Name: parallel rlc step response in surge protectors
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 14 s
Channel: JoVE

Considere uma lâmpada de rua com um protetor contra surtos RLC para proteger seus componentes de picos repentinos de tensão.
Essa configuração pode ser aproximada pelo circuito RLC paralelo mais simples com uma fonte CC de entrada gerando uma resposta em degrau.
Quando a chave é ligada, a aplicação da lei atual de Kirchhoff no nó superior produz uma equação diferencial de segunda ordem.
A solução completa para esta equação é uma combinação de respostas transitórias e de estado estacionário.
A resposta transitória diminui com o tempo e se assemelha às soluções RLC da série sem fonte em vários cenários de amortecimento.
Se o fator de amortecimento exceder a frequência de ressonância, a resposta é superamortecida.
Quando o fator de amortecimento é igual à frequência de ressonância, a resposta é criticamente amortecida.
Se o fator de amortecimento for menor que a frequência de ressonância, a resposta será subamortecida.
A resposta em estado estacionário corresponde à corrente final do indutor, correspondendo à corrente da fonte.
As constantes envolvidas podem ser deduzidas das condições iniciais do circuito.
A eliminação da corrente da fonte de entrada resulta apenas em uma resposta transitória.

Não há conflitos de interesse declarados.

circuito rlc paralelo

Parallel RLC Circuits

Postes de iluminação equipados com protetores contra surtos RLC são um excelente exemplo de aplicação da análise de circuitos em cenários práticos. Esses protetores contra surtos protegem os componentes da lâmpada contra picos repentinos de tensão.

Um modelo simplificado de circuito RLC paralelo com uma fonte de entrada DC gerando uma resposta ao degrau é empregado neste contexto. Quando a chave é ligada, a Lei dos Nós de Kirchhoff é aplicada, levando a uma equação diferencial de segunda ordem.

<img alt="Equation1" src="/files/ftp_upload/15101/15101_PT_Figure_1.svg" style="text-align: center; height: 32px;" />

Curiosamente, a solução desta equação compreende respostas transitórias e de estado estacionário. A resposta transitória diminui gradualmente ao longo do tempo, exibindo semelhanças com as soluções do circuito RLC da série livre de fonte sob diferentes condições de amortecimento. Se o fator de amortecimento ultrapassar a frequência de ressonância, a resposta será superamortecida.

<img alt="Equation2" src="/files/ftp_upload/15101/15101_PT_Figure_2.svg" style="text-align: center; height: 16px;" />

Quando esses dois fatores coincidem, a resposta é criticamente amortecida.

<img alt="Equation3" src="/files/ftp_upload/15101/15101_PT_Figure_3.svg" style="text-align: center; height: 16px;" />

A resposta fica subamortecida se o fator de amortecimento for menor que a frequência de ressonância.

<img alt="Equation4" src="/files/ftp_upload/15101/15101_PT_Figure_4.svg" style="text-align: center; height: 14px;" />

A resposta em estado estacionário corresponde à corrente final do indutor, alinhando-se com a corrente da fonte. A determinação das constantes envolvidas depende das condições iniciais do circuito.

Notavelmente, apenas a resposta transitória permanece quando a corrente da fonte de entrada é eliminada. Os circuitos RLC paralelos encontram amplas aplicações, particularmente em redes de comunicação e projetos de filtros. Compreender seu comportamento sob diferentes cenários de amortecimento contribui para uma proteção adequada contra surtos e para o projeto de circuitos em ambientes práticos.

Circuito RLC Paralelo

Considere uma lâmpada de rua com um protetor contra surtos RLC para proteger seus componentes de picos repentinos de tensão.
Esta configuração pode ser aproximada pelo mais simples ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

First and Second-Order Circuits

Circuitos de Primeira e Segunda Ordem

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

parallel rlc step response in surge protectors

Parallel RLC circuits help explain how a surge protector works in a street lamp. The circuit model uses a DC input source that creates a step response when the switch is turned on. This setup shows how the lamp’s components can be protected from sudden voltage spikes.

When the switch closes, Kirchhoff’s current law is applied to the parallel RLC circuit. That leads to a second-order differential equation. The solution has two parts: a transient response and a steady-state response.

The transient response fades over time. It follows the same kind of behavior seen in source-free series RLC circuit solutions, but the damping conditions can change the shape of the response. If the damping factor is greater than the resonant frequency, the response is overdamped. If the two are equal, the response is critically damped. If the damping factor is less than the resonant frequency, the response is underdamped.

The steady-state response matches the final inductor current. In this case, it also matches the source current. The constants in the solution are found from the initial conditions of the circuit.

If the input source current is removed, only the transient response remains. Parallel RLC circuits are also important in communications networks and filter design. Learning how these circuits behave under different damping conditions helps with surge protection and practical circuit design.

Parallel RLC Step Response in Surge Protectors

parallel-rlc-step-response-in-surge-protectors

first-order circuits

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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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parallel rlc circuits

Parallel RLC circuits help explain how a surge protector works in a street lamp. The circuit model uses a DC input source that creates a step response when the switch is turned on. This setup shows how the lamp’s components can be protected from sudden voltage spikes. When the switch closes, Kirchhoff’s current law is applied to the parallel RLC circuit. That leads to a second-order differential equation. The solution has two parts: a transient response and a steady-state response. The...

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key terms and concepts

Learn how a parallel RLC circuit models street lamp surge protection, with step response, KCL, damping cases, and transient versus steady-state behavior.

Parallel RLC Step Response in Surge Protectors | 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

Parallel RLC Step Response in Surge Protectors

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