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

Considere un sistema de encendido de automóvil que produce alto voltaje de la batería esencial para generar una chispa.
Este sistema se puede modelar como un circuito RLC en serie simple y se puede analizar la respuesta completa del circuito.
Aquí, el voltaje de CC de entrada sirve como una función de paso de forzamiento que da como resultado una respuesta de paso forzado que refleja las características de la función de forzamiento.
Aplicando la ley de voltaje de Kirchhoff al circuito se obtiene una ecuación diferencial de segundo orden.
Esta ecuación se asemeja a la ecuación diferencial de segundo orden de un circuito RLC sin fuente, lo que demuestra que la fuente de CC no altera la forma de las ecuaciones.
La solución completa a esta ecuación es una combinación de respuestas transitorias y de estado estacionario.
La respuesta transitoria, que disminuye con el tiempo, corresponde a la solución para circuitos sin fuente en escenarios sobreamortiguados, críticamente amortiguados e infraamortiguados.
La respuesta de estado estacionario corresponde al valor final del voltaje del condensador, que es idéntico al voltaje de la fuente.
Las constantes involucradas se pueden deducir de las condiciones iniciales del circuito.

No se han declarado conflictos de interés.

circuito rlc en serie con una fuente

Series RLC Circuit with Source

Considere el funcionamiento del sistema de encendido de un automóvil, un componente crucial responsable de generar una chispa al producir alto voltaje a partir de la batería. Este sistema puede describirse como un circuito RLC en serie simple, lo que permite un análisis en profundidad de su respuesta completa. En este contexto, el voltaje CC de entrada sirve como una función escalonada forzada, lo que da como resultado una respuesta escalonada forzada que refleja las características de la entrada. Al aplicar la ley de voltaje de Kirchhoff al circuito se obtiene una ecuación diferencial de segundo orden. Sorprendentemente, esta ecuación se parece mucho a la ecuación diferencial de segundo orden que caracteriza un circuito RLC sin fuente. Esta similitud subraya que la presencia de la fuente de CC no altera la forma fundamental de las ecuaciones. <img alt="Equation1" src="/files/ftp_upload/15100/15100_PT_Equation_1.svg" style="text-align: center; height: 34px;"> La solución completa a esta ecuación comprende respuestas tanto transitorias como de estado estacionario. <img alt="Equation2" src="/files/ftp_upload/15100/15100_PT_Equation_2.svg" style="text-align: center; height: 16px;"> La respuesta transitoria, que disminuye con el tiempo, se alinea con la solución para circuitos sin fuente y abarca escenarios que involucran comportamientos sobreamortiguados, críticamente amortiguados y subamortiguados. Por otro lado, la respuesta en estado estacionario corresponde al valor final del voltaje del capacitor, que es igual al voltaje de la fuente. Las constantes involucradas en estas respuestas se pueden determinar a partir de las condiciones iniciales del circuito.

Circuito RLC en serie con una fuente

Considere un sistema de encendido de automóvil que produce alto voltaje de la batería esencial para generar una chispa.
Este sistema se puede modelar como un ...

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Electrical Engineering

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Unit 1

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First and Second-Order Circuits

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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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