How it works
The FM signal s(t) = A_c·cos(ωct + 2πk_f∫m(τ)dτ) where k_f is the frequency sensitivity in Hz/V. For a sinusoidal message, β = k_f·A_m/f_m. The FM spectrum contains a carrier and theoretically infinite sidebands at spacings f_m, with amplitudes given by Bessel functions J_n(β). Carson's rule BW = 2(β + 1)f_m = 2(Δf + f_m) is an approximation containing about 98% of total power. Narrowband FM (β << 1) has bandwidth ≈ 2f_m, similar to AM but with different spectral structure.
Key points to remember
FM noise performance advantage over AM: output SNR of FM is 3β²(β+1) times better than AM for wideband FM, giving significant noise immunity at the cost of bandwidth. Pre-emphasis (boosting high frequencies before transmission with a 75 µs time constant in broadcast FM) and de-emphasis (complementary roll-off at receiver) together reduce high-frequency noise. Capture effect: when two FM signals arrive at a receiver, the stronger one captures the demodulator completely — unlike AM where both are heard simultaneously. Limiter stage in FM receiver removes amplitude variations before the discriminator, rejecting AM noise. Discriminator output noise power spectral density is proportional to f², giving parabolic noise spectrum.
Exam tip
The examiner always asks you to apply Carson's rule to find FM bandwidth for a given Δf and f_m, and then compare to AM bandwidth — state Carson's rule explicitly before substituting values, because the formula derivation earns partial marks.