Carson's rule estimates FM bandwidth as BW ≈ 2(Δf + f_m). What do Δf and f_m represent?

• A. Δf is instantaneous frequency; f_m is minimum modulating frequency.
• B. Δf is peak deviation; f_m is maximum modulating frequency.
• C. Δf is modulation index; f_m is carrier frequency.
• D. Δf is gate modulation; f_m is frequency of messenger.

Answer: (B)

Carson's rule estimates the occupied bandwidth of an FM signal using the peak frequency deviation and the highest frequency in the modulating signal. Here, Δf is the peak frequency deviation—the maximum amount the instantaneous carrier frequency can swing away from the carrier frequency due to modulation. f_m is the maximum (highest) frequency present in the modulating signal. The rule says the approximate bandwidth is BW ≈ 2(Δf + f_m), which accounts for the sidebands created by modulation around the carrier: the deviation spreads the spectrum, and the highest modulating frequency determines how far those sidebands extend. So the terms reflect the largest frequency swing and the fastest variation in the modulating signal, not instantaneous frequency, modulation index, carrier frequency, or any unrelated terms.