Detailed Notes: Operational Amplifier (Op-amp) | Analog Circuits - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


 
OPERATIOANL AMPLIFIERS 
Ideal op-amp, Output offset voltage, input bias current, input offset current, slew rate, gain 
bandwidth product, Inverting and non-inverting amplifier, Differentiator, integrator, 
Square-wave and triangular-wave generators. 
Introduction to Operational amplifiers: 
An electronic circuit is a group of electronic components connected for a specific purpose. 
A simple electronic circuit can be designed easily because it requires few discrete electronic 
components and connections. However, designing a complex electronic circuit is difficult, as 
it requires more number of discrete electronic components and their connections. It is also 
time taking to build such complex circuits and their reliability is also less. These difficulties 
can be overcome with Integrated Circuits. 
Integrated Circuit (IC) 
If multiple electronic components are interconnected on a single chip of semiconductor 
material, then that chip is called as an Integrated Circuit (IC). It consists of both active and 
passive components. 
This chapter discusses the advantages and types of ICs. 
Advantages of Integrated Circuits 
Integrated circuits offer many advantages. They are discussed below - 
? Compact size - For a given functionality, you can obtain a circuit of smaller size 
using ICs, compared to that built using a discrete circuit. 
? Lesser weight - A circuit built with ICs weighs lesser when compared to the weight 
of a discrete circuit that is used for implementing the same function of IC. using ICs, 
compared to that built using a discrete circuit. 
? Low power consumption - ICs consume lower power than a traditional 
circuit,because of their smaller size and construction. 
? Reduced cost - ICs are available at much reduced cost than discrete circuits because 
of their fabrication technologies and usage of lesser material than discrete circuits. 
? Increased reliability - Since they employ lesser connections, ICs offer increased 
reliability compared to digital circuits. 
? Improved operating speeds - ICs operate at improved speeds because of their 
switching speeds and lesser power consumption. 
Types of Integrated Circuits 
Integrated circuits are of two types - Analog Integrated Circuits and Digital Integrated 
Circuits. 
Analog Integrated Circuits 
Integrated circuits that operate over an entire range of continuous values of the signal 
amplitude are called as Analog Integrated Circuits. These are further classified into the 
two types as discussed here - 
Page 2


