Phasorábrázolás

Phasor representation, or phasorábrázolás in Hungarian, is a mathematical technique used to simplify the analysis of sinusoidal signals, particularly in electrical engineering and physics. It converts time-varying sinusoidal quantities, such as voltage and current, into complex numbers called phasors. These phasors represent the amplitude and phase of the sinusoid at a specific frequency.

The core idea is that a sinusoidal function of time, like A cos(ωt + φ), can be represented by a vector in the complex plane. The length of this vector corresponds to the amplitude A, and its angle with respect to the positive real axis represents the phase φ. The angular frequency ω is assumed to be constant for all signals being analyzed.

This representation is particularly useful for operations involving addition, subtraction, differentiation, and integration of sinusoids. Instead of performing complex trigonometric manipulations in the time domain, these operations are transformed into simpler algebraic operations in the phasor domain. For instance, differentiation in the time domain corresponds to multiplication by jω (where j is the imaginary unit) in the phasor domain, and integration corresponds to division by jω.

Phasors are widely applied in circuit analysis to determine steady-state responses to AC sources. They allow engineers to easily calculate impedance, admittance, and power, and to analyze circuits containing resistors, capacitors, and inductors. The phasor method significantly simplifies the understanding and solution of complex AC circuits by converting differential equations into algebraic equations.