Table of Contents

What is an Operational Amplifier?
Operational amplifiers, (op-amp), are linear devices that are used extensively in signal conditioning, filtering, or to perform mathematical operations such as adding, subtracting, integration, and differentiation.
They are used in combination with external feedback components such as resistors, capacitors and inductors between the input and output. The configuration of these components determines the function/operation of the op-amp.
They have a three-terminal device with two high impedance inputs. The input designated by a minus sign, (-), is called the "inverting" input, while the other input is designated by a plus sign, (+), is called the "non-inverting" input. The third terminal represents the op-amps output which can sink or source either a voltage or current. The output signal is the amplification factor or amplification gain (A) and is multiplied by the input signal. Depending on the nature of the input or output, there are four classifications for op-amp gain [2].

Input Output Classification
Voltage Voltage Voltage
Current Current Current
Voltage Current Transconductance
Current Voltage Trans-resistance

Figure 1. Operational Amplifier [1]

Equivalent Circuit

Op-Amp Parameter and Idealized Characteristic
Parameter Idealized Characteristic
Open Loop Gain (A_VO)
Infinite
Open loop gain is the gain of an op-amp without any feedback
Main function of an op-amp is to amplify an input signal, the larger than gain the better
Real op-amps typically have an open loop gain from 20,000 to 200,000
Input Impedance (Z_IN)
Infinite
Input impedance is the ratio of input voltage to input current
Assumed to be infinite to prevent any current flowing from the source into the input circuitry (I_IN = 0)
Real op-amps have some input current in from a few pico-amps to a few milli-amps
Output Impedance (Z_OUT)
Zero
Output impedance is assumed to be zero to act as a perfect internal voltage source with zero internal resistance in order to supply as much current as necessary
Real op-amps typically have output impedances of 100-20kΩ
Bandwidth (BW)
Infinite
Bandwidth is the frequency range over which the voltage gain of the amplifier is above 70.7% of its max output value
It is assumed to be infinite so that it can amplify any frequency signal
Real op-amps are limited by the Gain-Bandwidth product
Offset Voltage (V_IO)
Zero
The op-amps output is zero when the voltage difference between the two inputs is zero
Real op-amps have some offset voltage
The op-amp output is limited by the +V_supply and the -V_supply where they are the upper and lower limit of the op-amp respectively [2].

Figure 2. Equivalent Circuit of an Ideal Operational Amplifier [2]

Basic Configurations

Inverting Op-Amp
The main feature of this circuit is the gain that it produces which can be calculated as: [3]
This configuration has applications in audio mixers and provides low impedance. Another application is that since the output it generates is phase shifted 180 degrees, it can be used as a phase shifter [4].

Figure 3. Inverting Op-Amp Configuration [3]

Non-Inverting Op-Amp
The gain of the circuit can be calculated as:

This configuration is one of the most popular and widely used forms of op-amp circuits. It is primarily used in applications where high input impedance is required [3].

Figure 4. Non-Inverting Op-Amp Configuration [3]

Summing Amplifier
The summing amplifier also known as a linear mixer sums all the signals in a completely linear fashion. The other type of mixer is called a multiplying mixer and uses the non-linear properties of circuits to multiply two signals together and generate additional frequencies.
The output of the circuit can be calculated as:
Where R1x is the value of the resistor at the input. This configuration provides the ideal platform for audio mixing. The various inputs (R1a, R1b, R1c etc.) can be controlled independently as the virtual earth (a node of the circuit maintained at a steady reference potential without being directly connected [5]) of the inverting amplifier is not dependent on the conditions of any of the inputs [3].

Figure 5. Summing Op-Amp Configuration / Virtual Earth Mixer [4]

Differential Amplifier
The ideal voltage output of a differential amplifier is:
If all resistors are equal, that is: R1=R2=R3=R4, then the circuit will become a Unity Gain Differential Amplifier and V_out is simply:
The differential amplifier configuration can be used by adding more resistors in parallel with the input resistors to make it either add or subtract voltages applied to the respective inputs. A common method of doing this is to connect a "Resistive Bridge" (Wheatstone Bridge) to the input of the an op-amp [3].

Figure 6. Differential Op-Amp Configuration [4]

Integrator Amplifier
The ideal voltage output of an integrator amplifier is:
This can be re-written as:
Where ω = 2πƒ and V_out is a constant 1/RC times the integral of the input voltage V_IN with respect to time and is phase shifted 180° as indicated by the negative [4].
The integrator amplifier circuit has many applications. They are most commonly seen in analog-to-digital converters, ramp generators, and in wave shaping. They also see usage in analog computers to perform calculus operations [6].

Figure 7. Integrator Op-Amp Configuration [4]

Differentiator Amplifier
The ideal voltage of the differentiator amplifier is:
Thus the output voltage is a constant, -R_f*C times the derivative of the input voltage with a 180° phase shift as indicated by the negative [3].
The differentiator amplifier circuit are most commonly designed to operate on triangular and rectangular signals. They also see usage as wave shaping circuits to detect high frequency components in the input signal [7].

