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

I circuiti RLC paralleli sottosmorzati possono sostenere oscillazioni a una frequenza di risonanza, il che li rende adatti per l'uso negli oscillatori.
Un ingegnere elettrico ha il compito di progettare un circuito oscillatore modello con una frequenza naturale smorzata di 4 kilohertz e un fattore di smorzamento di 4 radianti al secondo.
Con una resistenza impostata di 200 ohm, è possibile determinare i valori precisi di capacità e induttanza.
Poiché il fattore di smorzamento per il circuito è il reciproco del doppio del prodotto della resistenza e della capacità, si ottiene il valore di capacità richiesto per la progettazione del circuito.
L'espressione matematica che correla la frequenza di risonanza, il fattore di smorzamento e la frequenza naturale smorzata viene utilizzata per ottenere la frequenza di risonanza.
La frequenza di risonanza è inversamente proporzionale alla radice quadrata del prodotto di induttanza e capacità.
I valori noti vengono sostituiti in questa equazione per ottenere l'induttanza richiesta.
La frequenza naturale smorzata è inferiore alla frequenza di risonanza e il valore di induttanza è inferiore a quattro volte il quadrato della resistenza moltiplicato per la capacità. Entrambe queste condizioni confermano un'oscillazione sottosmorzata.

Nessun conflitto di interessi dichiarato.

esempio di progettazione: circuito rlc parallelo

Si consideri la progettazione di un circuito oscillatore, un componente cruciale in vari dispositivi e sistemi elettronici. L'obiettivo è creare un circuito oscillatore con caratteristiche specifiche: una frequenza naturale smorzata di 4 kHz e un fattore di smorzamento di 4 radianti al secondo. Per ottenere ciò, viene utilizzato un circuito RLC parallelo, noto per la sua capacità di sostenere oscillazioni a una frequenza di risonanza. In questo caso, il fattore di smorzamento è fondamentale per ottenere le prestazioni desiderate.

Partendo da una resistenza fissa di 200 Ω, vengono determinati i valori necessari di capacità e induttanza per soddisfare le specifiche. Innanzitutto, si riconosce che il fattore di smorzamento è il reciproco del doppio del prodotto tra resistenza e capacità. Questa intuizione consente di individuare il valore di capacità richiesto per il circuito.

<img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;">

Successivamente, l'attenzione viene rivolta all'espressione matematica che collega la frequenza di risonanza, il fattore di smorzamento e la frequenza naturale smorzata. Manipolando questa equazione, è possibile estrarre informazioni sulla frequenza di risonanza.

<img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;">

La frequenza di risonanza, cruciale per la progettazione dell'oscillatore, è inversamente proporzionale alla radice quadrata del prodotto di induttanza e capacità. Grazie a queste conoscenze e ai valori noti, viene calcolata l'induttanza necessaria per soddisfare i criteri di progettazione.

<img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;">

Questi calcoli confermano che la frequenza naturale smorzata è effettivamente inferiore alla frequenza di risonanza e il valore dell'induttanza scende al di sotto di quattro volte il quadrato della resistenza moltiplicata per la capacità. Queste condizioni affermano che il circuito dell'oscillatore è stato progettato per mostrare le oscillazioni sottosmorzate richieste, dimostrando competenza nella progettazione precisa del circuito.

Esempio di Progettazione: Circuito RLC Parallelo

I circuiti RLC paralleli sottosmorzati possono sostenere oscillazioni a una frequenza di risonanza, il che li rende adatti per l'uso negli oscillatori.
Un ingegnere elettrico è ...

design-example-underdamped-parallel-rlc-circuit

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

First and Second-Order Circuits

Circuiti del primo e del secondo ordine

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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