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

オペアンプ回路を使用して一定の速度を維持するクルーズコントロールを備えた車を考えてみましょう。この回路は、オペアンプの機能を積分器および微分器として採用しています。
理想的な積分器と微分器は、帰還抵抗と入力抵抗をそれぞれコンデンサに置き換えることにより、反転オペアンプ回路から作成できます。
積分器は、入力信号の積分に比例して出力を生成するオペアンプ回路です。
逆に、微分器は、入力信号の変化率に比例した出力を生成します。
キルヒホッフの電流法則を両回路の反転ノードに適用し、抵抗とコンデンサの電流-電圧式を利用することで、出力電圧と入力電圧の関係式を導出できます。
積分器回路の方程式を両側で積分し、信号印加前にコンデンサが放電すると仮定すると、最終的な式は、出力電圧が入力の積分に比例することを示しています。
対照的に、微分回路の場合、出力電圧は入力信号の微分に比例します。

積分器と微分器

Integrator and Differentiator

オペアンプ回路は、自動車工学を含むさまざまな分野で重要な用途があります。そのような用途の 1 つは自動車のクルーズ コントロール システムであり、一定の速度を維持するためにオペアンプ回路が組み込まれています。これらのシステムでは、オペアンプは積分器と微分器の両方として機能します。

オペアンプ回路内の積分器は、入力信号の積分に正比例する出力を生成します。これは、一般的な反転増幅回路の帰還抵抗をコンデンサに置き換えることによって実現され、理想的な積分器が得られます。出力電圧と入力電圧に関する式は、キルヒホッフの電流法則を適用し、抵抗とコンデンサの電流と電圧の関係を利用することによって導出されます。この式を積分すると、出力電圧が入力信号の積分に対応することがわかります。

<img alt="Equation1" src="/files/ftp_upload/15081/15081_Equation_1.svg" style="text-align: center; height: 48px;">

逆に、オペアンプ回路内の微分器は、入力信号の変化率に比例した出力を生成します。これを実現するには、標準の反転アンプの入力抵抗をコンデンサに置き換えて、微分回路を作成する必要があります。出力電圧と入力電圧を結び付けるFigureは、キルヒホッフの電流法則を適用し、電流と電圧の関係を使用することによって確立されます。この場合、式は出力電圧が入力信号の微分値に比例することを示しています。

<img alt="Equation2" src="/files/ftp_upload/15081/15081_Equation_2.svg" style="text-align: center; height: 30px;">

これらのオペアンプ回路はエネルギー貯蔵アプリケーションで価値があり、そのコンパクトさとコスト効率の高さから、抵抗器とコンデンサを使用して設計されることが多いことに注目してください。積分器はアナログ コンピュータやさまざまなアプリケーションで広く使用されていますが、微分器は電気ノイズを増幅する傾向があり、電子的に不安定になるため、実際にはあまり一般的ではありません。

オペアンプ回路を使用して一定の速度を維持するクルーズコントロールを備えた車を考えてみましょう。この回路は、積分器としてのオペアンプの機能を採用しています...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Operational Amplifiers

演算増幅器（オペアンプ）

KEY TERMS AND CONCEPTS

主要用語と概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Op-Amp Circuits in Cruise Control

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