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
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