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

Stellen Sie sich einen AM-Radiotuner vor, der aus einer Parallelschaltung eines Widerstands, eines Kondensators und einer Induktivität besteht, die zusammen zur Eingangsdurchlassung der Schaltung beitragen.
Bei Resonanz ist der Imaginärteil der Admittanz Null, wodurch die Resonanzfrequenz umgekehrt mit der Quadratwurzel des Produkts aus Induktivität und Kapazität variiert.
Bei der Resonanzfrequenz wirkt die parallele Kombination von Induktivität und Kondensator wie ein offener Stromkreis. Infolgedessen zieht der Widerstand nur minimalen Strom und die Energie oszilliert zwischen dem Magnetfeld der Induktivität und dem elektrischen Feld des Kondensators.
Der Frequenzgang zeigt an, dass die Stromstärke zunächst abnimmt, bei der Resonanzfrequenz ein Minimum erreicht und mit zunehmender Frequenz zunimmt.
Bei den Frequenzen halber Leistung beträgt der Strom das 1,4142-fache des minimalen Stroms.
Die Bandbreite wird berechnet, indem die Differenz zwischen der höheren und der niedrigeren Halbwertsfrequenz bestimmt wird.
Der Qualitätsfaktor, der die Schärfe der Resonanzkurve angibt, kann in Form der Reaktanzen ausgedrückt werden.
Ein höherer Qualitätsfaktor führt zu Frequenzen halber Leistung, die symmetrisch um die Resonanzfrequenz verteilt sind, und einer schmaleren Bandbreite.

frequenzgang

Der parallele RLC-Schaltkreis ist eine Anordnung, bei der Widerstand (R), Induktor (L) und Kondensator (C) alle an dieselben Knoten angeschlossen sind und daher dieselbe Spannung über sie teilen. Der parallele RLC-Schaltkreis wird hinsichtlich der Admittanz (Y) analysiert, die die Leichtigkeit widerspiegelt, mit der Strom fließen kann. Die Admittanz wird wie folgt angegeben:

<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="text-align: center; height: 30px;">

Resonanz in einem parallelen RLC-Schaltkreis tritt auf, wenn die Nettoreaktanz Null ist, was bedeutet, dass sich die kapazitiven und induktiven Effekte gegenseitig aufheben. Dieser Zustand wird erreicht, wenn:

<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="text-align: center; height: 30px;">

Die Lösung für die Resonanzfrequenz ergibt:

<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="text-align: center; height: 34px;">

Bei dieser Resonanzfrequenz zeigt der Schaltkreis ein rein resistives Verhalten und der Strom durch den Widerstand ist maximal. Die im Schaltkreis verbrauchte Leistung ist bei Resonanz aufgrund des maximalen Stromflusses maximal. Bei den Halbleistungspunktfrequenzen beträgt der Strom ungefähr 0,707 des Maximalstroms, was zur Hälfte der maximalen Leistungsableitung führt. Die Bandbreite des parallelen RLC-Schaltkreises ist die Differenz zwischen diesen Halbleistungsfrequenzen und wird wie folgt ermittelt:

<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="text-align: center; height: 30px;">

Der Qualitätsfaktor (Q) ist ein dimensionsloser Parameter, der die Resonanzfrequenz mit der Bandbreite vergleicht und die Selektivität oder Schärfe des Resonanzpeaks angibt. In hochwertigen Schaltkreisen mit Q≥10 können die Halbleistungsfrequenzen wie folgt angenähert werden:

<img alt="Equation 5" src="/files/ftp_upload/15145/15145_Equation_5.svg" style="text-align: center; height: 30px;">

<img alt="Equation 6" src="/files/ftp_upload/15145/15145_Equation_6.svg" style="text-align: center; height: 30px;">

Ein höherer Q-Faktor bedeutet, dass der Schaltkreis hochselektiv ist und in einem engen Frequenzbereich um die Resonanzfrequenz herum stark resoniert. Diese Eigenschaft ist besonders bei Funkkommunikation von Vorteil, da sie das Filtern unerwünschter Frequenzen und Minimieren von Interferenzen ermöglicht. Parallelresonanzkreise sind besonders nützlich in Filteranwendungen, da sie als Bandsperren oder Sperrfilter fungieren und einen bestimmten Frequenzbereich blockieren, während andere durchgelassen werden. Dies macht sie in der Signalverarbeitung wertvoll, um unerwünschte Frequenzen oder Rauschen zu eliminieren.

Frequenzgang

Betrachten Sie einen AM-Radiotuner, der aus einer Parallelschaltung eines Widerstands, eines Kondensators und einer Induktivität besteht, die zusammen zur ...

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KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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.

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Parallel RLC Tuning at Resonance

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