Contents

- 1 What is Operational Amplifier
- 2 Double ended or differential input
- 3 Common mode operation of of operational amplifier
- 4 Common mode rejection
- 5 Differential inputs
- 6 Common Inputs
- 7 Output Voltage (Vo)
- 8 Common-mode rejection ratio (CMRR)
- 9 Output in term of CMRR
- 10 Characteristics of operational amplifier (OP AMP)

## What is Operational Amplifier

An operational amplifier (OP-AMP) is a very high gain differential Amplifier with high input impedance and low input impedance. It is direct coupled and uses negative feedback. It is called **operational amplifier** because it can perform mathematical operation like subtraction, addition, differentiation and integration etc. the symbolic representation of Operational amplifier is shown in the figure 10.

When a signal is applied to the **plus input** (i.e. input 1), whereas the **minus input** (i.e. input 2) is connected to the ground, we get an amplified signal at the output which has the same polarity as that of the input signal as shown in the figure 11(a).

Since, the polarity of a signal applied to the plus input is not changed, so input 1 or less input is known as a **non inverting input**.

When a signal is applied to **minus input** (i.e. input 2), whereas the **plus input** is grounded, we get an amplified signal at the output whose polarity is just opposite to the quality of the input signal as shown in the figure 11(b).

Since, the polarity of a signal applied to minus input is inverted, so input 2 or minus input is known as **inverting input**.

Thus, the symbolic representation of OP-AMP is shown in figure 12.

**Double ended or differential input**

Signal can also be applied between two input of Operational Amplifier as shown in the figure 13. In this case, no input is grounded and we get an amplified output signal. Both input and output signal are in phase.

The above operation of feeding a signal between two inputs is equivalent to two separate signals applied to two inputs as shown in figure 14. In this case, the resulting input signal is the difference between two inputs.

That is, **V _{d}=V_{1}-V_{2}**

Hence, double ended input is also known as the **differential input**.

## Common mode operation of of operational amplifier

Operational amplifier operates in common mode when the same input signal are applied to the both inputs as shown in the figure 15. For ideal operational amplifier, both the input signals are equally amplified.

These equally amplified signal are out of phase and hence no output signal is obtained. However, in actual practice, there is small output signal.

## Common mode rejection

A differential amplifier has the ability to amplify output input signals which are out of phase and cancel out or reject the common signal at the two inputs. A “noise” or an unwanted signal arising due to voltages is induced by magnetic field in the feeding wires is common to both the inputs.

A differential amplifier attenuates or rejects the noise or unwanted signal common to both the inputs and amplifies the difference signal applied to the inputs. This operating feature of the amplifier is known as **common mode rejection**.

## Differential inputs

When separate signal are applied to both the input of the operational amplifier, then the resulting input signal is the difference between the two inputs. This resulting signal is known as **difference signal**.

if V_{1} and V_{2} represent the two separate signals, then the difference signal is given by

## Common Inputs

If identical signals are applied to both the input of Operational Amplifier, then the resulting signal is the average of the sum of the two signals. This resulting signal is also known as **common signal**.

Let V_{1} and V_{2} represent two identical signals applied to two inputs, then the common signal is represented by,

## Output Voltage (V_{o})

Since the input signal to an OP-AMP may be difference signal or common signal, therefore, output voltage in general can be written as

A_{d} is known as **differential gain** of OP-AMP and A_{c} is the **common mode gain** of the OP-AMP.

**Case 1. If**

Output voltage,

**Case 2. If**

Output voltage

## Common-mode rejection ratio (CMRR)

Common-mode rejection is described by a numerical value known as common mode rejection ratio (CMRR). It is defined as the ratio of differential voltage gain (A_{d}) to the common mode voltage gain (A_{c}).

CMRR is decible (dB) can also be expressed as

## Output in term of CMRR

Since, output voltage V_{o} is given by (eqn. 3)

Using eqn. (6), we get

From eqn. (8), it is clear that if CMRR is very large, then the output voltage will be given by

Thus, the output voltage will be due to a difference signal for a large value of CMRR even when both the components V_{d} and V_{c} exist at the input.

## Characteristics of operational amplifier (OP AMP)

The characteristics of an ideal operational amplifier are:

- Input impedance is infinite.
- Output impedance is zero.
- Voltage gain is infinite.
- Frequency band width is infinite.
- There is no drifting of characteristics with temperature.
- Perfect balance i.e. output voltage is zero when equal voltage are applied to both the input terminals.