Simple Summing Amplifier Equation and Explanation

summing amplifier equation

Now we will move on to the next topic: “Summing Amplifier Equation’ along with its easy equation.

Summing Amplifier Equation

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 Figure.(1), is a variation of the inverting amplifier. It takes advantage of the fact that the inverting configuration can handle many inputs at the same time.

summing amplifier equation
Figure 1. The summing amplifier

We keep in mind that the current entering each op amp input is zero. Applying KCL at node a gives

summing amplifier equation
(1)

But

summing amplifier equation
(2)

We note that va = 0 and substitute Equation.(2) into Equation.(1). We get

summing amplifier equation
(3)

indicating that the output voltage is a weighted sum of the inputs. For this reason, the circuit in Figure.(1) is called summer. Needless to say, the summer can have more than three inputs.

Summing Amplifier Equation Example

Calculate vo and io in the op amp circuit in Figure.(2).

summing amplifier equation
Figure 2

Solution:
This is summer with two inputs. Using Equation.(3) gives

summing amplifier equationThe current io is the sum of the currents through the 10- and 2-kΩ resistors. Both of these resistors have voltage vo = −8 V across them, since va = vb = 0. Hence,

summing amplifier equation