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Well I admit that I did not thoroughly search the forum .
But there are lot’s of answers on how to find phase and gain margin using either mathematical expressions or graphical representations or both.
I am interested in mathematical proof behind all that. How Mr. Bode came up with the expressions for gain margin and phase margin. I imagine there were not based entirely on experimental results, but also on some theorems and lemmas.
You should know that the "Bode stability criterion" is nothing else than a visualization of Nyquist`s criterion using a separation between phase and magnitude response.
From the mathematical viewpoint both are equivalent.
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