PhaseModulated

Phasemodulated is an adjective used to describe a signal whose phase of a carrier is varied in time according to a modulating signal. This is a form of angle modulation, alongside amplitude and frequency modulation. In a phasemodulated carrier, the instantaneous phase φ(t) encodes the information, while the instantaneous amplitude remains approximately constant.

A typical mathematical model is s(t) = A cos(2π f_c t + φ(t)), where A is the carrier amplitude, f_c is the carrier frequency, and φ(t) = k_p m(t) for a baseband modulating signal m(t) and modulation index k_p. The instantaneous frequency is f_i(t) = f_c + (1/2π) dφ/dt, so changes in m(t) affect the derivative of φ and thus the observed frequency, although the primary effect is phase variation.

Generation and demodulation: Phasemodulated signals can be produced by directly varying the phase of a carrier with a phase modulator or by IQ modulation methods that impose a phase reference on the carrier. In digital communications, phase modulation underpins many schemes, with discrete phase shifts yielding phase-shift keying such as BPSK and QPSK. Demodulation is typically coherent, requiring a reference carrier and often a phase-locked loop or digital signal processing to recover φ(t) and thus the transmitted data.

Relationship to FM: PM is a type of angle modulation; FM corresponds to modulation of instantaneous frequency. PM can be related to FM by differentiating or integrating the baseband representation of the modulating signal, depending on how m(t) is defined.

Usage and context: The term "phasemodulated" is common in specifications and descriptions of radio links, oscillators, and digital communications to indicate that the carrier’s phase carries the information rather than its amplitude.