 
OPERATIOANL AMPLIFIERS 
Ideal op-amp, Output offset voltage, input bias current, input offset current, slew rate, gain 
bandwidth product, Inverting and non-inverting amplifier, Differentiator, integrator, 
Square-wave and triangular-wave generators. 
Introduction to Operational amplifiers: 
An electronic circuit is a group of electronic components connected for a specific purpose. 
A simple electronic circuit can be designed easily because it requires few discrete electronic 
components and connections. However, designing a complex electronic circuit is difficult, as 
it requires more number of discrete electronic components and their connections. It is also 
time taking to build such complex circuits and their reliability is also less. These difficulties 
can be overcome with Integrated Circuits. 
Integrated Circuit (IC) 
If multiple electronic components are interconnected on a single chip of semiconductor 
material, then that chip is called as an Integrated Circuit (IC). It consists of both active and 
passive components. 
This chapter discusses the advantages and types of ICs. 
Advantages of Integrated Circuits 
Integrated circuits offer many advantages. They are discussed below - 
? Compact size - For a given functionality, you can obtain a circuit of smaller size 
using ICs, compared to that built using a discrete circuit. 
? Lesser weight - A circuit built with ICs weighs lesser when compared to the weight 
of a discrete circuit that is used for implementing the same function of IC. using ICs, 
compared to that built using a discrete circuit. 
? Low power consumption - ICs consume lower power than a traditional 
circuit,because of their smaller size and construction. 
? Reduced cost - ICs are available at much reduced cost than discrete circuits because 
of their fabrication technologies and usage of lesser material than discrete circuits. 
? Increased reliability - Since they employ lesser connections, ICs offer increased 
reliability compared to digital circuits. 
? Improved operating speeds - ICs operate at improved speeds because of their 
switching speeds and lesser power consumption. 
Types of Integrated Circuits 
Integrated circuits are of two types - Analog Integrated Circuits and Digital Integrated 
Circuits. 
Analog Integrated Circuits 
Integrated circuits that operate over an entire range of continuous values of the signal 
amplitude are called as Analog Integrated Circuits. These are further classified into the 
two types as discussed here - 
? Linear Integrated Circuits - An analog IC is said to be Linear, if there exists a 
linear relation between its voltage and current. IC 741, an 8-pin Dual In-line Package 
(DIP)op-amp, is an example of Linear IC. 
? Radio Frequency Integrated Circuits - An analog IC is said to be Non-Linear, if 
there exists a non-linear relation between its voltage and current. A Non-Linear IC is 
also called as Radio Frequency IC. 
Digital Integrated Circuits 
If the integrated circuits operate only at a few pre-defined levels instead of operating for an 
entire range of continuous values of the signal amplitude, then those are called as Digital 
Integrated Circuits. 
Operational Amplifier, also called as an Op-Amp, is an integrated circuit, which can be used 
to perform various linear, non-linear, and mathematical operations. An op-amp is a direct 
coupled high gain amplifier. You can operate op-amp both with AC and DC signals. This 
chapter discusses the characteristics and types of op-amps. 
Construction of Operational Amplifier 
An op-amp consists of differential amplifier(s), a level translator and an output stage. A 
differential amplifier is present at the input stage of an op-amp and hence an op-amp 
consists of two input terminals. One of those terminals is called as the inverting 
terminal and the other one is called as the non-inverting terminal. The terminals are 
named based on the phase relationship between their respective inputs and outputs. 
Characteristics of Operational Amplifier 
The important characteristics or parameters of an operational amplifier are as follows - 
? Open loop voltage gain 
? Output offset voltage 
? Common Mode Rejection Ratio 
? Slew Rate 
This section discusses these characteristics in detail as given below - 
Open loop voltage gain 
The open loop voltage gain of an op-amp is its differential gain without any feedback path. 
Mathematically, the open loop voltage gain of an op-amp is represented as - 
Av=v0v1-v2Av=v0v1-v2 
Output offset voltage 
The voltage present at the output of an op-amp when its differential input voltage is zero is 
called as output offset voltage. 
Common Mode Rejection Ratio 
Common Mode Rejection Ratio (CMRR) of an op-amp is defined as the ratio of the closed 
loop differential gain, AdAd and the common mode gain, AcAc. 
Mathematically, CMRR can be represented as - 
CMRR=AdAcCMRR=AdAc 
Page 3


