Phase margin is a concept in control systems that quantifies the stability and robustness of a feedback system. It is an important parameter used in the design and analysis of control systems.

Definition:
Phase margin is defined as the amount of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability. It is usually expressed in degrees.

Explanation:
The gain crossover frequency is the frequency at which the magnitude of the open-loop transfer function is equal to 1 (0 dB). At this frequency, the phase of the transfer function is measured. The phase margin is then calculated as the difference between 180 degrees (or -180 degrees) and the phase at the gain crossover frequency.

Significance:
The phase margin provides a measure of how far the system's phase response is from the critical -180 degrees phase shift required for instability. A larger phase margin indicates a more stable system with a greater ability to tolerate disturbances and variations in the system parameters.

Positive phase margin:
Option B states that the phase margin is always positive for stable feedback systems, which is correct. A positive phase margin indicates that the system is stable. It implies that the system has a sufficient phase reserve, allowing it to respond robustly to disturbances and maintain stability. If the phase margin is zero or negative, it indicates that the system is on the verge of instability.

Calculation:
Option C states that the phase margin is calculated at the gain crossover frequency, which is true. The gain crossover frequency is determined by analyzing the Bode plot of the open-loop transfer function. Once the gain crossover frequency is identified, the phase at that frequency is measured, and the phase margin is calculated as the difference between 180 degrees (or -180 degrees) and the phase at the gain crossover frequency.

Conclusion:
In summary, phase margin is the amount of additional phase lag required to bring a system to the verge of instability. It is always positive for stable feedback systems and is calculated at the gain crossover frequency. The phase margin provides valuable insights into the stability and robustness of a control system, guiding the design and analysis process.