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

Circuitos RLC paralelos subamortecidos podem sustentar oscilações em uma frequência ressonante, tornando-os adequados para uso em osciladores.
Um engenheiro elétrico é encarregado de projetar um modelo de circuito oscilador com uma frequência natural amortecida de 4 kilohertz e um fator de amortecimento de 4 radianos por segundo.
Com uma resistência definida de 200 ohms, os valores precisos de capacitância e indutância podem ser determinados.
Como o fator de amortecimento do circuito é o recíproco de duas vezes o produto da resistência e capacitância, o valor de capacitância necessário para o projeto do circuito é obtido.
A expressão matemática que correlaciona a frequência ressonante, o fator de amortecimento e a frequência natural amortecida é usada para obter a frequência ressonante.
A frequência de ressonância é inversamente proporcional à raiz quadrada do produto da indutância e capacitância.
Os valores conhecidos são substituídos nesta equação para obter a indutância necessária.
A frequência natural amortecida é menor que a frequência ressonante e o valor da indutância é menor que quatro vezes o quadrado da resistência multiplicado pela capacitância. Ambas as condições confirmam a oscilação subamortecida.

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exemplo de projeto: circuito rlc paralelo

Considere projetar um circuito oscilador, um componente crucial em vários dispositivos e sistemas eletrônicos. O objetivo é criar um circuito oscilador com características específicas: frequência natural amortecida de 4 kHz e fator de amortecimento de 4 radianos por segundo. Para conseguir isso, é empregado um circuito RLC paralelo, conhecido por sua capacidade de sustentar oscilações em uma frequência ressonante. Neste caso, o fator de amortecimento é fundamental para alcançar o desempenho desejado.

Começando com uma resistência fixa de 200 Ω, são determinados os valores necessários de capacitância e indutância para atender às especificações. Primeiro, reconhece-se que o fator de amortecimento é o inverso do dobro do produto da resistência e da capacitância. Esse insight permite identificar o valor de capacitância necessário para o circuito.

<img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;" />

A seguir, a atenção se volta para a expressão matemática que conecta a frequência de ressonância, o fator de amortecimento e a frequência natural amortecida. Ao manipular esta equação, informações de frequência ressonante podem ser extraídas.

<img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;" />

A frequência ressonante, crucial para o projeto do oscilador, é inversamente proporcional à raiz quadrada do produto da indutância e da capacitância. Munido deste conhecimento e dos valores conhecidos, é calculada a indutância necessária para atender aos critérios de projeto.

<img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;" />

Estes cálculos confirmam que a frequência natural amortecida é de facto inferior à frequência de ressonância, e o valor da indutância cai abaixo de quatro vezes o quadrado da resistência multiplicado pela capacitância. Estas condições afirmam que o circuito oscilador foi projetado para exibir as oscilações subamortecidas necessárias, demonstrando proficiência no projeto preciso do circuito.

Exemplo de Projeto: Circuito RLC Paralelo

Circuitos RLC paralelos subamortecidos podem sustentar oscilações em uma frequência ressonante, tornando-os adequados para uso em osciladores.
Um engenheiro elétrico é ...

design-example-underdamped-parallel-rlc-circuit

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

First and Second-Order Circuits

Circuitos de Primeira e Segunda Ordem

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

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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...

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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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