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

오디오 시스템에서 필터 회로는 증폭기에서 증폭된 오디오 신호를 처리하여 저주파의 신호 성분을 강력하게 감쇠합니다.
저항기 R1 및 R2 및 커패시터 C1과 결합된 반전 구성의 연산 증폭기로 구성된 가장 간단한 필터 회로를 생각해 보십시오. 알려진 입력 신호에 대한 결과 출력 신호는 무엇입니까?
커패시터의 임피던스는 입력 전압에 대한 시간 도메인 표현식에서 파생된 각 주파수를 사용하여 계산됩니다.
주파수 영역 등가 회로는 극성 형태의 입력 신호와 임피던스 Z1 및 Z2를 나타냅니다. 임피던스 Z2 는 커패시터 C1 과 저항 R2 의 병렬 조합에 해당합니다.
Kirchoff의 현재 법칙과 옴의 법칙을 노드에 적용하면 이상적인 연산 증폭기에 대한 노드 방정식을 얻을 수 있습니다. 이 방정식을 재배열하면 입력 전압에 대한 출력의 비율이 임피던스의 음의 비율과 동일함을 나타냅니다.
알려진 값과 계산된 값을 이 방정식에 대입하면 출력 전압이 극성 형태로 결정된 다음 시간 도메인으로 변환됩니다.

연산 증폭기 ac 회로

오디오 시스템 내에서 필터 회로는 증폭기에서 증폭된 오디오 신호를 처리하는 데 중추적인 역할을 합니다. 주요 기능은 낮은 주파수의 신호 구성 요소를 크게 감쇠시켜 오디오 출력을 형성하는 것입니다. 이 회로의 작동을 기본 필터 구성에 중점을 두고 검토합니다. 이 구성에는 저항( R_1 및 R_2) 및 축전기(C_1)와 결합된 반전 설정으로 배열된 연산 증폭기가 포함됩니다.

<img alt="Figure1" src="/files/ftp_upload/15116/15116_PT_Figure_1.svg" style="text-align: center; height: 164px;">

알려진 입력 신호에 직면했을 때, 결과적인 출력 신호를 결정하는 것이 과제입니다. 첫 번째 단계에서는 입력 전압의 시간 영역 표현에서 파생된 각주파수를 사용하여 달성되는 축전기의 온저항을 계산합니다.

<img alt="Equation1" src="/files/ftp_upload/15116/15116_PT_Equation_1.svg" style="text-align: center; height: 36px;">

결과적으로 분석은 주파수 영역으로 전환되며, 여기서 입력 신호는 온저항 구성 요소 Z_1 및 Z_2 와 함께 극성 형식으로 표시됩니다. Z_2 는 축전기 C_1 과 저항 R_2 의 병렬 조합과 명시적으로 관련됩니다. 분석의 핵심은 키르히호프의 전류 법칙과 옴의 법칙을 회로의 특정 노드에 적용하여 이상적인 연산 증폭기에 대한 노드 방정식을 공식화하는 데 있습니다. 이 방정식을 다시 정리하면 중요한 통찰력을 얻을 수 있습니다. 입력 전압에 대한 출력 비율은 온저항 비율에 반비례합니다.

<img alt="Equation2" src="/files/ftp_upload/15116/15116_PT_Equation_2.svg" style="text-align: center; height: 36px;">

알려지고 계산된 값은 이 방정식에 능숙하게 대체되어 출력 전압을 극성 형태로 나타냅니다. 그런 다음 출력 전압을 나타내는 결과를 시간 영역으로 변환하여 입력 신호에 대한 필터 회로의 응답을 포괄적으로 이해할 수 있습니다. 분석을 위해 입력 단자에 전류가 유입되지 않고 입력 단자의 전압이 0으로 유지된다는 원리를 포함하여 이상적인 연산 증폭기 특성이 가정되는 경우가 많습니다.

