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

Le principe de superposition trouve son application dans l’analyse de circuits linéaires AC avec plusieurs sources indépendantes.
Considérons un circuit composé de deux résistances, d’une inductance et de deux sources sinusoïdales indépendantes de fréquences différentes. Le théorème de superposition peut être utilisé pour déterminer la chute de tension aux bornes de la résistance.
Selon le théorème de superposition, la sortie totale d’un circuit linéaire avec plusieurs entrées est égale à la somme des sorties individuelles de chaque entrée fonctionnant indépendamment.
Ainsi, le circuit peut être divisé en plusieurs circuits, chacun avec une seule entrée sinusoïdale. 
Étant donné que l’impédance dépend de la fréquence, il existe différents circuits dans le domaine fréquentiel pour chaque fréquence.
La règle de division de la tension et la loi d'Ohm sont appliquées pour déterminer la tension de sortie de chaque circuit.
Les tensions obtenues sont ensuite exprimées dans le domaine temporel.
La tension de sortie totale est la somme des tensions produites par chaque source individuellement.
Lorsque cette chute de tension est tracée graphiquement, il en résulte une sortie non sinusoïdale, même si toutes les entrées sont sinusoïdales.

théorème de superposition pour les circuits alternatifs

Imaginez un circuit en régime permanent où toutes ses entrées sont sinusoïdales, mais elles ne possèdent pas toutes la même fréquence. Un tel circuit n'est pas classé comme circuit à courant alternatif (AC) et, par conséquent, ses courants et tensions ne présenteront pas de comportement sinusoïdal. Cependant, ce circuit peut être analysé grâce au principe de superposition. Le principe de superposition stipule que la sortie d'un circuit linéaire à plusieurs entrées concurrentes est équivalente aux sorties cumulées lorsque chaque entrée fonctionne indépendamment. Les entrées du circuit sont les tensions des sources de tension indépendantes et les courants des sources de courant indépendantes. Lorsque toutes les entrées sauf une sont mises à zéro, les entrées restantes deviennent des sources de tension 0 V et des sources de courant 0 A. Etant donné que les sources de tension 0 V équivalent à des courts-circuits et les sources de courant 0 A correspondent à des circuits ouverts, les sources liées aux autres entrées sont remplacées par des circuits ouverts ou des courts-circuits. Ce qui reste est un circuit en régime permanent avec une seule entrée sinusoïdale, qualifié de circuit alternatif et analysé à l'aide de phaseurs et d'impédances. Ainsi, le principe de superposition est utilisé pour transformer un circuit avec plusieurs entrées sinusoïdales à fréquences variables en plusieurs circuits distincts, chacun avec une entrée sinusoïdale singulière. Chacun de ces circuits CA est ensuite analysé à l'aide de phaseurs et d'impédances pour déterminer sa sortie sinusoïdale. L'ensemble de ces sorties sinusoïdales coïncidera avec la sortie du circuit initial.

Théorème de superposition pour les circuits alternatifs

Le principe de superposition trouve son application dans l’analyse de circuits linéaires AC avec plusieurs sources indépendantes.
Considérons un circuit composé 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

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

analyzing-mixed-frequency-linear-circuits

sinusoidal sources

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graphical-and-analytic-representation-of-sinusoids

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phasors

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Series and Parallel Impedance Rules

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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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