FM Parameters & Carson Bandwidth Calculator

Frequency modulation encodes the message in the instantaneous frequency of the carrier: a peak deviation Δf proportional to the message amplitude, swinging at the message frequency f_m. The dimensionless ratio between them is the modulation index, β = Δf/f_m — the single parameter that determines the shape of the FM spectrum for a sinusoidal tone (through Bessel functions of argument β).

Unlike AM, an FM signal's spectrum is theoretically infinite — the Bessel series never quite ends. What Carson's rule provides is the practical answer: about 98% of the power lies within B = 2(Δf + f_m) = 2f_m(1 + β). That one-line estimate, published by John Carson in 1922, remains how FM channel bandwidths are allocated: broadcast FM's 75 kHz deviation with a 15 kHz audio bandwidth gives 2(75 + 15) = 180 kHz, matching the 200 kHz channel spacing with guard band.

The index also classifies the system. For β well below 1 (narrowband FM), only the first sideband pair matters and the bandwidth approaches 2f_m, like AM. For large β (wideband FM), bandwidth approaches 2Δf and the system trades that extra bandwidth for its famous noise advantage.

This calculator computes β, the Carson bandwidth, and the approximate count of significant sideband pairs (about β + 1), and plots how the bandwidth grows with deviation so the narrowband-to-wideband transition is visible.