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

댐핑이 부족한 병렬 RLC 회로는 공진 주파수에서 발진을 견딜 수 있으므로 발진기에 사용하기에 적합합니다.
한 전기 엔지니어가 4kW의 감쇠 고유 주파수와 초당 4라디안의 감쇠 계수를 갖는 모델 발진기 회로를 설계하는 임무를 맡고 있습니다.
200옴의 설정 저항으로 커패시턴스와 인덕턴스에 대한 정확한 값을 결정할 수 있습니다.
회로의 댐핑 계수는 저항과 커패시턴스의 곱의 두 배의 역수이기 때문에 회로 설계에 필요한 커패시턴스 값을 얻습니다.
공진 주파수, 감쇠 계수 및 감쇠된 고유 주파수를 상관시키는 수학적 표현을 사용하여 공진 주파수를 얻습니다.
공진 주파수는 인덕턴스와 커패시턴스의 곱의 제곱근에 반비례합니다.
알려진 값은 필요한 인덕턴스를 얻기 위해 이 방정식에 대체됩니다.
감쇠된 고유 주파수는 공진 주파수보다 낮고 인덕턴스 값은 저항 제곱에 커패시턴스를 곱한 값의 4배 미만입니다. 이 두 가지 조건 모두 저감쇠 진동을 확인합니다.

설계 예: 병렬 rlc 회로

다양한 전자 장치 및 시스템의 중요한 구성 요소인 발진기 회로 설계를 생각해 보세요. 목표는 4kHz의 감쇠 고유 주파수와 초당 4라디안의 감쇠 계수와 같은 특정 특성을 가진 발진기 회로를 만드는 것입니다. 이를 달성하기 위해 공진 주파수에서 진동을 유지하는 능력으로 알려진 병렬 RLC 회로가 사용됩니다. 이 경우 감쇠 계수는 원하는 성능을 달성하는 데 중추적인 역할을 합니다.

200Ω의 고정 저항으로 시작하여 사양에 맞게 전기용량과 유도계수에 필요한 값이 결정됩니다. 첫째, 댐핑 팩터는 저항과 전기용량의 곱의 두 배의 역수라는 것이 인식됩니다. 이러한 통찰력을 통해 회로에 필요한 전기용량 값을 정확히 찾아낼 수 있습니다.

<img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;">

다음으로 공진주파수, 감쇠계수, 감쇠고유주파수를 연결하는 수학적 표현에 주목한다. 이 방정식을 조작하면 공진주파수 정보를 추출할 수 있습니다.

<img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;">

발진기 설계에 중요한 공진 주파수는 유도계수와 전기용량 곱의 제곱근에 반비례합니다. 이러한 지식과 알려진 값을 바탕으로 설계 기준을 충족하는 데 필요한 유도계수가 계산됩니다.

<img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;">

이러한 계산을 통해 감쇠된 고유 주파수가 실제로 공진 주파수보다 낮고 유도계수 값이 저항에 전기용량을 곱한 값의 제곱의 4배 아래로 떨어진다는 사실이 확인되었습니다. 이러한 조건은 발진기 회로가 필요한 저감쇠 발진을 나타내도록 설계되었으며 정밀한 회로 설계의 숙련도를 보여줍니다.

설계 예: 병렬 RLC 회로

댐핑이 부족한 병렬 RLC 회로는 공진 주파수에서 발진을 견딜 수 있으므로 발진기에 사용하기에 적합합니다.
전기 엔지니어는 ...

design-example-underdamped-parallel-rlc-circuit

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

First and Second-Order Circuits

1차 및 2차 회로

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

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RC Circuit Charging After a DC Step

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rl circuit without source

RL Circuit Decay After Source Removal

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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

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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...

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Second-Order Op Amp Low-Pass Filters

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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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