• 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

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

  1. Input impedance Zi= ∞
  2. Output impedance Zo= 0
  3. Infinite voltage gain A= ∞
  4. Infinite bandwidth (Bw)= ∞
  5. 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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