The gain crossover frequency is when:

• A. Phase becomes −180°
• B. Magnitude equals 0 dB
• C. Gain becomes infinite
• D. Phase equals +180°

Answer: (B)

The gain crossover frequency is defined as the frequency at which the magnitude of the open-loop transfer function equals 0 dB. At this point, the system's output is equal to the input when measured in decibels, indicating that the output is neither being amplified nor attenuated. This frequency is crucial for analyzing the stability and performance of control systems.

When evaluating system stability, particularly in feedback systems, identifying the gain crossover frequency allows engineers to assess other important characteristics, such as the phase margin. It is at this frequency that you can start to see how close the system is to instability, as the phase at the gain crossover can then be analyzed to understand how much additional phase lag can be tolerated before oscillation occurs.

The other options, while they relate to frequency response and system behavior, do not describe the gain crossover frequency accurately. The phase becoming -180° is not specific to the gain crossover itself and can happen at different frequencies. Similarly, infinite gain is not a practical or defined scenario in standard system analysis, and +180° phase is not indicative of the gain crossover frequency either. Thus, the correct context for understanding gain crossover is its relation to a 0 dB magnitude.