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FM Modulation

Frequency Modulation - encoding information in signal frequency

80 Hz
5 Hz
5

Message Signal m(t)

Instantaneous Frequency f(t) = f_c + Δf·m(t)

FM Signal s(t) = cos(2πf_c t + β·sin(2πf_m t))

AM Spectrum (for comparison)

FM Spectrum (Bessel function sidebands)

s(t) = A_c cos(2πf_c t + β·sin(2πf_m t)) where β = Δf/f_m

How FM Works

Modulation Index (β): β = Δf/f_m where Δf is the frequency deviation. Higher β = wider bandwidth but more noise immunity.

Bandwidth: Carson's rule: BW ≈ 2(Δf + f_m) = 2f_m(β + 1). FM uses more bandwidth than AM!

Sidebands: FM produces infinite sidebands with amplitudes given by Bessel functions J_n(β).

Constant Envelope: FM signals have constant amplitude - better for nonlinear amplifiers.

Applications: FM radio (88-108 MHz), analog TV audio, two-way radios, satellite communications.