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

Quando un circuito RL è collegato a una sorgente CC, la sua risposta completa è suddivisa in risposte transitorie e stazionarie.
La risposta transitoria è la risposta temporanea del circuito che decade esponenzialmente a zero man mano che il tempo si avvicina all'infinito.
L'induttore agisce quindi come un cortocircuito e la tensione di sorgente scende attraverso il resistore.
In questo istante, la corrente nel circuito diventa costante ed è uguale al rapporto tra la tensione della sorgente e la resistenza. Questa è la risposta allo stato stazionario.
Sostituendo lo stato stazionario e la risposta transitoria si ottiene la risposta totale del circuito RL.
Il termine costante è determinato sostituendo la corrente iniziale attraverso l'induttore in un tempo pari a zero.
La risposta completa al passo, rappresentata graficamente, mostra che la corrente iniziale diminuisce esponenzialmente fino a un valore stazionario.
Se la corrente iniziale è zero, la risposta completa al gradino mostra l'aumento esponenziale della corrente a un valore stazionario.
La risposta in tensione diminuisce esponenzialmente fino a zero con una tensione iniziale uguale alla tensione della sorgente.

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circuito rl con sorgente

Quando un circuito RL (resistore-induttore), è collegato a una sorgente CC, la risposta completa del circuito può essere divisa in due parti: la risposta transitoria e la risposta a regime.

La risposta transitoria del circuito è la sua reazione temporanea all'improvvisa applicazione della sorgente CC. Questa risposta è caratterizzata da una corrente che decade esponenzialmente fino a zero quando il tempo si avvicina all'infinito. Durante questo periodo di transizione, l'induttore si comporta come un cortocircuito, provocando una caduta della tensione sorgente attraverso il resistore.

Una volta che la risposta transitoria è scesa a zero, il circuito entra nella fase stazionaria. In questa fase, la corrente nel circuito diventa stabile, eguagliando il rapporto tra la tensione sorgente e la resistenza del circuito. Questa è la risposta allo stato stazionario.

Il termine costante nella risposta transitoria, può essere determinato sostituendo la corrente iniziale attraverso l'induttore nel momento in cui l'interruttore è chiuso (t=0). Questo ci dà la condizione iniziale per la risposta transitoria.

Tracciando la risposta al gradino completa del circuito, si vede che la corrente iniziale diminuisce esponenzialmente fino a raggiungere un valore stazionario. Da questa risposta in corrente si deriva la risposta in tensione, che segue anch'essa un decadimento esponenziale da un valore massimo a zero.

Se la corrente iniziale nel circuito è zero, la risposta al gradino completa mostra che la corrente aumenta in modo esponenziale, fino a raggiungere il valore di regime. Di conseguenza, la risposta in tensione inizia dalla tensione della sorgente e diminuisce esponenzialmente fino a zero.

In conclusione, comprendere la risposta completa di un circuito RL a una sorgente CC, fornisce preziose informazioni su come questi circuiti reagiscono ai cambiamenti improvvisi della tensione di ingresso. Questa conoscenza è essenziale per la progettazione e l'analisi dei circuiti elettronici, in particolare in applicazioni quali il filtraggio dell'alimentazione e l'elaborazione del segnale, dove gli induttori sono ampiamente utilizzati.

Circuito RL con Sorgente

Quando un circuito RL è collegato a una sorgente CC, la sua risposta completa è suddivisa in risposte transitorie e stazionarie.
La risposta transitoria è la ...

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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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