Name: oscillator design with a parallel rlc circuit
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 17 s
Channel: JoVE

アンダーダンピングされた並列RLC回路は、共振周波数で発振を維持できるため、発振器での使用に適しています。
電気技師は、減衰固有振動数が4キロヘルツ、減衰係数が毎秒4ラジアンのモデル発振器回路を設計する任務を負っています。
200Ωの抵抗を設定すると、静電容量とインダクタンスの正確な値を決定できます。
回路の減衰係数は、抵抗と静電容量の積の2倍の逆数であるため、回路設計に必要な静電容量値が得られます。
共振周波数、減衰係数、減衰固有振動数を相関させる数式を使用して、共振周波数を求めます。
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ます。
既知の値をこの式に代入して、必要なインダクタンスを求めます。
減衰された固有振動数は共振周波数よりも低く、インダクタンス値は抵抗に容量を掛けた2乗の4倍未満です。これらの条件は両方とも、減衰不足の振動を確認します。

利益相反は宣言されていません。

並列 rlc 回路

さまざまな電子デバイスやシステムの重要なコンポーネントである発振器回路の設計を例に考えてみましょう。 目的は、4 kHz の減衰固有周波数と 4 ラジアン/秒の減衰係数という特定の特性を備えた発振回路を作成することです。 これを達成するために、共振周波数での発振を維持する能力で知られる並列 RLC 回路が使用されます。 この場合、所望の性能を達成するには減衰率が極めて重要です。

200 Ω の固定抵抗から始まり、仕様を満たすために必要な容量とインダクタンスの値が決定されます。 まず、減衰係数は抵抗と静電容量の積の 2 倍の逆数であることが認識されます。 この洞察により、回路に必要な静電容量値を正確に特定できるようになります。

<img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;">

次に、共振周波数、減衰率、減衰固有振動数を結び付ける数式に注目します。 この式を操作することにより、共振周波数情報を抽出することができます。

<img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;">

発振器の設計にとって重要な共振周波数は、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ます。 この知識と既知の値を利用して、設計基準を満たすために必要なインダクタンスが計算されます。

<img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;">

これらの計算により、減衰した固有振動数が実際に共振周波数よりも低く、インダクタンス値が抵抗と静電容量の二乗の 4 倍を下回ることが確認されます。 これらの条件は、発振回路が必要な低減衰発振を示すように設計されていることを裏付けており、正確な回路設計の熟練度を示しています。

並列 RLC 回路

アンダーダンピングされた並列RLC回路は、共振周波数で発振を維持できるため、発振器での使用に適しています。
電気技師とは...

design-example-underdamped-parallel-rlc-circuit

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

First and Second-Order Circuits

一次および二次回路

KEY TERMS AND CONCEPTS

主要な用語と概念

Design Example: Underdamped Parallel RLC Circuit

oscillator design with a parallel rlc circuit

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design.

The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance and damping factor.

Next, the resonant frequency is found from the link between resonant frequency, damping factor, and damped natural frequency. Resonant frequency is important in oscillator design because it is the frequency a parallel RLC circuit tends to sustain. It is also tied to inductance and capacitance through the square root of their product.

With the capacitance known, the inductance is then computed from the resonant frequency equation. The results show that the damped natural frequency is lower than the resonant frequency. They also show that the inductance is below four times the square of the resistance multiplied by capacitance, which supports underdamped oscillations in the circuit.

Oscillator Design with a Parallel RLC Circuit

oscillator-design-with-a-parallel-rlc-circuit

first-order circuits

First-Order Circuits in Flashing Lamps

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second-order circuits

RLC Damping and Resonant Frequency

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series rlc circuit without source

Natural Response of a Source-Free RLC Circuit

A source-free RLC circuit is a series circuit with a resistor, inductor, and capacitor, but no external energy source. It begins with the energy already stored in the capacitor and inductor. That stored energy drives the circuit at first. The circuit is described by a second-order differential equation. This equation shows how the resistor, inductor, and capacitor interact over time. The resistor removes energy from the circuit, so the solution has an exponential form. When the exponential...

types of responses of series rlc circuits

types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

A source-free series RLC circuit shows three response patterns based on damping. The circuit is described by a second-order differential equation. Its complete solution is made from two distinct solutions. Those solutions depend on the roots, which are written in terms of the damping factor and the resonant frequency. When the damping factor is greater than the resonant frequency, both roots are real and negative. This gives an overdamped response. The circuit output decays slowly over time. <br...

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Forced Response in a Series RLC Circuit

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design example: underdamped parallel rlc circuit

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design. The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance...

key terms and concepts

Learn how a parallel RLC circuit is sized for oscillator use by finding capacitance and inductance from a target damped natural frequency and damping factor.

Oscillator Design with a Parallel RLC Circuit | 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

Oscillator Design with a Parallel RLC Circuit

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