Name: analyzing an op amp audio filter
Uploaded: 2024-04-11T12:48:50.000Z
Duration: 1 min 18 s
Channel: JoVE

In einem Audiosystem verarbeitet die Filterschaltung das verstärkte Audiosignal eines Verstärkers, wodurch die Signalanteile bei tiefen Frequenzen stark gedämpft werden.
Betrachten Sie die einfachste Filterschaltung, die aus einem Operationsverstärker in invertierender Konfiguration besteht, der mit den Widerständen R1 und R2 und dem Kondensator C1 gekoppelt ist. Was ist das resultierende Ausgangssignal für ein bekanntes Eingangssignal?
Die Impedanz des Kondensators wird anhand der Kreisfrequenz berechnet, die aus dem Zeitbereichsausdruck für die Eingangsspannung abgeleitet wird.
Die Frequenzbereichs-Ersatzschaltung stellt das Eingangssignal in polarer Form und die Impedanzen Z1 und Z2 dar. Die Impedanz Z2 entspricht der parallelen Kombination von Kondensator C1 und Widerstand R2.
Wendet man das Kirchoffsche Stromgesetz und das Ohmsche Gesetz auf den Knoten an, erhält man eine Knotengleichung für einen idealen Operationsverstärker. Diese Gleichung zeigt, wenn sie neu angeordnet wird, dass das Verhältnis der Ausgangs- zur Eingangsspannung dem negativen Verhältnis der Impedanzen entspricht.
Durch das Einsetzen der bekannten und berechneten Werte in diese Gleichung wird die Ausgangsspannung in polarer Form bestimmt, die dann in den Zeitbereich umgerechnet wird.

ac-schaltkreise von operationsverstärkern

Innerhalb eines Audiosystems spielt die Filterschaltung eine entscheidende Rolle bei der Verarbeitung des verstärkten Audiosignals von einem Verstärker. Seine Hauptfunktion besteht darin, Signalkomponenten mit niedrigeren Frequenzen erheblich zu dämpfen und so die Audioausgabe zu formen. Die Funktionsweise dieser Schaltung wird untersucht, wobei der Schwerpunkt auf der grundlegenden Filterkonfiguration liegt. Bei dieser Konfiguration handelt es sich um einen Operationsverstärker, der in einer invertierenden Anordnung angeordnet ist und mit Widerständen (R1 und R2) und einem Kondensator (C1) gekoppelt ist. <img alt="Figure1" src="/files/ftp_upload/15116/15116_PT_Figure_1.svg" style="text-align: center; height: 164px;"> Bei einem bekannten Eingangssignal besteht die Herausforderung darin, das resultierende Ausgangssignal zu bestimmen. Der erste Schritt umfasst die Berechnung der Impedanz des Kondensators, die durch die Verwendung der Winkelfrequenz erreicht wird, die aus dem Zeitbereichsausdruck der Eingangsspannung abgeleitet wird. <img alt="Equation1" src="/files/ftp_upload/15116/15116_PT_Equation_1.svg" style="text-align: center; height: 36px;"> Dadurch geht die Analyse in den Frequenzbereich über, wo das Eingangssignal in Polarform neben den Impedanzkomponenten Z1 und Z2 dargestellt wird. Z2 bezieht sich explizit auf die Parallelschaltung von Kondensator C1 und Widerstand R2. Der Kern der Analyse besteht darin, das Kirchhoffsche Stromgesetz und das Ohmsche Gesetz an einem bestimmten Knoten in der Schaltung anzuwenden und so eine Knotengleichung für einen idealen Operationsverstärker zu formulieren. Wenn diese Gleichung neu geordnet wird, offenbart sie eine entscheidende Erkenntnis: Das Verhältnis der Ausgangs- zur Eingangsspannung ist umgekehrt proportional zum Verhältnis der Impedanzen. <img alt="Equation2" src="/files/ftp_upload/15116/15116_PT_Equation_2.svg" style="text-align: center; height: 36px;"> Die bekannten und berechneten Werte werden geschickt in diese Gleichung eingesetzt, um die Ausgangsspannung in Polarform anzuzeigen. Das Ergebnis, das die Ausgangsspannung darstellt, kann dann in den Zeitbereich umgewandelt werden, was ein umfassendes Verständnis der Reaktion der Filterschaltung auf das Eingangssignal liefert. Für die Analyse werden oft ideale Operationsverstärkereigenschaften angenommen, einschließlich des Prinzips, dass kein Strom in einen seiner Eingangsanschlüsse fließt und dass die Spannung an seinen Eingangsanschlüssen Null bleibt.

AC-Schaltkreise von Operationsverstärkern

In einem Audiosystem verarbeitet die Filterschaltung das verstärkte Audiosignal von einem Verstärker und dämpft die Signalanteile stark ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

AC Circuit Analysis

Analyse von Wechselstromschaltungen

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

Op Amp AC Circuits

analyzing an op amp audio filter

An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1.

The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the time-domain form of the input voltage, so the work moves into the frequency domain.

In the frequency domain, the input signal is written in polar form. The impedances Z1 and Z2 are then used, with Z2 representing the parallel combination of capacitor C1 and resistor R2. At the same time, the ideal op amp assumptions are used. No current enters either input terminal, and the voltage across the input terminals is zero.

The final step is applying Kirchhoff's current law and Ohm's law at one node in the circuit. This creates a nodal equation for the ideal op amp. When that equation is rearranged, the output-to-input voltage ratio is shown to be inversely proportional to the impedance ratio. The known values are then substituted to find the output voltage in polar form, and that result can be converted back to the time domain for a full description of the filter response.

Analyzing an Op Amp Audio Filter

sinusoidal sources

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phasors

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op amp ac circuits

An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1. The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the...

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key terms and concepts

Learn how an op amp audio filter reduces low-frequency signals. Follow impedance, nodal analysis, and polar-to-time-domain output calculations.

Analyzing an Op Amp Audio Filter | 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

Analyzing an Op Amp Audio Filter

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