 
OPERATIOANL AMPLIFIERS 
Ideal op-amp, Output offset voltage, input bias current, input offset current, slew rate, gain 
bandwidth product, Inverting and non-inverting amplifier, Differentiator, integrator, 
Square-wave and triangular-wave generators. 
Introduction to Operational amplifiers: 
An electronic circuit is a group of electronic components connected for a specific purpose. 
A simple electronic circuit can be designed easily because it requires few discrete electronic 
components and connections. However, designing a complex electronic circuit is difficult, as 
it requires more number of discrete electronic components and their connections. It is also 
time taking to build such complex circuits and their reliability is also less. These difficulties 
can be overcome with Integrated Circuits. 
Integrated Circuit (IC) 
If multiple electronic components are interconnected on a single chip of semiconductor 
material, then that chip is called as an Integrated Circuit (IC). It consists of both active and 
passive components. 
This chapter discusses the advantages and types of ICs. 
Advantages of Integrated Circuits 
Integrated circuits offer many advantages. They are discussed below - 
? Compact size - For a given functionality, you can obtain a circuit of smaller size 
using ICs, compared to that built using a discrete circuit. 
? Lesser weight - A circuit built with ICs weighs lesser when compared to the weight 
of a discrete circuit that is used for implementing the same function of IC. using ICs, 
compared to that built using a discrete circuit. 
? Low power consumption - ICs consume lower power than a traditional 
circuit,because of their smaller size and construction. 
? Reduced cost - ICs are available at much reduced cost than discrete circuits because 
of their fabrication technologies and usage of lesser material than discrete circuits. 
? Increased reliability - Since they employ lesser connections, ICs offer increased 
reliability compared to digital circuits. 
? Improved operating speeds - ICs operate at improved speeds because of their 
switching speeds and lesser power consumption. 
Types of Integrated Circuits 
Integrated circuits are of two types - Analog Integrated Circuits and Digital Integrated 
Circuits. 
Analog Integrated Circuits 
Integrated circuits that operate over an entire range of continuous values of the signal 
amplitude are called as Analog Integrated Circuits. These are further classified into the 
two types as discussed here - 
? Linear Integrated Circuits - An analog IC is said to be Linear, if there exists a 
linear relation between its voltage and current. IC 741, an 8-pin Dual In-line Package 
(DIP)op-amp, is an example of Linear IC. 
? Radio Frequency Integrated Circuits - An analog IC is said to be Non-Linear, if 
there exists a non-linear relation between its voltage and current. A Non-Linear IC is 
also called as Radio Frequency IC. 
Digital Integrated Circuits 
If the integrated circuits operate only at a few pre-defined levels instead of operating for an 
entire range of continuous values of the signal amplitude, then those are called as Digital 
Integrated Circuits. 
Operational Amplifier, also called as an Op-Amp, is an integrated circuit, which can be used 
to perform various linear, non-linear, and mathematical operations. An op-amp is a direct 
coupled high gain amplifier. You can operate op-amp both with AC and DC signals. This 
chapter discusses the characteristics and types of op-amps. 
Construction of Operational Amplifier 
An op-amp consists of differential amplifier(s), a level translator and an output stage. A 
differential amplifier is present at the input stage of an op-amp and hence an op-amp 
consists of two input terminals. One of those terminals is called as the inverting 
terminal and the other one is called as the non-inverting terminal. The terminals are 
named based on the phase relationship between their respective inputs and outputs. 
Characteristics of Operational Amplifier 
The important characteristics or parameters of an operational amplifier are as follows - 
? Open loop voltage gain 
? Output offset voltage 
? Common Mode Rejection Ratio 
? Slew Rate 
This section discusses these characteristics in detail as given below - 
Open loop voltage gain 
The open loop voltage gain of an op-amp is its differential gain without any feedback path. 
Mathematically, the open loop voltage gain of an op-amp is represented as - 
Av=v0v1-v2Av=v0v1-v2 
Output offset voltage 
The voltage present at the output of an op-amp when its differential input voltage is zero is 
called as output offset voltage. 
Common Mode Rejection Ratio 
Common Mode Rejection Ratio (CMRR) of an op-amp is defined as the ratio of the closed 
loop differential gain, AdAd and the common mode gain, AcAc. 
Mathematically, CMRR can be represented as - 
CMRR=AdAcCMRR=AdAc 
Note that the common mode gain, AcAc of an op-amp is the ratio of the common mode 
output voltage and the common mode input voltage. 
Slew Rate 
Slew rate of an op-amp is defined as the maximum rate of change of the output voltage due 
to a step input voltage. 
Mathematically, slew rate (SR) can be represented as - 
SR=MaximumofdV0dtSR=MaximumofdV0dt 
Where, V0V0 is the output voltage. In general, slew rate is measured in 
either V/µSecV/µSec or V/mSecV/mSec. 
Types of Operational Amplifiers 
An op-amp is represented with a triangle symbol having two inputs and one output. 
Op-amps are of two types: Ideal Op-Amp and Practical Op-Amp. 
They are discussed in detail as given below - 
Ideal Op-Amp 
An ideal op-amp exists only in theory, and does not exist practically. The equivalent 
circuit of an ideal op-amp is shown in the figure given below - 
 
 
An ideal op-amp exhibits the following characteristics - 
? Input impedance Zi=8OZi=8O 
? Output impedance Z0=0OZ0=0O 
? Open loop voltage gaine Av=8Av=8 
? If (the differential) input voltage Vi=0VVi=0V, then the output voltage will 
be V0=0VV0=0V 
? Bandwidth is infinity. It means, an ideal op-amp will amplify the signals of any 
frequency without any attenuation. 
? Common Mode Rejection Ratio (CMRR) is infinity. 
? Slew Rate (SR) is infinity. It means, the ideal op-amp will produce a change in the 
output instantly in response to an input step voltage. 
Practical Op-Amp 
Practically, op-amps are not ideal and deviate from their ideal characteristics because of 
some imperfections during manufacturing. The equivalent circuit of a practical op-amp is 
shown in the following figure - 
Page 4


