Carson's Rule for estimating FM bandwidth is BW ≈ 2(Δf + f_m). What do Δf and f_m represent?

• A. Δf is peak frequency deviation; f_m is the highest modulating frequency.
• B. Δf is carrier frequency; f_m is modulation index.
• C. Δf is LO frequency; f_m is IF frequency.
• D. Δf is total bandwidth; f_m is modulation depth.

Answer: (A)

Carson’s Rule estimates how wide an FM signal’s spectrum will be by looking at how far the carrier frequency can swing and how fast the modulating signal changes. The two quantities are: peak frequency deviation, Δf, which is the maximum distance the instantaneous carrier frequency moves from its unmodulated value, and the highest modulating frequency, f_m, which is the highest frequency component in the modulating signal. The rule says the approximate bandwidth is BW ≈ 2(Δf + f_m) because the frequency deviations create upper and lower sidebands around the carrier, extending out by about Δf plus the highest modulation frequency on each side, doubling the total span. For example, if Δf = 5 kHz and f_m = 3 kHz, the approximate bandwidth is 16 kHz. Other options mix up the terms: the carrier frequency or LO/IF frequencies aren’t what set FM bandwidth, and modulation index or total bandwidth aren’t the two parameters in Carson’s formula.