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I'm reading about Gain Margin and Phase Margin in a book and having trouble understanding why they calculate the Phase margin like this:

<G(Wcrossover) - (-180) = PM

Why not: <G(Wcrossover) - (180) = PM

Looking at this Nyquist plot, if you take 180 from the phase of G at the Wcrossover, it gives you the Phase Margin.

Plot

Where Am I mistaken?

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  • $\begingroup$ I think it has to do with sign convention? arg(G) has "more lag" when more+, PM has "less lag" when more+ (?) $\endgroup$
    – Pete W
    Jul 18, 2021 at 20:59
  • $\begingroup$ @PeteW Why the phase of (-1) is -pi and not pi? $\endgroup$
    – siji
    Jul 18, 2021 at 21:15
  • $\begingroup$ @PeteW This is driving me crazy.. they are saying that the gain of -1 is 1, which is correct. But they are also saying that the phase of -1 (which is the stability point) has a phase of -pi, and not pi... any help here? $\endgroup$
    – siji
    Jul 18, 2021 at 21:16
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    $\begingroup$ phase is in angles. in complex plane, rotation by pi is halfway around the circle... equivalent to multiply by -1 ... -pi means lag, +pi means lead. If you have sine wave in time domain, +/- pi is the same, but if e.g. you have a step it's not $\endgroup$
    – Pete W
    Jul 18, 2021 at 21:40

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