Operational Amplifier Basics
 Boris Poupet
 bpoupet@hotmail.fr
 13 min

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Introduction
This tutorial is an introduction to the Operational Amplifiers, also known as opamps. The fundamental goal of opamps is to amplify a voltage difference and it is the reason why we also describe them as differential amplifiers.
Opamps have been invented the exact same year as the transistors (1947) and they were originally designed with vacuum tubes in order to perform basic mathematical operations. Massproduction only started in the ’50s when the opamps were heavy, not reliable, and cost much. Not before the late ’60s were produced large amounts of transistorbased opamps available for just a few $.
Nowadays, opamps are one of the most used electronic components, their cost is only of a few cents of $, and thanks to their interesting properties they are used for many applications.
In the first section, we will present in detail the architecture and definitions surrounding opamps. Moreover, we briefly discuss the internal circuitry of opamps.
The second section focuses on the concept of the ideal opamp which is a model describing the functioning of a perfect opamp.
Real opamps will be discussed in the third section where we will look into the differences that must be considered.
Presentation
An opamp is usually represented as a triangle with 5 pins from which 4 are inputs and one is the output.
The output is labeled V_{out }and it is the pin where the output voltage is collected. V_{+} and V_{–} are respectively the noninverting and inverting inputs. V_{S+} and V_{S} are respectively the positive power supply and negative power supply rails.
We can note that in most of the opamps representations, the power supply voltages and pins are not represented in order to simplify the drawing. Most of the time, the power configuration is just assumed or not relevant to perform calculations on a specific opamp.
The internal circuitry of opamps generally consists of a succession of bipolar or fieldeffect transistors and other passive components that are assembled in three distinct stages as shown in Figure 2:
The goal of the differential stage is to preamplify the differential signal V_{+}V_{– }. The special configuration used to realize this process is called a transistor longtailed pair circuit or differential pair. Moreover, this configuration provides a high input impedance.
The amplification stage is usually a high gain class A amplifier, the capacitor is used to assures the frequency compensation. Note that many amplification stages can be interconnected in order to provide a higher amplification output.
Finally, the buffer stage provides no amplification (unitary gain) but has a low output impedance and, therefore, provides high output currents. It is also used in order to adapt the impedances and protect against shortcircuits.
Openloop gain
A few major characteristics can be associated with opamps and we will dictate their electronic behavior here. The first one is the openloop gain (A_{OL}), it is a factor that represents the amplification applied to the input differential voltage:
The term “openloop” refers to the fact that no feedback is applied from the output to the inverting input of the opamp. We will come back to that notion later on in the tutorial, however, in order to get an idea now of this concept, we show in Figure 3 the distinction made between openloop and closedloop opamps:
Input and output impedances
The input impedance Z_{in} represents the ratio V_{in}/I_{in} with V_{in}=V_{+}V_{–} and I_{in} being the input current. Similarly, we can also define an output impedance Z_{out} which represents the ratio V_{out}/I_{out }with V_{out}=A_{OL}.V_{in }and I_{out} being the output current.
Figure 4 below shows a representation of an opamp that takes into account these impedances:
Bandwidth
Opamps can be used in DC but also in the AC regime, such as for example for the amplification of audio signals. For this reason, one of the important characteristics of opamps is their bandwidth (B). This means that the gain (A_{OL}) is dependent on the input frequency.
The bandwidth is measured in Hertz (Hz) and represents the range of frequencies that an opamp can amplify efficiently. More precisely, the frequencies for which the gain is higher than 3 dB are included in the bandwidth. The limit frequencies for which the gain is exactly equal to 3 dB are called cutoff frequencies and often labeled f_{3dB}.
Opamps behave actually as firstorder lowpass filters, this means that the gain can be approximated as a constant from the DC regime up until its cutoff frequency. For higher frequencies, a loss of 20 dB/decade is observed as shown in Figure 5:
To get more detail about this topic, we recommend reading the tutorial about Bode diagrams.
Offset voltage
The offset voltage V_{off} can be read at the output terminal when no input is applied to the amplifier. For example, if an opamp has an offset voltage of 1 V, it means that the output voltage will constantly be shifted of +1 V, even when no input signal is applied.
Ideal opamp model
This model describes an idealized opamp that is free of any parasitic phenomena. It is of course not possible to build such an opamp with ideal characteristics but only approach it.
The ideal opamp model consists of idealizing its main characteristics previously presented in the presentation section:
 Infinite openloop gain (A_{OL}=+∞)
 Infinite input impedance (Z_{in}=+∞)
 Zero output impedance (Z_{out}=0)
 Infinite bandwidth (B=+∞)
 Zero offset voltage (V_{off}=0)
This set of idealized characteristics highlights the fact that an ideal opamp does not disturb the amplified signal. An ideal opamp is usually represented with a sign “∞” within the triangle shape.
One very important property is that in an openloop configuration, the output of an ideal opamp can only take two values called the saturation voltages (V_{sat}). If the differential input V_{in} is positive (reciprocally negative), the output is +V_{sat }(reciprocally V_{sat}).
The value of V_{sat} is slightly lower than the absolute value of the supply V_{S}.
In the following subsections, we will see two different modes that can be adopted for an ideal opamp depending on which input the feedback is applied.
Saturated mode
In this mode, feedback is applied to the noninverting input (+) of the opamp. This means that any increase in the output voltage will increase the differential input. This kind of configuration is also known as a comparator and represented in Figure 8:
Linear mode
If instead the feedback is applied to the inverting input () of the opamp, the function of the amplifier is completely different.
In this configuration, any increase of the output voltage tends to decrease the differential input and therefore, also tends to maintain a differential input close to zero.
The relation between the input and output voltages is given by Equation 2:
In a closedloop configuration with negative feedback, the characteristic V_{out}=f(V_{in}) is therefore linear according to Equation 2 up until V_{sat} and +V_{sat} where a plateau emerges.
Real opamps
Opamps that can be found in real electronic circuits have limited and nonideal characteristics:
 Finite openloop gain typically ranges from 10^{5} to 10^{6}
 Finite input impedance: 10^{5} up to 10^{12} Ω
 Nonzero output impedance: 50 to 200 Ω
 Finite bandwidth
 Nonzero offset voltage: 1μV up to 50 mV
The gain of real opamps depends moreover on the frequency with a variation that can be described as a first order lowpass frequency. Another important information is that the product gainbandwidth of opamps is constant, this implies that “slow” opamps can have higher gains and “fast” opamps tend to have a lower gain.
The input impedance is not purely resistive as a parallel capacitor of a few pF modelizes the lowpass filter behavior of the opamp and tends to reduce the impedance when the frequency increases.
Conclusion
We have presented the basics of operational amplifiers in this introductory tutorial. Opamps are integrated circuits that are powered with two supply inputs and which goal is to amplify the differential input voltage.
We have briefly presented their internal circuitry and shown that at least three stages are necessary to perform amplification.
Many characteristics can define an opamp, however, five in particular are extremely important and are presented in detail in the first section. Moreover, we explain that two configurations can be adopted leading to different behaviors: the openloop or closedloop.
The ideal opamp model is detailed in a second section where its idealized characteristics and behavior are summarized.
Finally, we highlight the differences between this ideal model and real opamps that can be found in many modern circuitry. The most important consequences of these differences are the finite gain and bandwidth which limits the amplification and frequency abilities.