Summing amplifiers or adders are the amplifier circuits which can add more than one input signal. It is possible to apply more than one input signal to an inverting or non-inverting terminal of op-amp.

The summing amplifier then add all these input signals to produce their addition at the output.

Depending on the polarity of the output voltage the adder circuit can be classified into two categories as

- Inverting summing amplifier
- Non-inverting summing amplifier

## Inverting Summing Amplifier Using Op-Amp

The summing amplifier is same as that inverting amplifier except that is has several input terminals. The negative feedback applied through resister R_{f} from the output to the input terminal.

Following figure shows the circuit diagram of an inverting configuration of summing amplifier (Inverting adder) using op-amp.

As shown in figure, the input voltages V_{1}, V_{2} and V_{3} are applied through resistance R_{1}, R_{2} and R_{3} respectively to the inverting terminal of op-amp.

Let the current flowing through resistance R_{1}, R_{2} and R_{3} be I_{1}, I_{2} and I_{3} respectively.

Let V_{A} is the voltage at non-inverting terminal and V_{B} is the voltage at inverting terminal respectively.

Applying Kirchhoff’s current law (KCL) at node B,

*( KCL: Sum of current going toward node is equal to sum of currents going away from the node.)*

…(1)

According to the concept of virtual ground, as node A is grounded, node B is also grounded, i.e., V_{A}= V_{B}= 0,

Putting V_{B}= 0 in equation (1) we get

…(2)

Therefore, equation (2) will become

…(3)

Where R_{1}≠R_{2}≠R_{3}

It is known as **“scaling amplifier”** or **“Weighted amplifier”.**

If R_{f}=R_{1}=R_{2}=R_{3}=R then,

we get,

This circuit is called as **“Inverting Adder”** or **“Inverting Summing Amplifier”.**

If R_{1}=R_{2}=R_{3}=R and R_{f }=Ri/3

Equation (3) becomes,

Thus, the magnitude of output voltage is equal to the average of three input voltages. This is called **“Averaging amplifier”.**

## Non-inverting Summing Amplifier Using Op-Amp

Non-inverting Summing Amplifier or non-inverting adder is the circuit in which the output is proportional to the sum of the input and also the output is in phase with input.

The negative feedback applied through resister R_{f} from the output to the input terminal. Following figure shows the circuit diagram of non-inverting configuration of summing amplifier (non-inverting adder) using op-amp.

As shown in figure, the input voltages V_{1}, V_{2} and V_{3} are applied through resistance R_{1}, R_{2} and R_{3} respectively to the **non-inverting** terminal of op-amp.

Let the current flowing through resistance R_{1}, R_{2} and R_{3} be I_{1}, I_{2} and I_{3} respectively.

Let V_{A} is the voltage at non-inverting terminal.

Applying Kirchhoff’s current law (KCL) at node A,

*( KCL: Sum of current going toward node is equal to sum of currents going away from the node.)*

* *

Also,

Above equation can be rearranged as

…(4)

Let R_{1}=R_{2}=R_{3}=R;

Equation (4) will become,

…(5)

But for non-inverting amplifier output voltage is given by

As input voltage at non-inverting terminal is V_{in }= V_{A},

…(6)

From equation (5) and (6),

…(7)

To make output voltage as sum of all input voltages (V_{1}+V_{2}+V_{3}),

Therefore, equation (7) becomes,