Electrical – A question about loop gain, feedback and stability of an op amp circuit

Some comments from my side:

1.) The stability check in the BODE diagram concerns the LOOP GAIN response only (because once you did mention "closed-loop system" in your text.)

2.) The shown system is "conditionally stable". That means: It is stable - regardless the properties at the frequency A. However, if you REDUCE the gain within the loop until the gain crosses the point A (the phase remains unchanged) the closed-loop system will be unstable.

Such conditional stable system should be avoided because a gain reduction can happen due to aging or other damping effects. Remember: Classical feedback systems with a continuos decreasing loop phase will become unstable (under closed-loop conditions) for rising gain values (beyond a certain limit) only.

As to your next question - the input signal Vi does not influence stability properties at all. Stability is determined by the loop components only. That is the reason, we investigate the loop gain only.

EDIT: Here is an explanation why the closed loop (your example) will be stable: If a closed-loop system is unstable, this point of instability also must be "stable". That means - either we will have "stable" and continuous oscillations or the output is latched at one of the supply voltage rails. In both cases, this point of instability is fixed.

Now - what happens at the point A in your example? Here we have a rising phase which is identical to a NEGATIVE group delay at this point (group delay is defined as the negative phase slope). This is an indication for the unability of the closed-loop system to let the amplitudes rise (oscillations or latching at the supply rail). Rather, the system returns to a stable operating point.

A final information: The stability check investigates either (a) the -180deg line or (b) the -360 deg line. This depends on what you are investigating: (a) Either the simple product GH or (b) the loop gain LG which is LG=-GH.

why they tell to roll off the open loop gain

Saying it this way is just a convenience but the practicality is that there will be negative feedback applied that both shapes the amplifier gain to what you want AND corrects for instability.

First of all, familiarize yourself with the important features of the open-loop gain. This is for an OPA192: -

This op-amp is pretty stable when you connect negative feedback and you can see that in the open-loop response because, for instability to occur, the phase angle would have be passing through 0 degrees when the gain was at some positive dB value. Clearly the OPA192 is going to be stable when resistive negative feedback elements are used.

Now let's consider the OPA338 op-amp. The graph below shows the OPA338 (unity gain unstable) and the OPA337 (unity gain stable): -

My question is that why they tell to roll off the open loop gain

If your basic amplifier is unstable, the open-loop gain can be "tweaked" using a combination of both attenuation and feedback components to make an unstable amplifier stable at the gain you require when you eventually apply the required negative feedback.

However, the bottom line is that you might apply feedback components to correct the open-loop response that are barely indistinguishable from the components you apply to give you the desired gain.

It's a little "pretty" and "theoretical" to say you should "roll-off the open loop gain" but it's a useful way look at things. practicality means that the feedback you need for the desired performance merges with other components to prevent instability.