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

After learning what is operational amplifier, we will also learn:

- Ideal op amp
- Summing amplifier
- Difference amplifier
- Cascaded op amp circuits
- Digital to analog converter

## 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.

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

But

We note that *v*_{a }= 0 and substitute Equation.(2) into Equation.(1). We get

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 *v*_{o }and *i*_{o }in the op amp circuit in Figure.(2).

**Solution:**

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

The current *i*_{o }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,