# Summing Amplifier or Op-amp Adder – Applications

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

## Summing Amplifier Circuit

The summing amplifier circuit is shown in figure 1. The input V1 , V2, and V3 are applied. Vo 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 I1, I2 and I3 flowing through resistances R1, R2 and R3 respectively.

\label{eq:poly}

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

\label{eq:poly}

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

\label{eq:poly}

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

Apply KCL at node Q

\label{eq:poly}

$I_1+I_2+I_3 = I$

Apply KCL at node P

$I = 0+I_f$

\label{eq:poly}

$I = I_f$

\label{eq:poly}

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

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

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

putting values of I1, I2 and I3 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

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

$\quicklatex{color=”#000000″ size=20} \boxed{V_o=-(V_1+V_2+V_3)}$

This site uses Akismet to reduce spam. Learn how your comment data is processed.