연산 증폭기 AC 회로

오디오 시스템에서 필터 회로는 증폭기에서 증폭된 오디오 신호를 처리하여 신호 성분을 낮은 온도로 강력하게 감쇠합니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

AC Circuit Analysis

교류 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Measuring Sinusoid Phase on an Oscilloscope

Measuring sinusoid phase on an oscilloscope helps compare two sinusoidal voltages with the same amplitude and period. An oscilloscope is an instrument used to display and analyze waveforms. The process starts by reading the peak-to-peak value, which is twice the amplitude of the sinusoid. This shows the maximum voltage swing of the waveform. Next, the period and angular frequency are measured. The period is the time for one complete cycle. Angular frequency, often written as omega, is the rate...

phasors

Phasors for AC Circuit Analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis. Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in...

phasor arithmetics

Phasor Rules for AC Circuit Analysis

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time. Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its...

phasor relationships for circuit elements

phasor-relationships-for-circuit-elements

AC Circuit Phasors: Resistor, Inductor, Capacitor

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier. For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction. An inductor works differently because its voltage depends on the rate of change of current. The...

kirchoff's laws using phasors

AC Circuit Rules with Phasor Diagrams

AC circuit analysis uses Kirchhoff's voltage law and Kirchhoff's current law with phasors. In household wiring, AC power from a distribution panel is sent to appliances connected in parallel. These rules help describe how voltage and current behave in sinusoidal steady state. Kirchhoff's voltage law, or KVL, says that the sum of phasor voltages around a closed loop in an AC circuit is zero. The voltages can first be written in the time domain and then changed into phasor form. In phasor...

impedances and admittance

AC Circuit Response: Impedance and Admittance

AC circuit response changes with frequency, and impedance describes how resistors, inductors, and capacitors affect sinusoidal current flow. In phasor form, voltage and current are used to show this behavior in a clear way. Impedance is a key idea in AC circuit analysis because it measures opposition to current in an alternating circuit. These components behave differently in AC than in DC. In DC circuits, inductors act like short circuits and capacitors act like open circuits. In AC circuits,...

impedance combination

Series and Parallel Impedance Rules

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

node analysis for ac circuits

AC Circuit Node Method in an Angioplasty Model

AC circuit node analysis is used to study an angioplasty system with a catheter turbine. The system helps remove plaque deposits from coronary arteries. Its electrical model is similar to a dual-node RLC circuit driven by a current-controlled voltage source. The analysis begins by collecting the input source voltage, inductance, and capacitance values. These measurements are used to find the driving voltage for the catheter shaft. The circuit is then viewed in the frequency domain, where...

mesh analysis for ac circuits

Impedance Matching with Mesh Currents

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students. The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input...

source transformation for ac circuits

AC Source Conversion in Circuit Analysis

AC source conversion is a circuit analysis method used in the frequency domain. It changes a voltage source in series with an impedance into a current source in parallel with the same impedance, or it converts a current source back into a voltage source. The source values must keep the correct relationship during each change. This method helps solve for an unknown voltage in a circuit that includes a current source and components such as resistors, capacitors, and inductors. Each of these...

th&#233venin equivalent circuits

Finding Voltage and Impedance in Circuit A

The household power distribution system can be simplified with Thevenin's theorem. In this system, distribution lines and transformers form the main network. Electrical appliances can be treated as load impedance, which makes the circuit easier to analyze. An AC circuit can be split into two parts, circuit A and circuit B, with a single pair of terminals between them. Circuit A can then be replaced by its Thevenin equivalent circuit. That equivalent has a voltage source in series with an...

norton equivalent circuits

Norton Current in AC Circuit Analysis

Norton’s theorem helps simplify complex AC circuits by replacing a two-terminal linear network with a smaller equivalent circuit. That equivalent circuit uses an impedance in parallel with a constant current source. The method lets students break one complicated circuit into two parts and analyze them more easily. To build the Norton equivalent, the source is replaced by its internal impedance. The result is the Norton impedance, which is the same as the Thévenin impedance. This parallel...

superposition theorem for ac circuits

Analyzing Mixed-Frequency Linear Circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources. When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This...

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...

design example: capacitance multiplier circuit

design-example-capacitance-multiplier-circuit

Capacitance Multiplier Circuit for Larger Capacitance

A capacitance multiplier circuit creates a larger effective capacitance from a small physical capacitor. In integrated circuit technology, this approach is useful when a small capacitor is not enough. The circuit can multiply capacitance by as much as 1000, so a 10-pF capacitor can act like a 100-nF capacitor. The design uses two op-amps. The first op-amp works as a voltage follower, which helps isolate the generated capacitance from the loading caused by the second stage. The second op-amp...

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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