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

Düşük sönümlü paralel RLC devreleri, rezonans frekansında salınımları sürdürebilir ve bu da onları osilatörlerde kullanıma uygun hale getirir.
Bir elektrik mühendisi, 4 kilohertz sönümlü doğal frekansa ve saniyede 4 radyan sönümleme faktörüne sahip bir model osilatör devresi tasarlamakla görevlendirilir.
200 ohm'luk bir ayar direnci ile kapasitans ve endüktans için kesin değerler belirlenebilir.
Devre için sönümleme faktörü, direnç ve kapasitansın çarpımının iki katının tersi olduğundan, devre tasarımı için gerekli kapasitans değeri elde edilir.
Rezonans frekansını, sönümleme faktörünü ve sönümlü doğal frekansı ilişkilendiren matematiksel ifade, rezonans frekansını elde etmek için kullanılır.
Rezonans frekansı, endüktans ve kapasitans ürününün karekökü ile ters orantılıdır.
Gerekli endüktansı elde etmek için bilinen değerler bu denklemin yerine ikame edilir.
Sönümlü doğal frekans, rezonans frekansından daha düşüktür ve endüktans değeri, kapasitans ile çarpılan direncin karesinin dört katından daha azdır. Bu koşulların her ikisi de düşük sönümlü salınımı doğrular.

Herhangi bir çıkar çatışması beyan edilmedi.

tasarım Örneği: paralel rlc devresi

Çeşitli elektronik cihaz ve sistemlerde önemli bir bileşen olan bir osilatör devresi tasarlamayı düşünün. Amaç, belirli özelliklere sahip bir osilatör devresi oluşturmaktır: 4 kHz'lik sönümlü doğal frekans ve saniyede 4 radyanlık sönümleme faktörü. Bunu başarmak için, salınımları rezonans frekansında sürdürme yeteneği ile bilinen paralel bir RLC devresi kullanılır. Bu durumda sönümleme faktörü istenen performansın elde edilmesinde çok önemlidir.

200 Ω'luk sabit bir dirençten başlayarak spesifikasyonları karşılayacak kapasite ve endüktans için gerekli değerler belirlenir. İlk olarak, sönümleme faktörünün direnç ve kapasitans çarpımının iki katının tersi olduğu kabul edilmektedir. Bu anlayış, devre için gerekli kapasitans değerinin tam olarak belirlenmesine olanak sağlar.

<img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;" />

Daha sonra, rezonans frekansını, sönüm faktörünü ve sönümlü doğal frekansı birbirine bağlayan matematiksel ifadeye dikkat çekilir. Bu denklemi değiştirerek rezonans frekansı bilgisi çıkarılabilir.

<img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;" />

Osilatör tasarımı için çok önemli olan rezonans frekansı, endüktans ve kapasitans çarpımının kareköküyle ters orantılıdır. Bu bilgi ve bilinen değerlerle donatılarak tasarım kriterlerini karşılamak için gerekli endüktans hesaplanır.

<img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;" />

Bu hesaplamalar, sönümlü doğal frekansın gerçekten de rezonans frekansından daha düşük olduğunu ve endüktans değerinin, direncin karesinin kapasitansla çarpımının dört katının altına düştüğünü doğrulamaktadır. Bu koşullar, osilatör devresinin gerekli sönümsüz salınımları sergileyecek şekilde tasarlandığını doğrulamakta ve hassas devre tasarımındaki yeterliliği ortaya koymaktadır.

Tasarım Örneği: Paralel RLC Devresi

Düşük sönümlü paralel RLC devreleri, rezonans frekansında salınımları sürdürebilir ve bu da onları osilatörlerde kullanıma uygun hale getirir.
Bir elektrik mühendisi ...

design-example-underdamped-parallel-rlc-circuit

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

First and Second-Order Circuits

Birinci ve İkinci Dereceden Devreler

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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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...

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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 Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

Oscillator Design with a Parallel RLC Circuit

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