Name: series resonance and rlc filter behavior
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 24 s
Channel: JoVE

Prenons l’exemple d’un émetteur radio qui intègre un filtre passe-bande de résonance de la série RLC.
La réponse en fréquence de ce circuit indique que l'amplitude du courant augmente initialement, atteint un pic à la fréquence de résonance et diminue à mesure que la fréquence augmente.
La dissipation de puissance, correspondant à la valeur maximale du courant, est la plus élevée à la résonance.
Aux fréquences de demi-puissance, le courant est 0,707 fois le courant maximum et la puissance dissipée est la moitié du maximum.
La fréquence de résonance est la moyenne géométrique de ces fréquences de demi-puissance.
La bande passante, définie comme la gamme de fréquences entre les fréquences de demi-puissance, est égale au rapport entre la résistance et l’inductance.
Le facteur de qualité, représentant la netteté de la courbe de résonance, relie l’énergie maximale stockée dans le circuit à l’énergie dissipée par cycle d’oscillation.
À la résonance, l’énergie réactive oscille entre les éléments réactifs, ce qui permet d’exprimer le facteur de qualité en termes de réactances.
Ce facteur peut être exprimé comme le rapport entre la fréquence de résonance et la largeur de bande.
Un facteur de qualité plus élevé implique une bande passante plus étroite, augmentant ainsi la sélectivité.

réponse en fréquence

Characteristics of Series Resonant Circuit

La résonance série se produit dans un circuit contenant des éléments inductifs (L), capacitifs (C) et résistifs (R) connectés séquentiellement. À la fréquence de résonance, les réactances inductives et capacitives sont égales en amplitude mais de signe opposé, s’annulant efficacement. Cela fait que l'impédance du circuit est minimale, principalement déterminée par la résistance R. La fréquence de résonance d'un circuit RLC est définie comme:

<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">

La puissance dissipée dans la résistance est proportionnelle au carré du courant. Cela montre que la dissipation de puissance est également maximale lorsque le courant est maximal dans une condition de résonance. Cette puissance maximale est donnée par:

<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">

où Imax est le courant maximum à la résonance.

La bande passante d'un circuit est définie comme la plage de fréquences sur laquelle la puissance dissipée diminue jusqu'à la moitié de sa valeur maximale. Cela se produit aux fréquences de demi-puissance, où le courant diminue à environ 70,7 % de son niveau maximum. La bande passante est calculée comme la différence entre les fréquences de demi-puissance supérieures et inférieures.

À la résonance, la puissance réactive ne se dissipe pas mais oscille entre l'inductance et le condensateur, tandis que la puissance résistive est dissipée dans la résistance. Le facteur de qualité concerne l'énergie maximale stockée dans le circuit par rapport à l'énergie dissipée par cycle. En application, un émetteur radio avec un facteur Q plus élevé pour son filtre RLC peut mieux isoler un signal souhaité du bruit de fréquence proche. Le compromis est la bande passante : un Q plus élevé réduit la bande passante, ce qui pourrait limiter l'applicabilité du filtre dans les systèmes nécessitant une gamme de fréquences plus complète.

Un circuit de résonance de la série RLC illustre l'ingénierie de précision dans la transmission radio en fonctionnant comme un filtre passe-bande efficace. Ce circuit est précisément conçu pour permettre un pic d'amplitude de courant à la fréquence de résonance, permettant une transmission et une réception de fréquence sélective.

Réponse en fréquence

Prenons l’exemple d’un émetteur radio qui intègre un filtre passe-bande de résonance de la série RLC.
La réponse en fréquence de ce circuit indique que le ...

characteristics-of-series-resonant-circuit

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

series resonance and rlc filter behavior

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance.

The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum value. Because power loss in the resistor depends on the square of the current, the power dissipated in the resistor is also highest at resonance.

Bandwidth describes the range of frequencies over which the power falls to half of its maximum value. These are the half-power frequencies, where the current drops to about 70.7% of its peak value. The bandwidth is found by subtracting the lower half-power frequency from the higher one.

At resonance, reactive power does not turn into heat. Instead, it moves back and forth between the inductor and the capacitor. The resistor is where real power is dissipated. The quality factor, or Q factor, compares the maximum energy stored in the circuit with the energy lost each cycle.

This behavior is useful in radio transmitters and similar systems. A higher-Q RLC filter can separate a desired signal from nearby frequency noise more effectively. The trade-off is a narrower bandwidth, which can limit use in systems that need a wider frequency range. In this way, a series resonant circuit works as a band-pass filter that favors one frequency range over others.

Series Resonance and RLC Filter Behavior

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series resonance

Series Resonance in RLC Circuits

Series resonance in an RLC circuit happens when the inductive reactance and capacitive reactance are equal. An RLC circuit contains a resistor, an inductor, and a capacitor. The impedance of the circuit is the ratio of the supply voltage to the circuit current. At resonance, the imaginary part of the impedance becomes zero. The frequency at which this occurs is called the resonant frequency. It depends on the inductance (L) and capacitance (C) of the circuit. Mathematically, the resonant...

characteristics of series resonant circuit

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance. The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum...

parallel resonance

Parallel RLC Tuning at Resonance

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key terms and concepts

Learn how series resonance in an RLC circuit creates maximum current, minimum impedance, bandwidth limits, and filter behavior used in radio systems.

Series Resonance and RLC Filter Behavior | 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

Series Resonance and RLC Filter Behavior

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