Transfer function from Gain Margin and Phase Margin

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It is not possible to derive the transfer function of a system solely from the open loop gain margin and phase margin, as these metrics are specific to the closed-loop gain condition. Open loop gain margin refers to the stability of the system at a certain frequency, while phase margin indicates the phase difference at the point where loop gain equals 0dB. Both margins provide insights into system stability but do not contain sufficient information to reconstruct the transfer function. Additional data about the system's dynamics is required for a complete analysis. Therefore, without more information, the transfer function cannot be inferred from gain and phase margins alone.
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Would it be possible to get the Transfer Function of a System if Open Loop Gain Margin and Phase Margin are known.
 
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What do you mean by open loop gain margin? I only know about loop gain margin at certain frequency with given the closed loop gain and open loop gain plot. Loop gain is the log subtraction of the open loop gain minus close loop gain at a given frequency. People use that to calculate the error of the closed loop feedback.

Phase margin usually refer the the phase from 180 at the open loop gain line crossing the close loop gain line OR at the point loop gain equal to 0dB.
 
Yungman is right. I would add that the answer is "no". The gain and phase margins are two numbers specified or measured where the closed-loop gain is 1. You cannot deduce or infer the transfer function unless much more is known about the system.
 

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