Why is a peak in the gain a sign of instability in a closed loop op-amp circuit?

Question

I watched a tutorial video that mentioned that when there is a peak in gain (dB), it is a sign of instability in the op-amp circuit. Is this statement always correct? If yes, can any one please explain why?

Answer 1

1.) A peak in the frequency response for a closed-loop gain is NOT an indication for instability. It rather indicates that the phase margin is smaller than app. 65 deg (for a 2nd order system). This is very often the case for lowpass filters having a Q-factor larger than 0.707 (Chebyshev response).

2.) Instability can be observed when an amplifier shows continuous oscillation (measurement or simulation). However, in case of simulation it is necessary to switch-on the power supplies at t=0 (start of simulation) - otherwise the simulator can find a stable bias point, even in case of positive feedback.

3.) Simulations in the frequency domain (Bode diagram): One should know that the magnitude response does NOT show a behaviour which indicates instability. However, the phase response has a positive slope at frequencies where the magnitude has a negatve slope. This is an unexpected behaviour for a stable amplifier and an indication for instability.

Answer 2

Is this statement always correct?

I apologize for the brief answer, but the answer is no. A peak in gain (dB), it is not always a sign of instability in an Op-Amp circuit.

A system is unstable if it's transfer function has a pole in the right half-plane. The existence of peak in gain does not entail that a system's transfer function has a pole in the right half-plane.

A peak in gain does indicate that the system may take some time to settle after a disturbance. This may be undesirable. But, as a phenomenon, it is distinguished from instability.

Answer 3

TLDR: Not always an indication of instability - a peak might be intended.

However, an internally-compensated op amp is very often used to amplify linearly, where two resistors are chosen to set closed-loop gain. One expects gain to be the same at all frequencies, up to the gain-bandwidth product of the op amp...higher frequencies than this will be amplified less.

^{simulate this circuit – Schematic created using CircuitLab}

output_1 might be flat as expected.
A little capacitance at the op amp's inverting node causes problems, especially when the chosen resistors have large values. The capacitance might be internal, because large opamp input transistors are used.

Capacitance can also be added from layout. output_2 can introduce peaking at a frequency somewhat below the point where gain-bandwidth falls off. This peaking is likely not intended. In extreme cases, peaking can result in oscillation.
One can decrease peaking by choosing lower values of R3/R4, and/or decreasing capacitance at the inverting node.

Answer 4

I did a research and I noticed for having a stable circuit there should be at least 45 degree phase margin. There is a way that we can calculate phase margin form the gain-frequency plot as follows:

So, it shows the higher the gain overshoot, the lower the phase margin, so we can conclude, when there is a peaking in gain, we must check the phase margin to be sure there is at least 45 degree phase margin. For calculating the phase margin, there is a simple way, we can apply a step input to the closed-loop system, then by investigating the output response overshoot, we can define the phase margin as follows:

This shows the higher the overshoot, the lower phase margin there is. So, overshoot is gain-frequency is correlated to the time-domain step response as well. Then, overshoot in gain frequency should be considered as a warning of stability issues.

Reference Texas instrument