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

Stellen Sie sich eine Funksendeeinheit vor, die einen Resonanz-Bandpassfilter der RLC-Serie enthält.
Der Frequenzgang dieser Schaltung zeigt an, dass die Stromstärke zunächst zunimmt, bei der Resonanzfrequenz ihren Höhepunkt erreicht und mit zunehmender Frequenz abnimmt.
Die Verlustleistung, die dem maximalen Stromwert entspricht, ist bei Resonanz am höchsten.
Bei den Frequenzen mit halber Leistung beträgt der Strom das 0,707-fache des maximalen Stroms, und die Verlustleistung beträgt die Hälfte des Maximums.
Die Resonanzfrequenz ist das geometrische Mittel dieser Halbwertsfrequenzen.
Die Bandbreite, definiert als der Frequenzbereich zwischen den Halbwertsfrequenzen, entspricht dem Verhältnis von Widerstand zu Induktivität.
Der Qualitätsfaktor, der die Schärfe der Resonanzkurve darstellt, setzt die maximal in der Schaltung gespeicherte Energie in Beziehung zur pro Schwingungszyklus abgegebenen Energie.
Bei der Resonanz oszilliert die Blindenergie zwischen den Blindelementen, was den Qualitätsfaktor in Form von Reaktanzen zum Ausdruck bringt.
Dieser Faktor kann als Verhältnis der Resonanzfrequenz zur Bandbreite ausgedrückt werden.
Ein höherer Qualitätsfaktor impliziert eine geringere Bandbreite und damit eine höhere Selektivität.

frequenzgang

Characteristics of Series Resonant Circuit

Serienresonanz tritt in einem Schaltkreis auf, der induktive (L), kapazitive (C) und resistive (R) Elemente enthält, die in Reihe geschaltet sind. Bei der Resonanzfrequenz sind die induktiven und kapazitiven Reaktanzen gleich groß, haben aber entgegengesetzte Vorzeichen, wodurch sie sich gegenseitig aufheben. Dies führt dazu, dass die Impedanz des Schaltkreises minimal ist und in erster Linie durch den Widerstand R bestimmt wird. Die Resonanzfrequenz eines RLC-Schaltkreises ist definiert als:

<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">

Die Verlustleistung im Widerstand ist proportional zum Quadrat des Stroms. Dies zeigt, dass die Verlustleistung auch dann maximal ist, wenn der Strom in einem Resonanzzustand maximal ist. Diese maximale Leistung ergibt sich aus:

<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">

wobei I_max der maximale Strom bei Resonanz ist.

Die Bandbreite eines Schaltkreises ist definiert als der Frequenzbereich, über den die Verlustleistung auf die Hälfte ihres Maximalwerts abnimmt. Dies geschieht bei den Halbleistungsfrequenzen, bei denen der Strom auf etwa 70,7 % seines Maximalpegels absinkt. Die Bandbreite wird als Differenz zwischen der höheren und der niedrigeren Halbleistungsfrequenz berechnet.

Bei Resonanz wird Blindleistung nicht abgeführt, sondern oszilliert zwischen der Induktivität und dem Kondensator, während Widerstandsleistung im Widerstand abgeführt wird. Der Qualitätsfaktor bezieht sich auf die im Schaltkreis gespeicherte maximale Energie im Vergleich zur pro Zyklus abgeführten Energie. In der Anwendung kann ein Funksender mit einem höheren Q-Faktor für seinen RLC-Filter ein gewünschtes Signal besser von nahegelegenem Frequenzrauschen isolieren. Der Kompromiss ist die Bandbreite: Ein höherer Q-Faktor reduziert die Bandbreite, was die Anwendbarkeit des Filters in Systemen einschränken könnte, die einen umfassenderen Frequenzbereich erfordern.

Ein RLC-Serienresonanzkreis ist ein Beispiel für Präzisionstechnik bei der Funkübertragung, indem er als effektiver Bandpassfilter fungiert. Dieser Schaltkreis ist präzise konstruiert, um einen Spitzenwert der Stromstärke bei der Resonanzfrequenz zuzulassen und so eine selektive Frequenzübertragung und -empfang zu ermöglichen.

Frequenzgang

Stellen Sie sich eine Funksendeeinheit vor, die einen Resonanz-Bandpassfilter der RLC-Serie enthält.
Der Frequenzgang dieser Schaltung zeigt an, dass die ...

characteristics-of-series-resonant-circuit

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Frequency Response

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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-i

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transfer function and bode plots-ii

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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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