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Does complex conjugate poles lead to gain peaking?

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Chinmaye

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Dear all,
I heard in a lecture that complex conjugate poles lead to peaking. Could someone please explain this to me?
 

It is a simple math. Take any 2nd order polynomial with negative discriminant, i.e. s^2+s+1, replace s with iw and calculate the modulus. Then you will clearly seen nonmonotonicity of function.
 

Peaking is caused due to lesser phase margin or higher Q right? It is a sign of unstability. I didnt understand what does it have to do with complex conjugate poles.
 

Phase margin is a parameter of the open loop characteristic of a feedback system. After you close the loop the sytem will form another transfer characteristic, the closed loop transfer function, which can has complex conjugate poles. See phase margin as a relation between the closed loop transfer function's complex conjugate poles and the open loop characteristic.
Another important thing if the pahse margin is lower than 0° (of the open loop charateristic) the closed loop's complex conjugate poles will appear on the right half plane with positive sign. This is also equivalent with oscillation or unstability.
 
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