Carson's rule for FM bandwidth is given by which expression?

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Multiple Choice

Carson's rule for FM bandwidth is given by which expression?

Carson’s rule estimates FM bandwidth by combining how far the carrier frequency can swing (the peak deviation) with how high the modulating signal goes. The practical bandwidth is about twice the sum of those two quantities: B ≈ 2(Δf + f_m). Here, Δf is the peak frequency deviation and f_m is the highest frequency present in the modulating signal. The reason this works is that FM produces many sidebands on both sides of the carrier, and the outermost significant sidebands extend roughly to ±(Δf + f_m) from the carrier. Doubling that extent accounts for both the upper and lower sides, giving the total bandwidth. This is an approximation that’s widely used in practice. The other expressions miss either the need to include the modulation-frequency content or the fact that energy sits on both sides of the carrier.

Carson’s rule estimates FM bandwidth by combining how far the carrier frequency can swing (the peak deviation) with how high the modulating signal goes. The practical bandwidth is about twice the sum of those two quantities: B ≈ 2(Δf + f_m). Here, Δf is the peak frequency deviation and f_m is the highest frequency present in the modulating signal. The reason this works is that FM produces many sidebands on both sides of the carrier, and the outermost significant sidebands extend roughly to ±(Δf + f_m) from the carrier. Doubling that extent accounts for both the upper and lower sides, giving the total bandwidth. This is an approximation that’s widely used in practice. The other expressions miss either the need to include the modulation-frequency content or the fact that energy sits on both sides of the carrier.

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