Name: matching load impedance for maximum power
Uploaded: 2024-07-08T13:19:54.000Z
Duration: 1 min 20 s
Channel: JoVE

Stellen Sie sich einen linearen Wechselstromkreis vor, der mit einer Last verbunden ist, dargestellt durch sein Thevenin-Äquivalent.
Der Strom, der durch die Last fließt, wird anhand der rechteckigen Form des Thevenins und der Lastimpedanz bestimmt.
Die durchschnittliche Leistung, die an die Last abgegeben wird, wird aus dem Stromausdruck abgerufen.
Um den Lastwiderstand für die maximale Leistung zu bestimmen, wird die Ableitung der Leistung in Bezug auf den Widerstand für die maximale Leistung auf Null gesetzt.
In ähnlicher Weise wird die Lastreaktanz für maximale Leistung erreicht.
Für die maximale durchschnittliche Leistungsübertragung ist die Reaktanz der Lastimpedanz also der Nachteil der Reaktanz der Thevenin-Impedanz, und ihr Widerstand entspricht dem Widerstand der Thevenin-Impedanz.
Durch Ersetzen dieser Werte wird die maximale Leistung erreicht.
Gemäß dem Theorem der maximalen durchschnittlichen Leistung entspricht die Lastimpedanz dem komplexen Konjugat der Thevenin-Impedanz.
Bei rein ohmschen Lasten erfolgt die maximale durchschnittliche Leistungsübertragung, wenn die Lastimpedanz der Größe der Thevenin-Impedanz entspricht.
Bei der drahtlosen Kommunikation wird die Impedanz der Antenne an die Impedanz der Übertragungsleitung oder des Empfängerkreises angepasst, wodurch die Energieübertragung maximiert, eine optimale Signalstärke gewährleistet und die Kommunikationsqualität und -reichweite verbessert wird.

das theorem der maximalen leistungsübertragung

Betrachten Sie einen linearen Wechselstrom-Thevenin-Äquivalentschaltkreis, der an eine Lastimpedanz angeschlossen ist.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="text-align: center; height: 16px;">

Die angeschlossene Last zieht den Strom und der Schaltkreis liefert die Leistung an die Last. Der durch die Last fließende Wechselstrom wird anhand der Rechteckform von Spannungen, Strömen, Netzwerkimpedanz und Lastimpedanz bestimmt. Die an die Last gelieferte Durchschnittsleistung ergibt sich aus dem Produkt des Quadrats von Strom und Lastwiderstand.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="text-align: center; height: 16px;">

<img alt="Equation 2" src="/files/ftp_upload/15125/15125_Equation_2.svg" style="text-align: center; height: 16px;">

Die an die Last gelieferte maximale Leistungsübertragung wird durch Berechnung der Leistungsableitung in Bezug auf den Lastwiderstand bestimmt. Die Ableitung wird dann für den maximalen Zustand mit Null gleichgesetzt. Für eine maximale durchschnittliche Leistungsübertragung ist also die Reaktanz der Lastimpedanz der negative Wert der Reaktanz der Thevenin-Impedanz und ihr Widerstand gleich dem Widerstand der Thevenin-Impedanz. Wenn diese Bedingungen erfüllt sind, wird die Lastimpedanz als komplex konjugiert zur Thevenin-Impedanz des Schaltkreises bezeichnet. Die maximale Leistung wird erreicht, wenn die Lastimpedanz die oben genannte Bedingung erfüllt.

<img alt="Equation 3" src="/files/ftp_upload/15125/15125_Equation_3.svg" style="text-align: center; height: 44px;">

<img alt="Equation 4" src="/files/ftp_upload/15125/15125_Equation_4.svg" style="text-align: center; height: 36px;">

<img alt="Equation 5" src="/files/ftp_upload/15125/15125_Equation_5.svg" style="text-align: center; height: 16px;">

Gemäß dem Theorem der maximalen Durchschnittsleistung ist die Lastimpedanz gleich der komplex konjugierten Thevenin-Impedanz. Bei rein ohmschen Lasten erfolgt die maximale durchschnittliche Leistungsübertragung, wenn die Lastimpedanz gleich der Größe der Thevenin-Impedanz ist.

Bei der drahtlosen Kommunikation wird die Impedanz der Antenne an die Impedanz der Übertragungsleitung oder des Empfängerschaltkreises angepasst, wodurch die Leistungsübertragung maximiert, optimale Signalstärke sichergestellt und Kommunikationsqualität und -reichweite verbessert werden.

Das Theorem der maximalen Leistungsübertragung

Stellen Sie sich einen linearen Wechselstromkreis vor, der mit einer Last verbunden ist, dargestellt durch sein Thevenin-Äquivalent.
Der Strom, der durch die Last fließt, wird mit dem ...

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KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

The Maximum Power Transfer Theorem

matching load impedance for maximum power

Maximum power transfer in an AC circuit depends on matching the load impedance to the Thevenin equivalent of the source network. The load draws current, and the circuit delivers power to that load. To analyze the current, the voltages, currents, network impedance, and load impedance are written in rectangular form.

The average power delivered to the load comes from the square of the current multiplied by the load resistance. To find the condition for maximum power, the power is differentiated with respect to the load resistance. That derivative is then set equal to zero.

For maximum average power transfer, the load reactance must be the negative of the Thevenin reactance. The load resistance must also equal the Thevenin resistance. When both conditions are met, the load impedance is the complex conjugate of the circuit's Thevenin impedance.

For a purely resistive load, maximum average power transfer occurs when the load impedance equals the magnitude of the Thevenin impedance. This idea is used in wireless communications, where an antenna is matched to a transmission line or receiver circuit. Good matching improves power transfer, signal strength, communication quality, and range.

Matching Load Impedance for Maximum Power

matching-load-impedance-for-maximum-power

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the maximum power transfer theorem

Maximum power transfer in an AC circuit depends on matching the load impedance to the Thevenin equivalent of the source network. The load draws current, and the circuit delivers power to that load. To analyze the current, the voltages, currents, network impedance, and load impedance are written in rectangular form. The average power delivered to the load comes from the square of the current multiplied by the load resistance. To find the condition for maximum power, the power is differentiated...

key terms and concepts

Learn how AC load impedance matching and complex conjugate conditions help maximize power transfer in Thevenin equivalent circuits and wireless communication.

Matching Load Impedance for Maximum Power | 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

Matching Load Impedance for Maximum Power

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