Carson's Rule: If Δf doubles while f_m remains the same, what happens to the FM bandwidth?

• A. BW approximately doubles.
• B. BW remains the same.
• C. BW halves.
• D. BW quadruples.

Answer: (A)

Carson's Rule says FM bandwidth is about BW ≈ 2(Δf + f_m), where Δf is the peak frequency deviation and f_m is the highest modulating frequency. If Δf doubles while f_m stays the same, the new bandwidth is BW' ≈ 2(2Δf + f_m) = 4Δf + 2f_m, compared with the original BW = 2Δf + 2f_m. The increase depends on how large Δf is relative to f_m. When Δf is much larger than f_m (a common case in FM), BW' is about twice BW. If Δf and f_m are comparable, the increase is still substantial but not exactly double (for example, if Δf = f_m, BW' is about 1.5 times BW). So the best answer is that the FM bandwidth increases approximately by a factor of two.