FrequencyModulation

Frequency modulation is a modulation technique in which information is encoded by varying the instantaneous frequency of a carrier wave around a fixed center frequency, while the carrier amplitude remains constant. The instantaneous frequency can be expressed as f_i(t) = f_c + k_f m(t), where f_c is the carrier frequency, m(t) is the modulating signal, and k_f is the frequency sensitivity (Hz per unit of m). The modulation index is often defined as β = Δf / f_m, with Δf representing the peak frequency deviation and f_m the highest frequency in the modulating signal.

Bandwidth in frequency modulation is determined by the deviation and the modulating spectrum. Carson's rule provides a practical estimate: BW ≈ 2(Δf + f_m). Wideband FM uses larger deviations and broader bandwidth, suitable for high-fidelity transmissions, while narrowband FM employs smaller deviations for efficient voice communications.

History and use: Frequency modulation was developed and popularized by Edwin Howard Armstrong in the 1930s, offering improved noise resistance compared with amplitude modulation. It is widely used for FM radio broadcasting in the VHF band, as well as professional communications links, telemetry, and various measurement systems. In audio applications, FM can carry stereo signals and data streams (for example RDS in some implementations).

Demodulation and characteristics: FM demodulation relies on devices that convert frequency variations back into voltage variations, such as discriminators, phase-locked loops, or digital signal processing schemes. A key advantage of FM is its resilience to amplitude nonlinearity and certain noise types, since information is encoded in frequency, not amplitude. A drawback is the greater bandwidth requirement and, for high-fidelity systems, the need for more complex transmitters and receivers.