2nd order circuit's bode plot

[BlackMelon]

Hello,

The pictures show the circuit and the gain and phase plot. In the plot, I don't know about the letter phi and the phrase "link the close loop with open loop". Could you give me some advice or link to study further?

Thank you
BlackMelon

 

[LvW]

The plot shows the loop gain (magnitude and phase).
The stability criterion requires to determine the phase difference between the actual loop phase at the "cross-over frequency" (magnitude 0dB) and zero phase. This difference must be positive (for a stable closed-loop) and, hence , is called "phase margin (phi)m".
The open-loop response - and, in particular, the phase margin determine the closed-loop response (magnitude peaking) in the "critical" area (around the cross.over frequency). This magnitude peaking is related to the Q factor (pole quality). This Q factor is defined in the denominator of the last equation .
The angular frequencies wo and w2 can also be derived from the plot.

EDIT: The whole plot is misleading. The same plot was used on page 9 of the contribution for explaining phase and gain margin. That`s OK. And now - the same plot was used in conjunction with given functions for open and closed-loop gains. This is misleading because the shown plot does NOT belong to a simple 2nd order function with real poles only (as given with the function).
So - what is the problem to be solved?

 

[BlackMelon]

The plot shows the loop gain (magnitude and phase).
The stability criterion requires to determine the phase difference between the actual loop phase at the "cross-over frequency" (magnitude 0dB) and zero phase. This difference must be positive (for a stable closed-loop) and, hence , is called "phase margin (phi)m".

According to this:http://www.mathworks.com/help/control/ref/margin.html, the phase margin is measured at the gain cross-over frequency as you said. But it's done by subtracting the phase at that point by -180 degree, not 0 degree. So, did you state it in another point of view? (I mean what you said might be correct but in a different explanation from www.mathworks.com)

 

[BlackMelon]

So - what is the problem to be solved?

I just want to study the app note, DC-DC Converters Feedback and Control, to design a feedback compensation for my forward converter. I have to take phase lag/lead between an AC variation of my output and duty cycle variation into account, because I don't want the converter to act like positive feedback.