Closed loop gain A' of the above op amp system is given as:
A' = A / (1 + β*A)
where A is the open loop gain which is a positive huge number.
Here as a side note, my understanding is that β being positive means β doesn't cause any phase shift so this causes subtraction hence negative feedback. And I assume β being negative means β causes 180 degrees phase shift and causes positive feedback(subtraction becomes addition at Σ).
But in a text I encounter the following:
Condition for negative feedback: |1 + β*A| > 1
Condition for positive feedback: |1 + β*A| < 1
So if the above conditions are correct,
does that mean that even the β causes 180 degree shift, it is not enough to create positive feedback?
I mean |1 + β*A| can still be greater than 1 even β is negative.
Which one is correct?
1-) β being negative causes 180 degree phase shift so there is positive feedback
2-) Condition for positive feedback: |1 + β*A| < 1 . β being negative alone is not enough for positive feedback salutation.
Here is the text where I encountered these conditions:
Best Answer
I'm sure you'll agree intuitively that positive feedback will increase the gain thus |1 + AB| must be < 1 so that |A/(1+AB)| > |A|. Similarly, we can argue that negative feedback will decrease the gain thus requiring |1 + AB| > 1.
The derivations of these formulas assume the systems are Linear (https://en.wikipedia.org/wiki/Linear_time-invariant_theory).The examples you gave that seem to violate this, are cases where the loop gain is so large linearity is no longer satisfied. For example with B = -10 and A = 10000 you find that the closed loop gain is negative, this doesn't make much sense if the open loop gain is positive and if we consider values of AB between 0 and -1 we find the closer to -1 we are the larger the gain gets, yet it is still positive. Then at -1 the gain goes to infinity. Past this point, we can no longer apply those formulas, hence the contradiction.
For more information see, Positive feedback and unstability