Difference Amplifiers

A dual input, balanced output difference amplifier circuit is shown in fig. 1.

Fig. 1

Inverting & Non – inverting Inputs:

In differential amplifier the output voltage v_O is given by

               V_O = A_d (v₁ – v₂)
When     v₂ = 0, v_O = A_d v₁
& when   v₁ = 0, v_O = - A_d v₂

Therefore the input voltage v₁ is called the non inventing input because a positive voltage v₁ acting alone produces a positive output voltage v_O. Similarly, the positive voltage v₂ acting alone produces a negative output voltage hence v₂ is called inverting input. Consequently B₁ is called noninverting input terminal and B₂ is called inverting input terminal.

Common mode Gain:

A common mode signal is one that drives both inputs of a differential amplifier equally. The common mode signal is interference, static and other kinds of undesirable pickup etc.

The connecting wires on the input bases act like small antennas. If a differential amplifier is operating in an environment with lot of electromagnetic interference, each base picks up an unwanted interference voltage. If both the transistors were matched in all respects then the balanced output would be theoretically zero. This is the important characteristic of a differential amplifier. It discriminates against common mode input signals. In other words, it refuses to amplify the common mode signals.

The practical effectiveness of rejecting the common signal depends on the degree of matching between the two CE stages forming the differential amplifier. In other words, more closely are the currents in the input transistors, the better is the common mode signal rejection e.g. If v₁ and v₂ are the two input signals, then the output of a practical op-amp cannot be described by simply

v₀ = A_d (v₁ – v₂ )

In practical differential amplifier, the output depends not only on difference signal but also upon the common mode signal (average).

        v_d = (v₁ – v_d )

and v_C = ½ (v₁ + v₂ )

The output voltage, therefore can be expressed as

v_O = A₁ v₁ + A₂ v₂

Where A₁ & A₂ are the voltage amplification from input 1(2) to output under the condition that input 2 (1) is grounded.

The voltage gain for the difference signal is A_d and for the common mode signal is A_C.

The ability of a differential amplifier to reject a common mode signal is expressed by its common mode rejection ratio (CMRR). It is the ratio of differential gain A_d to the common mode gain A_C.

Date sheet always specify CMRR in decibels CMRR = 20 log CMRR.

Therefore, the differential amplifier should be designed so that r is large compared with the ratio of the common mode signal to the difference signal. If r = 1000, v_C = 1mV, v_d = 1 m V, then

It is equal to first term. Hence for an amplifier with r = 1000, a 1m V difference of potential between two inputs gives the same output as 1mV signal applied with the same polarity to both inputs.

 Dual Input, Unbalanced Output Differential Amplifier:

In this case, two input signals are given however the output is measured at only one of the two-collector w.r.t. ground as shown in fig. 2. The output is referred to as an unbalanced output because the collector at which the output voltage is measured is at some finite dc potential with respect to ground..

Fig. 2

In other words, there is some dc voltage at the output terminal without any input signal applied. DC analysis is exactly same as that of first case.

AC Analysis:

The output voltage gain in this case is given by

The voltage gain is half the gain of the dual input, balanced output differential amplifier. Since at the output there is a dc error voltage, therefore, to reduce the voltage to zero, this configuration is normally followed by a level translator circuit.

Differential amplifier with swamping resistors:

By using external resistors R'_E in series with each emitter, the dependence of voltage gain on variations of r'_e can be reduced. It also increases the linearity range of the differential amplifier.

Fig. 3, shows the differential amplifier with swamping resistor R'_E. The value of R'_E is usually large enough to swamp the effect of r'_e.

Fig. 3

 Example-1

Consider example-1 of lecture-2. The specifications are given again for the dual input, unbalanced-output differential amplifier: R_C = 2.2 kΩ, R_B= 4.7 kΩ, R_in1 = R_in2= 50Ω, +V_CC = 10V, -V_EE= -10 V, β_dc =100 and V_BE= 0.715V.

Determine the voltage gain, input resistance and the output resistance.

Solution:

Since the component values remain unchanged and the biasing arrangement is same, the I_CQ and V_CEQ values as well as input and output resistance values for the dual input, unbalanced output configuration must be the same as those for the dual input, balanced output configuration.

Thus, I_CQ = 0.988 mA
V_CEQ = 8.54 V
R_i1 = R_i2 = 5.06 kΩ
R_o = 2.2 kΩ

The voltage gain of the dual input, unbalanced output differential amplifier is given by

Example-2

Repeat Example-1 for single input, balanced output differential amplifier.

Solution:

Because the same biasing arrangement and same component values are used in both configurations, the results obtained in Example-1 for the dual input, balanced output configuration are also valid for the single input, balanced output configuration.

That is,

I_CQ= 0.988 mA
V_CEQ = 8.54 V
V_d = 86.96
R_i = 5.06 kΩ
R_o1 = R_o2 = 2.2 kΩ