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

Gdy obwód RL jest podłączony do źródła prądu stałego, jego pełna odpowiedź jest podzielona na reakcje w stanie nieustalonym i ustalonym.
Odpowiedź przejściowa to tymczasowa odpowiedź obwodu, która wykładniczo zanika do zera, gdy czas zbliża się do nieskończoności.
Cewka indukcyjna działa wtedy jak zwarcie, a napięcie źródła spada na rezystorze.
W tym momencie prąd w obwodzie staje się stały i wyrównuje stosunek napięcia źródła do rezystancji. To jest reakcja w stanie ustalonym.
Podstawienie odpowiedzi w stanie ustalonym i nieustalonej daje całkowitą odpowiedź obwodu RL.
Składnik stały jest określany przez podstawienie prądu początkowego przepływającego przez cewkę indukcyjną w czasie równym zero.
Pełna odpowiedź krokowa, przedstawiona graficznie, pokazuje, że prąd początkowy wykładniczo maleje do wartości w stanie ustalonym.
Jeśli prąd początkowy wynosi zero, pełna odpowiedź krokowa pokazuje wykładniczy wzrost prądu do wartości w stanie ustalonym.
Odpowiedź napięciowa wykładniczo spada do zera przy napięciu początkowym równym napięciu źródłowemu.

obwód rl ze źródłem

Kiedy obwód RL (rezystor-cewka indukcyjna) jest podłączony do źródła prądu stałego, pełną odpowiedź obwodu można podzielić na dwie części: odpowiedź przejściową i reakcję w stanie ustalonym.

Odpowiedź przejściowa obwodu jest jego tymczasową reakcją na nagłe przyłączenie źródła prądu stałego. Odpowiedź ta charakteryzuje się prądem, który wykładniczo maleje do zera w miarę zbliżania się czasu do nieskończoności. Podczas tego okresu przejściowego cewka indukcyjna zachowuje się jak zwarcie, powodując spadek napięcia źródła na rezystorze.

Gdy odpowiedź przejściowa spadnie do zera, obwód wchodzi w fazę stanu ustalonego. W tej fazie prąd w obwodzie staje się stabilny, równy stosunkowi napięcia źródła do rezystancji obwodu. Jest to reakcja w stanie ustalonym.

Stały składnik odpowiedzi przejściowej można wyznaczyć zastępując prąd początkowy płynący przez cewkę indukcyjną w momencie zamknięcia przełącznika (t=0). Daje nam to warunek początkowy dla odpowiedzi przejściowej.

Wykres pełnej odpowiedzi krokowej obwodu pokazuje, że początkowy prąd maleje wykładniczo, aż osiągnie wartość ustaloną. Z tej odpowiedzi prądowej wyprowadzana jest odpowiedź napięciowa, która również następuje wykładniczo od wartości maksymalnej do zera.

Jeśli początkowy prąd w obwodzie wynosi zero, pełna odpowiedź skokowa pokazuje, że prąd rośnie wykładniczo, aż osiągnie wartość stanu ustalonego. Odpowiednio, odpowiedź napięciowa zaczyna się od napięcia źródła i maleje wykładniczo do zera.

Podsumowując, zrozumienie pełnej reakcji obwodu RL na źródło prądu stałego dostarcza cennych informacji na temat reakcji tych obwodów na nagłe zmiany napięcia wejściowego. Wiedza ta jest niezbędna do projektowania i analizowania obwodów elektronicznych, szczególnie w zastosowaniach takich jak filtrowanie zasilania i przetwarzanie sygnałów, gdzie szeroko stosowane są cewki indukcyjne.

Obwód RL ze źródłem

Gdy obwód RL jest podłączony do źródła prądu stałego, jego pełna odpowiedź jest podzielona na reakcje w stanie nieustalonym i ustalonym.
Odpowiedzią przejściową jest ...

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

First and Second-Order Circuits

Obwody pierwszego i drugiego rzędu

KEY TERMS AND CONCEPTS

KLUCZOWE TERMINY I POJĘCIA

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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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 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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