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

RLC 계열 공진 대역 통과 필터를 통합한 무선 송신기 장치를 생각해 보십시오.
이 회로의 주파수 응답은 전류 크기가 초기에 증가하고, 공진 주파수에서 최고조에 도달하고, 주파수가 증가함에 따라 감소함을 나타냅니다.
최대 전류 값에 해당하는 전력 손실은 공진에서 가장 높습니다.
절반 전력 주파수에서 전류는 최대 전류의 0.707배이고 소비되는 전력은 최대 전류의 절반입니다.
공진 주파수는 이러한 반전력 주파수의 기하 평균입니다.
반전력 주파수 사이의 주파수 범위로 정의되는 대역폭은 인덕턴스에 대한 저항의 비율과 같습니다.
공진 곡선의 선명도를 나타내는 품질 계수는 회로에 저장된 최대 에너지를 진동 주기당 소산되는 에너지와 관련시킵니다.
공진에서 반응 에너지는 반응성 요소 사이에서 진동하여 리액턴스 측면에서 품질 계수의 표현을 생성합니다.
이 계수는 대역폭에 대한 공진 주파수의 비율로 표현할 수 있습니다.
품질 계수가 높을수록 대역폭이 좁아지므로 선택성이 높아집니다.

주파수 응답

Characteristics of Series Resonant Circuit

직렬 공진은 유도성(L), 용량성(C), 저항성(R) 요소가 순차적으로 연결된 회로에서 발생합니다. 공진 주파수에서 유도성 리액턴스와 용량성 리액턴스는 크기는 동일하지만 부호는 반대이므로 서로 효과적으로 상쇄됩니다. 이로 인해 회로의 온저항이 최소화되고 주로 저항 R에 의해 결정됩니다. RLC 회로의 공진 주파수는 다음과 같이 정의됩니다.
<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">
저항기의 전력 손실은 전류의 제곱에 비례합니다. 이는 공진 상태에서 전류가 최대일 때 전력소모도 최대임을 보여줍니다. 이 최대 전력은 다음과 같이 제공됩니다.
<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">
여기서 I_max는 공진 시 최대 전류입니다.
회로의 대역폭은 소비되는 전력이 최대값의 절반으로 감소하는 주파수 범위로 정의됩니다. 이는 전류가 최대 레벨의 약 70.7%로 감소하는 반전력 주파수에서 발생합니다. 대역폭은 더 높은 반전력 주파수와 더 낮은 반전력 주파수 간의 차이로 계산됩니다.
공진 시 무효 전력은 소멸되지 않고 대신 인덕터와 커패시터 사이에서 진동하는 반면, 저항 전력은 저항기에서 소멸됩니다. 품질 계수는 회로에 저장된 최대 에너지와 사이클당 소산되는 에너지와 관련이 있습니다. 응용 분야에서 RLC 필터의 Q 인자가 더 높은 무선 송신기는 근처의 주파수 잡음에서 원하는 신호를 더 잘 분리할 수 있습니다. 단점은 대역폭입니다. Q가 높을수록 대역폭이 줄어들어 보다 포괄적인 주파수 범위가 필요한 시스템에서 필터의 적용 가능성이 제한될 수 있습니다.
RLC 시리즈 공진 회로는 효과적인 대역 통과 필터 역할을 하여 무선 전송의 정밀 엔지니어링을 보여줍니다. 이 회로는 공진 주파수에서 전류 크기의 피크를 허용하도록 정밀하게 설계되어 선택적인 주파수 전송 및 수신이 가능합니다.

RLC 계열 공진 대역 통과 필터를 통합한 무선 송신기 장치를 생각해 보십시오.
이 회로의 주파수 응답은 ...

characteristics-of-series-resonant-circuit

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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...

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Circuit Gain and Phase Shift

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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 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

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...

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Op Amp Gain and Bode Plot Basics

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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 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 and RLC Filter Behavior

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