Name: rlc damping and resonant frequency
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 17 s
Channel: JoVE

تسمى الدائرة الكهربائية التي تتكون من عنصرين غير قابلين للاختزال لتخزين الطاقة بدائرة من الدرجة الثانية.
تتضمن بعض الأمثلة دوائر RLC بالإضافة إلى دوائر RC و RL ذات المكثفات المزدوجة والمحاثات ، على التوالي.
تتميز هذه الدوائر بمعادلة تفاضلية من الدرجة الثانية تربط بين إشارات الإدخال والإخراج للدائرة.
تنشأ إشارات الإدخال بشكل عام من مصادر الجهد أو التيار ، في حين أن الإخراج عادة ما يكون الجهد عبر المكثف و / أو التيار عبر المحرض.
ضع في اعتبارك دائرة RLC ، حيث تقود الطاقة الأولية المخزنة في المكثف والمحث الدائرة.
يؤدي تطبيق قانون جهد كيرشوف على الدائرة وأخذ مشتق الوقت إلى معادلة تفاضلية من الدرجة الثانية.
تعرف معاملات هذه المعادلة ، معبرا عنها من حيث المقاومة والسعة والحث ، باسم معامل التخميد وتردد الرنين.
يشير معامل التخميد إلى التخميد الناتج عن المقاوم ويحدد معدل تبديد الطاقة في النظام.
يمثل تردد الرنين تردد التذبذب الطبيعي للدائرة حيث يتم تبادل الطاقة بين المحرض والمكثف.

لم يتم الإعلان عن أي تضارب في المصالح.

دوائر الدرجة الثانية

Second-Order Circuits

<div style="direction:rtl">يؤدي دمج عنصرين أساسيين لتخزين الطاقة في الدوائر الكهربائية إلى ظهور دوائر من الدرجة الثانية، تشمل دوائر RLC ودوائر ذات مكثفات مزدوجة أو محاثات (دوائر RC وRL) يتم تحديد دوائر الدرجة الثانية بواسطة المعادلات التفاضلية من الدرجة الثانية التي تربط إشارات الإدخال والإخراج. تنشأ إشارات الإدخال عادة من مصادر الجهد أو التيار، حيث يمثل الإخراج غالبا الجهد عبر المكثف و/ أو التيار عبر المحث. على سبيل المثال، في دائرة RLC، الطاقة الأولية المخزنة في المكثف والمحث هي التي تبدأ الدائرة. يؤدي تطبيق قانون كيرشوف للجهد وإجراء مشتق زمني إلى الحصول على معادلة تفاضلية من الدرجة الثانية. <img alt="Equation1" src="/files/ftp_upload/15097/15097_PT_Equation_1.svg" style="text-align: center; height: 36px;"> وتتجلى معاملاتها، التي تحددها المقاومة والسعة والمحاثة، في صورة معامل التخميد وتردد الرنين. <img alt="Equation2" src="/files/ftp_upload/15097/15097_PT_Equation_2.svg" style="text-align: center; height: 34px;"> <img alt="Equation3" src="/files/ftp_upload/15097/15097_PT_Equation_3.svg" style="text-align: center; height: 36px;"> يلعب معامل التخميد دورًا حاسمًا في هذه الدوائر، مما يدل على مدى التخميد الناتج بشكل أساسي عن المقاوم. فهو يؤثر بشكل مباشر على وتيرة تبدد الطاقة داخل النظام، ويتحكم بشكل فعال في معدل فقدان الطاقة. ومن ناحية أخرى، فإن تردد الرنين هو خاصية رئيسية تمثل تردد التذبذب الفطري للدائرة. فهو يقيس مدى سرعة تبادل الطاقة بين المحرِّض والمكثف في الدائرة، مما يوضح الميل الطبيعي للدائرة للتذبذب عند تردد معين. يحدد معامل التخميد مدى سرعة فقدان الطاقة في النظام بسبب المقاومة. وفي الوقت نفسه، يسلط تردد الرنين الضوء على سرعة التذبذب المتأصلة في الدائرة مع تحول الطاقة بين المحرِّض والمكثف. يعد هذان العاملان حاسمين في فهم وتحليل سلوك دوائر الدرجة الثانية.</div>

تسمى الدائرة الكهربائية التي تتكون من عنصرين غير قابلين للاختزال لتخزين الطاقة بدائرة من الدرجة الثانية.
تتضمن بعض الأمثلة دوائر RLC بالإضافة إلى ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

First and Second-Order Circuits

الدوائر ذات الرتبة الأولى والثانية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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 current through the inductor, or both. In an RLC circuit, energy already stored in the capacitor and inductor starts the circuit response.

To analyze an RLC circuit, Kirchhoff's voltage law is applied and then differentiated with respect to time. This step produces a second-order differential equation. The equation's coefficients depend on resistance, capacitance, and inductance.

Those coefficients show up as the damping coefficient and the resonant frequency. The damping coefficient describes how much the resistor slows the circuit down. It also shows how quickly energy is lost from the system.

The resonant frequency is the circuit's natural oscillation frequency. It shows how fast energy moves back and forth between the inductor and capacitor. Together, the damping coefficient and resonant frequency are key to understanding how second-order circuits behave.

RLC Damping and Resonant Frequency

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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RL Circuit Decay After Source Removal

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second-order circuits

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...

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Natural Response of a Source-Free RLC Circuit

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types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

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key terms and concepts

Learn how second-order circuits use capacitors, inductors, and resistors. Explore damping coefficient, resonant frequency, and RLC circuit response.

RLC Damping and Resonant Frequency | 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

RLC Damping and Resonant Frequency

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