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How to relate the loop gain phase margin with a closed loop damping ratio in MFB LPF?

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spbhu

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Hi all expert:
I have a question here: for a standard 2nd order system, the forward gain is: A=ωn²/(s²+2ξωn), the feedback factor:β=1, hence the loop gain Aβ=ωn²/(s²+2ξωn), the phase margin can be calculated as: Φ=2ξ/√√(1+4ξ^4)-2ξ², hence
the phase margin can be related to the damping ratio ξ here!

The problem is : if Multiple feedback topology is used as in a LPF, how can we relate the loop gain phase margin with the closed loop damping ratio ?
Can anybody help me or suggest any paper which have make reserch in this area?
Thanks very much...
 

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