 
OPERATIOANL AMPLIFIERS 
Ideal op-amp, Output offset voltage, input bias current, input offset current, slew rate, gain 
bandwidth product, Inverting and non-inverting amplifier, Differentiator, integrator, 
Square-wave and triangular-wave generators. 
Introduction to Operational amplifiers: 
An electronic circuit is a group of electronic components connected for a specific purpose. 
A simple electronic circuit can be designed easily because it requires few discrete electronic 
components and connections. However, designing a complex electronic circuit is difficult, as 
it requires more number of discrete electronic components and their connections. It is also 
time taking to build such complex circuits and their reliability is also less. These difficulties 
can be overcome with Integrated Circuits. 
Integrated Circuit (IC) 
If multiple electronic components are interconnected on a single chip of semiconductor 
material, then that chip is called as an Integrated Circuit (IC). It consists of both active and 
passive components. 
This chapter discusses the advantages and types of ICs. 
Advantages of Integrated Circuits 
Integrated circuits offer many advantages. They are discussed below - 
? Compact size - For a given functionality, you can obtain a circuit of smaller size 
using ICs, compared to that built using a discrete circuit. 
? Lesser weight - A circuit built with ICs weighs lesser when compared to the weight 
of a discrete circuit that is used for implementing the same function of IC. using ICs, 
compared to that built using a discrete circuit. 
? Low power consumption - ICs consume lower power than a traditional 
circuit,because of their smaller size and construction. 
? Reduced cost - ICs are available at much reduced cost than discrete circuits because 
of their fabrication technologies and usage of lesser material than discrete circuits. 
? Increased reliability - Since they employ lesser connections, ICs offer increased 
reliability compared to digital circuits. 
? Improved operating speeds - ICs operate at improved speeds because of their 
switching speeds and lesser power consumption. 
Types of Integrated Circuits 
Integrated circuits are of two types - Analog Integrated Circuits and Digital Integrated 
Circuits. 
Analog Integrated Circuits 
Integrated circuits that operate over an entire range of continuous values of the signal 
amplitude are called as Analog Integrated Circuits. These are further classified into the 
two types as discussed here - 
? Linear Integrated Circuits - An analog IC is said to be Linear, if there exists a 
linear relation between its voltage and current. IC 741, an 8-pin Dual In-line Package 
(DIP)op-amp, is an example of Linear IC. 
? Radio Frequency Integrated Circuits - An analog IC is said to be Non-Linear, if 
there exists a non-linear relation between its voltage and current. A Non-Linear IC is 
also called as Radio Frequency IC. 
Digital Integrated Circuits 
If the integrated circuits operate only at a few pre-defined levels instead of operating for an 
entire range of continuous values of the signal amplitude, then those are called as Digital 
Integrated Circuits. 
Operational Amplifier, also called as an Op-Amp, is an integrated circuit, which can be used 
to perform various linear, non-linear, and mathematical operations. An op-amp is a direct 
coupled high gain amplifier. You can operate op-amp both with AC and DC signals. This 
chapter discusses the characteristics and types of op-amps. 
Construction of Operational Amplifier 
An op-amp consists of differential amplifier(s), a level translator and an output stage. A 
differential amplifier is present at the input stage of an op-amp and hence an op-amp 
consists of two input terminals. One of those terminals is called as the inverting 
terminal and the other one is called as the non-inverting terminal. The terminals are 
named based on the phase relationship between their respective inputs and outputs. 
Characteristics of Operational Amplifier 
The important characteristics or parameters of an operational amplifier are as follows - 
? Open loop voltage gain 
? Output offset voltage 
? Common Mode Rejection Ratio 
? Slew Rate 
This section discusses these characteristics in detail as given below - 
Open loop voltage gain 
The open loop voltage gain of an op-amp is its differential gain without any feedback path. 
Mathematically, the open loop voltage gain of an op-amp is represented as - 
Av=v0v1-v2Av=v0v1-v2 
Output offset voltage 
The voltage present at the output of an op-amp when its differential input voltage is zero is 
called as output offset voltage. 
Common Mode Rejection Ratio 
Common Mode Rejection Ratio (CMRR) of an op-amp is defined as the ratio of the closed 
loop differential gain, AdAd and the common mode gain, AcAc. 
Mathematically, CMRR can be represented as - 
CMRR=AdAcCMRR=AdAc 
Note that the common mode gain, AcAc of an op-amp is the ratio of the common mode 
output voltage and the common mode input voltage. 
Slew Rate 
Slew rate of an op-amp is defined as the maximum rate of change of the output voltage due 
to a step input voltage. 
Mathematically, slew rate (SR) can be represented as - 
SR=MaximumofdV0dtSR=MaximumofdV0dt 
Where, V0V0 is the output voltage. In general, slew rate is measured in 
either V/µSecV/µSec or V/mSecV/mSec. 
Types of Operational Amplifiers 
An op-amp is represented with a triangle symbol having two inputs and one output. 
Op-amps are of two types: Ideal Op-Amp and Practical Op-Amp. 
They are discussed in detail as given below - 
Ideal Op-Amp 
An ideal op-amp exists only in theory, and does not exist practically. The equivalent 
circuit of an ideal op-amp is shown in the figure given below - 
 
