Home > Textbooks > Basic Electronics > Operational Amplifiers > Summing Amplifier >

Operational Amplifiers

# Summing Amplifier

The process of adding and subtracting voltages is performed by a summing amplifier.
The figure above shows an arrangement for the summation of three voltages
*v*_{1}, *v*_{2}, and *v*_{3}, applied
to input resistors *R*_{1}, *R*_{2}, and
*R*_{3} respectively.

The three input currents *i*_{1}, *i*_{2}, and
*i*_{3} may be equated to the current *i*_{f}
through *R*_{f}

The currents are equal to

Since *v*_{A} is approximately equal to zero (the virtual ground),
the currents which are added can be seen to be

The rearrangement of the equation gives

This equation tells us that each input voltage is multiplied by a gain determined by the value of its own input resistor and the common feedback resistor. In addition, each amplified input voltage is algebraically added to the other amplified input voltages. In the special case, when each resistance ratio is 1, the circuit merely algebraically adds all of the input voltages. Subtraction occur when the signs of some of the input voltages are negative. Note that the total algebraic sum of the input voltages is inverted by the operational amplifier.

Now let’s consider a few examples. Consider the summing
amplifier circuit shown in the figure below. Input voltage *v*_{1} (+5 V)
will have a gain of 1/2. Input voltage *v*_{2} (+3 V) will have a gain of 1.
Input voltages of +5 V and +3 V will produce the following currents:
current *i*_{1} = 2.5 μA and *i*_{2} = 3 μA (i.e.
*v*_{1}/*R*_{1} and *v*_{2}/*R*_{2}).
The output voltage is then -*i*_{f}*R*_{f} or –5.5 V.

The circuit conditions under slightly different input
voltages (*v*_{1} = -10 V, *v*_{2} = +3 V) are
considered next. Note that current *i*_{1} flows in the
opposite direction when *v*_{1} is negative. Under these conditions,
*i*_{1} = -5 μA and *i*_{2} = 3 μA.
The current which flows through *R*_{f} must be the sum of
*i*_{1} and *i*_{2}. This
sum, -2 μA, flows through the feedback resistor and
indicates an output voltage of +2 V.