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

Wenn eine RL-Schaltung an eine Gleichstromquelle angeschlossen ist, wird ihr gesamtes Ansprechverhalten in Einschwing- und stationäre Reaktionen unterteilt.
Das Einschwingverhalten ist das temporäre Verhalten der Schaltung, das exponentiell auf Null abklingt, wenn sich die Zeit der Unendlichkeit nähert.
Die Induktivität fungiert dann als Kurzschluss, und die Quellenspannung fällt über dem Widerstand ab.
In diesem Moment wird der Strom in der Schaltung konstant und entspricht dem Verhältnis der Quellenspannung zum Widerstand. Dies ist die stationäre Reaktion.
Durch das Ersetzen des stationären Zustands und des Einschwingverhaltens ergibt sich das Gesamtverhalten der RL-Schaltung.
Der konstante Term wird bestimmt, indem der Anfangsstrom durch die Induktivität zu einem Zeitpunkt gleich Null eingesetzt wird.
Die vollständige Sprungantwort, die grafisch dargestellt wird, zeigt, dass der Anfangsstrom exponentiell auf einen stationären Wert abnimmt.
Wenn der Anfangsstrom Null ist, zeigt die vollständige Schrittantwort den exponentiellen Anstieg des Stroms auf einen stationären Wert an.
Der Spannungsgang sinkt exponentiell auf Null ab, wenn die Anfangsspannung der Quellspannung entspricht.

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rl-schaltkreis mit quelle

Wenn ein RL-Schaltkreis (Widerstand-Induktivität) an eine Gleichstromquelle angeschlossen ist, kann das vollständige Verhalten des Schaltkreises in zwei Teile unterteilt werden: das Einschwingverhalten und das stationäre Verhalten. Das Einschwingverhalten der Schaltung ist ihre vorübergehende Reaktion auf das plötzliche Anlegen der Gleichstromquelle. Diese Reaktion ist durch einen Strom gekennzeichnet, der exponentiell auf Null abfällt, wenn sich die Zeit der Unendlichkeit nähert. Während dieser Übergangszeit verhält sich die Induktivität wie ein Kurzschluss, wodurch die Quellenspannung am Widerstand abfällt. Sobald das Einschwingverhalten auf Null abgeklungen ist, tritt die Schaltung in ihre stationäre Phase ein. In dieser Phase stabilisiert sich der Strom im Stromkreis und entspricht dem Verhältnis der Quellenspannung zum Widerstand des Stromkreises. Dies ist die stationäre Reaktion. Der konstante Term im Einschwingverhalten kann durch Ersetzen des Anfangsstroms durch die Induktivität zum Zeitpunkt des Schließens des Schalters (t=0) bestimmt werden. Dies gibt uns die Anfangsbedingung für das Einschwingverhalten. Die Darstellung der vollständigen Sprungantwort der Schaltung zeigt, dass der Anfangsstrom exponentiell abnimmt, bis er einen stationären Wert erreicht. Aus dieser Stromantwort wird die Spannungsantwort abgeleitet, die ebenfalls einem exponentiellen Abfall von einem Maximalwert auf Null folgt. Wenn der Anfangsstrom im Stromkreis Null ist, zeigt die vollständige Sprungantwort, dass der Strom exponentiell ansteigt, bis er den stationären Wert erreicht. Dementsprechend beginnt die Spannungsreaktion bei der Quellenspannung und nimmt exponentiell auf Null ab. Zusammenfassend lässt sich sagen, dass das Verständnis der vollständigen Reaktion eines RL-Schaltkreises auf eine Gleichstromquelle wertvolle Erkenntnisse darüber liefert, wie diese Schaltkreise auf plötzliche Änderungen der Eingangsspannung reagieren. Dieses Wissen ist für den Entwurf und die Analyse elektronischer Schaltkreise von entscheidender Bedeutung, insbesondere bei Anwendungen wie der Filterung von Stromversorgungen und der Signalverarbeitung, bei denen Induktivitäten häufig zum Einsatz kommen.

RL-Schaltkreis mit Quelle

Wenn eine RL-Schaltung an eine Gleichstromquelle angeschlossen ist, wird ihr gesamtes Ansprechverhalten in Einschwing- und stationäre Reaktionen unterteilt.
Das Einschwingverhalten ist das ...

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Einheit 1

First and Second-Order Circuits

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KEY TERMS AND CONCEPTS

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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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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 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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