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

RL回路がDC電源に接続されている場合、その完全な応答は過渡応答と定常状態の応答に分割されます。
過渡応答は、時間が無限大に近づくにつれて指数関数的にゼロに減衰する回路の一時的な応答です。
その後、インダクタは短絡として機能し、ソース電圧は抵抗の両端で低下します。
この瞬間、回路内の電流は安定し、ソース電圧と抵抗の比に等しくなります。これが定常状態の応答です。
定常状態と過渡応答を代入すると、RL回路の全応答が得られます。
定数項は、インダクタを流れる初期電流をゼロに等しい時間に代入することによって決定されます。
グラフで示された完全なステップ応答は、初期電流が定常状態の値まで指数関数的に減少することを示しています。
初期電流が 0 の場合、完全なステップ応答は、電流が定常状態の値まで指数関数的に増加していることを示します。
電圧応答は、初期電圧がソース電圧と等しいとゼロまで指数関数的に減少します。

利益相反は宣言されていません。

ソースを使用した rl 回路

RL (抵抗インダクタ) 回路が DC 電源に接続されている場合、回路の完全な応答は、過渡応答と定常状態応答の 2 つの部分に分割できます。

回路の過渡応答は、DC 電源の突然の印加に対する一時的な反応です。 この応答は、時間が無限大に近づくにつれて指数関数的にゼロまで減衰する電流によって特徴付けられます。 この過渡期間中、インダクタは短絡のように動作し、抵抗器の両端の電源電圧が降下します。

過渡応答がゼロに減衰すると、回路は定常状態に入ります。 この段階では、回路内の電流は安定し、電源電圧と回路の抵抗の比に等しくなります。 これが定常状態の応答です。

過渡応答の定数項は、スイッチが閉じているとき (t=0) にインダクタを流れる初期電流を代入することで決定できます。 これにより、過渡応答の初期条件が得られます。

回路の完全なステップ応答をプロットすると、初期電流が定常状態の値に達するまで指数関数的に減少することがわかります。 この電流応答から電圧応答が導出されますが、これも最大値からゼロまで指数関数的に減衰します。

回路内の初期電流がゼロの場合、完全なステップ応答は、電流が定常状態の値に達するまで指数関数的に増加することを示します。 同様に、電圧応答は電源電圧で始まり、ゼロまで指数関数的に減少します。

結論として、DC 電源に対する RL 回路の完全な応答を理解することで、これらの回路が入力電圧の突然の変化にどのように反応するかについて貴重な洞察が得られます。 この知識は、電子回路の設計と解析、特にインダクタが広範囲に使用される電源フィルタリングや信号処理などのアプリケーションにおいて不可欠です。

ソースを使用した RL 回路

RL回路がDC電源に接続されている場合、その完全な応答は過渡応答と定常状態の応答に分割されます。
過渡応答は...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

First and Second-Order Circuits

一次および二次回路

KEY TERMS AND CONCEPTS

主要な用語と概念

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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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...

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key terms and concepts

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

RL Step Response Under a DC Source

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