phaseshift

Phase shift is the difference in phase between two periodic signals or between a signal and a reference. For a sinusoidal signal of angular frequency ω, a signal with phase φ can be written as v(t) = V0 sin(ωt + φ). The phase difference between two signals v1(t) = V1 sin(ωt) and v2(t) = V2 sin(ωt + φ) is φ, measured in radians or degrees. If one signal is delayed by τ seconds, the corresponding phase shift is φ = ωτ. Phase shift may vary with frequency, a phenomenon known as dispersion, which causes different frequency components to accumulate different phase shifts.

In optics and electronics, phase shifts arise in different ways. In optics, they result from propagation through media with different refractive indices or from devices such as waveplates that retard one polarization component. In electronic systems, RC, RL, and RLC networks produce phase shifts between input and output; all-pass filters are designed to provide phase shifts across a band with minimal amplitude change. In communications, phase shift keying encodes information by discrete changes in the carrier’s phase, illustrating a practical use of phase shifts in digital modulation.

Phase shifts are central to interferometry and metrology, where path length differences translate into phase differences that produce constructive or destructive interference. In signal processing, phase information is used in demodulation, beamforming, and image reconstruction. The term phase shift can be context-dependent, referring to any phase angle difference in a given domain.