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

抵抗、コンデンサ、およびインダクタの並列接続で構成されるAMラジオチューナについて考えてみましょう。これらは、回路の入力アドミタンスに総合的に寄与します。
共振では、アドミタンスの虚数部がゼロになり、共振周波数はインダクタンスとキャパシタンスの積の平方根に反比例して変化します。
共振周波数では、インダクタとコンデンサの並列組み合わせが開回路として機能します。その結果、抵抗器の消費電流は最小限に抑えられ、インダクタの磁場とコンデンサの電界の間でエネルギーが振動します。
周波数応答は、電流の大きさが最初に減少し、共振周波数で最小に達し、周波数が増加するにつれて増加することを示しています。
ハーフパワー周波数では、電流は最小電流の1.4142倍です。
帯域幅は、高い半分の電力周波数と低い半分の電力周波数の差を決定することによって計算されます。
共振曲線の鋭さを示す品質係数は、リアクタンスで表すことができます。
品質係数が高いほど、共振周波数の周囲に対称的に分布する半電力周波数が得られ、帯域幅が狭くなります。

周波数応答

並列 RLC 回路は、抵抗器 (R)、インダクタ (L)、コンデンサ (C) がすべて同じノードに接続され、その結果、それらの間で同じ電圧を共有する配置です。並列 RLC 回路は、電流が流れる容易さを表すアドミタンス (Y) の観点から分析されます。アドミタンスは次のように求められます:

<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="height: 30px;">

並列 RLC 回路の共振は、正味リアクタンスがゼロのときに発生します。つまり、容量効果と誘導効果が互いに打ち消されます。この条件は、次の場合に達成されます:
<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="height: 30px;">
共振周波数を解くと、次のようになります:
<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="height: 34px;">
この共振周波数では、回路は純粋に抵抗的な動作を示し、抵抗器を流れる電流は最大になります。回路で消費される電力は、最大電流により共振時に最大になります。半電力点周波数では、電流は最大電流の約 0.707 となり、最大電力消費の半分になります。並列 RLC 回路の帯域幅は、これらの半電力周波数の差であり、次を使用して求められます。
<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="height: 30px;">
品質係数 (Q) は、共振周波数と帯域幅を比較する無次元パラメータであり、共振ピークの選択性または鋭さを示します。Q≥10 の高品質回路では、半電力周波数は次を使用して概算できます。
<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;">
Q 係数が高いほど、回路の選択性が高く、共振周波数周辺の狭い範囲の周波数で強く共振することを意味します。この特性は無線通信で特に有益であり、不要な周波数をフィルタリングして干渉を最小限に抑えることができます。並列共振回路は、バンドストップ フィルターまたはノッチ フィルターとして機能し、特定の周波数範囲をブロックしながら他の周波数範囲を通過させるフィルタリング アプリケーションで特に役立ちます。このため、不要な周波数やノイズを除去する信号処理で役立ちます。

抵抗、コンデンサ、インダクタの並列接続で構成されるAMラジオチューナーを考えてみましょう。

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Frequency Response

周波数特性

KEY TERMS AND CONCEPTS

主要用語および概念

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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series resonance

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characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

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parallel resonance

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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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Parallel RLC Tuning at Resonance

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