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

Si consideri un sintonizzatore radio AM che comprende un collegamento in parallelo di un resistore, un condensatore e un induttore, che contribuiscono collettivamente all'ammettenza di ingresso del circuito.
In risonanza, la parte immaginaria dell'ammettenza è zero, facendo sì che la frequenza di risonanza vari inversamente con la radice quadrata del prodotto dell'induttanza e della capacità.
Alla frequenza di risonanza, la combinazione parallela dell'induttore e del condensatore agisce come un circuito aperto. Di conseguenza, il resistore assorbe una corrente minima e l'energia oscilla tra il campo magnetico dell'induttore e il campo elettrico del condensatore.
La risposta in frequenza indica che l'ampiezza della corrente inizialmente diminuisce, raggiunge un minimo alla frequenza di risonanza e aumenta all'aumentare della frequenza.
Alle frequenze a metà potenza, la corrente è 1,4142 volte la corrente minima.
La larghezza di banda viene calcolata determinando la differenza tra le frequenze di metà potenza più alte e più basse.
Il fattore di qualità, che indica la nitidezza della curva di risonanza, può essere espresso in termini di reattanze.
Un fattore di qualità più elevato produce frequenze a metà potenza distribuite simmetricamente attorno alla frequenza di risonanza e una larghezza di banda più stretta.

risposta in frequenza

Il circuito RLC parallelo è una disposizione in cui il resistore (R), l'induttore (L) e il condensatore (C), sono tutti collegati agli stessi nodi e di conseguenza, condividono la stessa tensione ai loro capi. Il circuito RLC parallelo viene analizzato in termini di ammettenza (Y), che riflette la facilità con cui la corrente può fluire. L'ammettenza è data da:


<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="height: 30px;">

La risonanza in un circuito RLC parallelo, si verifica quando la reattanza netta è zero, il che significa che gli effetti capacitivo e induttivo si annullano a vicenda. Questa condizione si realizza quando:


<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="height: 30px;">

Risolvendo per la frequenza di risonanza si ottiene:

<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="height: 34px;">

Questa frequenza di risonanza è il punto in cui il circuito mostrerà un comportamento puramente resistivo e la corrente attraverso il resistore sarà massima. La potenza dissipata nel circuito è massima in risonanza a causa del massimo flusso di corrente. Alle frequenze del punto di metà potenza, la corrente è circa 0,707 della corrente massima, portando a metà della dissipazione di potenza massima. La larghezza di banda del circuito RLC parallelo, è la differenza tra queste frequenze a metà potenza e si trova utilizzando:

<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="height: 30px;">

Il fattore di merito (Q) è un parametro adimensionale che confronta la frequenza di risonanza con la larghezza di banda, indicando la selettività o la nitidezza del picco di risonanza. Nei circuiti di alta qualità in cui Q≥10, le frequenze di metà potenza possono essere approssimate utilizzando:

<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 fattore Q più alto significa che il circuito è altamente selettivo, risuonando fortemente in una gamma ristretta di frequenze attorno alla frequenza di risonanza. Questa proprietà è particolarmente vantaggiosa nelle comunicazioni radio, poiché consente di filtrare le frequenze indesiderate e ridurre al minimo le interferenze. I circuiti di risonanza paralleli sono particolarmente utili nelle applicazioni di filtraggio, agendo come filtri elimina banda o notch, bloccando una gamma di frequenza specifica e consentendo il passaggio di altre. Ciò li rende preziosi nell'elaborazione del segnale per eliminare frequenze o rumore indesiderati.

Risposta in Frequenza

Si consideri un sintonizzatore radio AM che comprende un collegamento in parallelo di un resistore, un condensatore e un induttore, che contribuiscono collettivamente al circuito ...

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

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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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

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electrical engineering

Parallel RLC Tuning at Resonance

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