Name: series resonance and rlc filter behavior
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 24 s
Channel: JoVE

RLCシリーズ共振バンドパスフィルタを組み込んだ無線送信機ユニットを考えてみましょう。
この回路の周波数応答は、電流の大きさが最初に増加し、共振周波数でピークに達し、周波数が増加するにつれて減少することを示しています。
最大電流値に対応する電力損失は、共振時に最も大きくなります。
半電力周波数では、電流は最大電流の0.707倍であり、消費される電力は最大電流の半分です。
共振周波数は、これらの半電力周波数の幾何平均です。
半電力周波数間の周波数範囲として定義される帯域幅は、抵抗とインダクタンスの比に等しくなります。
共振曲線の鋭さを表す品質係数は、回路に蓄積された最大エネルギーを発振サイクルごとに消費されるエネルギーに関連付けます。
共振時には、無効エネルギーが無効要素間で振動し、リアクタンスの観点から品質係数の表現が得られます。
この係数は、帯域幅に対する共振周波数の比率として表すことができます。
品質係数が高いほど、帯域幅が狭くなるため、選択性が向上します。

周波数応答

Characteristics of Series Resonant Circuit

直列共振は、誘導性 (L)、容量性 (C)、抵抗性 (R) の要素が順番に接続された回路で発生します。共振周波数では、誘導性リアクタンスと容量性リアクタンスは大きさは同じですが、符号が反対で、実質的に互いに打ち消し合います。これにより、回路のインピーダンスは最小になり、主に抵抗 R によって決まります。RLC 回路の共振周波数は次のように定義されます:

<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">

抵抗器の電力消費は電流の 2 乗に比例します。これは、共振状態で電流が最大になると、電力消費も最大になることを示しています。この最大電力は次のように求められます:

<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">

ここで、I_max は共振時の最大電流です。

回路の帯域幅は、消費される電力が最大値の半分に減少する周波数範囲として定義されます。これは、電流が最大レベルの約 70.7% に減少する半電力周波数で発生します。帯域幅は、高半電力周波数と低半電力周波数の差として計算されます。

共振では、無効電力は消費されず、インダクタとコンデンサの間で振動し、抵抗電力は抵抗器で消費されます。品質係数は、回路に蓄積される最大エネルギーとサイクルごとに消費されるエネルギーの関係です。アプリケーションでは、RLC フィルタの Q 係数が高い無線送信機は、目的の信号を近くの周波数ノイズからより適切に除去できます。トレードオフは帯域幅です。Q が高いほど帯域幅が狭くなり、より包括的な周波数範囲を必要とするシステムではフィルタの適用範囲が制限される可能性があります。

RLC 直列共振回路は、効果的なバンドパスフィルタとして機能することで、無線送信における精密電気回路の例です。この回路は、共振周波数で電流振幅のピークを許容するように精密に設計されており、選択的な周波数の送信と受信が可能です。

RLCシリーズ共振バンドパスフィルタを組み込んだ無線送信機ユニットを考えてみましょう。
この回路の周波数応答は、...

characteristics-of-series-resonant-circuit

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

series resonance and rlc filter behavior

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance.

The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum value. Because power loss in the resistor depends on the square of the current, the power dissipated in the resistor is also highest at resonance.

Bandwidth describes the range of frequencies over which the power falls to half of its maximum value. These are the half-power frequencies, where the current drops to about 70.7% of its peak value. The bandwidth is found by subtracting the lower half-power frequency from the higher one.

At resonance, reactive power does not turn into heat. Instead, it moves back and forth between the inductor and the capacitor. The resistor is where real power is dissipated. The quality factor, or Q factor, compares the maximum energy stored in the circuit with the energy lost each cycle.

This behavior is useful in radio transmitters and similar systems. A higher-Q RLC filter can separate a desired signal from nearby frequency noise more effectively. The trade-off is a narrower bandwidth, which can limit use in systems that need a wider frequency range. In this way, a series resonant circuit works as a band-pass filter that favors one frequency range over others.

Series Resonance and RLC Filter Behavior

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transfer function and bode plots-ii

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series resonance

Series Resonance in RLC Circuits

Series resonance in an RLC circuit happens when the inductive reactance and capacitive reactance are equal. An RLC circuit contains a resistor, an inductor, and a capacitor. The impedance of the circuit is the ratio of the supply voltage to the circuit current. At resonance, the imaginary part of the impedance becomes zero. The frequency at which this occurs is called the resonant frequency. It depends on the inductance (L) and capacitance (C) of the circuit. Mathematically, the resonant...

characteristics of series resonant circuit

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance. The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum...

parallel resonance

Parallel RLC Tuning at Resonance

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key terms and concepts

Learn how series resonance in an RLC circuit creates maximum current, minimum impedance, bandwidth limits, and filter behavior used in radio systems.

Series Resonance and RLC Filter Behavior | 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

Series Resonance and RLC Filter Behavior

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