So I read about Stability/Negative Feedback in amplifiers here https://www.allaboutcircuits.com/technical-articles/negative-feedback-part-4-introduction-to-stability/
I understand that an LTI feedback amplifier has a closed-loop gain of
I also understand that the Loop gain is defined to be AB and that for a loop gain magnitude less than one, there will some oscillations but these will die out as time goes on - thus being stable. Now, that contradicts with the equation up there.
If we set the Loop gain AB < 1 to something like AB = 0.5 and then consider at a 180 degree phase shift, which will mean that $$G_{CL}=\frac{A}{1-(0.5)}=2A$$ Now that suggests to me that for a loop gain magnitude less than 1 (0.5 here) and at a phase shift of 180 degrees, the amplifier should be unstable as the oscillations would build up with a CL gain of 2A? That contradicts the previous intuition I had. How come the equation isn't matching up with what I thought?