FM Bandwidth
FM's noise immunity comes at a cost: it consumes more spectrum than AM. How much? Carson's Rule gives engineers a fast, practical answer used worldwide.
FM Uses More Spectrum
An FM signal produces infinite sidebands via Bessel functions — theoretically infinite bandwidth. In practice we count only sidebands with significant power, which leads us to Carson's Rule.
Carson's Rule
Proposed by John Carson in 1922, this rule captures 98% of FM signal power within the stated bandwidth. It is the industry standard for FM planning.
Breaking It Down
- BW — total occupied bandwidth (Hz)
- Δf — maximum frequency deviation
- fm — highest message frequency
- Factor 2 — upper + lower sidebands
In Terms of β
Since β = Δf / fm, Carson's Rule can be rewritten using the modulation index. Higher β means wider bandwidth — but better noise immunity.
Narrowband FM
When β << 1, deviation is small. Carson's Rule simplifies to BW ≈ 2fm — same as AM. Used in walkie-talkies and aviation voice.
Wideband FM
When β >> 1, deviation dominates. Carson's Rule becomes BW ≈ 2Δf. Commercial FM broadcast is wideband: β ≈ 5, delivering superior audio quality.
Commercial FM Radio
Standard FM broadcast: Δf = 75 kHz, fm = 15 kHz.
Channels spaced 200 kHz apart
Guard band = 20 kHz | β = 75/15 = 5
BW Calculator
Bandwidth vs. Noise
Wider FM bandwidth buys noise performance. For tone modulation the output SNR improves as 3β² over AM — both at the same received power, with AM’s SNR taken in its own 2fm channel. Doubling β quadruples it.
FM in the Wild
- FM broadcast: β = 5, BW = 180 kHz
- Aviation voice (NBFM): β < 0.5, BW ≈ 16 kHz
- Land mobile (police/fire): β ≈ 1.5
- Satellite telemetry: narrow FM for efficiency
- TV audio (legacy): β ≈ 2.5
What You Learned
Carson's Rule BW ≈ 2(Δf + fm) captures 98% of FM power. Low β → narrowband. High β → wideband with better noise immunity. Commercial FM: β = 5, 200 kHz channels.