 
An ideal op-amp exhibits the following characteristics - 
? Input impedance Zi=8OZi=8O 
? Output impedance Z0=0OZ0=0O 
? Open loop voltage gaine Av=8Av=8 
? If (the differential) input voltage Vi=0VVi=0V, then the output voltage will 
be V0=0VV0=0V 
? Bandwidth is infinity. It means, an ideal op-amp will amplify the signals of any 
frequency without any attenuation. 
? Common Mode Rejection Ratio (CMRR) is infinity. 
? Slew Rate (SR) is infinity. It means, the ideal op-amp will produce a change in the 
output instantly in response to an input step voltage. 
Practical Op-Amp 
Practically, op-amps are not ideal and deviate from their ideal characteristics because of 
some imperfections during manufacturing. The equivalent circuit of a practical op-amp is 
shown in the following figure - 
 
 
A practical op-amp exhibits the following characteristics - 
? Input impedance, ZiZi in the order of Mega ohms. 
? Output impedance, Z0Z0 in the order of few ohms.. 
? Open loop voltage gain, AvAv will be high. 
 
When you choose a practical op-amp, you should check whether it satisfies the following 
conditions - 
? Input impedance, ZiZi should be as high as possible. 
? Output impedance, Z0Z0 should be as low as possible. 
? Open loop voltage gain, AvAv should be as high as possible. 
? Output offset voltage should be as low as possible. 
? The operating Bandwidth should be as high as possible. 
? CMRR should be as high as possible. 
? Slew rate should be as high as possible. 
A circuit is said to be linear, if there exists a linear relationship between its input and the 
output. Similarly, a circuit is said to be non-linear, if there exists a non-linear relationship 
between its input and output. Op-amps can be used in both linear and non-linear 
applications. The following are the basic applications of op-amp - 
? Inverting Amplifier 
? Non-inverting Amplifier 
? Voltage follower 
Inverting Amplifier 
An inverting amplifier takes the input through its inverting terminal through a resistor R1R1, 
and produces its amplified version as the output. This amplifier not only amplifies the input 
but also inverts it (changes its sign). 
 
