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?
Best Answer
I think, some clarification is necessary:
When A is the open-loop gain of the amplifier (without feedback) and beta is the feedback factor, it is important if the feedback network is connected to the inverting (negative feedback) or the non-inverting input of the opamp.
In most cases (amplification) we have negative feedback and the closed-loop gain is
Gcl=A/(1+A*beta)
However, with respect to the correct sign, it is important to realize that the quantity we call LOOP GAIN includes the negative sign at the summing node, hence
Loop Gain LG=-A*beta
It is important to include the negative sign at the summing node in the loop gain definition because that is the way we are measuring/simulating the loop gain function: We open the loop at a suitable point and measure the total gain (and phase) of the whole loop - of course including the minus sign).
Therefore:
Gcl=A/(1-LG)
Note that Barkhausen`s oscillation condition (there is no "stability criterion" from Barkhausen) requires LG=1 for a circuit to oscillate (unity loop gain with a phase shift of zero deg).
That means: All feedback circuits are stable for LG<1 (examples: pos. feedback with LG=0.5 or negative feedback with LG<0).
I hope this clarifies some points.