Name: forced response in a series rlc circuit
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 12 s
Channel: JoVE

Considere um sistema de ignição de automóvel que produz alta tensão da bateria, essencial para gerar uma faísca.
Este sistema pode ser modelado como um circuito RLC em série simples e a resposta completa do circuito pode ser analisada.
Aqui, a tensão CC de entrada serve como uma função de degrau forçado, resultando em uma resposta de degrau forçado que espelha as características da função de força.
A aplicação da lei de tensão de Kirchhoff ao circuito produz uma equação diferencial de segunda ordem.
Esta equação se assemelha à equação diferencial de segunda ordem de um circuito RLC livre de fonte, mostrando que a fonte CC não altera a forma das equações.
A solução completa para esta equação é uma combinação de respostas transitórias e de estado estacionário.
A resposta transitória, que diminui com o tempo, corresponde à solução para circuitos livres de fonte em cenários superamortecidos, criticamente amortecidos e subamortecidos.
A resposta em estado estacionário corresponde ao valor final da tensão do capacitor, que é idêntico à tensão da fonte.
As constantes envolvidas podem ser deduzidas das condições iniciais do circuito.

Não há conflitos de interesse declarados.

circuito em série rlc com uma fonte

Series RLC Circuit with Source

Considere a operação de um sistema de ignição de automóvel, um componente crucial responsável por gerar uma faísca ao produzir alta voltagem a partir da bateria. Este sistema pode ser descrito como um circuito RLC em série simples, permitindo uma análise aprofundada de sua resposta completa.

Neste contexto, a tensão DC de entrada serve como uma função de degrau forçado, resultando em uma resposta de degrau forçada que reflete as características da entrada. A aplicação da Lei das Malhas de Kirchhoff ao circuito produz uma equação diferencial de segunda ordem. Notavelmente, esta equação se assemelha fortemente à equação diferencial de segunda ordem que caracteriza um circuito RLC sem fonte. Esta semelhança ressalta que a presença da fonte DC não altera a forma fundamental das equações.

<img alt="Equation1" src="/files/ftp_upload/15100/15100_PT_Equation_1.svg" style="text-align: center; height: 34px;" />

A solução completa para esta equação compreende respostas transitórias e de estado estacionário.

<img alt="Equation2" src="/files/ftp_upload/15100/15100_PT_Equation_2.svg" style="text-align: center; height: 16px;" />

A resposta transitória, que diminui com o tempo, alinha-se com a solução para circuitos livres de fonte e abrange cenários que envolvem comportamentos sobreamortecidos, criticamente amortecidos e subamortecidos. Por outro lado, a resposta em estado estacionário corresponde ao valor final da tensão do capacitor, que é igual à tensão da fonte. As constantes envolvidas nestas respostas podem ser determinadas a partir das condições iniciais do circuito.

Circuito em Série RLC com uma Fonte

Considere um sistema de ignição de automóvel que produz alta tensão da bateria, essencial para gerar uma faísca.
Este sistema pode ser modelado como um ...

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

forced response in a series rlc circuit

A series RLC circuit with a DC source can model an automobile ignition system. The circuit shows how a battery can produce the high voltage needed for a spark. In this case, the input DC voltage acts like a forcing step function.

Applying Kirchhoff's voltage law leads to a second-order differential equation. A second-order differential equation is an equation with a term for the second derivative. The form of this equation is very similar to the one used for a source-free RLC circuit, so the DC source does not change the basic equation structure.

The full response of the circuit has two parts: transient response and steady-state response. The transient response fades with time and matches the source-free circuit solution. It can be overdamped, critically damped, or underdamped.

The steady-state response is the final capacitor voltage. That final value equals the source voltage. The constants in both parts of the solution come from the initial conditions of the circuit.

Forced Response in a Series RLC Circuit

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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

Forced Response in a Series RLC Circuit

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