## Differential Amplifier opamp

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Definition of Differential Amplifier

A differential amplifier is one which amplifies only difference between two signals. Ideally difference amplifier should not amplify signal content common to both input signals. Practically the common mode signal gain will be finite. The efficiency of differential amplifier is quantified in terms of parameter called Common Mode Rejection Ratio. Common Mode Rejection Ratio of an differential amplifier is defined as follows

CMMR = 20 * log10 (Ad/Ac)

Where,

Ad is differential mode signal gain

Ac is common mode signal gain.

## Need for differential amplifier

Consider a transducer which provides a small signal at its output terminals which has to be sent to the measuring instrument. The medium carrying these signals for example copper wire may induce an interference signal which is comparable or larger than the transducer output signal. This noise signal is common to both output terminals. Hence by using differential amplifier at the front end of the amplifier this noise signal can be attenuated to a large extent so that its amplitude is negligible to the transducer output signal.

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## Design and Operation of Differential Amplifier

Differential amplifier Design and Operation with circuit diagram:

Consider the simplest design of differential amplifier with one opamp, four resistors R1, R2, R3 and R4. V1 and v2 are the two input voltages applied to non-inverting and inverting terminals of an opamp. In this configuration opamp is given negative feedback hence the concept of virtual ground holds and V+ = V-. The above diagram can be simplified and can be redrawn as follows

Due to high input resistance of opamp, it draws no current. Hence

Similarly at the non inverting terminal applying Kirchhoff’s current law

Substituting for Va from Equation 1 into equation 2

From the equations it is evident that for the output to be of the form Ad*(V1-V2)

Solving further and rearranging terms

Therefore for the above configuration to work as differential amplifier

where differential gain

## Common Mode Gain of Differential Amplifier

Assume that the resistors are not perfectly matched and let V1=V1d+Vn and V2=V2d+Vn where differential input signal is Vd = V1d-V2d and Vn is the common input signal. From equation 3 by substituting equations for V1 and V2 we get

Any practical resistance will have tolerance represented in percentage values. Let us assume that the deviations of resistances from their rated values are represented by ∆Ri where i =1, 2, 3, 4.Assuming these tolerances have little effect on differential signals then

From the ratio of differential gain to common mode gain it is obvious that CMMR depends on how close the ratio

is matched to unity.

## Input resistance of Differential Amplifier

For the special case of R3=R1 and R4=R2, the directions of currents are represented by arrows. Using the concept of virtual ground existing the input terminals of the opamp, applying Kirchhoff’s voltage law in the input mesh assuming a current of I amps, we get