faseforskelle

Phase difference, or faseforskelle in Danish, is the offset between two periodic signals that share the same frequency. It indicates which signal leads or lags the other in time, and is commonly expressed in degrees or radians.

Mathematically, if two sinusoidal signals are written as x1(t) = A1 sin(ωt + φ1) and x2(t) = A2 sin(ωt + φ2), the phase difference is Δφ = φ2 − φ1. A positive Δφ means x2 leads x1, while a negative Δφ means x2 lags behind x1. For signals with the same frequency, this phase difference is constant; for more complex signals, the concept applies to individual frequency components in a Fourier sense.

When the signals have different frequencies, a constant phase difference generally does not exist. In such cases, phase information is defined for each steady-state frequency component and can be summarized using cross-spectral methods, such as the cross-spectrum or the phase spectrum obtained from Fourier analysis.

Measurement methods include using an oscilloscope with two channels to observe the time offset, or constructing Lissajous figures to infer phase difference from the ratio of sine and cosine components. In power systems, phase difference between voltage and current affects real power flow and relates to the power factor, cos(Δφ).

Applications span electrical engineering, signal processing, acoustics, and communications. Understanding phase differences helps in designing filters, synchronization systems, and in assessing interference and signal integrity.