Name: load matching in thevenin circuits
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 16 s
Channel: JoVE

In der Praxis ist eine Schaltung so ausgelegt, dass sie maximale Leistung von einer Quelle zu einer Last liefert.
Eine Thevenin-Ersatzschaltung kann die maximale Leistung bestimmen, die eine lineare Schaltung liefern kann.
Die abgegebene Leistung ist das Produkt aus dem Lastwiderstand und dem Quadrat des Stroms. Er variiert, wenn sich der Lastwiderstand ändert.
Um den Lastwiderstandswert zu ermitteln, der die Leistung maximiert, wird die Differentialrechnung verwendet. Wenn Sie diese Gleichung vereinfachen, erhalten Sie den optimalen Wert für den Lastwiderstand.
Dieser Widerstandswert wird in die zweite Ableitung der Leistung eingesetzt, was zu einem negativen Wert führt, der die Bedingung für die maximale Leistung bestätigt.
Der erhaltene Widerstandswert ermöglicht die Berechnung der maximalen Leistung. Wenn der Lastwiderstand nicht mit dem Thevenin-Widerstand übereinstimmt, weicht die tatsächlich abgegebene Leistung von diesem Maximum ab.
Nach dem Theorem der maximalen Leistungsübertragung erfolgt die höchste Kraftübertragung, wenn der Lastwiderstand dem Thevenin-Widerstand entspricht.
Stellen Sie sich eine Batterie bekannter Parameter vor, die mit zwei Widerständen bekannter Werte verbunden ist. Der Widerstand, der dem Innenwiderstand der Batterie entspricht, erhält die maximale Leistung.

maximale kraftübertragung

Zahlreiche praktische Anwendungen in Ingenieurdisziplinen wie der Telekommunikation erfordern die Optimierung der Leistungsabgabe an eine angeschlossene Last. Dieses Vorgehen bringt jedoch inhärente interne Verluste mit sich, die der der Last zugeführten Leistung entsprechen oder diese übersteigen können. Die Thevenin-Ersatzschaltung ist hilfreich, um die maximale Leistung zu ermitteln, die eine lineare Schaltung an eine Last liefern kann. Dabei wird davon ausgegangen, dass der Belastungswiderstand einstellbar ist. Durch Ersetzen der gesamten Schaltung durch ihr Thevenin-Äquivalent unter Beibehaltung der Last, wie in Figure 1 dargestellt, <img alt="Figure1" src="/files/ftp_upload/15055/15055_PT_Figure_1.svg" style="text-align: center; height: 140px;"> Figure 1: Schaltung für maximale Leistungsübertragung  Die an die Last abgegebene Leistung ist gegeben durch <img alt="Equation1" src="/files/ftp_upload/15055/15055_PT_Equation_1.svg" style="text-align: center; height: 40px;">.................(1) Für einen gegebenen Stromkreis sind der äquivalente Widerstand und die Spannung von Thevenin festgelegt. Die Schwankung der an die Last abgegebenen Leistung mit dem Lastwiderstand ist bei kleinen oder großen Lastwiderstandswerten gering, bei einigen Lastwiderstandswerten zwischen Null und Unendlich jedoch maximal. Die maximale Leistung tritt auf, wenn der Lastwiderstand dem Thevenin-Widerstand entspricht, ausgedrückt als 
 <img alt="Equation2" src="/files/ftp_upload/15055/15055_PT_Equation_2.svg" style="text-align: center; height: 14px;">.................(2) 
 Dies ist als Maximum-Power-Transfer-Theorem bekannt. Unter Verwendung der Gleichungen 1 und 2 erhält man den Ausdruck für die maximale übertragene Leistung und wird ausgedrückt als: 
 <img alt="Equation3" src="/files/ftp_upload/15055/15055_PT_Equation_3.svg" style="text-align: center; height: 40px;">..................(3) Diese Gleichung gilt nur, wenn Gleichung 2 gültig ist. Andernfalls wird die an die Last gelieferte Leistung mithilfe von Gleichung bestimmt. 1.

Maximale Kraftübertragung

In der Praxis ist eine Schaltung so ausgelegt, dass sie maximale Leistung von einer Quelle zu einer Last liefert.
Eine Thevenin-Ersatzschaltung kann die maximale ...

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DC Circuit Analysis

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Maximum Power Transfer

load matching in thevenin circuits

Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load.

The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load resistance is assumed to be adjustable, so the power delivered to it can be tested across different values.

For a fixed circuit, the Thevenin equivalent voltage and resistance do not change. The load power changes only a little when the load resistance is very small or very large. It reaches a maximum at one value between zero and infinity.

The maximum power occurs when the load resistance equals the Thevenin resistance. This condition is called the maximum power transfer theorem. Using the load-power equation and this matching rule, the maximum transferred power can be found. If the matching condition is not met, the load power is determined from the general power equation instead.

Load Matching in Thevenin Circuits

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Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load. The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load...

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Learn how Thevenin equivalent circuits predict maximum power transfer when load resistance matches Thevenin resistance in linear circuits.

Load Matching in Thevenin Circuits | 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

Load Matching in Thevenin Circuits

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