Name: op-amp gain, feedback, and saturation
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 17 s
Channel: JoVE

考虑运算放大器的等效电路模型。输出部分由一个与输出电阻串联的电压控制源组成。
在输入部分，v1 和 v2 分别表示反相端和同相端对地的电压。
运算放大器的输出电压等于输入电压差与开环增益的乘积。
对于较小的电压差，运算放大器表现为线性。若电压超过电源电压，运算放大器将进入饱和状态。
施加的电压与负反馈的结合可确保运算放大器在其线性范围内工作。
现代放大器具有高增益和高输入电阻，因此可被近似视为理想运算放大器。
理想的运算放大器具有无限大的开环增益、无限大的输入电阻和零输出电阻。在理想运算放大器中，两个输入端的电流以及输入失调电压均为零。
此外，它具有无限的带宽，能够放大任意频率的信号，并具有无限的压摆率，表明其输出电压随时间快速变化的能力。

运算放大器的特性

运算放大器，俗称运放，是一种专门设计的电子电路元件。其目的是与其他电路元件之间互相配合来执行定义的信号处理操作。思考一个运算放大器中的等效电路模型，如图1所示；其中的输出部分包括与输出电阻Ro所并联的压控源。 

<img alt="Figure1" src="/files/ftp_upload/15077/15077_PT_Figure_1.svg" style="text-align: center; height: 166px;"> 

图1：非理想运算放大器的等效电路 

图1显示了输入电阻Ri等于输入端子处可观察到的戴维南等效电阻。类似地，输出电阻Ro则对应于输出端可辨别的戴维南等效电阻。差分输入电压 (vd) 计算了为同相端子相对于地的电压与反相端子相对于地的电压之间的差值。 

运算放大器能够识别这两个输入之间的差异，并按增益A来对其进行放大，从而生成出现在位于输出端的电压。在这里，A代表了开环电压增益-这样命名是因为它表示了在输出到没有任何外部输入反馈的情况下，运算放大器所产生的增益。 

反馈是用来研究运算放大器电路时所需要理解的一个完整概念。负反馈可以通过将输出反馈到运算放大器的反相端子来进行实现。当存在从输出到输入的反馈路径时，从而将所得到输出电压与输入电压之比称为闭环增益。 

运算放大器确实有其实际的局限性。其中的一个限制是其输出电压的幅度不能超过 |VCC|。在本质上，电源的电压能够决定并限制其输出电压。根据差分输入电压可以得知，运算放大器能够以其中的三种模式之一来进行运行：正饱和、线性区或负饱和。如果尝试增加vd来使其超出线性范围，那么运算放大器就会达到饱和，从而产生vo = VCC或vo = -VCC这两个等式。

运算放大器，通常称为运放（op-amp），是一种专门设计的电子电路元件。其作用是与……协同工作。

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

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 the noninverting terminal voltage and the inverting terminal voltage, both measured relative to ground. The op-amp compares these two input voltages and amplifies the difference by the gain A to produce an output voltage.

A is called the open-loop voltage gain because it describes the op-amp without feedback from the output back to the input. Feedback is important in op-amp circuits. Negative feedback is created by connecting the output to the inverting terminal. When that feedback path exists, the output-to-input ratio is the closed-loop gain.

Op-amps also have practical limits. Their output voltage cannot exceed the magnitude of the supply voltage, |VCC|. The power supply sets this limit. Depending on the differential input voltage, the op-amp can operate in positive saturation, the linear region, or negative saturation. If v d is pushed beyond the linear range, the output saturates at either v o = VCC or v o = -VCC.

Op-Amp Gain, Feedback, and Saturation

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...

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...

characteristics of opamp

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...

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 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...

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

Learn how an op-amp compares input voltages, uses open-loop and closed-loop gain, and reaches positive or negative saturation when output limits are exceeded.

Op-Amp Gain, Feedback, and Saturation | 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 Gain, Feedback, and Saturation

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