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Root Locus for Dominant-Pole Compensation

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akbarza

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hi


in Gray& Meyer book ( Analysis_and_Design_of_Analog_Integrated_Circuits_5th ) in section 9.5.3 in paragraph 3 is written:

"Assume that maximum bandwidth in this amplifier is required, but that little or no peaking is allowed. This means that with maximum loop gain applied, the poles should not go beyond the points marked X and Y on the locus where an angle of 45◦ is made between the negative real axis and a line drawn from X or Y to the origin. "
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my question is about 45 degree. i don't know where this value come and how effects peaking and the value off peaking.
anyone can explain where this value come and effect of it on peaking.
i have attached the pic in the book about this subject.

root_locus.PNG

thanks
 

my question is about 45 degree. i don't know where this value come and how effects peaking and the value off peaking.
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The 45-degree value is not a strict threshold, but rather a reference metric to determine from which gain your system will begin to have a much more oscillatory than damped characteristic. The above system is of 2nd order, which is quite explored and there are many figures of merit well known in the technical literature showing the waveform in the time domain for each damping factors. Keep im mind that for the highest imaginary component (y-axis) and the smaller real component (x-axis), there will be a greater predominance of unstably behavior, taking longer to converge to a steady state.
 
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