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

Nelle applicazioni pratiche, un circuito è progettato per fornire la massima potenza da una sorgente a un carico.
Un circuito equivalente a Thevenin può determinare la potenza massima che un circuito lineare può fornire.
La potenza erogata è il prodotto della resistenza di carico e del quadrato della corrente. Varia al variare della resistenza al carico.
Per identificare il valore di resistenza al carico che massimizza la potenza, viene utilizzato il calcolo differenziale. Semplificando questa equazione si ottiene il valore ottimale di resistenza al carico.
Questo valore di resistenza viene sostituito nella derivata seconda della potenza, risultando in un valore negativo, confermando la condizione per la massima potenza.
Il valore di resistenza ottenuto permette il calcolo della potenza massima. Se la resistenza di carico non corrisponde alla resistenza di Thevenin, la potenza effettiva erogata si discosterà da questo massimo.
Secondo il teorema del trasferimento di potenza massima, il trasferimento di potenza più elevato si verifica quando la resistenza di carico corrisponde alla resistenza di Thevenin.
Si consideri una batteria di parametri noti, collegata con due resistori di valori noti. La resistenza che corrisponde alla resistenza interna della batteria riceve la massima potenza.

massimo trasferimento di potenza

Numerose applicazioni pratiche nell'ambito delle discipline ingegneristiche, come le telecomunicazioni, richiedono l'ottimizzazione dell'erogazione di energia a un carico collegato. Questo perseguimento comporta però perdite interne intrinseche, che possono essere pari o superiori alla potenza fornita al carico. Il circuito equivalente di Thevenin è utile per trovare la potenza massima che un circuito lineare può fornire a un carico. In questo contesto si presuppone che la resistenza al carico possa essere regolata.

Sostituendo l'intero circuito con il suo equivalente di Thevenin preservando il carico come mostrato in Figure 1,

<img alt="Figure1" src="/files/ftp_upload/15055/15055_PT_Figure_1.svg" style="text-align: center; height: 140px;">

Figure 1: Circuito utilizzato per il massimo trasferimento di potenza

la potenza resa al carico è data da

<img alt="Equation1" src="/files/ftp_upload/15055/15055_PT_Equation_1.svg" style="text-align: center; height: 40px;">.................(1)

Per un dato circuito, la resistenza e la tensione equivalenti di Thevenin sono fisse. La variazione della potenza erogata al carico con resistenza di carico è piccola per valori piccoli o grandi di resistenza di carico ma massima per valori di resistenza di carico compresi tra zero e infinito. La potenza massima si verifica quando la resistenza di carico è uguale alla resistenza di Thevenin espressa come

<img alt="Equation2" src="/files/ftp_upload/15055/15055_PT_Equation_2.svg" style="text-align: center; height: 14px;">.................(2)

Questo è noto come teorema del massimo trasferimento di potenza. Utilizzando le equazioni 1 e 2 si ottiene l'espressione della potenza massima trasferita che è espressa come

<img alt="Equation3" src="/files/ftp_upload/15055/15055_PT_Equation_3.svg" style="text-align: center; height: 40px;">..................(3)

Questa equazione si applica solo quando è valida l'equazione 2, altrimenti la potenza erogata al carico viene determinata utilizzando l'Eq. 1.

Massimo trasferimento di potenza

Nelle applicazioni pratiche, un circuito è progettato per fornire la massima potenza da una sorgente a un carico.
Un circuito equivalente a Thevenin può determinare il massimo ...

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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.

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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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