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

특정 주파수의 신호를 정확하게 선택하는 라디오 튜너를 생각해 보십시오.
튜너는 직렬 연결된 저항기, 커패시터 및 인덕터로 구성됩니다.
RLC 주파수 영역 회로 임피던스는 공급 전압과 회로 전류의 비율입니다.
공진은 이 임피던스의 허수 부분이 0일 때 발생합니다.
이것은 유도 리액턴스가 용량성 리액턴스와 같다는 것을 의미합니다.
이 조건이 충족되는 주파수를 공진 주파수라고 하며 인덕턴스 및 커패시턴스 곱의 제곱근에 반비례합니다.
이 공진 주파수에서 인덕터와 커패시터 직렬 조합은 단락과 같아 회로를 순전히 저항하게 만듭니다.
그 결과 전압과 전류가 위상이 같아 단일 역률이 생성됩니다.
임피던스는 최소 크기에 도달하여 회로를 통해 최대 전류가 흐를 수 있습니다.
인덕터와 커패시터 양단의 전압이 소스 전압을 크게 초과합니다.
공진은 선택한 채널의 신호 강도를 높이고 전반적인 방송 품질을 향상시킵니다.

계열 공명

Series Resonance

RLC 회로 온저항은 공급 전압과 회로 전류의 비율로 정의됩니다. 이러한 회로의 공진은 이 온저항의 허수부가 0일 때 발생합니다. 이 특정 조건은 유도성 리액턴스가 용량성 리액턴스와 정확히 동일하다는 것을 의미합니다. 이런 일이 발생하는 주파수를 공진 주파수라고 합니다. 수학적으로 공진 주파수는 유도계수(L)와 전기용량(C) 곱의 제곱근에 반비례합니다.
이 공진 주파수에서 유도자와 축전기의 직렬 조합은 단락 회로처럼 동작합니다. 결과적으로 회로는 순전히 저항성으로 작동합니다. 즉, 온저항은 최소이고 회로는 최대 전류 흐름을 허용합니다. 이는 또한 전압과 전류가 동상이 되어 단일 역률을 달성하는 결과를 낳습니다.
공진이 달성되면 온저항은 최소 크기에 도달하여 회로를 통해 최대 전류 흐름을 허용합니다. 또한 공진 시 유도자와 축전기 양단의 전압은 회로의 품질 요소로 인해 소스 전압을 크게 초과할 수 있으며, 이는 공진 주파수에서 회로의 효율성을 나타냅니다. 이 현상은 선택한 주파수에 대한 신호 강도를 향상시켜야 하는 라디오 튜너 및 필터와 같은 응용 분야에서 매우 중요합니다.
직렬 공진 회로는 공진 주파수가 특징이며, 회로는 최대 전류에서 순수 저항 동작을 나타냅니다. 공진 상태에서 유도성 및 용량성 리액턴스 전류는 표준 값보다 몇 배나 증가합니다. 그러나 유도성 리액턴스와 용량성 리액턴스가 서로의 효과를 상쇄하기 때문에 이 효과는 관찰되지 않습니다. 공진 주파수는 특정 주파수를 선택하거나 거부하는 기능이 필수적인 무선 송신기 및 수신기의 튜닝 회로를 비롯한 다양한 응용 분야에서 매우 중요합니다.

특정 주파수의 신호를 정확하게 선택하는 라디오 튜너를 생각해 보십시오.
튜너는 직렬 연결 저항기, 커패시터 및 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

주파수 응답

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 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

Series Resonance in RLC Circuits

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