Name: impedance matching with mesh currents
Uploaded: 2024-04-11T12:48:49.000Z
Duration: 1 min 12 s
Channel: JoVE

В радиосвязи цепь согласования импеданса выравнивает импеданс радиопередатчика и приемника.
Рассмотрим базовую схему согласования импеданса, состоящую из резистора, за которым следуют конденсатор и катушка индуктивности, расположенные параллельно.
Если входные и выходные сигналы известны, можно рассчитать ток, протекающий через конденсатор.
Угловая частота, извлекаемая из выражения входного напряжения во временной области, используется для определения импеданса катушки индуктивности и конденсатора.
Преобразованная схема в частотной области представляет импедансы, а также входные и выходные сигналы в полярной форме.
Для анализа назначаются токи сетки, и к каждой сетке применяется закон напряжения Кирхгофа, в результате чего получается набор линейных одновременных уравнений.
Эти уравнения могут быть представлены в матричной форме, а затем правило Крамера может быть использовано для решения для токов сетки.
Ток в общей ветви — это разница между токами сетки.
Путем подстановки рассчитанных токов сетки ток на конденсаторе получается в полярной форме, а затем преобразуется во временную область.

Анализ сеток для цепей переменного тока

В задачах радиосвязи необходимо учитывать важность согласования импедансов. Крайне важно обеспечить эффективную передачу сигналов между радиопередатчиками и приемниками. Для достижения этого баланса предлагается использовать схемы согласования импеданса, имеющие определённую фундаментальную конфигурацию, состоящую из резистора, конденсатора и индуктора.

Процесс согласования этих импедансов начинается с четкого понимания входных и выходных сигналов. Как только эти сигналы станут известны, следующим шагом будет расчет тока, протекающего через конденсатор в этой цепи.

Угловая частота, полученная из выражения входного напряжения во временной области, играет решающую роль. Это определяющий фактор при определении значений импеданса индуктора и конденсатора.

<img alt="Equation1" src="/files/ftp_upload/15111/15111_PT_Equation_1.svg" style="text-align: center; height: 16px;" />

<img alt="Equation2" src="/files/ftp_upload/15111/15111_PT_Equation_2.svg" style="text-align: center; height: 40px;" />

Затем схема преобразуется в частотную область. Это представление включает импедансы, входные и выходные сигналы, выраженные в полярной форме, что упрощает анализ. Чтобы глубже изучить работу схемы, назначаются токи сетки и применяется закон напряжений Кирхгофа (KVL), основополагающий принцип анализа сетки. Важно отметить, что анализ сетки особенно эффективен для плоских цепей.

Результатом этого тщательного анализа является набор линейных одновременных уравнений, которые можно элегантно представить в матричной форме. Применяется правило Крамера, чтобы выявить токи сетки, что позволяет определить ток, проходящий через конденсатор.

Подстановка рассчитанных токов сетки дает ток, протекающий через конденсатор, первоначально выраженный в полярной форме. Наконец, эти данные преобразуются во временной домен, что позволяет понять и оптимизировать схему согласования импедансов.

В радиосвязи цепь согласования импеданса выравнивает импеданс радиопередатчика и приемника.
Рассмотрим базовую схему согласования импеданса ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

AC Circuit Analysis

Анализ цепей переменного тока

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

Mesh Analysis for AC Circuits

impedance matching with mesh currents

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students.

The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input voltage. That frequency is used to find the impedance of the inductor and the capacitor, since both depend on frequency in AC circuits.

Next, the circuit is moved into the frequency domain. In this form, the signals and impedances are written in polar form, which makes the math easier to handle. Mesh currents are then assigned to the planar circuit, and Kirchhoff's voltage law, or KVL, is applied around each loop.

The result is a set of linear equations. These equations can be written in matrix form. Cramer's rule is then used to solve for the mesh currents and find the current shared by the capacitor. After substituting the mesh currents, the capacitor current is converted from polar form back into the time domain to complete the impedance-matching analysis.

Impedance Matching with Mesh Currents

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phasors

Phasors for AC Circuit Analysis

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Phasor Rules for AC Circuit Analysis

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AC Circuit Phasors: Resistor, Inductor, Capacitor

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AC Circuit Rules with Phasor Diagrams

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Series and Parallel Impedance Rules

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mesh analysis for ac circuits

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students. The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input...

source transformation for ac circuits

AC Source Conversion in Circuit Analysis

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Norton Current in AC Circuit Analysis

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key terms and concepts

Learn how mesh currents, KVL, and Cramer's rule are used to analyze an AC impedance-matching circuit and find capacitor current in radio communication.

Impedance Matching with Mesh Currents | 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

Impedance Matching with Mesh Currents

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