Page 5


 
OPERATIOANL AMPLIFIERS 
Ideal op-amp, Output offset voltage, input bias current, input offset current, slew rate, gain 
bandwidth product, Inverting and non-inverting amplifier, Differentiator, integrator, 
Square-wave and triangular-wave generators. 
Introduction to Operational amplifiers: 
An electronic circuit is a group of electronic components connected for a specific purpose. 
A simple electronic circuit can be designed easily because it requires few discrete electronic 
components and connections. However, designing a complex electronic circuit is difficult, as 
it requires more number of discrete electronic components and their connections. It is also 
time taking to build such complex circuits and their reliability is also less. These difficulties 
can be overcome with Integrated Circuits. 
Integrated Circuit (IC) 
If multiple electronic components are interconnected on a single chip of semiconductor 
material, then that chip is called as an Integrated Circuit (IC). It consists of both active and 
passive components. 
This chapter discusses the advantages and types of ICs. 
Advantages of Integrated Circuits 
Integrated circuits offer many advantages. They are discussed below - 
? Compact size - For a given functionality, you can obtain a circuit of smaller size 
using ICs, compared to that built using a discrete circuit. 
? Lesser weight - A circuit built with ICs weighs lesser when compared to the weight 
of a discrete circuit that is used for implementing the same function of IC. using ICs, 
compared to that built using a discrete circuit. 
? Low power consumption - ICs consume lower power than a traditional 
circuit,because of their smaller size and construction. 
? Reduced cost - ICs are available at much reduced cost than discrete circuits because 
of their fabrication technologies and usage of lesser material than discrete circuits. 
? Increased reliability - Since they employ lesser connections, ICs offer increased 
reliability compared to digital circuits. 
? Improved operating speeds - ICs operate at improved speeds because of their 
switching speeds and lesser power consumption. 
Types of Integrated Circuits 
Integrated circuits are of two types - Analog Integrated Circuits and Digital Integrated 
Circuits. 
Analog Integrated Circuits 
Integrated circuits that operate over an entire range of continuous values of the signal 
amplitude are called as Analog Integrated Circuits. These are further classified into the 
two types as discussed here - 
? Linear Integrated Circuits - An analog IC is said to be Linear, if there exists a 
linear relation between its voltage and current. IC 741, an 8-pin Dual In-line Package 
(DIP)op-amp, is an example of Linear IC. 
? Radio Frequency Integrated Circuits - An analog IC is said to be Non-Linear, if 
there exists a non-linear relation between its voltage and current. A Non-Linear IC is 
also called as Radio Frequency IC. 
Digital Integrated Circuits 
If the integrated circuits operate only at a few pre-defined levels instead of operating for an 
entire range of continuous values of the signal amplitude, then those are called as Digital 
Integrated Circuits. 
Operational Amplifier, also called as an Op-Amp, is an integrated circuit, which can be used 
to perform various linear, non-linear, and mathematical operations. An op-amp is a direct 
coupled high gain amplifier. You can operate op-amp both with AC and DC signals. This 
chapter discusses the characteristics and types of op-amps. 
Construction of Operational Amplifier 
An op-amp consists of differential amplifier(s), a level translator and an output stage. A 
differential amplifier is present at the input stage of an op-amp and hence an op-amp 
consists of two input terminals. One of those terminals is called as the inverting 
terminal and the other one is called as the non-inverting terminal. The terminals are 
named based on the phase relationship between their respective inputs and outputs. 
Characteristics of Operational Amplifier 
The important characteristics or parameters of an operational amplifier are as follows - 
? Open loop voltage gain 
? Output offset voltage 
? Common Mode Rejection Ratio 
? Slew Rate 
This section discusses these characteristics in detail as given below - 
Open loop voltage gain 
The open loop voltage gain of an op-amp is its differential gain without any feedback path. 
Mathematically, the open loop voltage gain of an op-amp is represented as - 
Av=v0v1-v2Av=v0v1-v2 
Output offset voltage 
The voltage present at the output of an op-amp when its differential input voltage is zero is 
called as output offset voltage. 
Common Mode Rejection Ratio 
Common Mode Rejection Ratio (CMRR) of an op-amp is defined as the ratio of the closed 
loop differential gain, AdAd and the common mode gain, AcAc. 
Mathematically, CMRR can be represented as - 
CMRR=AdAcCMRR=AdAc 
Note that the common mode gain, AcAc of an op-amp is the ratio of the common mode 
output voltage and the common mode input voltage. 
Slew Rate 
Slew rate of an op-amp is defined as the maximum rate of change of the output voltage due 
to a step input voltage. 
Mathematically, slew rate (SR) can be represented as - 
SR=MaximumofdV0dtSR=MaximumofdV0dt 
Where, V0V0 is the output voltage. In general, slew rate is measured in 
either V/µSecV/µSec or V/mSecV/mSec. 
Types of Operational Amplifiers 
An op-amp is represented with a triangle symbol having two inputs and one output. 
Op-amps are of two types: Ideal Op-Amp and Practical Op-Amp. 
They are discussed in detail as given below - 
Ideal Op-Amp 
An ideal op-amp exists only in theory, and does not exist practically. The equivalent 
circuit of an ideal op-amp is shown in the figure given below - 
 
