# Why do we take gain and phase margin from these points in stability?

In the following graph, why do we take the phase margin from -180 degrees and the gain margin from 0 dB in stability? An inverting amplifier will start to oscillate when the feedback network causes:

1. a gain of 1 (0dB) and
2. with an 180 degree phase shift.

If you get near these two prerequisites for oscillation you'll notice that the amplifier will show first signs of oscillation like overshooting and taking relatively long to dampen to the end value. This is best visible with response to a step or a square wave signal.

By keeping sufficient margin, these effects can be minimized to an acceptable level.

• Note that in a power supply (DC) world (assuming there is a feedback loop), phase margin must be maintained at all frequencies where there is gain >=0dB in the loop. Failure to do that can yield output transients if noise occurs at frequencies where there is no phase margin. This has happened to me on an inherited design which reached the positive output limit (+7%) and then shut down the output switches until the loop was back in regulation. This can be very tricky to fault-find. – Peter Smith Sep 21 '15 at 8:15

In a unity, negative feedback loop, the transfer function is of the form $s \mapsto {g(s) \over 1+g(s)}$. The poles of the system will be the values of $s$ for which $1+g(s) = 0$, or $g(s) = -1$.

In the complex frequency plane, the point $-1$ corresponds to a magnitude of 1 and a phase of 180°, so one measure of how 'close' the system is to being unstable is to see how many degrees the open loop phase is at unity gain, and similarly for the gain margin.

Generally, for such things, I find it more satisfactory to look at a Nyquist diagram rather than Bode plots, albeit you lose the nice frequency parameterization.

Note that despite the nice characterisation by two precise numbers, the measure of stability is qualitative rather than quantitative.