**Summing Amplifier** is an electronic circuit that produces output as a weighted sum of the applied inputs. It is also known as **Op-amp adder**. Basically it performs mathematical operation of addition. In this article, we will see the summing amplifier circuit, its working and its applications.

**Contents**show

## Summing Amplifier Circuit

The summing amplifier circuit is shown in figure 1. The input V_{1 }, V_{2}, and V_{3} are applied. V_{o} is the output voltage. The non-inverting terminal of the op-amp is connected to the ground. This means that the voltage of the non-inverting terminal is zero volts.

### Analysis

The analysis of the summing amplifier circuit is shown in figure 2. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V_{−}) is equal to the voltage of the non-inverting terminal (V_{+} = 0V), according to the **virtual short concept**.

V_{− }= V_{+} = 0V

The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

The currents I_{1}, I_{2} and I_{3} flowing through resistances R_{1}, R_{2} and R_{3} respectively.

\begin{equation} \label{eq:poly}

I_1=\frac{V_{1}-0}{R_1}=\frac{V_{1}}{R_1}

\end{equation}

\begin{equation} \label{eq:poly}

I_2=\frac{V_{2}-0}{R_2}=\frac{V_{2}}{R_2}

\end{equation}

\begin{equation} \label{eq:poly}

I_3=\frac{V_{3}-0}{R_3}=\frac{V_{3}}{R_3}

\end{equation}

Apply KCL at node **Q**

\begin{equation} \label{eq:poly}

$I_1+I_2+I_3 = I$

\end{equation}

Apply KCL at node **P**

$I = 0+I_f$

\begin{equation} \label{eq:poly}

$I = I_f$

\end{equation}

\begin{equation} \label{eq:poly}

I_f=\frac{0-V_{o}}{R_f}=-\frac{V_{o}}{R_f}

\end{equation}

From equations (4), (5) and (6), we have

$\Rightarrow I_1+I_2+I_3=-\frac{V_{o}}{R_f}$

putting values of I_{1}, I_{2} and I_{3} from equations (1), (2) and (3), we have

$\Rightarrow \frac{V_{1}}{R_1}+\frac{V_{2}}{R_2}+\frac{V_{3}}{R_3}=-\frac{V_{o}}{R_f}$

$\Rightarrow V_o=-(\frac{R_f}{R_1}V_1+\frac{R_f}{R_2}V_2+\frac{R_f}{R_3}V_3)$

Therefore,

\[

\quicklatex{color=”#000000″ size=20}

\boxed{V_o=-(\frac{R_f}{R_1}V_1+\frac{R_f}{R_2}V_2+\frac{R_f}{R_3}V_3)}

\]

If $R_1=R_2=R_3=R_f=R$

Then, we have

$V_o=-(\frac{R}{R}V_1+\frac{R}{R}V_2+\frac{R}{R}V_3)$

\[

\quicklatex{color=”#000000″ size=20}

\boxed{V_o=-(V_1+V_2+V_3)}

\]