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?