Phase margin is defined as what in a feedback system?

• A. The difference between the loop phase at the gain crossover and -180 degrees
• B. The phase difference between input and output signals
• C. The gain margin at the frequency where the phase is -180 degrees
• D. The amount of attenuation in the feedforward path

Answer: (A)

Phase margin measures how much extra phase shift the loop can tolerate before the closed-loop system becomes unstable. It is defined at the gain crossover frequency, which is the frequency where the loop gain magnitude is 1 (0 dB). At that same frequency, you look at how far the loop’s phase is from −180 degrees. The phase margin is the difference between that actual phase and −180 degrees. For example, if the loop phase at the gain crossover is −135 degrees, the phase margin is 45 degrees. If it’s −180 degrees, the margin is zero, meaning the system is on the edge of instability. If it’s more negative than −180, the margin would be negative, indicating instability for that gain. This distinguishes it from the phase difference between input and output signals, and from gain margin (which is measured at the phase crossover frequency where the phase is −180 degrees and indicates how much the gain could be increased before instability). The option describing the difference between the loop phase at the gain crossover and −180 degrees is the correct one.