Name: series resonance in rlc circuits
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 17 s
Channel: JoVE

特定の周波数の信号を正確に選択するラジオチューナーについて考えてみましょう。
チューナーは、直列接続された抵抗、コンデンサ、およびインダクタで構成されています。
RLC周波数領域回路インピーダンスは、回路電流に対する電源電圧の比率です。
共振は、このインピーダンスの虚数部がゼロに等しいときに発生します。
これは、誘導性リアクタンスが容量性リアクタンスと等しいことを意味します。
この条件が満たされる周波数は共振周波数と呼ばれ、インダクタンス積とキャパシタンス積の平方根に反比例します。
この共振周波数では、インダクタとコンデンサの直列の組み合わせは短絡のようになり、回路は純粋に抵抗性になります。
これにより、電圧と電流が同相になり、統一力率が生まれます。
インピーダンスは最小の大きさに達し、回路に最大電流が流れることができます。
インダクタとコンデンサの両端の電圧がソース電圧を大幅に上回っています。
レゾナンスは、選択したチャンネルの信号強度を向上させ、全体的な放送品質を向上させます。

直列共振

Series Resonance

RLC 回路のインピーダンスは、供給電圧と回路電流の比として定義されます。このような回路の共振は、このインピーダンスの虚数部がゼロになったときに発生します。この特定の条件は、誘導性リアクタンスが容量性リアクタンスと正確に等しいことを意味します。これが発生する周波数は、共振周波数と呼ばれます。数学的には、共振周波数はインダクタンス (L) と容量 (C) の積の平方根に反比例します。

この共振周波数では、インダクタとコンデンサの直列接続は短絡のように動作します。その結果、回路は純粋に抵抗的に動作し、インピーダンスが最小になり、回路は最大電流の流れを可能にします。これにより、電圧と電流が同位相になり、力率が 1 になります。
共振が達成されると、インピーダンスが最小値に達し、回路を流れる電流が最大になります。さらに、共振時には、回路の品質係数により、インダクタとコンデンサの両端の電圧がソース電圧を大幅に超えることがあります。これは、回路の共振周波数での効率を示します。この現象は、選択した周波数の信号強度を強化する必要があるラジオチューナーなどのアプリケーションでは重要です。
直列共振回路は共振周波数によって特徴付けられ、回路は最大電流で純粋に抵抗的な動作を示します。共振状態では、誘導性リアクタンス電流と容量性リアクタンス電流が標準値から何倍にも増加します。それでも、誘導性リアクタンスと容量性リアクタンスが互いの効果を打ち消すため、この効果は現れません。共振周波数は、特定の周波数を選択または拒否する機能が不可欠な、無線送信機と受信機のチューニング回路を含むさまざまなアプリケーションで重要です。

特定の周波数の信号を正確に選択するラジオチューナーについて考えてみましょう。
チューナーは、直列接続された抵抗、コンデンサ、および...

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 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 frequency is inversely proportional to the square root of L times C. This means the resonant frequency changes when either L or C changes.

At the resonant frequency, the series inductor and capacitor act like a short circuit. The circuit then behaves as a purely resistive circuit. Its impedance is at the minimum value, and the current becomes maximum. The voltage and current are also in phase, so the power factor is unity.

Resonance can also cause the voltage across the inductor and capacitor to become much larger than the source voltage. This depends on the quality factor of the circuit, which shows how efficient the circuit is at resonance. The current through the inductive and capacitive parts rises many times above its normal value, but their effects cancel each other. These features are useful in radio tuners and filters, where a selected frequency must be strengthened or isolated.

Series Resonance in RLC Circuits

network function of a circuit

How Transfer Functions Shape Circuit Response

Transfer functions show how a circuit responds as signal frequency changes. They describe the link between input and output in frequency response analysis. This makes them useful for studying how circuits behave in electronics and engineering. A transfer function is a mathematical tool that relates phasor output to phasor input. It can be written as voltage gain, current gain, transfer impedance, or transfer admittance. The poles and zeros are the most important parts of the function. Zeros...

frequency response of a circuit

Inductive Circuit Frequency Response

Inductive circuit frequency response shows how a circuit with an inductor reacts to different frequencies. The analysis starts in the time domain and then moves into the frequency domain. In that step, the inductor is replaced by an impedance, and the circuit is written with phasors, which are sinusoidal signals shown with magnitude and phase. The transfer function describes how the output changes compared with the input at each frequency. A key parameter is the time constant, which is the...

