# Op-Amp as Summing Amplifier

Op-Amp can be used as a summing amplifier by applying multiple inputs either to the inverting or to the non-inverting op-amp terminals.

## Inverting Summing Amplifier

Fig.1 Inverting Summing Amplifier

As shown in Fig.1, the op-amp is used as a summing amplifier in the inverting configuration. The inputs to the op-amp (V1, V2, and V3) are applied using the resistors R1, R2, and R3 respectively. The output of the op-amp can be given as

Proof:

Here, assume the op-amp is an ideal op-amp. As shown in Fig.2, let’s say, the current flowing through resistor R1, R2 and R3 are I1, I2, and I3. And current flowing through resistor Rf is IF.

Fig.2 Currents in the Inverting Summing Amplifier

For an ideal op-amp, no current is flowing into the op-amp terminal. So, applying KCL at node A, it can be written as

If R1 = R2 = R3 = R then

When Rf = R, then Vout = – (V1 + V2 + V3)

And when R1 = R2 = R3 = R and the ratio of Rf and R is selected such that,

where n=number of inputs being applied to the inverting terminal.

Then it can be used as a averaging circuit. For example, in the above circuit when R1= R2 = R3 = R and R = 3 Rf then Vo = – (V1 + V2 + V3)/3

That means output is the average of the three input signals.

## Applications of Summing Amplifier

• Summing, Averaging, and Scaling
• For providing DC offset
• Digital to Analog Converters
• Audio Mixer

## Non-Inverting Summing Amplifier

Fig.3 Non-Inverting Summing Amplifier

Fig.3 Shows the non-inverting summing amplifier. Where the two inputs V1 and V2 are applied to the non-inverting op-amp terminal through resistor R1 and R2.

The output of the op-amp can be given as

Proof:

The output can be found by applying the superposition theorem. To find the output, let’s consider only one input at a time. If V1 is acting alone and V2 = 0 (as shown in fig.4), then voltage V1+ at the non-inverting input is

Fig. 4 Non-Inverting Summing Amplifier (When V2 = 0)

Similarly, as shown in Fig.5, when voltage V1 = 0 and V2 is acting alone then voltage V2+ can be given as

Fig.5 Non-Inverting Summing Amplifier (When V1 = 0)

Considering both inputs simultaneously, the total voltage at the non-inverting input terminal

That means overall output voltage of the op-amp is

When R1 = R2 = R then output of the op-amp

And when Rf = Ra then output