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A question on Root Locus: why 45 degree is used?

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jeepx5

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A question on Root Locus

In Grey's book the following contant is mentioned
Assuming the maximum bandwidth in this amplifier is required, but that little or no peaking is allowed. This means that with the maximum loop gain applied, the poles should not go beyond the points marked X and Y on the locus where an angle of 45 degree is mad between the negative real axis and a line drawn from X or Y to the origin.
My question is why 45 degree? And how to obtain the 45 degree?
Is the 45 degree is a golden rule for every feed back system?
 

tycheng

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A question on Root Locus

could you describe that question more clearly?
 

jeepx5

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Re: A question on Root Locus

In order to achieve the maximum bandwidth with no peaking, the maximum loop gain is when the poles reaches the cross section between the root locus and the lines who has an 45 degree at the origin with the real axis.
my question is why 45degree?

Added after 5 minutes:

The fig follows
 

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