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 R_{f} is I_{F}.

**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 R_{f} = R, then Vout = – (V_{1 }+ V_{2} + V_{3})

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 R_{1}= R_{2} = R_{3} = R and R = 3 R_{f} then Vo = – (V_{1} + V_{2 }+ V_{3})/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 R_{1} and R_{2}.

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 V_{1} is acting alone and V_{2} = 0 (as shown in fig.4), then voltage V_{1}+ at the non-inverting input is

**Fig. 4 Non-Inverting Summing Amplifier (When V _{2} = 0)**

Similarly, as shown in Fig.5, when voltage V1 = 0 and V2 is acting alone then voltage V_{2}+ can be given as

**Fig.5 Non-Inverting Summing Amplifier (When V _{1} = 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 R _{1} = R_{2} = R then output of the op-amp**

**And when R _{f }= R_{a} then output**

For more information about inverting and non-inverting summing amplifier, please check this video: