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

Consider a car with cruise control using an op amp circuit to maintain a constant speed. This circuit employs the function of an op amp as an integrator and differentiator.
An ideal integrator and differentiator can be created from an inverting operational amplifier circuit by replacing the feedback and input resistors with capacitors, respectively.
An integrator is an op amp circuit that generates an output in proportion to the integral of the input signal.
Conversely, a differentiator produces an output proportional to the rate of change of the input signal.
By applying Kirchhoff&#39;s current law at the inverting node of both circuits and utilizing the current-voltage expressions for the resistor and capacitor, an equation relating the output and input voltages can be derived.
Upon integrating the equation for the integrator circuit on both sides and assuming the capacitor discharges before signal application, the final expression demonstrates that the output voltage is proportional to the input&#39;s integral.
In contrast, for the differentiator circuit, the output voltage is proportional to the derivative of the input signal.

integrator and differentiator

Integrator and Differentiator

Op-amp circuits have significant applications in various fields, including automotive engineering. One such application is cruise control systems in cars, where op-amp circuits are integral for maintaining a constant speed. In these systems, op-amps function as both integrators and differentiators.
An integrator within an op-amp circuit produces an output directly proportional to the integral of the input signal. This is achieved by replacing the feedback resistor in a typical inverting amplifier circuit with a capacitor, resulting in an ideal integrator. An equation relating output and input voltages is derived by applying Kirchhoff's current law and utilizing current-voltage relationships for resistors and capacitors. When integrated, this equation demonstrates that the output voltage corresponds to the integral of the input signal.
<img alt="RC circuit voltage equation \(v_o = -\frac{1}{RC} \int_{0}^{t} v_i(t) \, dt\)." src="/files/ftp_upload/15081/15081_Equation_1.svg" style="text-align: center; height: 48px;" data-altupdatedat="1754904545000" data-alt="RC circuit integral equation diagram, depicting voltage output calculation formula." />
Conversely, a differentiator within an op-amp circuit yields an output proportional to the input signal's rate of change. Achieving this involves replacing the input resistor with a capacitor in a standard inverting amplifier, creating a differentiator circuit. An equation linking output and input voltages is established by applying Kirchhoff's current law and employing current-voltage relations. In this case, the equation indicates that the output voltage is proportional to the derivative of the input signal.
<img alt="RC integrator formula \(v_o = -RC \frac{dv_i}{dt}\), electronic circuit equation." src="/files/ftp_upload/15081/15081_Equation_2.svg" style="text-align: center; height: 30px;" data-altupdatedat="1754904545000" data-alt="RC circuit differentiator equation \(v_o = -RC \frac{dv_i}{dt}\); electrical concepts." />
It is worth noting that these op-amp circuits are valuable in energy storage applications and are often designed using resistors and capacitors due to their compactness and cost-effectiveness. While integrators are widely employed in analog computers and various applications, differentiators are less common in practice due to their tendency to amplify electrical noise, making them electronically unstable.

Op-amp circuits have significant applications in various fields, including automotive engineering. One such application is cruise control systems in cars, ...

Education

JoVE Core

Electrical Engineering

Unit 1

Operational Amplifiers

KEY TERMS AND CONCEPTS

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...

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...

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...

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...

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