gain

Circuit Gain and Phase Shift

Circuit gain and phase shift describe how a linear circuit changes a sinusoidal input voltage or current. These properties matter in circuits with reactive elements, because the response depends on the input frequency. As the frequency changes, the gain and phase shift also change. Gain compares the size of the output sinusoid to the size of the input sinusoid. If Vin is the input and Vout is the output, the gain K is the ratio of the output amplitude to the input amplitude. A gain greater...

bode plots

Reading Frequency Response on Bode Plots

Bode plots show how a circuit or system responds across frequency. They use a logarithmic frequency scale on the x-axis and gain in decibels on the y-axis. This format makes it easier to display a wide range of frequencies and to see how circuit parts affect behavior over that range. A network function gives the ratio of output to input for a system. Its complex form provides both magnitude and phase angle. The logarithmic gain on a Bode plot comes from the magnitude, calculated by multiplying...

transfer function and bode plots-i

Transfer Function Gain and Origin Effects

Transfer function gain and poles or zeros at the origin shape a system's Bode plot. The transfer function is often written in standard form after the polynomial coefficients are normalized. In that form, the constant gain, zeros, poles, and quadratic terms all appear clearly. The poles and zeros mark critical frequencies where the output magnitude and phase change noticeably. The constant gain K creates a fixed magnitude and phase term. Its magnitude is 20 log 10 K in decibels, and its phase...

transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

Bode plots show how a transfer function changes with frequency. The standard form includes constant gain, poles and zeros at the origin, simple poles and zeros, and quadratic poles and zeros. Each part shapes the system response in a different way. A simple zero sets the magnitude trend first. The Bode magnitude plot stays flat at low frequencies, near 0 dB, and then rises at 20 dB per decade after the corner or break frequency, ω1. That corner frequency is where the straight-line...

bode plots construction

Reading Frequency Response with Bode Plots

Bode plots show the frequency response of a system with a magnitude plot and a phase plot. Both plots use a logarithmic frequency axis. In control system analysis, this makes it easier to see how a transfer function changes with frequency. To build a Bode plot, start with the transfer function H(ω). After normalization, the function includes constant gain, zeros, and poles. Each term affects the plot in a different way. A constant gain of 10 gives a starting magnitude of 20 dB, since 20...

series resonance

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

characteristics-of-series-resonant-circuit

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...

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...

frequency response of op amp circuits

Op Amp Gain and Bode Plot Basics

Operational amplifiers are used for signal conditioning, filtering, and mathematical tasks such as addition, subtraction, integration, and differentiation. Their frequency response shows how amplifier gain changes as the input frequency changes. This makes the gain of an op-amp a key idea in circuit design. At low frequencies, an op-amp can hold a constant gain called the dc gain, A0. As frequency rises, the gain starts to drop after the corner frequency, or break frequency, ω1. In other...

passive filters

Audio Frequency Control with Passive Filters

Passive filters shape the frequency spectrum of electrical signals. They use only passive parts such as resistors, inductors, and capacitors. Because they do not need an external power source, they can let selected frequency ranges pass or block others in many applications. Low-pass filters pass signals below the cutoff frequency, ωc, and reduce signals above it. In audio systems, they can send bass frequencies to woofers or subwoofers. For an RC low-pass filter, the transfer function H(s)...

active filters

Active Filter Design and Frequency Response

Active filters use op-amps, resistors, and capacitors to shape a signal's frequency response. They remove unwanted frequency components while keeping the parts of the signal that are needed. The design depends on the choice of resistor and capacitor values, which set the cutoff points and help define the overall response. A first-order low-pass active filter passes signals below a cutoff frequency and reduces signals above it. Its transfer function includes the low-frequency gain, also called...

scaling

Circuit Component Scaling for Filters

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels. This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study.

design example

Touch-Tone Filter Design Example

Touch-tone telephony uses dual-tone multi-frequency (DTMF) signaling and a filter design example to show how keypad tones are separated. It replaced the old rotary dial with a matrix-style keypad arranged in four rows and three columns. Each of the 12 buttons produces a unique signal pair. Every key press creates two sinusoidal tones at the same time. One tone comes from a low-frequency group between 697 and 941 Hz. The other comes from a high-frequency group between 1209 and 1477 Hz. This...

key terms and concepts

Learn how series resonance works in an RLC circuit, why impedance drops at the resonant frequency, and how radio tuners use this effect.

Series Resonance in RLC Circuits | 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 in RLC Circuits

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