# What is an Operational Amplifier? Op-Amp Integrator and Op-Amp Differentiator

An op-amp or operational amplifier is a linear device and extensively used in filtering, signal conditioning, or mainly used for performing mathematical operations such as addition, subtraction, differentiation, and integration. Basically, an op-amp uses external feedback components among the input as well as output terminals of op-amp like resistors and capacitors. These components will resolve the operation of the op-amp with good features like capacitive, resistive, etc. The amplifier can execute a variety of functions. An operational amplifier is a three terminal device includes two inputs and one output, where the inputs are inverting and non-inverting, and the outputs can be voltage or current.

## What is an Operational Amplifier?

An op-amp or operational is one type of integrated circuit that utilizes exterior voltage for amplifying the input using a very high gain. The main intention of this circuit is designed to enhance the low-level signal power. Please refer the link to know more about Various Op Amp Applications in Electronics

## What is an Operational Amplifier Differentiator?

In an op-amp differentiator circuit, the output voltage is directly proportional to the input voltage rate of change with respect to time, which means that a quick change of the input voltage signal, then the high o/p voltage will change in response. As the output of an op-amp differentiator circuit is proportional to the change in input. When the inputs of the differentiator circuit are standard waveforms like sine, square, triangular then the output waveforms will be very different.

If the input is square wave then there will be small spikes in other output waveforms. These spikes will be imperfect with the slope of the ends of the input waveform and maximum circuit output.

If the input is triangular waveform then the output changes to a square waveform in the ow with the increasing and declining levels of the input waveform.

If the input is sine wave from then it is changed to a cosine waveform which gives the signal with 90° phase shift, which is very useful in some situations.

### Operational Amplifier Differentiator Circuit

This is one type of amplifier, and the connection of this amplifier can be done among the input as well as output and includes very-high gain. The operational amplifier differentiator circuit can be used in analog computers to perform mathematical operations such as summation, multiplication, subtraction, integration, and differentiation.

The operational amplifier circuit generates an output voltage which is proportional to the time derivative input voltage. So this op-amp circuit is called as the differentiator. Assume the ground terminal which is denoted with G in the above circuit, where the flow of current through the ground terminal is equivalent to the flow of current out, we can write is as

In the above circuit, the op-amp node voltage at inverting terminal is zero then the flow of current through the capacitor can be written as

** I _{in} = I_{f}**

Where **I _{f }= -V_{out}/R_{f}**

The capacitor charge equals the voltage with capacitance times across the capacitor

**Q = C X V _{in}**

Therefore the charge rate change is

**dQ/dt = C dV _{in}/dt**

But the dQ/dt is the current through the capacitor

**I _{in = }**

**C dV**

_{in}/dt =**I**

_{f}**-V _{out}/R_{f } = **

**C dV**

_{in}/dtAn ideal output voltage (Vout) for the operational amplifier differentiator is written as

**Vout =** **–**** R _{f }C **

**dV**

_{in}/dtThus, the output voltage is a constant input voltage derivative – R_{f }C times of the input Vin voltage with respect to time. Here sign minus (–) specifies the phase shift (180^{o}) as the input signal is given to the input inverting terminal of the op-amp.

## What is an Operational Amplifier Integrator?

In most of the operational amplifier circuits, the feedback connection which is used is because of resistive in nature by a straight resistive line outlining as a minimum portion of the network. But for the op-amp integrator, the feedback will be provided by the capacitor among the input and output of the operational amplifier.

As an op-amp integrator performs the function of mathematical integration. However, it can be used in analog computers. The operation of this circuit is, it generates an output which is proportional to the input voltage with time. So the output voltage will be determined with the primary output voltage at any time.

From the above waveforms, it can be observed that as the input residues at zero. but when a step i/p voltage is given to the input, then the output will be raised. Similarly, when the step input voltage comebacks to zero position, then the output residue at the voltage it last achieved.

### Operational Amplifier Integrator Circuit

The operational amplifier integrator circuit can be built with an operational amplifier and a capacitor among the inverting input as well as the output, & a resistor from the inverting i/p to **e**ntire input of the circuit.

One of the applications of an op-amp is an integrator; it can be formed by altering the positions of resistor and capacitor. This circuit can generate an o/p voltage which is proportional to the input voltage time integral. Thus this circuit is named as an integrator circuit. Assume the ground terminal which is denoted with G in the above circuit, where the flow of current through the ground terminal is equivalent to the flow of current out, we can write is as

If **I _{in} + I_{f} = 0**

**I _{in} = – I_{f}**

**Vin –Va/R = -C d/dt (V0-Va)**

**Where Va = 0**

**Vin/R = -C d/dt V0**

Integrate the above equation, we can get the following

**1/R **

**Or **

**Vout**** = −∫****Vin/R**** ****C**** ****dt**** +****c**

Therefore the Vout voltage is equal to the constant -1/RC and integral of input voltage Vin

The circuit of operational amplifier integrator allows precise integration of the i/p signal to be attained. The applications of this circuit mainly include analog computers. Nowadays, an integration task is mandatory in analog applications, wherever the IC circuit is the perfect solution.

The op-amp differentiator has several applications of electronic circuit design. This circuit is used in analog computers where it is capable of providing a differentiation operation on the analog input voltage. This can be used in process instrumentation to check the rate of change of different points. Op-amp differentiator may be required in signal conditioning applications.

Thus, from the above information finally, we can conclude that op-amp integrated circuits are linear devices which are perfect for DC amplification, and used commonly in filtering, signal conditioning, mathematical operations like integration, differentiation, etc. Here is a question for you, **what are the different types of an operational amplifier?**