Name: rl step response under a dc source
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 14 s
Channel: JoVE

Lorsqu’un circuit RL est connecté à une source CC, sa réponse complète est divisée en réponses transitoires et en réponses stationnaires.
La réponse transitoire est la réponse temporaire du circuit qui décroît exponentiellement jusqu'à zéro lorsque le temps s'approche de l'infini.
L’inductance agit alors comme un court-circuit et la tension de la source chute aux bornes de la résistance.
À cet instant, le courant dans le circuit devient stable et est égal au rapport entre la tension de la source et la résistance. C’est la réponse à l’état stationnaire.
En substituant l’état stationnaire et la réponse transitoire, on obtient la réponse totale du circuit RL.
Le terme constant est déterminé en substituant le courant initial traversant l’inductance à un temps égal à zéro.
La réponse complète de l’étape, représentée graphiquement, montre que le courant initial diminue de façon exponentielle jusqu’à une valeur d’état stable.
Si le courant initial est nul, la réponse de l’étape complète montre l’augmentation exponentielle du courant jusqu’à une valeur d’état stable.
La réponse en tension diminue exponentiellement jusqu’à zéro avec une tension initiale égale à la tension source.

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circuit rl avec source

Lorsqu'un circuit RL (Résistance-Inductance) est connecté à une source CC, la réponse complète du circuit peut être divisée en deux parties : la réponse transitoire et la réponse en régime permanent. La réponse transitoire du circuit est sa réaction temporaire à l'application soudaine de la source CC. Cette réponse est caractérisée par un courant qui décroît de façon exponentielle jusqu'à zéro à mesure que le temps s'approche de l'infini. Pendant cette période de transition, l'inductance se comporte comme un court-circuit, provoquant une chute de la tension source aux bornes de la résistance. Une fois que la réponse transitoire est tombée à zéro, le circuit entre dans sa phase d'état stationnaire. Dans cette phase, le courant dans le circuit devient stable, égalant le rapport entre la tension de la source et la résistance du circuit. C'est la réponse en régime permanent. Le terme constant dans la réponse transitoire peut être déterminé en remplaçant le courant initial à travers l'inductance au moment où l'interrupteur est fermé (t = 0). Cela nous donne la condition initiale de la réponse transitoire. Le tracé de la réponse échelonnée complète du circuit montre que le courant initial diminue de façon exponentielle jusqu'à ce qu'il atteigne une valeur stable. De cette réponse en courant est dérivée la réponse en tension, qui suit également une décroissance exponentielle depuis une valeur maximale jusqu'à zéro. Si le courant initial dans le circuit est nul, la réponse échelonnée complète montre que le courant augmente de façon exponentielle jusqu'à ce qu'il atteigne la valeur stable. En conséquence, la réponse en tension commence à la tension source et diminue de façon exponentielle jusqu'à zéro. En conclusion, comprendre la réponse complète d'un circuit RL à une source CC fournit des informations précieuses sur la façon dont ces circuits réagissent aux changements soudains de tension d'entrée. Ces connaissances sont essentielles pour concevoir et analyser des circuits électroniques, en particulier dans des applications telles que le filtrage d'alimentation et le traitement du signal, où les inductances sont largement utilisées.

Circuit RL avec Source

Lorsqu’un circuit RL est connecté à une source CC, sa réponse complète est divisée en réponses transitoires et en réponses stationnaires.
La réponse transitoire est la ...

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First and Second-Order Circuits

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RL Circuit with Source

rl step response under a dc source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied.

During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source voltage drops across the resistor.

The constant term in the transient response comes from the initial inductor current at the moment the switch closes, which is t = 0. That initial value gives the starting condition for the response. As the transient dies out, the circuit reaches steady state.

In steady state, the current becomes stable. Its value equals the source voltage divided by the resistance. The current response can be plotted to show the exponential change toward this final value.

The voltage response is also derived from the current response. When the current decays from an initial value, the voltage drops exponentially from a maximum value to zero. If the initial current is zero, the current instead rises exponentially to the steady-state value, and the voltage starts at the source voltage and falls to zero.

Understanding the complete response of an RL circuit to a DC source helps explain how these circuits react to sudden changes in input voltage. This idea is useful in circuit design and analysis. It is especially important in applications such as power supply filtering and signal processing, where inductors are used extensively.

RL Step Response Under a DC Source

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Explore how an RL circuit responds to a DC source, including transient and steady-state behavior, exponential current change, and voltage decay.

RL Step Response Under a DC Source | 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

RL Step Response Under a DC Source

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