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

Considere uma unidade transmissora de rádio que incorpore um filtro passa-banda de ressonância da série RLC.
A resposta de frequência deste circuito indica que a magnitude da corrente aumenta inicialmente, atinge o pico na frequência de ressonância e diminui à medida que a frequência aumenta.
A dissipação de energia, correspondente ao valor máximo da corrente, é maior na ressonância.
Nas frequências de meia potência, a corrente é 0,707 vezes a corrente máxima e a potência dissipada é metade da máxima.
A frequência de ressonância é a média geométrica dessas frequências de meia potência.
A largura de banda, definida como a faixa de frequência entre as frequências de meia potência, é igual à razão entre resistência e indutância.
O fator de qualidade, representando a nitidez da curva de ressonância, relaciona a energia máxima armazenada no circuito com a energia dissipada por ciclo de oscilação.
Na ressonância, a energia reativa oscila entre os elementos reativos, produzindo uma expressão do fator de qualidade em termos de reatâncias.
Este fator pode ser expresso como a razão entre a frequência de ressonância e a largura de banda.
Um fator de qualidade mais alto implica uma largura de banda mais estreita, aumentando assim a seletividade.

resposta de frequência

Characteristics of Series Resonant Circuit

A ressonância em série ocorre em um circuito contendo elementos indutivos (L), capacitivos (C) e resistivos (R) conectados sequencialmente. Na frequência de ressonância, as reatâncias indutiva e capacitiva são iguais em magnitude, mas opostas em sinal, cancelando-se efetivamente. Isso faz com que a impedância do circuito seja mínima, determinada principalmente pela resistência R. A frequência de ressonância de um circuito RLC é definida como:
<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">
A dissipação de potência no resistor é proporcional ao quadrado da corrente. Isto mostra que a dissipação de potência também é máxima quando a corrente é máxima numa condição de ressonância. Esta potência máxima é dada por:
<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">
onde I_max é a corrente máxima na ressonância.
A largura de banda de um circuito é definida como a faixa de frequência na qual a potência dissipada diminui para metade do seu valor máximo. Isto ocorre nas frequências de meia potência, onde a corrente reduz para cerca de 70,7% do seu nível máximo. A largura de banda é calculada como a diferença entre as frequências de meia potência mais altas e mais baixas.
Na ressonância, a potência reativa não se dissipa, mas oscila entre o indutor e o capacitor, enquanto a potência resistiva é dissipada no resistor. O fator de qualidade refere-se à energia máxima armazenada no circuito versus a energia dissipada por ciclo. Na aplicação, um transmissor de rádio com um fator Q mais alto para seu filtro RLC pode isolar melhor um sinal desejado do ruído de frequência próximo. A desvantagem é a largura de banda: um Q mais alto reduz a largura de banda, o que poderia limitar a aplicabilidade do filtro em sistemas que exigem uma faixa de frequência mais abrangente.
Um circuito de ressonância da série RLC exemplifica a engenharia de precisão na transmissão de rádio, funcionando como um filtro passa-faixa eficaz. Este circuito é projetado com precisão para permitir um pico na magnitude da corrente na frequência de ressonância, permitindo transmissão e recepção seletiva de frequência.

Resposta de Frequência

Considere uma unidade transmissora de rádio que incorpore um filtro passa-banda de ressonância da série RLC.
A resposta de frequência deste circuito indica que o ...

characteristics-of-series-resonant-circuit

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

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transfer function and bode plots-i

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Bode Plot Slope and Phase Changes

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Reading Frequency Response with Bode Plots

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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 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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