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

В аудиосистеме схема фильтра обрабатывает усиленный звуковой сигнал от усилителя, сильно ослабляя компоненты сигнала низкими частотами.
Рассмотрим простейшую схему фильтра, состоящую из операционного усилителя в инвертирующей конфигурации, соединенного с резисторами R1 и R2 и конденсатора C1. Что такое результирующий выходной сигнал для известного входного сигнала?
Импеданс конденсатора рассчитывается с использованием угловой частоты, полученной из выражения входного напряжения во временной области.
Эквивалентная схема в частотной области представляет входной сигнал в полярной форме и импедансах Z1 и Z2. Импеданс Z2 соответствует параллельной комбинации конденсатора C1 и резистора R2.
Применение современного закона Кирхгофа и закона Ома в узле дает узловое уравнение для идеального операционного усилителя. Это уравнение при перестановке показывает, что отношение выходного напряжения к входному напряжению равно отрицательному отношению импедансов.
Путем подстановки известных и расчетных значений в это уравнение выходное напряжение определяется в полярной форме, которая затем преобразуется во временную область.

ОУ в цепях переменного тока

В аудиосистеме схема фильтра играет ключевую роль в обработке усиленного аудиосигнала от усилителя. Его основная функция — значительное ослабление компонентов сигнала с более низкими частотами, что формирует выходной аудиосигнал. Работа этой схемы рассматривается с упором на базовую конфигурацию фильтра. Эта конфигурация включает в себя операционный усилитель, выполненный в инвертирующей схеме, соединенный с резисторами (R1 и R2) и конденсатором (C1</sub.).

<img alt="Figure1" src="/files/ftp_upload/15116/15116_PT_Figure_1.svg" style="text-align: center; height: 164px;" />

Когда мы сталкиваемся с известным входным сигналом, проблема заключается в определении результирующего выходного сигнала. Первый шаг включает в себя расчет импеданса конденсатора, который достигается за счет использования угловой частоты, полученной из выражения входного напряжения во временной области.

<img alt="Equation1" src="/files/ftp_upload/15116/15116_PT_Equation_1.svg" style="text-align: center; height: 36px;" />

В результате анализ переходит в частотную область, где входной сигнал представлен в полярной форме вместе с компонентами импеданса Z1 и Z2. Z2 явно относится к параллельной комбинации конденсатора C1 и резистора R2. Суть анализа основана на применении закона токов Кирхгофа и закона Ома в конкретном узле схемы, тем самым формулируя узловое уравнение для идеального операционного усилителя. Это уравнение, если его переформулировать, открывает важное понимание: отношение выходного напряжения к входному обратно пропорционально отношению импедансов.

<img alt="Equation2" src="/files/ftp_upload/15116/15116_PT_Equation_2.svg" style="text-align: center; height: 36px;" />

Известные и рассчитанные значения подставляются в это уравнение, чтобы представить выходное напряжение в полярной форме. Результат, представляющий выходное напряжение, затем может быть преобразован во временную область, что дает лучшее понимание отклика схемы фильтра на входной сигнал. Для анализа часто предполагаются идеальные свойства операционного усилителя, включая принцип, согласно которому ток не поступает ни на одну из его входных клемм, а напряжение на входных клеммах остается нулевым.

В аудиосистеме схема фильтра обрабатывает усиленный аудиосигнал от усилителя, сильно ослабляя компоненты сигнала с низким ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

AC Circuit Analysis

Анализ цепей переменного тока

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

AC Waveform Basics and Phase

Alternating current, or AC, changes direction and magnitude over time, unlike direct current, or DC, which flows in one direction with constant polarity. AC is the main form of electricity used for modern power transmission and distribution because it can travel long distances efficiently. In homes, power supplies use sinusoidal sources to deliver electricity. A sinusoidal source creates a voltage that rises and falls in a smooth wave-like pattern. This waveform is called a sinusoid, which is...

graphical and analytic representation of sinusoids

graphical-and-analytic-representation-of-sinusoids

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phasors

Phasors for AC Circuit Analysis

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Phasor Rules for AC Circuit Analysis

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phasor relationships for circuit elements

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AC Circuit Phasors: Resistor, Inductor, Capacitor

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kirchoff's laws using phasors

AC Circuit Rules with Phasor Diagrams

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AC Circuit Response: Impedance and Admittance

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impedance combination

Series and Parallel Impedance Rules

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node analysis for ac circuits

AC Circuit Node Method in an Angioplasty Model

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Impedance Matching with Mesh Currents

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AC Source Conversion in Circuit Analysis

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Finding Voltage and Impedance in Circuit A

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norton equivalent circuits

Norton Current in AC Circuit Analysis

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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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