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

RLCサージプロテクタを備えた街路灯を考えて、突然の電圧スパイクからコンポーネントを保護します。
この設定は、ステップ応答を生成する入力DCソースを備えた最も単純な並列RLC回路によって近似できます。
スイッチがオンになったときに、キルヒホッフの電流法則を最上位ノードに適用すると、2 次微分方程式が得られます。
この方程式の完全な解は、過渡応答と定常状態応答の組み合わせです。
過渡応答は時間とともに減少し、さまざまなダンピングシナリオでソースフリーの直列RLCソリューションに似ています。
減衰係数が共振周波数を超えると、応答は過剰に減衰します。
減衰係数が共振周波数と等しい場合、応答は臨界減衰します。
減衰係数が共振周波数よりも小さい場合、応答は減衰不足になります。
定常状態の応答は、ソース電流と一致する最終的なインダクタ電流に対応します。
関連する定数は、回路の初期条件から推測できます。
入力ソース電流をなくすと、過渡応答のみになります。

利益相反は宣言されていません。

並列 rlc 回路

Parallel RLC Circuits

RLC サージ保護装置を備えた街路灯は、回路解析を実際のシナリオに適用する優れた例です。 これらのサージプロテクターは、突然の電圧スパイクからランプのコンポーネントを保護します。

この背景では、ステップ応答を生成する DC 入力ソースを備えた単純化された並列 RLC 回路モデルが使用されます。 スイッチがオンになると、キルヒホッフの電流法則が適用され、2 階微分Figureが導かれます。

<img alt="Equation1" src="/files/ftp_upload/15101/15101_PT_Figure_1.svg" style="text-align: center; height: 32px;">

興味深いことに、このFigureの解には過渡応答と定常状態応答の両方が含まれています。 過渡応答は時間の経過とともに徐々に減少し、さまざまな減衰条件下でのソースフリーの直列 RLC 回路ソリューションとの類似性を示します。 減衰率が共振周波数を超えると、応答は過減衰になります。

<img alt="Equation2" src="/files/ftp_upload/15101/15101_PT_Figure_2.svg" style="text-align: center; height: 16px;">

これら 2 つの要素が一致すると、応答が大幅に減衰します。

<img alt="Equation3" src="/files/ftp_upload/15101/15101_PT_Figure_3.svg" style="text-align: center; height: 16px;">

ダンピングファクターが共振周波数よりも小さい場合、応答はアンダーダンピングになります。

<img alt="Equation4" src="/files/ftp_upload/15101/15101_PT_Figure_4.svg" style="text-align: center; height: 14px;">

定常状態の応答は、ソース電流と一致する最終的なインダクタ電流に対応します。 関連する定数の決定は、回路の初期条件に依存します。

特に、入力ソースの電流が除去されると、過渡応答のみが残ります。 並列 RLC 回路は、特に通信ネットワークやフィルタ設計において広範囲に応用されています。 さまざまな減衰シナリオにおけるそれらの動作を理解することは、実際の設定における適切なサージ保護と回路設計に役立ちます。

並列 RLC 回路

RLCサージプロテクタを備えた街路灯を考えて、突然の電圧スパイクからコンポーネントを保護します。
この設定は、最も単純な...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

First and Second-Order Circuits

一次および二次回路

KEY TERMS AND CONCEPTS

主要な用語と概念

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...

rc circuit without source

RC Capacitor Discharge After Power Loss

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit. Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in...

rc circuit with source

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...

rl circuit without source

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...

rl circuit with source

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

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design. The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance...

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Parallel RLC Step Response in Surge Protectors

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