Phase margin formula is:

• A. 180° − φgc
• B. 90° + φpc
• C. 180° + φgc
• D. φgc − 180°

Answer: (C)

The correct expression for phase margin in control systems is derived from the gain and phase relationships of a system at the gain crossover frequency (where the magnitude of the open-loop transfer function is 1, or 0 dB).

Phase margin is defined as the amount of additional phase lag at the gain crossover frequency that would lead the system to become unstable. In other words, it measures how far the system can be pushed before reaching the stability boundary, which is a phase of -180°.

The formula for phase margin is 180° plus the phase angle of the open-loop transfer function at the gain crossover frequency (φgc). Thus, adding φgc indicates how close the actual system’s phase is to passing through -180°, which would indicate potential instability.

Therefore, the correct formula, 180° + φgc, accurately reflects this relationship, allowing for the evaluation of system stability based on its phase response.