How is the cutoff frequency defined in terms of H(jω) magnitude?

How is the cutoff frequency defined in terms of H(jω) magnitude?

• A. The magnitude equals the maximum.
• B. The magnitude equals one-half of the maximum magnitude.
• C. The magnitude equals zero.
• D. The magnitude equals 1/√2 of the maximum magnitude.

Answer: (D)

The cutoff frequency is the point where the magnitude of the frequency response has fallen to 1/√2 of its maximum value. This is the -3 dB point, tied to the fact that power ∝ |H(jω)|^2, so reducing power by half corresponds to reducing the magnitude by 1/√2. If the passband gain is normalized to 1, then the cutoff occurs at |H(jωc)| = 1/√2. The other options don’t match this standard definition: maximum magnitude would mean no attenuation, zero would imply complete attenuation, and half of the maximum does not correspond to the half-power point.

The cutoff frequency is the point where the magnitude of the frequency response has fallen to 1/√2 of its maximum value. This is the -3 dB point, tied to the fact that power ∝ |H(jω)|^2, so reducing power by half corresponds to reducing the magnitude by 1/√2. If the passband gain is normalized to 1, then the cutoff occurs at |H(jωc)| = 1/√2. The other options don’t match this standard definition: maximum magnitude would mean no attenuation, zero would imply complete attenuation, and half of the maximum does not correspond to the half-power point.