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

Prendi in considerazione un lampione con un limitatore di sovratensione RLC per proteggere i suoi componenti da picchi di tensione improvvisi.
Questa configurazione può essere approssimata dal più semplice circuito RLC parallelo con una sorgente CC in ingresso che genera una risposta al gradino.
Quando l'interruttore viene attivato, l'applicazione della legge corrente di Kirchhoff al nodo superiore produce un'equazione differenziale del secondo ordine.
La soluzione completa di questa equazione è una combinazione di risposte transitorie e stazionarie.
La risposta ai transienti diminuisce nel tempo e assomiglia alle soluzioni RLC in serie senza sorgente in vari scenari di smorzamento.
Se il fattore di smorzamento supera la frequenza di risonanza, la risposta viene sovrasmorzata.
Quando il fattore di smorzamento è uguale alla frequenza di risonanza, la risposta è smorzata in modo critico.
Se il fattore di smorzamento è inferiore alla frequenza di risonanza, la risposta è sottosmorzata.
La risposta in stato stazionario corrisponde alla corrente finale dell'induttore, corrispondente alla corrente sorgente.
Le costanti in gioco possono essere dedotte dalle condizioni iniziali del circuito.
L'eliminazione della corrente della sorgente di ingresso si traduce esclusivamente in una risposta transitoria.

Nessun conflitto di interessi dichiarato.

circuito rlc parallelo

Parallel RLC Circuits

I lampioni dotati di limitatori di sovratensione RLC, sono un eccellente esempio di applicazione dell'analisi dei circuiti in scenari pratici. Questi limitatori di sovratensione salvaguardano i componenti della lampada da improvvisi picchi di tensione.

In questo contesto, viene impiegato un modello circuitale RLC parallelo semplificato, con una sorgente di ingresso CC che genera una risposta al gradino. Quando l'interruttore è acceso, viene applicata la legge della corrente di Kirchhoff, portando a un'equazione differenziale di secondo ordine.

<img alt="Equation1" src="/files/ftp_upload/15101/15101_PT_Figure_1.svg" style="text-align: center; height: 32px;">

È interessante notare che la soluzione di questa equazione comprende sia risposte transitorie che stazionarie. La risposta transitoria diminuisce gradualmente nel tempo, mostrando somiglianze con le soluzioni circuitali RLC della serie senza sorgente in diverse condizioni di smorzamento. Se il fattore di smorzamento supera la frequenza di risonanza, la risposta risulta eccessivamente smorzata.

<img alt="Equation2" src="/files/ftp_upload/15101/15101_PT_Figure_2.svg" style="text-align: center; height: 16px;">

Quando questi due fattori coincidono, la risposta viene smorzata in modo critico.

<img alt="Equation3" src="/files/ftp_upload/15101/15101_PT_Figure_3.svg" style="text-align: center; height: 16px;">

La risposta risulta sottosmorzata se il fattore di smorzamento è inferiore alla frequenza di risonanza.

<img alt="Equation4" src="/files/ftp_upload/15101/15101_PT_Figure_4.svg" style="text-align: center; height: 14px;">

La risposta allo stato stazionario, corrisponde alla corrente finale dell'induttore, allineandosi con la corrente della sorgente. La determinazione delle costanti coinvolte si basa sulle condizioni iniziali del circuito.

In particolare, quando viene eliminata la corrente della sorgente di ingresso, rimane solo la risposta transitoria. I circuiti RLC paralleli trovano ampie applicazioni, in particolare nelle reti di comunicazione e nella progettazione di filtri. Comprendere il loro comportamento in diversi scenari di smorzamento, contribuisce a un'adeguata protezione dalle sovratensioni e alla progettazione dei circuiti in contesti pratici.

Circuito RLC Parallelo

Prendi in considerazione un lampione con un limitatore di sovratensione RLC per proteggere i suoi componenti da picchi di tensione improvvisi.
Questa configurazione può essere approssimata dal più semplice ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

First and Second-Order Circuits

Circuiti del primo e del secondo ordine

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

Second-order circuits use two energy storage elements, such as a capacitor and an inductor, to shape how current and voltage change over time. These circuits include RLC circuits, along with RC and RL circuits that have two capacitors or two inductors. Their behavior is described by second-order differential equations that connect the input signal to the output signal. The input usually comes from a voltage source or a current source. The output is often the voltage across the capacitor, the...

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...

series rlc circuit with source

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...

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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design-example-underdamped-parallel-rlc-circuit

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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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