Gain crossover frequency is defined as the frequency at which the open-loop magnitude equals 1.

• A. The phase angle equals -180 degrees.
• B. The gain is zero.
• C. The magnitude of the open-loop transfer function is zero.
• D. The magnitude of the open-loop transfer function equals 1.

Answer: (D)

In frequency-response analysis, the gain crossover frequency is the frequency where the loop gain has unit magnitude. In other words, |L(jω)| = 1 (0 dB). This point marks where the loop transitions from amplifying to attenuating as frequency increases, and it’s the key point used to assess stability margins—most notably the phase margin, which is determined from the loop phase at this frequency.

The other statements describe different ideas: the phase being -180 degrees relates to the phase crossover frequency, not the gain crossover. A magnitude of zero would mean there is no loop gain at all, which isn’t a crossing point. And a magnitude being exactly 1 is the defining condition for the gain crossover, not any other magnitude.