FMModulation

FM modulation is a method of transmitting information by varying the instantaneous frequency of a carrier wave in proportion to a message signal. The carrier amplitude remains constant, which makes FM robust to amplitude noise and distortion. It is a form of angle modulation and is widely used for high-fidelity audio broadcasting and communications.

Mathematically, with carrier s_c(t) = A_c cos(2π f_c t) and instantaneous frequency f_i(t) = f_c + k_f m(t), the transmitted signal is s(t) = A_c cos(2π f_c t + φ(t)), where φ(t) = 2π k_f ∫ m(τ) dτ. For a sinusoidal modulating signal m(t) = A_m cos(ω_m t), this becomes s(t) = A_c cos(2π f_c t + β sin(ω_m t)) with β = k_f A_m / ω_m, and the general modulation index β = Δf / f_m, where Δf = k_f A_m is the peak frequency deviation and f_m is the modulating frequency.

Bandwidth is typically described by Carson's rule: B ≈ 2(Δf + f_m). Δf is the peak frequency deviation. Wideband FM uses larger Δf, while narrowband FM employs smaller deviation for two-way radio and data services, trading bandwidth for higher spectral efficiency.

Demodulation of FM can be achieved with slope or limiter discriminators, Foster-Seeley or ratio detectors, or phase-locked loop (PLL) receivers; many modern receivers use digital signal processing techniques. FM’s enhanced noise immunity stems from its reliance on frequency, not amplitude, which makes it well suited to broadcast and communications applications.

FM was developed by Edwin Howard Armstrong in the 1930s and has become the standard for high-fidelity broadcasting and various mobile and communication systems.