I have a wrong mental model about phase margin in control theory.

I see that a phase of -180° is bad. If my input is a sine wave and I have negative feedback, which has a -180° phase shift, the feedback will become positive --> oscillation.

But why is positive phase margin good? Would a phase shift of +180° degree not be equally bad? I assume the best would be it is 0 every where. But I don't see why +45° is better then -45°.

When I am thinking about this I always try to imagine a sinusoidal signal, since one can not know how the input signal will actually look like. This is the reason I am treating positive and negative phase margins equally.


I just found one big mistake I have made. @Chu also pointed this out. The phase margin is 180° minus the phase at unity gain. Therefor all negativ phase margins mean an actual phase of smaller then -180°

This means my questions is almost obsolete. The actual questions should be now: Is a positive phase margin bigger than 180° bad and possible to achieve?

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    \$\begingroup\$ By definition, phase margin is (180 + phase angle) when the open loop gain is unity (= 0 dB). Positive phase margin thus indicates a stable closed loop. \$\endgroup\$ – Chu Jun 6 '19 at 9:11
  • \$\begingroup\$ I just wanted to post an edit about this :) \$\endgroup\$ – Mr.Sh4nnon Jun 6 '19 at 9:11
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    \$\begingroup\$ A phase margin bigger than +180 degrees can be considered a phase margin less than -180 degrees. Think of a circle. \$\endgroup\$ – Andy aka Jun 6 '19 at 9:36
  • \$\begingroup\$ Okay so it would be equally bad. However a phase margin bigger 180° would mean "looking in the future" wouldn't it? So practically I would not see that kind of problem? \$\endgroup\$ – Mr.Sh4nnon Jun 6 '19 at 9:41
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    \$\begingroup\$ +180 == -180, but since the feedback signal comes with a delay it starts with 0 deg and then the phase difference is increasing (in the negative way), the reaction comes delayed. So a phase angle of +160 deg is more appropriate to say -200 deg. \$\endgroup\$ – Marko Buršič Jun 6 '19 at 11:59

What really matters is what the gain and phase are for a given frequency, phase margin is how much phase is allowed at a given frequency. If the signal is very attenuated (below 0 or something like -80dB, then most of the time it doesn't matter what the phase is).

A better way to look at it would be not to worry about what phase margin is, but how much phase there is at a given frequency. You find the 0dB point, and then look at the phase, if it is lower than -180deg then you have a problem, it will make the system unstable.

Either find the 0dB point or -180deg point then find out how much phase margin you have.

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Source: https://www.sciencedirect.com/topics/engineering/gain-margin

  • \$\begingroup\$ Thank you very much. Your answer and the previus comments made my mistake clear. \$\endgroup\$ – Mr.Sh4nnon Jun 6 '19 at 15:53

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