Differential amplifiers are widely used in linear integrated circuits. They are a fundamental component of every operational amplifier. which, as we shall learn. is an extremely versatile device with a broad range of practical applications. We will study the circuit theory of differential amplifiers in some detail, in preparation for a more comprehensive investigation of the capabilities (and limitations) of operational amplifiers.

**Difference Voltages**

A differential amplifier is also called a difference amplifier because it amplifies the difference between two signal voltages. Let us refine the notion of a difference voltage by reviewing some simple examples. We have already encountered difference voltages in our stud / of transistor amplifiers. Recall, for example. that the collector-to-emitter voltage of a BJT is the difference between the collector-to-ground voltage and the emitter-to-ground voltage:

The basic idea here is that a difference voltage is the mathematical difference between two other voltages, each of whose values is given with respect to ground. Suppose the voltage at point A in a circuit is 12 V with respect to ground and the voltage at point B is 3 V with respect to ground. The notation VAS for the difference voltage means the voltage that would be measured if the positive side of a voltmeter were connected to point A and the negative side to point B; in this case, VA8 = VA – Vo = 12 – 3 = 9 V. If the voltmeter connections were reversed, we would measure VilA = VB – VA = 3 – 12 = – 9 V. Thus, VOA = – VAB. To help get used to thinking in terms of difference voltages, consider the system shown in Figure 12-1, where two identical amplifiers are driven by two different signal voltages. Although a differential amplifier does not behave in exactly the same way as this amplifier arrangement, the concepts of input and output difference voltages arc similar. The two signal input voltages, VI and V2, are shown as sine waves, one greater in amplitude than the other. For illustrative purposes. their peak.

Values arc 3 Vand I V, respectively. If the voltage gain of each amplifier is A, then the amplifier outputs are AVI and Avz. The input difference voltage, VIZ = VI – Vz, is a sine wave and the output difference voltage, AVI – AVl = A(vi – Vl), is seen to be an amplified version of the input difference voltage. In our illustration, the gain A is 10 and the input difference voltage is (3 V pk) – (1 V pk) = 2 V pk. The output difference voltage is A(vi – Vl) = 10(3 V-I V) = 10(2 V) = 20 V pk.