- Introduction

In today’s article, we are going to study about ‘ **operational amplifier** ‘ How beneficial it is and what is theory of **operational amplifier. **And hence We will also read about some more topics like **operational amplifier**, inverting signal, non inverting signal, ideal **operational amplifier**, condition for Ideal **operational amplifier**, inverting **operational amplifier** etc given in Detail. So, take your notebooks in you hand and get ready to study physics in an easy and sorted way.

# Operational amplifier

The **operational amplifier** in which two input are present. One Input is for inverting and second input is for non inverting, and we have only one output (Vo).

**For inverting**

If Input is amplified (Vi) on inverting terminal and non inverting terminal would be grounded then we get a invert amplified output corresponding to the input signal. For example- If we give a positive Cycle then we get a negative amplified cycle in output. And if we give a negative cycle on input then we get a positive amplified cycle at the output.

**Non inverting**

If we apply Input signal on non inverting terminal at that time inverting terminal will be grounded. Than we get amplified output in same phase, corresponding to the input signal. For example- If we apply positive signal on non inverting terminal than we get a positive amplified signal at the output. If we apply a negative cycle on non inverting terminal than we get a negative amplified output.

## Ideal operational amplifier

- When an
**operational amplifier**is used without any feedback it means the circuit is open loop circuit. **Operational amplifier**working in this condition in which there is no feedback, that is called ideal operational amplifier.

## Condition for Ideal operational amplifier

- Input impedance Zi= ∞
- Output impedance Zo= 0
- Infinite voltage gain A= ∞
- Infinite bandwidth (Bw)= ∞
- Perfect balance condition →Vout =0 when V1= V2.

## Inverting operational amplifier

We know that open loop gain of the operational amplifier is-

A= Vo/Vi = output voltage/ Input voltage

Here we apply the signal on inverting terminal. Z1 is the resistance connected on the inverting terminal. In which I current is flow. Therefore voltage is IZ1.

∴ Vs= IZ1 + Vi

I= (Vs- Vi)/ Z1 …(1)

Z2 is feedback impedance.

∴ Vi= IZ2 + Vo

IZ2 = Vi- Vo

I= (Vi- Vo)/ Z2 …(2)

Equating (1) and (2) we get,

(Vs- Vi)/ Z1 = (Vi- Vo)/ Z2

Vo/ Z2 = Vi/ Z2 -( Vs- Vi)/Z1

And, Vo/ Z2 = Vi/Z2 – Vs/Z1 + Vi/Z1

Vo/ Z2 = Vi [1/Z1 + 1/Z2] – Vs/ Z1 …(3)

Here we know that there is no feedback. I.e. **operational amplifier** makes the open loop gain.

∴A = -Vo/Vi

Vi= -Vo/A …(4)

Put the value from (4) in (3)

Vo= -Vo/A [1/Z1 + 1/Z2] – Vs/ Z1

And hence Vo/Z2 + Vo/A [1/Z1 + 1/Z2] = – Vs/ Z1

Vo [1/Z2 + 1/A [1/Z1 + 1/Z2]]= – Vs/ Z1

### Closed loop gain-

Af= Vo/Vs

From above equation,

Vo/Z2 [1/1 + 1/A [ 1/1 + Z2/Z1]] = -Vs/Z1

Vo/Z2 [ 1+ 1/A (1+ Z2/Z1)] = – Vs/ Z1

Consequently, Vo/Vs [ 1+ 1/A (1+ Z2/Z1)] = – Z2/ Z1

Vo/Vs= -(Z2/ Z1)/ [ 1+ 1/A (1+ Z2/Z1)]

Af= -(Z2/ Z1)/ [ 1+ 1/A (1+ Z2/Z1)]

If A= ∞ for ideal **operation amplifier**.

Af= -Z2/Z1

I.e. the gain is equal to the ratio of feedback impedance to input impedance.

**Input impedance-**

We know, I= (Vs- Vi)/ Z1

If Vi= 0

I= Vs/Z1 = Zi → input impedance

And,

I= (Vi- Vo)/ Z2

If Vi= 0

I= -Vo/ Z2 = Zo → output impedance

**Conclusion**

So our article is finished and after completely reading this article, one can easily tell what is **operational amplifier**. And we have also discussed some more topics **operational amplifier**, inverting signal, non inverting signal, ideal **operational amplifier**, condition for Ideal **operational amplifier**, inverting operational amplifier etc.

So one can say that they got a detailed information about **operational amplifier,** and basic information about other topics.

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