# Bode Plot Stability Criteria

Why is -180° taken as a reference or phase margin in Bode plots? If the phase plot (grid impedance and inverter impedance versus frequency) exceeds -180° at the gain crossover frequency, then the system will be unstable in a grid-tied inverter system. So why is -180° taken as a critical point?

• Welcome to engineering.SE! Please refrain from all caps questions (thank you PProteus for the edit).Regarding your question I'm lacking the time (and possibly) understanding to give you a satysfying answer. However have a look at the Nyquist Stability Criterion. I recall that one was able to determine the phase margin from the nyquist plot / criterion. – idkfa Jul 28 '17 at 14:57
• It's not clear to me what you mean by reference or phase margin. Whether or not there is something "special" about -180° depends on your specific application... – PProteus Jul 28 '17 at 15:36
• Are you familiar with the Nyquist stability criterion? – fibonatic Jul 29 '17 at 12:56

In short: using the Nyquist stability criterion it is possible to determine the stability of a closed loop system based on the open loop transfer function. Assuming a system consisting of a plant $P$, a controller $C$ and negative feedback the open loop transfer equals $PC$ while the closed loop transfer equals $(I + PC)^{-1}PC$. The closed loop response blows up (i.e. becomes unstable) as $PC$ approaches $-1$. An open loop transfer $PC$ equal to $-1$ implies a magnitude of $1$ and a phase equal to $-180$ degrees.