Name: analyzing mixed-frequency linear circuits
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 13 s
Channel: JoVE

Il principio di sovrapposizione trova applicazione nell'analisi di circuiti lineari in corrente alternata con più sorgenti indipendenti.
Si consideri un circuito costituito da due resistori, un induttore e due sorgenti sinusoidali indipendenti con frequenze diverse. Il teorema della sovrapposizione può essere utilizzato per determinare la caduta di tensione attraverso il resistore.
Secondo il teorema di sovrapposizione, l'uscita totale di un circuito lineare con più ingressi è uguale alla somma delle singole uscite di ciascun ingresso che operano in modo indipendente.
Quindi, il circuito può essere diviso in più circuiti, ciascuno con un singolo ingresso sinusoidale. 
Poiché l'impedenza dipende dalla frequenza, esistono circuiti nel dominio della frequenza diversi per ogni frequenza.
La regola della divisione della tensione e la legge di Ohm vengono applicate per determinare la tensione di uscita di ciascun circuito.
Le tensioni ottenute vengono quindi espresse nel dominio del tempo.
La tensione di uscita totale è la somma delle tensioni prodotte da ciascuna sorgente individualmente.
Quando questa caduta di tensione viene tracciata graficamente, si ottiene un'uscita non sinusoidale, anche se tutti gli ingressi sono sinusoidali.

teorema di sovrapposizione per circuiti ac

Considera di incontrare un circuito in uno stato stazionario in cui tutti i suoi ingressi sono sinusoidali, ma non possiedono tutti la stessa frequenza. Un circuito di questo tipo non è classificato come circuito a corrente alternata (CA) e, di conseguenza, le sue correnti e tensioni non presenteranno un comportamento sinusoidale. Tuttavia, questo circuito può essere analizzato utilizzando il principio di sovrapposizione.

Il principio di sovrapposizione stabilisce che l'uscita di un circuito lineare con diversi ingressi contemporanei è equivalente alle uscite cumulative, quando ciascun ingresso funziona in modo indipendente. Gli ingressi al circuito sono le tensioni provenienti dalle sorgenti di tensione indipendenti e le correnti dalle sorgenti di corrente indipendenti.

Quando tutti gli ingressi tranne uno sono impostati su zero, gli ingressi rimanenti diventano sorgenti di tensione da 0 V e sorgenti di corrente da 0 A. Dato che le sorgenti di tensione da 0 V, equivalgono a cortocircuiti e le sorgenti di corrente da 0 A corrispondono a circuiti aperti, le sorgenti collegate agli altri ingressi vengono sostituite da circuiti aperti o cortocircuiti. Ciò che rimane è un circuito stazionario con un singolo ingresso sinusoidale, che si qualifica come un circuito CA e viene analizzato utilizzando fasori e impedenze.

Pertanto, il principio di sovrapposizione viene utilizzato per trasformare un circuito con più ingressi sinusoidali a frequenze variabili, in diversi circuiti separati, ciascuno con un singolo ingresso sinusoidale. Ciascuno di questi circuiti CA viene quindi analizzato utilizzando fasori e impedenze per determinarne l'uscita sinusoidale. L'insieme di queste uscite sinusoidali, coinciderà con l'uscita del circuito iniziale.

Teorema di Sovrapposizione per Circuiti AC

Il principio di sovrapposizione trova applicazione nell'analisi di circuiti lineari in corrente alternata con più sorgenti indipendenti.
Considera un circuito composto 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

Superposition Theorem for AC Circuits

analyzing mixed-frequency linear circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources.

When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This leaves a steady-state circuit with only one sinusoidal input.

That single-input circuit can then be treated as an AC circuit. It is analyzed with phasors, which represent sinusoidal signals, and impedances, which describe how circuit parts oppose current in AC. The same process is repeated for each source in the original circuit.

The final result is found by adding the separate sinusoidal outputs together. This sum matches the output of the full circuit with multiple sinusoidal inputs at different frequencies. In this way, superposition turns one mixed-input circuit into several simpler AC circuits.

Analyzing Mixed-Frequency Linear Circuits

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phasors

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Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources. When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This...

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key terms and concepts

Learn how superposition breaks a linear circuit with multiple sinusoidal sources into simpler AC circuits, then combines the results into one output.

Analyzing Mixed-Frequency Linear Circuits | 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

Analyzing Mixed-Frequency Linear Circuits

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