Name: parallel rlc tuning at resonance
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 23 s
Channel: JoVE

Рассмотрим AM-радиотюнер, состоящий из параллельного соединения резистора, конденсатора и катушки индуктивности, которые в совокупности вносят свой вклад в входной сигнал схемы.
При резонансе мнимая часть адмиттанса равна нулю, в результате чего резонансная частота изменяется обратно пропорционально квадратному корню из произведения индуктивности и емкости.
На резонансной частоте параллельная комбинация катушки индуктивности и конденсатора действует как разомкнутая цепь. В результате резистор потребляет минимальный ток, а энергия колеблется между магнитным полем индуктора и электрическим полем конденсатора.
Частотная характеристика указывает на то, что величина тока сначала уменьшается, достигает минимума на резонансной частоте и увеличивается по мере увеличения частоты.
На частотах половинной мощности ток в 1,4142 раза превышает минимальный ток.
Ширина полосы рассчитывается путем определения разницы между более высокой и нижней частотами полумощности.
Добротность, которая указывает на резкость резонансной кривой, может быть выражена в терминах реактивного сопротивления.
Более высокий добротность дает частоты половинной мощности, симметрично распределенные вокруг резонансной частоты и более узкую полосу пропускания.

Частотная характеристика

Параллельная схема RLC представляет собой схему, в которой резистор (R), катушка индуктивности (L) и конденсатор (C) подключены к одним и тем же узлам и, как следствие, имеют одно и то же напряжение. Параллельная цепь RLC анализируется с точки зрения проводимости (Y), которая отражает легкость протекания тока. Допуск осуществляется по следующей схеме:
<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="height: 30px;">
Резонанс в параллельной цепи RLC возникает, когда чистое реактивное сопротивление равно нулю, что означает, что емкостный и индуктивный эффекты нейтрализуют друг друга. Это условие достигается, когда:
<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="height: 30px;">
Решение для резонансной частоты дает:
<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="height: 34px;">
На этой резонансной частоте схема будет проявлять чисто резистивное поведение, а ток через резистор будет максимальным. Мощность, рассеиваемая в цепи, максимальна при резонансе из-за максимального протекания тока. На частотах точки половинной мощности ток составляет примерно 0,707 максимального тока, что приводит к половине максимальной рассеиваемой мощности. Полоса пропускания параллельной цепи RLC представляет собой разницу между этими частотами половинной мощности и находится с помощью следующего уравнения:
<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="height: 30px;">
Добротность (Q) — это безразмерный параметр, который сравнивает резонансную частоту с шириной полосы, указывая на избирательность или остроту резонансного пика. В высококачественных схемах, где Q≥10, частоты половинной мощности можно аппроксимировать с помощью:
<img alt="Equation 5" src="/files/ftp_upload/15145/15145_Equation_5.svg" style="height: 30px;">
<img alt="Equation 6" src="/files/ftp_upload/15145/15145_Equation_6.svg" style="height: 30px;">
 Более высокая добротность означает, что схема очень избирательна и сильно резонирует в узком диапазоне частот около резонансной частоты. Это свойство особенно полезно в радиосвязи, позволяя фильтровать нежелательные частоты и минимизировать помехи. Цепи с параллельным резонансом особенно полезны в приложениях фильтрации, действующих как полосовые или режекторные фильтры, блокируя определенный диапазон частот, пропуская при этом другие. Это делает их ценными при обработке сигналов для устранения нежелательных частот или шума.

Рассмотрим радиотюнер AM, состоящий из параллельного соединения резистора, конденсатора и катушки индуктивности, которые в совокупности вносят свой вклад в ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Frequency Response

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

Parallel Resonance

parallel rlc tuning at resonance

A parallel RLC circuit uses a resistor, inductor, and capacitor connected to the same nodes. Because they share the same voltage, the circuit is analyzed with admittance, which describes how easily current can flow. In a parallel RLC circuit, admittance helps show how the circuit responds as the frequency changes.

Resonance happens when the net reactance is zero. At that point, the capacitive and inductive effects cancel each other out. The resonant frequency is found from this condition. At resonance, the circuit behaves as a purely resistive circuit, and the current through the resistor reaches its maximum.

Power dissipation is also greatest at resonance because the current is highest. The half-power point frequencies are the points where the current is about 0.707 of the maximum current. At those frequencies, the power dissipation is half of its maximum value. The bandwidth of the parallel RLC circuit is the difference between the two half-power frequencies.

The quality factor, or Q, compares the resonant frequency with the bandwidth. It shows how sharp or selective the resonance peak is. For high-quality circuits where Q is 10 or greater, the half-power frequencies can be approximated with a simpler method. A higher Q means the circuit responds strongly to a narrow range of frequencies around resonance.

This selective behavior is useful in radio communications. It can help filter unwanted frequencies and reduce interference. Parallel resonance circuits are also used as band-stop or notch filters. In these filters, a specific frequency range is blocked while other frequencies pass through, which is useful for removing unwanted signals or noise.

Parallel RLC Tuning at Resonance

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transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

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Reading Frequency Response with Bode Plots

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series resonance

Series Resonance in RLC Circuits

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characteristics of series resonant circuit

characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

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parallel resonance

A parallel RLC circuit uses a resistor, inductor, and capacitor connected to the same nodes. Because they share the same voltage, the circuit is analyzed with admittance, which describes how easily current can flow. In a parallel RLC circuit, admittance helps show how the circuit responds as the frequency changes. Resonance happens when the net reactance is zero. At that point, the capacitive and inductive effects cancel each other out. The resonant frequency is found from this condition. At...

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key terms and concepts

Explore how a parallel RLC circuit behaves at resonance, including admittance, bandwidth, Q factor, and its use in radio tuning and notch filtering.

Parallel RLC Tuning at Resonance | 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

Parallel RLC Tuning at Resonance

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