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

В практическом применении цепь предназначена для передачи максимальной мощности от источника к нагрузке.
Схема, эквивалентная Тевенину, может определить максимальную мощность, которую может выдать линейная цепь.
Подаваемая мощность является произведением сопротивления нагрузки на квадрат тока. Оно меняется в зависимости от изменения сопротивления нагрузке.
Чтобы определить значение сопротивления нагрузки, которое максимизирует мощность, используется дифференциальное исчисление. Упрощение этого уравнения позволяет получить оптимальное значение сопротивления нагрузке.
Это значение сопротивления подставляется во вторую производную мощности, в результате чего получается отрицательное значение, подтверждающее условие максимальной мощности.
Полученное значение сопротивления позволяет рассчитать максимальную мощность. Если сопротивление нагрузке не соответствует сопротивлению Тевенина, фактическая подаваемая мощность будет отклоняться от этого максимума.
Согласно теореме о максимальной передаче мощности, наибольшая передача мощности происходит, когда сопротивление нагрузки соответствует сопротивлению Тевенина.
Рассмотрим батарею с известными параметрами, соединенную с двумя резисторами известных значений. Сопротивление, соответствующее внутреннему сопротивлению аккумулятора, получает максимальную мощность.

Максимальная передача мощности

Многочисленные практические применения в рамках инженерных дисциплин, такие как телекоммуникации, требуют оптимизации подачи мощности на подключенную нагрузку. Однако это влечет за собой внутренние потери, которые могут быть равны мощности, подаваемой на нагрузку, или превышать ее. Эквивалентная схема Тевинина помогает определить максимальную мощность, которую линейная схема может передать нагрузке. При этом предполагается, что сопротивление нагрузки можно регулировать.

При замене всей схемы ее эквивалентом Тевинина, сохраняя при этом нагрузку, как показано на рисунке 1,

<img alt="Figure1" src="/files/ftp_upload/15055/15055_PT_Figure_1.svg" style="text-align: center; height: 140px;" />

Figure 1: Схема, используемая для передачи максимальной мощности.

мощность, подаваемая на нагрузку, определяется выражением

<img alt="Equation1" src="/files/ftp_upload/15055/15055_PT_Equation_1.svg" style="text-align: center; height: 40px;" />.................(1)

Для данной цепи эквивалентное сопротивление и напряжение Тевинина фиксированы. Изменение мощности, подаваемой на нагрузку, в зависимости от сопротивления нагрузки, невелико для малых или больших значений сопротивления нагрузки, но максимально для некоторых значений сопротивления нагрузки от нуля до бесконечности. Максимальная мощность возникает, когда сопротивление нагрузки равно сопротивлению Тевинина, выраженному как

<img alt="Equation2" src="/files/ftp_upload/15055/15055_PT_Equation_2.svg" style="text-align: center; height: 14px;" />.................(2)

Это известно как теорема о максимальной передаче мощности. Используя уравнения 1 и 2, получается выражение для максимальной передаваемой мощности, которое выражается как

<img alt="Equation3" src="/files/ftp_upload/15055/15055_PT_Equation_3.svg" style="text-align: center; height: 40px;" />..................(3)

Это уравнение применимо только тогда, когда справедливо уравнение 2, в противном случае мощность, передаваемая на нагрузку, определяется уравнением. 1.

В практическом применении цепь предназначена для передачи максимальной мощности от источника к нагрузке.
Эквивалентная схема Тевенина может определить максимальную ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

DC Circuit Analysis

Анализ цепей постоянного тока

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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maximum power transfer

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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key terms and concepts

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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