What is the phase margin in a Bode plot?

The Bode plot consists of two parts: the magnitude plot (showing the gain in decibels) and the phase plot (showing the phase shift in degrees) of the system as a function of frequency.

At the frequency where the magnitude of the transfer function is 0 dB (unity gain), the corresponding phase angle is denoted as φm (phase margin). The phase margin is defined as the amount of phase shift (in degrees) required to bring the system to the brink of instability, where the magnitude of the transfer function is unity (0 dB). In other words, it is the difference between the phase angle at the crossover frequency and -180 degrees.

A system with a larger phase margin is more stable and robust because it can tolerate more phase shift without becoming unstable. Typically, a phase margin of 45 degrees or more is considered good for most control systems.

If the phase margin is too small or negative, the system may become unstable, leading to oscillations or even instability in the closed-loop system. Therefore, designers use the phase margin as a design parameter to ensure the stability and performance of control systems.

To summarize, the phase margin in a Bode plot measures how far the phase angle is from -180 degrees at the frequency where the magnitude is 0 dB. It is a crucial parameter to assess the stability of control systems and is used in the design and analysis of feedback control systems.