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

Параллельные RLC-цепи с недостаточным демпфированием могут выдерживать колебания на резонансной частоте, что делает их пригодными для использования в генераторах.
Перед инженером-электриком ставится задача спроектировать схему модели генераторной схемы с затухающей собственной частотой 4 килогерц и коэффициентом демпфирования 4 радиана в секунду.
При заданном сопротивлении 200 Ом можно определить точные значения емкости и индуктивности.
Поскольку коэффициент демпфирования для схемы является величиной, обратной величине, в два раза превышающей произведение сопротивления и емкости, получается требуемое значение емкости для схемы схемы.
Для получения резонансной частоты используется математическое выражение, коррелирующее резонансную частоту, коэффициент демпфирования и собственную частоту затухания.
Резонансная частота обратно пропорциональна квадратному корню из произведения индуктивности и емкости.
Известные значения подставляются в это уравнение для получения требуемой индуктивности.
Затухающая собственная частота ниже резонансной, а величина индуктивности меньше четырехкратного квадрата сопротивления, умноженного на емкость. Оба эти условия подтверждают недостаточное затухание колебаний.

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Пример разработки: параллельная схема rlc

Рассмотрим возможность разработки схемы генератора, важнейшего компонента различных электронных устройств и систем. Цель состоит в том, чтобы создать схему генератора с конкретными характеристиками: затухающей собственной частотой 4 кГц и коэффициентом демпфирования 4 радиан в секунду. Для этого используется параллельная цепь RLC, известная своей способностью поддерживать колебания на резонансной частоте. В этом случае коэффициент демпфирования имеет решающее значение для достижения желаемой производительности.

Начиная с фиксированного сопротивления в 200 Ом, определяются необходимые значения емкости и индуктивности в соответствии со спецификациями. Во-первых, известно, что коэффициент демпфирования является обратной величиной удвоенного произведения сопротивления на емкость. Это выражение позволяет точно определить необходимое значение емкости для цепи.

<img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;" />

Далее, следует обратить внимание на математическое выражение, связывающее резонансную частоту, коэффициент демпфирования и затухающую собственную частоту. Манипулируя этим уравнением, можно получить информацию о резонансной частоте.

<img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;" />

Резонансная частота, имеющая критически важное значение для конструкции генератора, обратно пропорциональна квадратному корню из произведения индуктивности и емкости. Теперь, используя вышеупомянутые зависимости и известные значения, можно рассчитать необходимую индуктивность, которая будет отвечать критериям проекта.

<img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;" />

Эти расчеты подтверждают, что затухающая собственная частота действительно ниже резонансной частоты, а значение индуктивности падает ниже четырехкратного квадрата сопротивления, умноженного на емкость. Полученные расчеты подтверждают, что схема генератора была разработана так, чтобы производить интересующие нас недостаточно затухающие колебания, демонстрируя умение проектировать схемы.

Пример разработки: параллельная схема RLC

Параллельные RLC-цепи с недостаточным демпфированием могут выдерживать колебания на резонансной частоте, что делает их пригодными для использования в генераторах.
Инженер-электрик – это...

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Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

First and Second-Order Circuits

Схемы первого и второго порядка

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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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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