Figure 8. Differentiator Op-Amp Configuration [4]

Schmitt Trigger
A Schmitt trigger is a comparator circuit, a circuit that compares two voltages and outputs either a 1 or 0 depending on which is larger, that implements hysteresis, the dependence of the state of a system on its history, by applying positive feedback to the non-inverting input of the op-amp. In the non-inverting configuration, when V_in is greater than some chosen threshold as indicated by V_ref , then the output is high, or V_SAT . If the input becomes less than V_ref , the output will become V_-SAT . This dual threshold is called hysteresis and allows the Schmitt trigger to be used as a bistable multi-vibrator (latch or flip-flop). They are very similar to the basic inverting and non-inverting op-amp configurations except that the inputs are switched.
Schmitt triggers are usually used in signal conditioning applications to remove noise from signals in digital circuits, particularly in mechanical contact bounce in switches. Other applications include closed loop negative feedback, relaxation oscillators, function generators and switching power supplies [8].

Figure 9. Inverting Schmitt Trigger Configuration [8]
Figure 10. Non-Inverting Schmitt Trigger Configuration [8]

References
[1] “Introduction to Operational Amplifiers (Op-amps): Operational Amplifiers: Electronics Textbook,” All About Circuits. [Online]. Available: https://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/introduction-operational-amplifiers/. [Accessed: 25-Mar-2021].
[2] “Operational Amplifier Basics - Op-amp tutorial,” Basic Electronics Tutorials, 01-May-2020. [Online]. Available: https://www.electronics-tutorials.ws/opamp/opamp_1.html. [Accessed: 25-Mar-2021].
[3] E. Notes, “reference site for electronics, radio & wireless,” Electronics Notes. [Online]. Available: https://www.electronics-notes.com/. [Accessed: 05-Apr-2021].
[4] WatElectronics, “Inverting Amplifier Circuit Working Along With its Applications,” WatElectronics.com, 19-Nov-2019. [Online]. Available: https://www.watelectronics.com/inverting-amplifier-circuit-working-and-applications/. [Accessed: 05-Apr-2021].
[5] Author Ligo GeorgeFollow Me on LinkedIn, D. H. says: D. V. says: V. K. says: and P. G. says: “What is Virtual Ground in Opamp ?,” electroSome, 12-Apr-2018. [Online]. Available: https://electrosome.com/virtual-ground-opamp/. [Accessed: 13-Apr-2021].
[6] R. Teja, “Op Amp Integrator Circuit Design and Applications,” Electronics Hub, 10-Apr-2021. [Online]. Available: https://www.electronicshub.org/operational-amplifier-as-integrator/. [Accessed: 13-Apr-2021].
[7] Administrator, “Operational Amplifier as Differentiator Circuit Applications,” Electronics Hub, 25-Feb-2019. [Online]. Available: https://www.electronicshub.org/operational-amplifier-as-differentiator/#:~:text=BACK%20TO%20TOP-,Applications%20of%20Op%2Damp%20Differentiator,components%20in%20the%20input%20signal. [Accessed: 13-Apr-2021].
[8] Administrator, “Basics of Schmitt Trigger: How Schmitt Trigger Works?,” Electronics Hub, 30-Sep-2019. [Online]. Available: https://www.electronicshub.org/schmitt-trigger-basics/. [Accessed: 13-Apr-2021].

Contributors:
User Last Update
Mayurakhi Khan 1257 days ago
Faculty Advisors: Kim Pope, John Thistle, Allyson Giannikouris, Michael Lenover (alumni)

Input	Output	Classification
Voltage	Voltage	Voltage
Current	Current	Current
Voltage	Current	Transconductance
Current	Voltage	Trans-resistance

Parameter	Idealized Characteristic
Open Loop Gain (A_VO)	Infinite Open loop gain is the gain of an op-amp without any feedback Main function of an op-amp is to amplify an input signal, the larger than gain the better Real op-amps typically have an open loop gain from 20,000 to 200,000
Input Impedance (Z_IN)	Infinite Input impedance is the ratio of input voltage to input current Assumed to be infinite to prevent any current flowing from the source into the input circuitry (I_IN = 0) Real op-amps have some input current in from a few pico-amps to a few milli-amps
Output Impedance (Z_OUT)	Zero Output impedance is assumed to be zero to act as a perfect internal voltage source with zero internal resistance in order to supply as much current as necessary Real op-amps typically have output impedances of 100-20kΩ
Bandwidth (BW)	Infinite Bandwidth is the frequency range over which the voltage gain of the amplifier is above 70.7% of its max output value It is assumed to be infinite so that it can amplify any frequency signal Real op-amps are limited by the Gain-Bandwidth product
Offset Voltage (V_IO)	Zero The op-amps output is zero when the voltage difference between the two inputs is zero Real op-amps have some offset voltage

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