Differential Amplifier:

The function of a differential amplifier (DA) is to amplify the difference among two signals. Such an amplifier is required in many instrumentation and measurement systems, the most common instance being in detecting balance in bridge measurements. The DA also forms the input stage of several analog integrated circuits and is  significant building block of IC operational amplifiers.

Figure illustrates the circuit diagram of a differential amplifier with v₁ and v₂ as the input signals and v_o as the output signal. Ideally, we must have

                                                    V₀ = A_d (v₁ - v₂)

where the subscript d on the gain parameter A signifies 'differential'. In a practical DA, v₀ depends not only on the difference signal

                                                           v_d = v₁ - v₂

However also on the average or the common-mode signal

         v_c = (v₁ + v₂ ) /2

Figure: The Differential Amplifier

Generally, since the DA is a linear device (for small enough v1 and v2), we can write

V₀ = A₁ v₁ + A₂ v₂

where the gains A₁ and A₂ are easily described (and measured, if wanted). From Eqs. (25)

and (26), we have

v₁ = vc + ( v_d  /2)

and           v₂  = v_c  - (v_d  /2 )

From Eqs. (27), (28) and (29), we may obtain v₀ in terms of v_d and v_c :

v₀  =  [( A₁ - A₂ ) /2)]  and  A _c  = A₁ + A₂

Clearly, the differential and common-mode gains, A_d and A_c, are given by

A _d   = ( A₁ - A₂ )/ 2  and A_c  = A₁ + A₂

and may be calculated if one measures A₁ and A₂. A_d may be directly measured by setting

v₁ = - v₂; then A_d = v₀/(2v_d). Likewise A_c may be directly measured by setting v₁ = v₂; then

A_c = v₀/v₁.

An ideal differential amplifier is needed to be designed so as to attain as high A_d and as low A_c as possible. The ratio of A_d  to A_c is a figure of merit for a practical DA. The magnitude of this ratio is called the common-mode rejection ratio and is abbreviated as CMRR :

CMRR = |Ad / Ac|

Thus, one may write

V₀  = A_d  v_d   [ (1+( vc / vd) /? (CMRR)]

In order to approach the ideal characteristic, one must have a CMRR >> (v₀/v_d). Figure illustrates a typical differential amplifier circuit by using two BJTs. Ideally, transistors Q₁  and Q₂ are supposed to form a matched pair which is simply possible with IC technology.