Name: oscillator design with a parallel rlc circuit
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 17 s
Channel: JoVE

يمكن لدوائر RLC المتوازية غير المثبطة أن تحافظ على التذبذبات بتردد رنين ، مما يجعلها مناسبة للاستخدام في مؤشرات التذبذب.
تم تكليف مهندس كهربائي بتصميم دائرة مذبذب نموذجية بتردد طبيعي مثبط يبلغ 4 كيلو هرتز وعامل تخميد يبلغ 4 راديان في الثانية.
مع مقاومة محددة تبلغ 200 أوم ، يمكن تحديد القيم الدقيقة للسعة والحث.
نظرا لأن عامل التخميد للدائرة هو مقلوب ضعف ناتج المقاومة والسعة ، يتم الحصول على قيمة السعة المطلوبة لتصميم الدائرة.
يتم استخدام التعبير الرياضي المرتبط بتردد الرنين وعامل التخميد والتردد الطبيعي المخمد للحصول على تردد الرنين.
يتناسب تردد الرنين عكسيا مع الجذر التربيعي لحاصل ضرب الحث والسعة.
يتم استبدال القيم المعروفة في هذه المعادلة للحصول على الحث المطلوب.
التردد الطبيعي المخمد أقل من تردد الرنين ، وقيمة الحث أقل من أربعة أضعاف مربع المقاومة مضروبا في السعة. كلا الحالتين يؤكدان التذبذب الضعيف.

لم يتم الإعلان عن أي تضارب في المصالح.

مثال تصميمي: دارة rlc المتوازية

<div style="direction:rtl">فكر في تصميم دائرة مذبذبة، وهي مكون أساسي في الأجهزة والأنظمة الإلكترونية المختلفة. الهدف هو إنشاء دائرة مذبذبة ذات خصائص محددة: تردد طبيعي مخمد قدره 4 كيلو هرتز وعامل تخميد قدره 4 راديان في الثانية. ولتحقيق ذلك، يتم استخدام دائرة RLC متوازية، معروفة بقدرتها على الحفاظ على التذبذبات عند تردد الرنين. وفي هذه الحالة، يكون عامل التخميد عنصرًا محوريًا في تحقيق الأداء المطلوب. بدءًا من مقاومة ثابتة تبلغ 200 أوم، يتم تحديد القيم اللازمة للسعة والمحاثة لتلبية المواصفات. أولاً، من المسلم به أن عامل التخميد هو مقلوب ضعف حاصل ضرب المقاومة والسعة. تسمح هذه الرؤية بتحديد قيمة السعة المطلوبة للدائرة. <img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;"> بعد ذلك، يتم تحويل الانتباه إلى التعبير الرياضي الذي يربط بين تردد الرنين وعامل التخميد والتردد الطبيعي المخمد. ومن خلال معالجة هذه المعادلة، يمكن استخلاص معلومات تردد الرنين. <img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;"> تردد الرنين، وهو أمر حاسم لتصميم المذبذب، يتناسب عكسيا مع الجذر التربيعي لمنتج الحث والسعة. مسلحين بهذه المعرفة والقيم المعروفة، يتم حساب الحث اللازم للوفاء بمعايير التصميم. <img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;"> تؤكد هذه الحسابات أن التردد الطبيعي المخمد أقل بالفعل من تردد الرنين، وأن قيمة الحث تقل عن أربعة أضعاف مربع المقاومة مضروبًا في السعة. تؤكد هذه الشروط أن دائرة المذبذب قد تم تصميمها لإظهار التذبذبات المطلوبة تحت التخميد، وإظهار الكفاءة في تصميم الدائرة الدقيق.</div>

مثال تصميمي: دارة RLC المتوازية

يمكن لدوائر RLC المتوازية غير المثبطة أن تحافظ على التذبذبات بتردد رنين ، مما يجعلها مناسبة للاستخدام في مؤشرات التذبذب.
مهندس كهربائي هو ...

design-example-underdamped-parallel-rlc-circuit

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

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 and damping factor.

Next, the resonant frequency is found from the link between resonant frequency, damping factor, and damped natural frequency. Resonant frequency is important in oscillator design because it is the frequency a parallel RLC circuit tends to sustain. It is also tied to inductance and capacitance through the square root of their product.

With the capacitance known, the inductance is then computed from the resonant frequency equation. The results show that the damped natural frequency is lower than the resonant frequency. They also show that the inductance is below four times the square of the resistance multiplied by capacitance, which supports underdamped oscillations in the circuit.

Oscillator Design with a Parallel RLC Circuit

oscillator-design-with-a-parallel-rlc-circuit

first-order circuits

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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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design example: underdamped 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 is sized for oscillator use by finding capacitance and inductance from a target damped natural frequency and damping factor.

Oscillator Design with a Parallel RLC Circuit | 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

Oscillator Design with a Parallel RLC Circuit

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