Carson's Rule FM Bandwidth

Formula

Description

Carson's rule estimates the approximate bandwidth occupied by a frequency-modulated (FM) signal. The bandwidth depends on both the peak frequency deviation (Δf) and the highest modulating frequency (fm). For narrowband FM (Δf << fm), the bandwidth approaches 2×fm (similar to AM). For wideband FM (Δf >> fm), the bandwidth approaches 2×Δf. This rule captures about 98% of the signal power. It is the standard method for estimating FM channel bandwidth in communications system design.

Variables

• BW — Approximate occupied bandwidth (Hz)
• Δf — Peak frequency deviation (Hz)
• f_m — Maximum modulating frequency (Hz)

Practical Notes

Commercial FM radio: Δf = ±75 kHz, fm = 15 kHz, BW = 2(75+15) = 180 kHz, rounded to 200 kHz channel spacing. Narrowband FM (amateur radio, public safety): Δf = ±5 kHz, fm = 3 kHz, BW = 2(5+3) = 16 kHz. The modulation index β = Δf/fm determines the spectral shape: β < 0.5 is narrowband FM, β > 1 is wideband FM.