Gain margin is measured at:

• A. Phase crossover frequency
• B. Zero frequency
• C. Gain crossover frequency
• D. Resonant frequency

Answer: (A)

Gain margin is a critical parameter in control systems and stability analysis, and it is specifically measured at the gain crossover frequency. The gain crossover frequency is defined as the frequency at which the magnitude of the open-loop transfer function equals one (or 0 dB).

At this point, the phase of the system is also taken into account to determine the stability margin. The gain margin itself quantifies how much gain can be increased before the system reaches instability, which is identified by observing the phase at this crossover point. When the phase angle is -180 degrees at the gain crossover frequency, any further increase in gain will lead to instability.

Understanding the significance of the gain margin at the crucial gain crossover frequency helps in designing systems that are robust and stable under different operating conditions. Notably, the other frequencies mentioned like zero frequency, phase crossover frequency, and resonant frequency do not provide the comprehensive insight needed regarding stability and gain margin, which is specifically anchored around the gain crossover frequency.