These are linear devices having all the properties that are required for ideal DC amplification. It used for the signal condition, filtering or to perform mathematical operations such as add, subtract, differentiation and integration.
Operational amplifiers
An Operational Amplifier is a voltage amplifying device designed to be used with external feedback components such as capacitors and resistors between its input and output terminals.
These feedback components determine the operation of the amplifier and by the impact of the different feedback configurations, whether it is resistive, capacitive or both, the amplifier can perform a different verity of operations, giving rise to its name of Operational Amplifier.
An Operational Amplifier is basically a three terminal device which consists of two high impedance inputs and one input.
One of the inputs is Inverting Input, which marked with a negative or minus sign (–).
The other input is Noninverting Input, which marked with a positive or plus sign (+).
A third terminal behaves the operational amplifiers output port which can both source and sink either a voltage or a current.
Operational Amplifier Gain
In a linear operational amplifier, the amplification factor is the output signal, known as the amplifier’s gain ( A ) that is multiplied by the value of the input signal and depending upon the nature of these input and output signals, there are four different classifications of operational amplifier gain.
 Voltage– Voltage input and Voltage output
 Current– Current input and Current output
 Transconductance– Voltage input and Current output
 Transresistance– Current input and Voltage output
The output voltage signal of the Operational Amplifier is the difference between the signals of two individual inputs.
In other words, an output signal of an operational amplifier is the difference between the two input signals as the input stage of an Operational Amplifier is, in fact, a differential amplifier.
Equivalent Circuit of an Ideal Operational Amplifier
Opamp Parameter and Idealized Characteristic

Open Loop Gain, (Avo)
Infinite case
The main function of an opamp is the amplification of the input signal and the more openloop gain it has the better.
Openloop gain is the gain of the operational amplifier without positive or negative feedback.
For such an amplifier, the gain will be infinite but the typical real values range from about 20,000 to 200,000.

Input impedance, (Z_{IN})
Infinite case
The input impedance is the ratio of input voltage to the input current.
It is considered to be infinite to prevent any current flowing from the source into the amplifier’s input circuitry (I_{IN} = 0).
The real opamps have input leakage currents from the range of a few picoamper to a few milliamper.

Output impedance, (Z_{OUT})
Zero Impedance
The output impedance of the ideal opamp is assumed to be zero and it acting as a perfect internal voltage source having no internal resistance so that it can supply enough current as necessary to the load.
This internal resistance is useful in series with the load and it reducing the output voltage available to the load.
Real opamps have output impedances in the range of 10020kΩ.

Bandwidth
Infinite Case
An ideal opamp has an infinite frequency response and amplifies any frequency signal from DC to the high AC frequencies so it is assumed to have infinite bandwidth.
In real, the operational amplifier bandwidth is limited by the GainBandwidth product (GB), which is equal to the frequency where the amplifier’s gain becomes unity.

Offset Voltage, (V_{IO})
Zero amplification
The output of the amplifiers will be zero when the voltage difference is zero between the inverting and the noninverting inputs. The amplification is the same or when both inputs are grounded also included in this case. In real operational amplifiers have some amount of output offset voltage.
In idealized characteristics, we can see that the input resistance is infinite, so there are no current flows into either input terminal and that the differential input offset voltage is zero.
The real Opamp do not have infinite gain or bandwidth but it has a typical Open Loop Gain which is defined as the amplifiers output amplification without any external feedback signals connected to it and for a typical opamp is about 100dB at DC (zero Hz).
This output gain decreases linearly with respect to frequency down to Unity Gain, at about 1MHz
Operational Amplifiers Summary
The operational amplifier is a very high DC gain differential amplifier that uses one or more than one external feedback network to control the response and characteristics of an opamp.
We connect external resistors or capacitors to the opamp in different ways to form basic building Block circuits such as, Inverting, NonInverting, Summing, Voltage Follower, Integrator, Differential and Differentiator type amplifiers.
A perfect ideal operational amplifier is a device with certain special characteristics such as infinite input resistance R_{IN}, infinite openloop gain A_{O}, zero output resistance R_{OUT}, infinite bandwidth zero to infinite and zero offset voltage.Opamp is available in integrated circuit packages of single, dual or quad opamps within one single device.
The most commonly available and used of all operational amplifiers in basic electronic kits are μA741.