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

Considérons un circuit alternatif linéaire connecté à une charge, représenté par son équivalent thévenin.
Le courant circulant dans la charge est déterminé à l’aide de la forme rectangulaire du Thevenin et de l’impédance de la charge.
La puissance moyenne délivrée à la charge est obtenue à partir de l’expression courante.
Pour déterminer la résistance de charge pour la puissance maximale, la dérivée de la puissance par rapport à la résistance pour la puissance maximale est fixée à zéro.
De même, la réactance de charge pour une puissance maximale est obtenue.
Ainsi, pour un transfert de puissance moyen maximal, la réactance de l'impédance de charge est le négatif de la réactance de l'impédance de Thevenin, et sa résistance est égale à la résistance de l'impédance de Thevenin.
En substituant ces valeurs, la puissance maximale est obtenue.
Selon le théorème de la puissance moyenne maximale, l’impédance de charge est égale au conjugué complexe de l’impédance de Thevenin.
Pour les charges purement résistives, le transfert de puissance moyen maximal se produit lorsque l’impédance de la charge est égale à l’amplitude de l’impédance de Thevenin.
Dans les communications sans fil, l'impédance de l'antenne est adaptée à l'impédance de la ligne de transmission ou du circuit récepteur, ce qui maximise le transfert de puissance, garantit une force de signal optimale et améliore la qualité et la portée de la communication.

le théorème de transfert de puissance maximale

Considérons un circuit équivalent AC Thevenin linéaire connecté à une impédance de charge.

La charge connectée consomme le courant et le circuit fournit l'énergie à la charge. Le courant alternatif circulant à travers la charge est déterminé à l'aide de la forme rectangulaire des tensions, des courants, de l'impédance du réseau et de l'impédance de la charge. La puissance moyenne délivrée à la charge est obtenue à partir du produit du carré du courant et de la résistance de la charge.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="height: 18px;">
<img alt="Equation 2" src="/files/ftp_upload/15125/15125_Equation_2.svg" style="height: 18px;">

Le transfert de puissance maximal délivré à la charge est déterminé en calculant la dérivée de puissance par rapport à la résistance de la charge. La dérivée est alors égale à zéro pour la condition maximale. Ainsi, pour un transfert de puissance moyen maximal, la réactance de l'impédance de charge est la négative de la réactance de l'impédance Thevenin, et sa résistance est égale à la résistance de l'impédance Thevenin. Lorsque ces conditions sont remplies, l'impédance de charge est dite être le conjugué complexe de l'impédance de Thévenin du circuit. La puissance maximale est obtenue lorsque l'impédance de charge répond à la condition mentionnée ci-dessus.

<img alt="Equation 3" src="/files/ftp_upload/15125/15125_Equation_3.svg" style="height: 46px;">
<img alt="Equation 4" src="/files/ftp_upload/15125/15125_Equation_4.svg" style="height: 38px;">
<img alt="Equation 5" src="/files/ftp_upload/15125/15125_Equation_5.svg" style="height: 18px;">

Selon le théorème de la puissance moyenne maximale, l'impédance de charge est égale au conjugué complexe de l'impédance de Thévenin. Pour les charges purement résistives, le transfert de puissance moyen maximum se produit lorsque l'impédance de charge est égale à l'impédance de Thevenin.

Dans les communications sans fil, l'impédance de l'antenne est adaptée à l'impédance de la ligne de transmission ou du circuit récepteur, maximisant le transfert de puissance, garantissant une force de signal optimale et améliorant la qualité et la portée de la communication.

Le théorème de transfert de puissance maximale

Considérons un circuit alternatif linéaire connecté à une charge, représenté par son équivalent thévenin.
Le courant circulant dans la charge est déterminé à l’aide de la ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

AC Steady State Power

Puissance alternative en régime permanent

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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