methods for finding through simulations the small-signal phase and gain margins of feedback circuits based on op-amps are described and analyzed in this mostly tutorial paper. The testbenches employed by these methods are presented and the corresponding analytical expressions of the return...