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

I fasori sono rappresentazioni complesse dei sinusoidi in cui la grandezza del fasore è uguale all'ampiezza e l'angolo è uguale alla fase misurata dall'asse x positivo.
Semplificano l'analisi dei circuiti CA eliminando la dipendenza dal tempo della corrente e della tensione, trasformando il circuito nella sua forma CC equivalente.
I fasori possono essere rappresentati in forme rettangolari, polari o esponenziali utilizzando l'identità di Eulero.
Per ottenere il fasore di una sinusoide nella forma seno, prima convertirlo in forma coseno e poi esprimerlo come la parte reale del numero complesso.
Il fasore di questa sinusoide è uguale alla parte indipendente dal tempo del numero complesso.
Al contrario, la sinusoide di un dato fasore si ottiene moltiplicando il fasore per il fattore tempo e prendendo la sua parte reale.
I fasori possono essere rappresentati come vettori rotanti o sinori in senso antiorario su un piano complesso con una frequenza angolare costante, e i diagrammi che li raffigurano sono noti come diagrammi fasoriali.
La proiezione dei sinori rotanti sull'asse reale rappresenta le sinusoidi.

fasori

I fasori sono un potente strumento matematico utilizzato per analizzare i circuiti di corrente alternata (CA). Forniscono una rappresentazione numerica complessa delle sinusoidi, con la grandezza del fasore pari all'ampiezza della sinusoide e l'angolo del fasore che rappresenta la fase misurata dall'asse x positivo.

Uno dei vantaggi significativi derivanti dall'utilizzo dei fasori, è che semplificano l'analisi dei circuiti CA eliminando la dipendenza dal tempo della corrente e della tensione. Questa trasformazione consente di analizzare un circuito CA come se fosse la sua forma di corrente continua equivalente (CC), rendendo i calcoli più semplici.

I fasori possono essere rappresentati in diverse forme - rettangolare, polare o esponenziale - utilizzando l'identità di Eulero, una formula fondamentale nell'analisi complessa, che stabilisce una profonda relazione tra le funzioni trigonometriche ed esponenziali.

Per ottenere il fasore di una sinusoide in forma seno, bisogna prima convertirlo in forma coseno e poi esprimerlo come parte reale di un numero complesso. Il fasore di questa sinusoide è uguale alla parte indipendente dal tempo di questo numero complesso. Viceversa, la sinusoide di un dato fasore può essere ottenuta moltiplicando il fasore per un fattore tempo e prendendo la sua parte reale.

In un contesto grafico, i fasori possono essere visualizzati come vettori rotanti, o "sinori", che ruotano in senso antiorario su un piano complesso con una frequenza angolare costante. I diagrammi che raffigurano questi sinori rotanti, sono noti come diagrammi dei fasori.

Un concetto chiave per comprendere il diagramma dei fasori, è che la proiezione dei sinori rotanti sull'asse reale rappresenta i sinusoidi. Ciò significa che la posizione orizzontale del seno in qualsiasi momento, corrisponde al valore istantaneo della funzione sinusoidale che rappresenta.

Fasori

I fasori sono rappresentazioni complesse delle sinusoidi in cui la grandezza del fasore è uguale all'ampiezza e l'angolo è uguale alla fase misurata da ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

AC Circuit Analysis

Analisi dei circuiti in CA

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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Phasor Rules for AC Circuit Analysis

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AC Circuit Rules with Phasor Diagrams

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AC Circuit Response: Impedance and Admittance

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Series and Parallel Impedance Rules

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Norton Current in AC Circuit Analysis

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key terms and concepts

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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