What does a gain crossover frequency indicate in a root locus analysis?

• A. Frequency at which gain is infinite
• B. Frequency at which phase is zero
• C. Frequency at which gain equals unity
• D. Frequency at which poles meet

Answer: (C)

A gain crossover frequency is an important concept in control theory, particularly in the analysis of feedback systems using root locus techniques. This frequency specifically refers to the point in the system's frequency response where the magnitude of the open-loop transfer function equals unity (or 0 dB).

At this frequency, the system's output amplitude matches the input amplitude, which is critical for determining the stability and performance of the control system. Analyzing the gain crossover frequency helps designers assess how the system reacts to various inputs and how sensitive it is to feedback.

In systems under analysis, if the gain crossover frequency is determined, it allows for evaluating the phase margin—providing insights into system stability right at that point. Understanding this frequency helps in tuning controllers to achieve the desired stability and performance characteristics of a system.