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question about stability (phase margin and etc)

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lawfulgm

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fig1.png
pulse_response.png

Hi all, I have some question regarding the stability of a feedback system.
First figure shows closed loop AC frequency response (green), and feedback loop gain (purple), and feedback phase response (red).
From the first figure, at 710.97 Mhz, the loop phase response is 180' shifted from the starting phase (-180). At this frequency, the loop gain is much larger than 1 (22.7 dB)
However, from the step response, which is attached in the second figure, I am not experiencing any oscillation or instability problem.

It shows large over/undershoot but I think that is due to the low phase margin at 11.4 Ghz (only 28 ' of phase margin)

I understand that Barkhausen's criteria is a necessary condition but not a sufficient condition. However, this circuit has complex poles at higher frequency even when the loop gain is larger than 0dB, and I think it has enough sufficient condition to be oscillating.

If anyone has a good explanation on this phenomenon, please share you knowledge.

Thanks,
 

I think, the loop gain response (purple) has quite a "normal" form - however, with a max. slope of -40dB(dec.
It is somewhat surprising that the corresponding phase response shows a rising characteristic.
This could be an indication for zeros in the right half of the s-plane.
In this case, the BODE diagram must NOT be used for stability analyses.
Instead the complete NYQUIST criterion has to be applied.
 
Thanks for detailed analysis and answer!
but have two questions regarding your comments
Q1: just by looking at the phase response, how could you tell whether the step response may potentially have a ringing or not?

Q2: RHP zeros will create 90' phase lag. Then stability analysis using Bode plot should be sufficient enough... isn't it?
 

nyquist.png
Okay... the figure enclosed here shows that real part of -1 is encircled (Nyquist criterion) and hence it is unstable.
but still the pulse response doesn't show any oscillation/unstable behavior...

Does anyone know why?
 

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