Name: parallel rlc tuning at resonance
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 23 s
Channel: JoVE

Considérons un tuner radio AM comprenant une connexion parallèle d'une résistance, d'un condensateur et d'une inductance, qui contribuent collectivement à l'admission d'entrée du circuit.
À la résonance, la partie imaginaire de l’admission est nulle, ce qui fait que la fréquence de résonance varie inversement avec la racine carrée du produit de l’inductance et de la capacité.
À la fréquence de résonance, la combinaison parallèle de l’inductance et du condensateur agit comme un circuit ouvert. En conséquence, la résistance consomme un courant minimal et l'énergie oscille entre le champ magnétique de l'inductance et le champ électrique du condensateur.
La réponse en fréquence indique que l’amplitude du courant diminue initialement, atteint un minimum à la fréquence de résonance et augmente à mesure que la fréquence augmente.
Aux fréquences de demi-puissance, le courant est de 1,4142 fois le courant minimum.
La bande passante est calculée en déterminant la différence entre les fréquences supérieures et inférieures de demi-puissance.
Le facteur de qualité, qui indique la netteté de la courbe de résonance, peut être exprimé en termes de réactances.
Un facteur de qualité plus élevé donne des fréquences de demi-puissance réparties symétriquement autour de la fréquence de résonance et une bande passante plus étroite.

réponse en fréquence

Le circuit RLC parallèle est un arrangement dans lequel la résistance (R), l'inductance (L) et le condensateur (C) sont tous connectés aux mêmes nœuds et, par conséquent, partagent la même tension à leurs bornes. Le circuit RLC parallèle est analysé en termes d'admittance (Y), qui reflète la facilité avec laquelle le courant peut circuler. L'admission est donnée par :
<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="height: 30px;">
La résonance dans un circuit RLC parallèle se produit lorsque la réactance nette est nulle, ce qui signifie que les effets capacitifs et inductifs s'annulent. Cette condition est atteinte lorsque :
<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="height: 30px;">
La résolution de la fréquence de résonance donne :
<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="height: 34px;">
C'est à cette fréquence de résonance que le circuit présentera un comportement purement résistif et que le courant traversant la résistance sera à son maximum. La puissance dissipée dans le circuit est maximale à la résonance en raison du flux de courant maximal. Aux fréquences de demi-puissance, le courant représente environ 0,707 du courant maximum, ce qui correspond à la moitié de la dissipation de puissance maximale. La bande passante du circuit RLC parallèle est la différence entre ces fréquences demi-puissance et se trouve en utilisant :
<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="height: 30px;">
Le facteur de qualité (Q) est un paramètre sans dimension qui compare la fréquence de résonance à la bande passante, indiquant la sélectivité ou la netteté du pic de résonance. Dans les circuits de haute qualité où Q≥10, les fréquences demi-puissance peuvent être approximées en utilisant :
<img alt="Equation 5" src="/files/ftp_upload/15145/15145_Equation_5.svg" style="height: 30px;">
<img alt="Equation 6" src="/files/ftp_upload/15145/15145_Equation_6.svg" style="height: 30px;">
 Un facteur Q plus élevé signifie que le circuit est hautement sélectif et résonne fortement sur une plage étroite de fréquences autour de la fréquence de résonance. Cette propriété est particulièrement bénéfique dans les communications radio, car elle permet de filtrer les fréquences indésirables et de minimiser les interférences. Les circuits de résonance parallèle sont particulièrement utiles dans les applications de filtrage agissant comme des filtres coupe-bande ou coupe-bande, bloquant une plage de fréquences spécifique tout en permettant aux autres de passer. Cela les rend précieux dans le traitement du signal pour éliminer les fréquences ou le bruit indésirables.

Réponse en fréquence

Considérons un tuner radio AM comprenant une connexion parallèle d'une résistance, d'un condensateur et d'une inductance, qui contribuent collectivement à la ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Parallel Resonance

parallel rlc tuning at resonance

A parallel RLC circuit uses a resistor, inductor, and capacitor connected to the same nodes. Because they share the same voltage, the circuit is analyzed with admittance, which describes how easily current can flow. In a parallel RLC circuit, admittance helps show how the circuit responds as the frequency changes.

Resonance happens when the net reactance is zero. At that point, the capacitive and inductive effects cancel each other out. The resonant frequency is found from this condition. At resonance, the circuit behaves as a purely resistive circuit, and the current through the resistor reaches its maximum.

Power dissipation is also greatest at resonance because the current is highest. The half-power point frequencies are the points where the current is about 0.707 of the maximum current. At those frequencies, the power dissipation is half of its maximum value. The bandwidth of the parallel RLC circuit is the difference between the two half-power frequencies.

The quality factor, or Q, compares the resonant frequency with the bandwidth. It shows how sharp or selective the resonance peak is. For high-quality circuits where Q is 10 or greater, the half-power frequencies can be approximated with a simpler method. A higher Q means the circuit responds strongly to a narrow range of frequencies around resonance.

This selective behavior is useful in radio communications. It can help filter unwanted frequencies and reduce interference. Parallel resonance circuits are also used as band-stop or notch filters. In these filters, a specific frequency range is blocked while other frequencies pass through, which is useful for removing unwanted signals or noise.

Parallel RLC Tuning at Resonance

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parallel resonance

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key terms and concepts

Explore how a parallel RLC circuit behaves at resonance, including admittance, bandwidth, Q factor, and its use in radio tuning and notch filtering.

Parallel RLC Tuning at Resonance | 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

Parallel RLC Tuning at Resonance

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