Name: op-amp circuits in cruise control
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 13 s
Channel: JoVE

考虑一辆使用运算放大器电路实现巡航控制以保持恒定速度的汽车。该电路利用运算放大器作为积分器和微分器的功能。
通过分别将反相运算放大器电路中的反馈电阻和输入电阻替换为电容器，可以构建理想的积分器和微分器。
积分器是一种运算放大器电路，其输出与输入信号的积分成正比。
相反，微分器产生的输出与输入信号的变化率成正比。
通过对两个电路的反相节点应用基尔霍夫电流定律，并利用电阻和电容的电流-电压关系式，可以推导出输出电压与输入电压之间的关系方程。
通过对积分电路的方程两边进行积分，并假设电容在施加信号前已放电，最终表达式表明输出电压与输入信号的积分成正比。
相比之下，对于微分电路，输出电压与输入信号的导数成正比。

积分器和微分器

Integrator and Differentiator

运算放大器电路在包括汽车工程在内的各个领域都有着重要的应用。其中的一种应用是汽车中的巡航控制系统，其中运算放大器电路对于保持恒定的速度是不可或缺的。在这些系统中，运算放大器能够既充当积分器又充当微分器。 运算放大器电路中的积分器能够产生与输入信号积分成正比的输出。这是通过用电容器来替换典型反相放大器电路中的反馈电阻器来进行实现的，从而形成理想的积分器。通过应用基尔霍夫电流定律并利用电阻器和电容器的电流-电压关系来推导出与输出和输入电压相关的方程。在进行积分时，该方程表明了输出电压对应于输入信号的积分。 <img alt="Equation1" src="/files/ftp_upload/15081/15081_Equation_1.svg" style="text-align: center; height: 48px;"> 相反，运算放大器电路内的微分器能够产生与输入信号所产生的变化率成比例的输出。实现这一目标需要用标准反相放大器中的电容器来替换输入电阻器，从而创建出微分器电路。通过应用基尔霍夫电流定律并利用其中的电流-电压关系，从而建立出能够连接输出和输入电压的方程。在这种情况下，该方程表明了输出电压与输入信号的导数是成正比的。 <img alt="Equation2" src="/files/ftp_upload/15081/15081_Equation_2.svg" style="text-align: center; height: 30px;"> 值得注意的是，这些运算放大器电路在能量存储的应用中很有价值，并且由于其紧凑性和成本效益，通常使用电阻器和电容器来进行设计。虽然积分器能够广泛的应用在模拟计算机和各种应用中，但微分器在实践中是不太常见的，因为它们会放大电噪声，从而会导致其中的电子会处于不稳定的状态。

运算放大器电路在包括汽车工程在内的多个领域具有重要应用。其中一个应用是汽车中的巡航控制系统，……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Operational Amplifiers

运算放大器

KEY TERMS AND CONCEPTS

关键术语与概念

op-amp circuits in cruise control

Op-amp circuits are used in cruise control systems to help cars keep a constant speed. In these systems, operational amplifiers, or op-amps, can work as integrators and differentiators. Both circuits use resistors and capacitors, which makes them compact and cost-effective.

An integrator circuit produces an output that is proportional to the integral of the input signal. It is made by replacing the feedback resistor in a standard inverting amplifier with a capacitor. The output and input voltages can be related with Kirchhoff's current law and the current-voltage behavior of resistors and capacitors.

After integration, the equation shows that the output voltage matches the integral of the input signal. A differentiator circuit works in the opposite way. It produces an output proportional to the rate of change of the input signal by replacing the input resistor in a standard inverting amplifier with a capacitor.

The differentiator equation is also built with Kirchhoff's current law and current-voltage relations. In this case, the output voltage is proportional to the derivative of the input signal. Integrators are widely used in analog computers and other applications, while differentiators are less common because they can amplify electrical noise and become electronically unstable.

