anglemodulaation

Angle modulation, often called angle modulation, is a family of modulation schemes in which the instantaneous phase of a carrier is varied in accordance with a message signal, rather than its amplitude. The two main forms are phase modulation (PM) and frequency modulation (FM). A general representation uses a carrier with angular frequency ωc: s(t) = A cos[ωc t + φ(t)], where φ(t) is the instantaneous modulation phase.

In phase modulation, φ(t) = kp · m(t), where m(t) is the message signal and kp is a constant of proportionality. The instantaneous frequency becomes fi(t) = fc + (kp/2π) · dm/dt, meaning PM responds to the slope of the message. The carrier’s phase varies directly with the message, and the spectrum broadens according to the rate of change of m(t).

In frequency modulation, φ(t) = 2πkf ∫ m(τ) dτ, with kf a frequency sensitivity constant. The instantaneous frequency is fi(t) = fc + kf · m(t). FM modulates the carrier frequency directly, and the phase is the integral of that frequency variation. The amplitude of the carrier is typically kept constant.

Bandwidth and design considerations: Angle-modulated signals generally require wider bandwidth than the unmodulated carrier, with bandwidth increasing with the modulation index. Carson’s rule is a common approximation for the required bandwidth in FM and related schemes: BW ≈ 2(Δf + fm), where Δf is the peak frequency deviation and fm is the highest modulating frequency.

Applications and properties: Angle modulation is widely used in communications for its robustness to amplitude noise and its ability to convey information through phase or frequency changes. PM and FM are used in various radio systems, telemetry, and digital modulation schemes that rely on phase or frequency manipulation. Demodulation typically uses coherent detection methods for PM and FM.