Fasordomein

Fasordomein is a term used in signal processing and electrical engineering to describe the phasor domain, a representation that simplifies the analysis of linear systems under sinusoidal excitation. In Dutch-language texts, fasordomein refers to the use of complex numbers to capture amplitude and phase of steady-state signals, building on Euler’s formula to connect time-domain signals with their complex exponential form.

In the fasordomein, a sinusoidal signal x(t) = X cos(ωt + φ) is represented by a phasor X∠φ (or X e^{jφ}) in the complex plane. Time variation becomes a rotation of the phasor at angular frequency ω, so differentiation corresponds to multiplication by jω and integration to division by jω. Impedances and transfer functions are expressed as algebraic quantities in this domain, with components like ZR = R, ZL = jωL, and ZC = 1/(jωC).

The fasordomein is primarily used for steady-state analysis of linear time-invariant systems, such as AC circuits, filters, and control loops, where all signals share a common frequency ω. It enables straightforward algebraic manipulation to determine relationships between input and output phasors, gain, and phase shift, avoiding differential equations for these conditions.

Limitations include its focus on steady-state sinusoidal behavior; it does not capture transient responses, nonlinearities, or time-varying frequencies. It complements time-domain and Laplace-domain analyses. Conceptually, phasors in the fasordomein correspond to single-frequency components of a broader Fourier representation, with full signal analysis requiring more general transforms.