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

Si consideri un'unità trasmettitore radio che incorpora un filtro passa-banda di risonanza della serie RLC.
La risposta in frequenza di questo circuito indica che l'ampiezza della corrente inizialmente aumenta, raggiunge il picco alla frequenza di risonanza e diminuisce all'aumentare della frequenza.
La dissipazione di potenza, corrispondente al valore massimo di corrente, è massima in risonanza.
Alle frequenze a metà potenza, la corrente è 0,707 volte la corrente massima e la potenza dissipata è la metà della massima.
La frequenza di risonanza è la media geometrica di queste frequenze a metà potenza.
La larghezza di banda, definita come l'intervallo di frequenza tra le frequenze a metà potenza, è uguale al rapporto tra resistenza e induttanza.
Il fattore di qualità, che rappresenta la nitidezza della curva di risonanza, mette in relazione l'energia massima immagazzinata nel circuito con l'energia dissipata per ciclo di oscillazione.
Alla risonanza, l'energia reattiva oscilla tra gli elementi reattivi, producendo un'espressione del fattore di qualità in termini di reattanze.
Questo fattore può essere espresso come il rapporto tra la frequenza di risonanza e la larghezza di banda.
Un fattore di qualità più elevato implica una larghezza di banda più stretta, aumentando così la selettività.

risposta in frequenza

Characteristics of Series Resonant Circuit

La risonanza in serie si verifica in un circuito contenente elementi induttivi (L), capacitivi (C) e resistivi (R) collegati in sequenza. Alla frequenza di risonanza, le reattanze induttive e capacitive sono uguali in grandezza ma opposte in segno, annullandosi di fatto a vicenda. Ciò fa sì che l'impedenza del circuito sia minima, determinata principalmente dalla resistenza R. La frequenza di risonanza di un circuito RLC è definita come:

<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">

La dissipazione di potenza nel resistore è proporzionale al quadrato della corrente. Ciò dimostra che la dissipazione di potenza è massima anche quando la corrente è massima in condizione di risonanza. Tale potenza massima è data da:

<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">

dove Imax è la corrente massima alla risonanza.

La larghezza di banda di un circuito, è definita come l'intervallo di frequenza nel quale la potenza dissipata diminuisce fino alla metà del suo valore massimo. Ciò si verifica alle frequenze di metà potenza, dove la corrente si riduce a circa il 70,7% del suo livello massimo. La larghezza di banda, viene calcolata come la differenza tra le frequenze di metà potenza superiore e inferiore.

Durante la risonanza, la potenza reattiva non si dissipa, ma oscilla tra l'induttore e il condensatore, mentre la potenza resistiva viene dissipata nel resistore. Il fattore di merito indica l'energia massima immagazzinata nel circuito rispetto all'energia dissipata per ciclo. Nell'applicazione, un trasmettitore radio con un fattore Q più elevato per il suo filtro RLC, può isolare meglio il segnale desiderato dal rumore della frequenza vicina. Il compromesso è la larghezza di banda: un Q più elevato riduce la larghezza di banda, il che potrebbe limitare l'applicabilità del filtro nei sistemi che richiedono una gamma di frequenza più completa.

Un circuito di risonanza della serie RLC, esemplifica l'ingegneria di precisione nella trasmissione radio funzionando come un efficace filtro passa-banda. Questo circuito è progettato con precisione per consentire un picco di intensità di corrente alla frequenza di risonanza, consentendo la trasmissione e la ricezione selettiva della frequenza.

Risposta in Frequenza

Si consideri un'unità trasmettitore radio che incorpora un filtro passa-banda di risonanza della serie RLC.
La risposta in frequenza di questo circuito indica che il ...

characteristics-of-series-resonant-circuit

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Frequency Response

Risposta in frequenza

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

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Reading Frequency Response with Bode Plots

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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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