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

Phasoren sind komplexe Darstellungen der Sinuskurven, bei denen die Größe des Phasors der Amplitude und der Winkel der von der positiven x-Achse gemessenen Phase entspricht.
Sie vereinfachen die Analyse von Wechselstromkreisen, indem sie die Zeitabhängigkeit von Strom und Spannung beseitigen und die Schaltung in ihre äquivalente Gleichstromform umwandeln.
Phasoren können unter Verwendung der Eulerschen Identität in rechteckiger, polarer oder exponentieller Form dargestellt werden.
Um den Phasor einer Sinuskurve in der Sinusform zu erhalten, wandeln Sie ihn zuerst in die Kosinusform um und drücken ihn dann als den reellen Teil der komplexen Zahl aus.
Der Phasor dieser Sinuskurve entspricht dem zeitunabhängigen Teil der komplexen Zahl.
Umgekehrt erhält man die Sinuskurve eines gegebenen Phasors, indem man den Phasor mit dem Zeitfaktor multipliziert und seinen reellen Teil nimmt.
Phasoren können als rotierende Vektoren oder Sinoren gegen den Uhrzeigersinn auf einer komplexen Ebene mit konstanter Kreisfrequenz dargestellt werden, und die Diagramme, die sie darstellen, werden als Phasordiagramme bezeichnet.
Die Projektion der rotierenden Sinoren auf die reelle Achse stellt die Sinuskurven dar.

zeiger

Zeiger sind ein leistungsstarkes mathematisches Werkzeug zur Analyse von Wechselstromkreisen. Sie liefern eine komplexe Zahlendarstellung von Sinuskurven, wobei die Größe des Zeigers der Amplitude der Sinuskurve entspricht und der Winkel des Zeigers die von der positiven x-Achse aus gemessene Phase darstellt. Einer der wesentlichen Vorteile der Verwendung von Zeigern besteht darin, dass sie die Analyse von Wechselstromkreisen vereinfachen, indem sie die Zeitabhängigkeit von Strom und Spannung eliminieren. Diese Transformation ermöglicht die Analyse eines Wechselstromkreises, als wäre er dessen äquivalente Gleichstromform (DC), was die Berechnungen einfacher macht. Zeiger können in verschiedenen Formen dargestellt werden – rechteckig, polar oder exponentiell – mithilfe der Eulerschen Identität, einer grundlegenden Formel in der komplexen Analyse, die eine tiefe Beziehung zwischen trigonometrischen und exponentiellen Funktionen herstellt. Um den Zeiger einer Sinuskurve in Sinusform zu erhalten, muss man ihn zunächst in die Kosinusform umwandeln und ihn dann als Realteil einer komplexen Zahl ausdrücken. Der Zeiger dieser Sinuskurve entspricht dem zeitunabhängigen Teil dieser komplexen Zahl. Umgekehrt kann die Sinuskurve eines bestimmten Zeigers erhalten werden, indem man den Zeiger mit einem Zeitfaktor multipliziert und seinen Realteil bildet. In einem grafischen Kontext können Zeiger als rotierende Vektoren oder „Sinoren“ dargestellt werden, die sich auf einer komplexen Ebene mit einer konstanten Winkelfrequenz gegen den Uhrzeigersinn drehen. Die Diagramme, die diese rotierenden Sinoren darstellen, werden als Zeigerdiagramme bezeichnet. Ein Schlüsselkonzept zum Verständnis des Zeigerdiagramms besteht darin, dass die Projektion der rotierenden Sinoren auf die reale Achse die Sinuskurven darstellt. Dies bedeutet, dass die horizontale Position des Sinors zu jedem Zeitpunkt dem Momentanwert der von ihm dargestellten Sinusfunktion entspricht.

Zeiger

Phasoren sind komplexe Darstellungen der Sinuskurven, bei denen die Größe des Phasors gleich der Amplitude und der Winkel gleich der von ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

AC Circuit Analysis

Analyse von Wechselstromschaltungen

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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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