Although it is possible to obtain closely matched transistors for differential amplifiers. particularly in integrated circuits, it is not reasonable to expect that the paramcters of both devices will be exactly the same. or that they will track (change in the slime way) under variations in temperature or bias level. Differences in parameter value’ cause the amplifier to be unbalanced. in the sense that the gain of one side is different from that of the other. for example, our gain derivations for the ideal differential amplifier were based on the assumption that both transistors had identical values of Clearly, the voltage gains of both sides will not be identical if the vrlucs of arc not, in which case the outputs will not truly represent amplified versions of the input difference voltage, and the CMRR will suffer. In discrete circuits, an adjustable resistor can bc inserted between the emitter terminals to compensate for such variations, but this remedy is not practical in integrated circuits. To reduce the effect of variations in r., equal-valued resistors RI. can be inserted in series with the mitters, as shown in Figure 12-16. If the value of R; is substantially larger than r., then variations or differences in r; will have minimal consequence. However, the presence of additional emitter resistance decreases the voltage gain
of the amplifier. Equations 12-5 and 12-6, modified for the inclusion of RI:, become
A beneficial consequence of increased emitter resistance is the accompanying increase in differential input resistance. Equation 12-8 becomes
Another reality in practical differential amplifiers is that the current source biasing the amplifier does not have infinite resistance. Figure 12-17(a) shows the rUT amplifier biased with a current source having resistance U. We wish to invcstigate the effect of U on the common-mode rejection ratio, so both inputs arc shown connected to the common-mode voltage V,.tII. Since the circuit is symmetrical, we can determine Vol and Vo2 by analyzing the two equivalent half-circuits shown in Figure 12-17(b). Notice that the current-source resistance in each half-circuit must be 2R and the value of the current must be /12 to maintain equivalence.
This result shows that the differential common-mode gain is unaffected by source resistance R (assuming that both , and R; arc perfectly matched), However, the single-ended common-mode gain is given by equations 12-22 and 12-23, and from these it is clear that a large value of R is desirable.