Name: phasor rules for ac circuit analysis
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 13 s
Channel: JoVE

Consideriamo una sinusoide e il suo fasore corrispondente.
La derivata della sinusoide nel dominio del tempo è uguale al suo fasore moltiplicato per j-omega nel dominio del faso.
Allo stesso modo, quando si integra una sinusoide nel dominio del tempo, si trasforma nel suo fasore diviso per j-omega nel dominio del faso.
Queste trasformazioni producono la soluzione sinusoidale allo stato stazionario senza conoscere i valori iniziali.
Ora, consideriamo due fasori in forme rettangolari e polari. Per aggiungere questi due fasori, vengono utilizzate le loro forme rettangolari.
La parte reale del fasore risultante è la somma delle parti reali dei due fasori e la sua parte complessa è la somma delle parti complesse dei singoli fasori.
Allo stesso modo, per sottrarre due fasori, vengono utilizzate le loro forme rettangolari. Le parti reali e complesse del fasore risultante sono le differenze delle parti reali e immaginarie dei singoli fasori.
Le forme polari sono usate per moltiplicare e dividere due fasori qualsiasi, e il complesso coniugato di un fasore può essere espresso sia in forme rettangolari che polari.

aritmetica dei fasori

I fasori e le loro sinusoidi corrispondenti sono correlati, offrendo approfondimenti unici sul comportamento dei circuiti a corrente alternata (CA). Un modo per comprendere questa relazione è attraverso le operazioni di differenziazione e integrazione sia nel dominio del tempo che in quello dei fasori.

Quando la derivata di una sinusoide viene presa nel dominio del tempo, si trasforma nel suo corrispondente fasore moltiplicato per j-omega (jω) nel dominio dei fasori, dove j è l'unità immaginaria e ω è la frequenza angolare. Al contrario, quando una sinusoide è integrata nel dominio del tempo, si traduce nel suo corrispondente fasore diviso per j-omega nel dominio dei fasori. Queste trasformazioni forniscono un mezzo per trovare soluzioni stazionarie per la sinusoide, senza conoscere i valori iniziali della variabile.

Consideriamo quindi due fasori, ciascuno rappresentato in forma rettangolare e polare. Per sommare o sottrarre questi due fasori si utilizzano le loro forme rettangolari (che esprimono il fasore come un numero complesso con parti reali e immaginarie). La parte reale del fasore risultante è la somma (per addizione) o la differenza (per sottrazione) delle parti reali dei due fasori originali, e la sua parte immaginaria è la somma o differenza delle parti immaginarie dei singoli fasori.

Quando si moltiplicano o dividono due fasori qualsiasi, vengono utilizzate le loro forme polari (che esprimono il fasore come una grandezza e un angolo). La grandezza del fasore risultante è il prodotto (per la moltiplicazione) o il quoziente (per la divisione) delle grandezze dei due fasori originali, e l'angolo del fasore risultante è la somma o la differenza degli angoli dei singoli fasori.

Infine, il complesso coniugato di un fasore - che si ottiene cambiando il segno della sua parte immaginaria - può esprimersi sia in forma rettangolare che polare. Questa operazione è cruciale in molte applicazioni, compreso il calcolo della potenza nei circuiti CA.

In conclusione, i fasori rappresentano un potente strumento matematico nello studio dei circuiti CA, semplificando l'analisi e risolvendo problemi che sarebbero significativamente più complessi nel dominio del tempo.

Aritmetica dei Fasori

Consideriamo una sinusoide e il suo fasore corrispondente.
La derivata della sinusoide nel dominio del tempo è uguale al suo fasore moltiplicato per j-omega nel fasore ...

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

Phasor Arithmetics

phasor rules for ac circuit analysis

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time.

Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its phasor is divided by jω. These relationships help find steady-state solutions without needing the initial variable values.

Phasor addition and subtraction use rectangular form. In rectangular form, a phasor is written with real and imaginary parts. For addition, the real parts are added and the imaginary parts are added. For subtraction, the real parts are subtracted and the imaginary parts are subtracted.

Phasor multiplication and division use polar form. In polar form, a phasor is written as a magnitude and an angle. For multiplication, the magnitudes are multiplied and the angles are added. For division, the magnitudes are divided and the angles are subtracted.

The complex conjugate of a phasor is found by changing the sign of its imaginary part. It can be written in both rectangular and polar form. This operation is important in many applications, including power calculations in AC circuits. Together, these phasor tools simplify problems that are much harder to solve in the time domain.

Phasor Rules for AC Circuit Analysis

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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...

phasor arithmetics

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time. Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its...

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kirchoff's laws using phasors

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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key terms and concepts

Learn how phasors simplify AC circuit analysis through differentiation, integration, rectangular and polar forms, and complex conjugates in steady-state signals.

Phasor Rules 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

Phasor Rules for AC Circuit Analysis

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