Name: phasors for ac circuit analysis
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 12 s
Channel: JoVE

Les phaseurs sont des représentations complexes des sinusoïdes où l’amplitude du phaseur est égale à l’amplitude et l’angle est égal à la phase mesurée à partir de l’axe des x positifs.
Ils simplifient l’analyse des circuits AC en éliminant la dépendance temporelle du courant et de la tension, transformant ainsi le circuit en sa forme DC équivalente.
Les phaseurs peuvent être représentés sous des formes rectangulaires, polaires ou exponentielles en utilisant l'identité d'Euler.
Pour obtenir le phaseur d’une sinusoïde sous forme sinusoïde, convertissez-la d’abord sous forme cosinus, puis exprimez-la comme la partie réelle du nombre complexe.
Le phaseur de cette sinusoïde est égal à la partie indépendante du temps du nombre complexe.
À l’inverse, la sinusoïde d’un phaseur donné est obtenue en multipliant le phaseur par le facteur temps et en prenant sa partie réelle.
Les phaseurs peuvent être représentés sous forme de vecteurs rotatifs ou de sinus dans le sens inverse des aiguilles d’une montre sur un plan complexe avec une fréquence angulaire constante, et les diagrammes qui les décrivent sont connus sous le nom de diagrammes de phaseurs.
La projection des sinus en rotation sur l’axe réel représente les sinusoïdes.

phaseurs

Les phaseurs sont un outil mathématique puissant utilisé pour analyser les circuits à courant alternatif (AC). Ils fournissent une représentation numérique complexe des sinusoïdes, l'amplitude du phaseur étant égale à l'amplitude de la sinusoïde et l'angle du phaseur représentant la phase mesurée à partir de l'axe des x positif. L'un des avantages majeurs de l'utilisation des phaseurs est qu'ils simplifient l'analyse des circuits alternatifs en éliminant la dépendance temporelle du courant et de la tension. Cette transformation permet d'analyser un circuit CA comme s'il s'agissait de sa forme équivalente en courant continu (CC), ce qui rend les calculs plus simples. Les phaseurs peuvent être représentés sous différentes formes - rectangulaires, polaires ou exponentielles - en utilisant l'identité d'Euler, une formule fondamentale dans l'analyse complexe qui établit une relation profonde entre les fonctions trigonométriques et exponentielles. Pour obtenir le phaseur d'une sinusoïde sous forme sinusoïdale, il faut d'abord le convertir en forme cosinus, puis l'exprimer comme la partie réelle d'un nombre complexe. Le phaseur de cette sinusoïde est égal à la partie indépendante du temps de ce nombre complexe. A l’inverse, la sinusoïde d’un phaseur donné peut être obtenue en multipliant le phaseur par un facteur temps et en prenant sa partie réelle. Dans un contexte graphique, les phaseurs peuvent être visualisés comme des vecteurs en rotation, ou « sinors », tournant dans le sens inverse des aiguilles d'une montre sur un plan complexe avec une fréquence angulaire constante. Les diagrammes qui représentent ces sinors en rotation sont appelés diagrammes de phaseurs. Un concept clé pour comprendre le diagramme de phaseur est que la projection des sinors en rotation sur l'axe réel représente les sinusoïdes. Cela signifie que la position horizontale du sinor à tout moment correspond à la valeur instantanée de la fonction sinusoïdale qu'il représente.

Phaseurs

Les phaseurs sont des représentations complexes des sinusoïdes où l’amplitude du phaseur est égale à l’amplitude et l’angle est égal à la phase mesurée à partir de ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

AC Circuit Analysis

Analyse des circuits CA

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Phasors

phasors for ac circuit analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis.

Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in rectangular, polar, or exponential form.

Euler’s identity links trigonometric functions and exponential functions, and it helps convert between these phasor forms. To find the phasor of a sinusoid in sine form, the signal is first written in cosine form. It is then expressed as the real part of a complex number, and the phasor is the time-independent part of that number.

A sinusoid can also be recovered from a phasor. The phasor is multiplied by a time factor, and then the real part is taken. In a graph, phasors appear as rotating vectors, or sinors, on the complex plane.

These rotating sinors move counterclockwise with constant angular frequency. The diagrams that show them are called phasor diagrams. The projection of a sinor onto the real axis gives the sinusoid, so the horizontal position at any moment shows the instantaneous value of the wave.

Phasors for AC Circuit Analysis

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phasors

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis. Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in...

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Learn how phasors represent AC sinusoids, simplify circuit analysis, and appear as rotating vectors on the complex plane in phasor diagrams.

Phasors for AC Circuit Analysis | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Phasors for AC Circuit Analysis

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