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

考虑一个带有RLC浪涌保护器的路灯，用于保护其组件免受突然的电压尖峰影响。
该装置可通过最简单的并联RLC电路进行近似模拟，其中输入直流电源产生阶跃响应。
当开关闭合时，对顶部节点应用基尔霍夫电流定律可得到一个二阶微分方程。
该方程的完整解是瞬态响应和稳态响应的组合。
瞬态响应随时间逐渐衰减，在不同阻尼情况下类似于无源串联 RLC 电路的解。
如果阻尼因子超过谐振频率，则响应为过阻尼。
当阻尼因子等于共振频率时，系统的响应为临界阻尼。
如果阻尼因子小于共振频率，则响应为欠阻尼。
稳态响应对应于电感器的最终电流，与电源电流相匹配。
相关常数可根据电路的初始条件推导得出。
消除输入源电流后，仅产生瞬态响应。

并联 rlc 电路

Parallel RLC Circuits

配备 RLC 浪涌保护器的路灯是将电路分析应用于实际场景中的绝佳示例。这些电涌保护器能够使灯的组件免受突如其来的高电压所产生的影响。 在这种情况下，需要采用简化的并联 RLC 电路模型，该模型具有生成阶跃响应的直流输入源。当开关打开时，根据基尔霍夫电流定律能够得出二阶微分方程。 <img alt="Equation1" src="/files/ftp_upload/15101/15101_PT_Figure_1.svg" style="text-align: center; height: 32px;"> 有趣的是，该方程的解包括瞬态响应和稳态响应。瞬态响应会随着时间的推移而逐渐减弱，这与不同阻尼条件下的无源串联 RLC 电路解决方案是相似的。如果阻尼因数超过谐振频率，那么其中的响应就会变为过阻尼。 <img alt="Equation2" src="/files/ftp_upload/15101/15101_PT_Figure_2.svg" style="text-align: center; height: 16px;"> 当这两个因素匹配时，该响应过程就会严重减弱。 <img alt="Equation3" src="/files/ftp_upload/15101/15101_PT_Figure_3.svg" style="text-align: center; height: 16px;"> 如果阻尼系数小于谐振频率时，则该响应将会变为欠阻尼。 <img alt="Equation4" src="/files/ftp_upload/15101/15101_PT_Figure_4.svg" style="text-align: center; height: 14px;"> 稳态响应对应于最终的电感器电流，与源电流一致的是。确定其中涉及的常数取决于电路的初始条件。 值得注意的是，当消除输入的源电流时，仅保留瞬态响应。并行的 RLC 电路有着广泛的应用，特别是在通信网络和滤波器的设计过程中。了解它们在不同阻尼下的现象有助于在实际应用场景中提供足够的浪涌保护和电路设计。

并联 RLC 电路

考虑一个带有 RLC 浪涌保护器的路灯，用于保护其组件免受突发电压尖峰的影响。  
该装置可由最简单的……近似模拟。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

First and Second-Order Circuits

一阶与二阶电路

KEY TERMS AND CONCEPTS

关键术语与概念

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

First-Order Circuits in Flashing Lamps

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals. One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor...

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RC Capacitor Discharge After Power Loss

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RC Circuit Charging After a DC Step

An RC circuit with a DC source shows how a capacitor charges after a sudden voltage step. The applied source is treated as a unit step function, and the capacitor voltage is the step response of the circuit. This response describes how the circuit reacts right after the input changes. A capacitor cannot change its voltage instantly. So, immediately after the switch closes at t=0, the capacitor voltage stays at its initial value. Kirchhoff’s current law is then applied at that moment and...

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RL Circuit Decay After Source Removal

An RL circuit begins to decay after the DC source is removed. At that moment, the circuit becomes source-free. If the inductor has an initial current, I0, it also stores initial energy. That stored energy drives the natural response of the circuit. Kirchhoff’s voltage law is applied around the loop. The inductor voltage and resistor voltage are substituted into the equation. This gives a first-order differential equation for the current. Rearranging the terms produces a logarithmic form, which...

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RL Step Response Under a DC Source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied. During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source...

design example: frog muscle response

RL Circuit and Frog Leg Current Response

An RL circuit is used to model the frog leg’s response to electrical stimulation. In this setup, the student studies how current changes in a resistor-inductor circuit can trigger muscle contraction. The circuit provides a way to control and measure the electrical impulses involved in the experiment. When the switch is closed, the frog’s leg shows a brief contraction. At steady state, the inductor acts like a short circuit. That lets current bypass the resistor and produces a mild, short...

second-order circuits

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...

second-order op amp circuits

Second-Order Op Amp Low-Pass Filters

Second-order op-amp low-pass filters remove unwanted high-frequency noise from audio signals. They are used in audio systems to refine sound quality. These filters are often built as voltage followers and have two nodes with storage elements. The circuit analysis follows the same basic method used for second-order RLC circuits. In practice, bulky inductors are usually avoided because of their size and weight. For that reason, the focus here is on RC second-order op-amp circuits, which are...

design example: underdamped parallel rlc circuit

design-example-underdamped-parallel-rlc-circuit

Oscillator Design with a 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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