In locus of amplification factor , what does the 'locus' represent?

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The "locus of amplification factor" refers to the path traced by the poles of a transfer function as the gain varies from zero to infinity. This locus, often represented as a circle, is crucial for analyzing system stability under different gain values. It helps in adjusting system parameters to achieve desired performance characteristics, such as faster transient response or reduced steady-state error. Understanding this locus is essential for effective circuit design and optimization. The discussion emphasizes the importance of the locus in assessing system behavior in response to changes in amplification factor.
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In "locus of amplification factor", what does the 'locus' represent?

I am taking an applied class on complex variables and studying fractional linear transformations. I am given the amplificaton factor for a given circuit and asked to draw the "locus of the amplification factor." I can do this but my question is what exactly does this "locus" (which is a circle) represent? Thanks
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A locus is the movement of the poles of the transfer function as the gain (amplification factor) varies form zero to infinity, this can be used to test the stability of the system with different vales of gain, or it can be used to adjust the system for certain parameters (faster transit response or less steady state error).
 

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