**Differential Amplifier Circuit Operation:**

A Differential Amplifier Circuit Operation amplifies the difference between two inputs. The circuit shown in Fig. 14-23 is a combination of inverting and noninverting amplifiers. Resistors R_{1}, R_{2}, and the op-amp constitutes an inverting amplifier for a voltage (V_{i1}) applied to R_{1}. The same components (R_{1}, R_{2}, and the op-amp) also function as a noninverting amplifier for a voltage (V_{R4}) at the noninverting input terminal. It is seen that V_{R4} is derived from input voltage V_{i2} by the voltage divider R_{3} and R_{4}.

To understand the Differential Amplifier Circuit Operation, consider the output produced by each input voltage when the other input is zero:

with V_{i2} = 0,

with R_{3} = R_{1}, and R_{4} = R_{2},

When both inputs are present,

When R_{2 }= R_{1}, the output voltage (as calculated by Eq. 14-16) is the direct difference between the two inputs. With R_{2} greater than R_{1}, the output becomes an amplifier version of (V_{i2} – V_{i1}).

**Input resistances:**

Consider the input portion of the Differential Amplifier Circuit Operation reproduced in Fig. 14-24. The resistance at input terminal 1 is the same as the input impedance for an inverting amplifier: Z_{i1} = R_{1}. The input resistance at the op-amp noninverting input terminal, is very high (as in the case of a noninverting amplifier), and this is in parallel with resistor R_{4}. So, the input impedance at terminal 2 in Fig. 14-24 is Z_{i2} = R_{3} + R_{4}.

Equation 14-16 was derived by assuming that R_{3} = R_{1}, and R_{4} = R_{2}. It can be shown that the same result is obtained when the ratio R_{4}/R_{3} equals R_{2}/R_{1}, so that the actual resistor values do not have to be equal For equal resistances at the two input terminals

Then, calculate the resistances of R_{3} and R_{4} from,

A simple rule-of-thumb can be used for determining suitable resistance values for R_{3} and R_{4} when the two input resistances do not have to be exactly equal. Select, R_{4} = R_{2}/A_{CL}; which always makes R_{4} = R_{1}. Then, calculate R_{3} as, R_{3} = R_{1}/A_{CL}.

**Common Mode Voltages:**

A common-mode input voltage is a signal voltage (dc or ac) applied to both input terminals at the same time. This is illustrated in Fig. 14-26, where V_{i1}, V_{i2}, and the common-mode voltage (V_{n}) are all represented as inputs from dc sources. As shown, the input voltages at terminals 1 and 2 are changed from V_{i1} and V_{i2} to (V_{n} + V_{i1}) and (V_{n} + V_{i2}).

Equation 14-16 shows that the output voltage is the amplified difference between the two input voltages. So,

This shows that the common-mode input is completely cancelled. However, recall that the gain equation depends upon the resistor ratios (R_{4}/R_{3} and R_{2}/R_{1}) being equal If the ratios are not exactly equal, one input will experience a larger amplification than the other. Also, the common-mode voltage at one input terminal will be amplified by a larger amount than that applied to the other input terminal. In this case, common-mode inputs will not be completely cancelled.

Because it is difficult to perfectly match resistor ratios (especially for standard-value components), some common-mode output voltage is almost certain to be produced where a common-mode input exists. Figure 14-27 shows a circuit modification for minimizing common-mode outputs from a difference amplifier. Resistor R_{4} is made up of a fixed-value resistor and a small-value adjustable resistor connected in series. This provides adjustment of the ratio R_{4}/R_{3} to match R_{2}/R_{1}, so that common-mode outputs can be nulled to zero.