Op-Amp Circuits in Cruise Control

operational amplifiers

Operational Amplifier Pinout and Signal Use

An operational amplifier, or op-amp, is a flexible circuit building block used in many electronic designs. It can act like a voltage-controlled voltage source, and it can also be used to create a voltage- or current-controlled current source. When resistors and capacitors are connected to its terminals, an op-amp can perform mathematical operations on signals. Op-amps are able to sum signals, amplify a signal, integrate it, or differentiate it. These features make them useful in practical...

characteristics of opamp

Op-Amp Gain, Feedback, and Saturation

An operational amplifier, or op-amp, is an electronic circuit component used with other circuit parts to carry out a signal-processing task. It is often described with an equivalent circuit model. In that model, the output section includes a voltage-controlled source in parallel with the output resistance, R o. The model also shows the input resistance, R i, which is the Thevenin equivalent resistance seen at the input terminals. The differential input voltage, v d, is the difference between...

design example: vintage mixing console

Op-Amp Preamp for a Vintage Console

A sound engineer designs an op-amp pre-amplifier for a vintage mixing console. The console’s output is too low for modern recording equipment, so the signal must be boosted before it can be used. The goal is to build a preamp that raises the audio level without changing the console’s character. The design must meet three clear requirements. It needs a gain of 10, an input impedance above 10 kilo-ohms so the console is not overloaded, and a frequency range that covers the full audio spectrum...

cascaded op amps

Op Amp Stages in Series

Operational amplifiers can be connected in series as separate stages. This cascade works because op-amps have very high input resistance and very low output resistance. Those properties help each stage keep its input-output relationship while driving the next stage. In a cascaded op-amp circuit, the output of one stage becomes the input of the next. Each stage adds gain to the signal as it passes through. The overall gain is the product of the gain of each stage. This design can improve...

inverting and non-inverting opamps

Op-Amp Gain: Inverting, Noninverting, Buffer

Operational amplifiers can be used as inverting, noninverting, and buffer amplifiers. In these circuits, the output voltage depends on the input voltage and the resistor setup around the op-amp. In an inverting amplifier, the input voltage is sent through a resistor to the inverting terminal. The non-inverting terminal is grounded, and a feedback resistor links the inverting terminal to the output. Using Kirchhoff's Current Law and an ideal op-amp model, the gain can be found. This circuit...

sum and difference opamps

Op-Amp Adders and Subtractors

Operational amplifiers can be wired to add or subtract signals. In these two op-amp setups, the summing amplifier combines several input signals into one output, while the difference amplifier compares two inputs and amplifies their difference. A summing amplifier is also called an adder. Input signals, such as audio signals, enter through input resistors. These resistors send currents through the feedback resistor, which produces an output voltage. Using Kirchhoff's current law and Ohm's Law,...

characteristics of practical op amps

Op Amp Noise Rejection and Buffering

Practical op amps are used to separate useful signals from unwanted noise. A difference amplifier should ideally amplify only the difference between two input signals. In real circuits, though, the output depends on both differential gain and common-mode gain. The common-mode rejection ratio, or CMRR, measures how well an op amp rejects common-mode signals. Common-mode signals are the same on both inputs. A higher CMRR helps an op amp ignore noise and amplify the wanted signal, such as music...

integrator and differentiator

Op-amp circuits are used in cruise control systems to help cars keep a constant speed. In these systems, operational amplifiers, or op-amps, can work as integrators and differentiators. Both circuits use resistors and capacitors, which makes them compact and cost-effective. An integrator circuit produces an output that is proportional to the integral of the input signal. It is made by replacing the feedback resistor in a standard inverting amplifier with a capacitor. The output and input...

instrumentation amplifier

ECG Signal Amplifier Design

An ECG signal amplifier helps an electrocardiography machine measure the heart’s electrical activity. ECG electrodes detect tiny voltage changes on the skin that come from depolarization of the heart muscle during each heartbeat. These signals are in the microvolt range, so they can be easily hidden by noise or interference. To solve this problem, ECG machines use an instrumentation amplifier. This amplifier boosts the ECG waveform while reducing common-mode noise, which is interference that...

key terms and concepts

See how op-amp circuits support cruise control with integrator and differentiator setups, using resistors and capacitors to shape input signals.

Op-Amp Circuits in Cruise Control | 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

Op-Amp Circuits in Cruise Control

Description

Transcript

Tags