Which plot shows gain and phase margins together?

• A. Bode
• B. Polar
• C. Nichols
• D. Nyquist

Answer: (C)

The Nichols plot is the correct choice because it effectively displays both gain and phase margins on the same graph, allowing for a comprehensive analysis of system stability. In a Nichols plot, the gain (magnitude in decibels) is plotted against the phase (in degrees) for a range of frequencies. The intersections of the gain and phase curves provide clear visual indicators of gain and phase margins, making it easier to assess how close a system is to stability.

Gain margin indicates how much gain can be increased before the system becomes unstable, while phase margin indicates how much additional phase lag can be tolerated. By showing these margins on the same plot, the Nichols plot facilitates a more intuitive understanding of system dynamics and design requirements.

Other plotting methods, such as Bode, Polar, and Nyquist, have their own strengths in displaying specific information about system response and stability, but they typically do not combine gain and phase margins in the way that the Nichols plot does. The Bode plot presents gain and phase on separate graphs, while the Polar plot shows the frequency response in polar coordinates. The Nyquist plot visually represents stability criteria based on encirclements but does not explicitly show gain and phase margins simultaneously.