Name: forced response in a series rlc circuit
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 12 s
Channel: JoVE

Prenons l’exemple d’un système d’allumage automobile qui produit une haute tension à partir de la batterie, ce qui est essentiel pour générer une étincelle.
Ce système peut être modélisé comme un simple circuit RLC en série et la réponse complète du circuit peut être analysée.
Ici, la tension continue d’entrée sert de fonction d’étape de forçage, ce qui entraîne une réponse d’étape forcée qui reflète les caractéristiques de la fonction de forçage.
L'application de la loi de tension de Kirchhoff au circuit donne une équation différentielle du second ordre.
Cette équation ressemble à l’équation différentielle du second ordre d’un circuit RLC sans source, montrant que la source CC ne modifie pas la forme des équations.
La solution complète de cette équation est une combinaison de réponses transitoires et stationnaires.
La réponse transitoire, qui diminue avec le temps, correspond à la solution pour les circuits sans source dans les scénarios suramortis, critiques et sous-amortis.
La réponse en régime permanent correspond à la valeur finale de la tension du condensateur, qui est identique à la tension de la source.
Les constantes impliquées peuvent être déduites des conditions initiales du circuit.

Aucun conflit d’intérêts n’a été déclaré.

circuit rlc série avec une source

Series RLC Circuit with Source

Prenons le fonctionnement d'un système d'allumage automobile, un élément crucial responsable de la génération d'une étincelle en produisant une haute tension à partir de la batterie. Ce système peut être décrit comme un simple circuit RLC en série, permettant une analyse approfondie de sa réponse complète. Dans ce contexte, la tension continue d'entrée sert de fonction d'étape de forçage, ce qui entraîne une réponse échelonnée forcée qui reflète les caractéristiques de l'entrée. L'application de la loi de tension de Kirchhoff au circuit donne une équation différentielle du second ordre. Remarquablement, cette équation ressemble fortement à l’équation différentielle du second ordre caractérisant un circuit RLC sans source. Cette similitude souligne que la présence de la source DC ne modifie pas la forme fondamentale des équations. <img alt="Equation1" src="/files/ftp_upload/15100/15100_PT_Equation_1.svg" style="text-align: center; height: 34px;"> La solution complète de cette équation comprend à la fois des réponses transitoires et stables. <img alt="Equation2" src="/files/ftp_upload/15100/15100_PT_Equation_2.svg" style="text-align: center; height: 16px;"> La réponse transitoire, qui diminue avec le temps, s'aligne sur la solution pour les circuits sans source et englobe des scénarios impliquant des comportements suramortis, critiquement amortis et sous-amortis. En revanche, la réponse en régime permanent correspond à la valeur finale de la tension du condensateur, qui est égale à la tension source. Les constantes impliquées dans ces réponses peuvent être déterminées à partir des conditions initiales du circuit.

Circuit RLC série avec une source

Prenons l’exemple d’un système d’allumage automobile qui produit une haute tension à partir de la batterie, ce qui est essentiel pour générer une étincelle.
Ce système peut être modélisé comme un ...

Education

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Electrical Engineering

Génie électrique

Unit 1

Unité 1

First and Second-Order Circuits

Circuits du premier et du second ordre

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

forced response in a series rlc circuit

A series RLC circuit with a DC source can model an automobile ignition system. The circuit shows how a battery can produce the high voltage needed for a spark. In this case, the input DC voltage acts like a forcing step function.

Applying Kirchhoff's voltage law leads to a second-order differential equation. A second-order differential equation is an equation with a term for the second derivative. The form of this equation is very similar to the one used for a source-free RLC circuit, so the DC source does not change the basic equation structure.

The full response of the circuit has two parts: transient response and steady-state response. The transient response fades with time and matches the source-free circuit solution. It can be overdamped, critically damped, or underdamped.

The steady-state response is the final capacitor voltage. That final value equals the source voltage. The constants in both parts of the solution come from the initial conditions of the circuit.

Forced Response in a Series RLC Circuit

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electrical engineering

Forced Response in a Series RLC Circuit

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