5.6 Summing Amplifier

← Back to Fundamentals of Electric Circuits Overview

5.6 Summing Amplifier

Besides amplification, the op amp can perform addition and subtraction. The addition is performed by the summing amplifier covered in this section; the subtraction is performed by the difference amplifier covered in the next section.

A summing amplifier is an op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs.

The summing amplifier, shown in Fig. 5.21, is a v ariation of the inverting amplifier. It takes advantage of the fact that the inverting configuration can handle many inputs at the same time. We keep in mind

Figure 5.19 For Example 5.5.

4 kΩ

6 V ^v^o

–

a b

4 V

– +

Figure 5.20

4 kΩ

For Practice Prob. 5.5.

Figure 5.21 The summing amplifier.

–

10 kΩ

– that the current entering each op amp input is zero. Applying KCL at node a gives

i = i_1 + i_2 + i_3 \tag{5.13}

But

i_1 = \frac{v_1 - v_a}{R_1}, \quad i_2 = \frac{v_2 - v_a}{R_2}

i_3 = \frac{v_3 - v_a}{R_3}, \quad i = \frac{v_a - v_o}{R_f}

(5.14)

We note that v^a = 0 and substitute Eq. (5.14) into Eq. (5.13). We get

v_o = -\left(\frac{R_f}{R_1}v_1 + \frac{R_f}{R_2}v_2 + \frac{R_f}{R_3}v_3\right)

(5.15)

indicating that the output v oltage is a weighted sum of the inputs. F or this reason, the circuit in Fig. 5.21 is called a summer. Needless to say, the summer can have more than three inputs.

Example 5.6

Calculate vo and io in the op amp circuit in Fig. 5.22.

Figure 5.22 For Example 5.6.

Solution:

This is a summer with two inputs. Using Eq. (5.15) gives

v_o = -\left[\frac{10}{5}(2) + \frac{10}{2.5}(1)\right] = -(4 + 4) = -8

The current io is the sum of the currents through the 10- and 2-kΩ resistors. Both of these resistors have voltage v^o = −8 V across them, since v^a = v^b = 0. Hence,

i_o = \frac{v_o - 0}{10} + \frac{v_o - 0}{2}

mA = -0.8 - 4 = -4.8 mA

Find vo and io in the op amp circuit shown in Fig. 5.23.

Answer: −3.8 V, −1.425 mA.