# Summing Amplifier

## The Summing Amplifier

The **Summing Amplifier** is a very flexible circuit based upon the standard *Inverting Operational Amplifier* configuration. As its name suggests, the “summing amplifier” can be used for combining the voltage present on multiple inputs into a single output voltage.

We saw previously in the Inverting Operational Amplifier that the inverting amplifier has a single input voltage, ( Vin ) applied to the inverting input terminal. If we add more input resistors to the input, each equal in value to the original input resistor, Rin we end up with another operational amplifier circuit called a **Summing Amplifier**, “*summing inverter*” or even a “*voltage adder*” circuit as shown below.

### Summing Amplifier Circuit

The output voltage, ( Vout ) now becomes proportional to the sum of the input voltages, V1, V2, V3 etc. Then we can modify the original equation for the inverting amplifier to take account of these new inputs thus:

However, if all the input impedances, ( Rin ) are equal in value, we can simplify the above equation to give an output voltage of:

### Summing Amplifier Equation

We now have an operational amplifier circuit that will amplify each individual input voltage and produce an output voltage signal that is proportional to the algebraic “SUM” of the three individual input voltages V_{1}, V_{2} and V_{3}. We can also add more inputs if required as each individual input “see’s” their respective resistance, Rin as the only input impedance.

This is because the input signals are effectively isolated from each other by the “virtual earth” node at the inverting input of the op-amp. A direct voltage addition can also be obtained when all the resistances are of equal value and Rƒ is equal to Rin.

A **Scaling Summing Amplifier** can be made if the individual input resistors are “NOT” equal. Then the equation would have to be modified to:

To make the math’s a little easier, we can rearrange the above formula to make the feedback resistor R_{F} the subject of the equation giving the output voltage as:

This allows the output voltage to be easily calculated if more input resistors are connected to the amplifiers inverting input terminal. The input impedance of each individual channel is the value of their respective input resistors, ie, R_{1}, R_{2}, R_{3} … etc.

The **Summing Amplifier** is a very flexible circuit indeed, enabling us to effectively “Add” or “Sum” (hence its name) together several individual input signals. If the inputs resistors, R_{1}, R_{2}, R_{3} etc, are all equal a unity gain inverting adder can be made. However, if the input resistors are of different values a “scaling summing amplifier” is produced which gives a weighted sum of the input signals.