More than one gain crossover frequency

[varunag]

Hi

I was plotting the bode plot for $$\frac{1}{s^2 + 1}$$.
I found the following bode plot,
http://home.iitk.ac.in/~varunag/prob2q1-uncomp.jpg"

Here we can see two gain crossover frequencies. Thus two phase margins.
On googling, I found this paragraph in a book:

If there is more than one gain crossover frequency, there is more than one phase margin. For a stable system, the smallest candidate phase margin should be chosen

Which of the phase margins should be considered? and why?

TIA,
varunag

 

[berkeman]

Your plot looks to be unstable -- do you see why? Is the low frequency or high frequency area unstable?

As for the quote, you would chose the smallest phase margin point, because as things change in your circuit (temperature effects, component tolerances, noise, etc.), that is the point where you have the most chance of tending toward zero phase margin, and thus oscillations. Does that make sense?

 

[oswaler]

I would say that both phase margins should be considered and analyzed in order to fully understand the behavior and stability of the system. The phase margin is a measure of the system's stability and indicates how much the phase of the output signal can vary before the system becomes unstable. Therefore, having multiple gain crossover frequencies and phase margins suggests that the system may have complex dynamics and may exhibit different stability characteristics at different frequencies. It is important to study and understand all possible scenarios in order to make informed decisions and ensure the stability of the system. Additionally, the choice of phase margin may also depend on the specific application and requirements of the system. Thus, it is important to carefully analyze and consider all available information before making any conclusions.