 
An ideal op-amp exhibits the following characteristics - 
? Input impedance Zi=8OZi=8O 
? Output impedance Z0=0OZ0=0O 
? Open loop voltage gaine Av=8Av=8 
? If (the differential) input voltage Vi=0VVi=0V, then the output voltage will 
be V0=0VV0=0V 
? Bandwidth is infinity. It means, an ideal op-amp will amplify the signals of any 
frequency without any attenuation. 
? Common Mode Rejection Ratio (CMRR) is infinity. 
? Slew Rate (SR) is infinity. It means, the ideal op-amp will produce a change in the 
output instantly in response to an input step voltage. 
Practical Op-Amp 
Practically, op-amps are not ideal and deviate from their ideal characteristics because of 
some imperfections during manufacturing. The equivalent circuit of a practical op-amp is 
shown in the following figure - 
 
 
A practical op-amp exhibits the following characteristics - 
? Input impedance, ZiZi in the order of Mega ohms. 
? Output impedance, Z0Z0 in the order of few ohms.. 
? Open loop voltage gain, AvAv will be high. 
 
When you choose a practical op-amp, you should check whether it satisfies the following 
conditions - 
? Input impedance, ZiZi should be as high as possible. 
? Output impedance, Z0Z0 should be as low as possible. 
? Open loop voltage gain, AvAv should be as high as possible. 
? Output offset voltage should be as low as possible. 
? The operating Bandwidth should be as high as possible. 
? CMRR should be as high as possible. 
? Slew rate should be as high as possible. 
A circuit is said to be linear, if there exists a linear relationship between its input and the 
output. Similarly, a circuit is said to be non-linear, if there exists a non-linear relationship 
between its input and output. Op-amps can be used in both linear and non-linear 
applications. The following are the basic applications of op-amp - 
? Inverting Amplifier 
? Non-inverting Amplifier 
? Voltage follower 
Inverting Amplifier 
An inverting amplifier takes the input through its inverting terminal through a resistor R1R1, 
and produces its amplified version as the output. This amplifier not only amplifies the input 
but also inverts it (changes its sign). 
 
            
Note that for an op-amp, the voltage at the inverting input terminal is equal to the voltage at 
its non-inverting input terminal. Physically, there is no short between those two terminals 
but virtually, they are in short with each other. In the circuit shown above, the non-
inverting input terminal is connected to ground. That means zero volts is applied at the non-
inverting input terminal of the op-amp. According to the virtual short concept, the voltage 
at the inverting input terminal of an op-amp will be zero volts. 
The nodal equation at this terminal's node is as shown below - 
0-ViR1+0-V0Rf=00-ViR1+0-V0Rf=0 
=>-ViR1=V0Rf=>-ViR1=V0Rf 
=>V0=(-RfR1)Vt=>V0=(-RfR1)Vt 
=>V0Vi=-RfR1=>V0Vi=-RfR1 
The ratio of the output voltage V0V0 and the input voltage ViVi is the voltage-gain or gain 
of the amplifier. Therefore, the gain of inverting amplifier is equal to -RfR1-RfR1. 
Note that the gain of the inverting amplifier is having a negative sign. It indicates that there 
exists a 180
0
 phase difference between the input and the output. 
Non-Inverting Amplifier 
A non-inverting amplifier takes the input through its non-inverting terminal, and produces 
its amplified version as the output. As the name suggests, this amplifier just amplifies the 
input, without inverting or changing the sign of the output. The circuit diagram of a non-
inverting amplifier is shown in the following figure - 
 
 
In the above circuit, the input voltage ViVi is directly applied to the non-inverting input 
terminal of op-amp. So, the voltage at the non-inverting input terminal of the op-amp will 
be ViVi. By using voltage division principle, we can calculate the voltage at the inverting 
input terminal of the op-amp as shown below - 
=>V1=V0(R1R1+Rf)=>V1=V0(R1R1+Rf) 
According to the virtual short concept, the voltage at the inverting input terminal of an op-
amp is same as that of the voltage at its non-inverting input terminal. 
=>V1=Vi=>V1=Vi 
=>V0(R1R1+Rf)=Vi=>V0(R1R1+Rf)=Vi 
=>V0Vi=R1+RfR1=>V0Vi=R1+RfR1 
=>V0Vi=1+RfR1=>V0Vi=1+RfR1