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

在音频系统中，滤波电路处理来自放大器的已放大音频信号，显著衰减低频信号成分。
考虑一个最简单的滤波电路，该电路由一个反相配置的运算放大器以及电阻 R1 和 R2 与电容 C1 组成。对于已知的输入信号，其输出信号为何？
电容器的阻抗是利用输入电压时域表达式导出的角频率来计算的。
频域等效电路以极坐标形式表示输入信号以及阻抗 Z1 和 Z2。阻抗 Z2 对应于电容 C1 与电阻 R2 的并联组合。
在节点处应用基尔霍夫电流定律和欧姆定律，可得到理想运算放大器的节点方程。对该方程进行整理后可知，输出电压与输入电压之比等于阻抗之比的负值。
将已知值和计算值代入该方程后，可确定极坐标形式的输出电压，然后将其转换为时域形式。

运算放大器交流电路

在音频系统中，滤波器电路在处理来自放大器中放大音频信号方面起着至关重要的作用。其主要的功能是显著衰减较低频率的信号分量，从而来塑造音频的输出。在此过程中需要对该电路的操作过程进行检查，并且需要重点关注基本滤波器的配置。该配置中含有一个运算放大器，并且将其布置在反相的设置中，同时需要与电阻器（R1 和 R2）和电容器（C1）发生耦合。 <img alt="Figure1" src="/files/ftp_upload/15116/15116_PT_Figure_1.svg" style="text-align: center; height: 164px;"> 当面对已知的输入信号时，其中所具备的挑战在于确定其最终的输出信号。第一步涉及到计算电容器中的阻抗，这是通过使用从输入电压的时域表达式中所推导出的角频率来实现的。 <img alt="Equation1" src="/files/ftp_upload/15116/15116_PT_Equation_1.svg" style="text-align: center; height: 36px;"> 因此，对转换出频域进行分析，其中输入信号以极坐标的形式与阻抗分量 Z1和 Z2来一起进行表示。其中 Z2与电容器 C1和电阻器 R2的并联组合是明确具有相关性的。分析的核心在于将基尔霍夫电流定律和欧姆定律应用到电路中的特定节点上，从而以此来推导出理想运算放大器的节点方程。对方称进行重新排列后，可以观察到该方程揭示了一个重要的结论：输出电压与输入电压之比与阻抗之比成反比。 <img alt="Equation2" src="/files/ftp_upload/15116/15116_PT_Equation_2.svg" style="text-align: center; height: 36px;"> 巧妙地将已知的值和计算得出的值代入到该方程中，同时以极坐标形式来计算出其中的输出电压。然后，将代表输出电压的结果转换到时域中，从而来全面的了解滤波器电路对输入信号所产生的响应。为了能够进一步进行分析，通常会参照理想运算放大器中的特性，其中包括没有电流能够进入到任何一个输入端子以及其输入端子上的电压保持为零的原则。

在音频系统中，滤波电路处理来自放大器的已放大音频信号，显著衰减具有低频的信号分量……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

AC Circuit Analysis

交流电路分析

KEY TERMS AND CONCEPTS

关键术语与概念

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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