Summing Amplifier

The Summing Amplifier is a very flexible circuit based upon the standard Inverting Operational Amplifier configuration. We saw previously in the Inverting Amplifier tutorial that the Inverting Amplifier has a single input signal applied to the Inverting input terminal. If we add another input resistor 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 the final equation for the output voltage is given as:

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 V₁, V₂ and V₃. 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 Rf 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:

We can also rearrange the formula to make the feedback resistor R_F the subject and the output voltage is found from

Allowing the output voltage to be easily calculated if more input resistors are connected to the amplifiers input. The input impedance of each individual channel is the value of their respective input resistors, ie, R₁, R₂, R₃ ... etc.

The Summing Amplifier is a very flexible circuit indeed, enabling us to effectively "Add" or "Sum" together several individual input signals. If the inputs resistors, R₁, R₂, R₃ 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.

Example No1

Find the output voltage of the following Summing Amplifier circuit.

Summing Amplifier

Using the previously found formula for the gain of the circuit

we can now substitute the values of the resistors in the circuit as follows,

we know that the output voltage is the sum of the two amplified input signals and is calculated as:

then the output voltage of the Summing Amplifier circuit above is given as -45 mV and is negative.

If the input resistances of a summing amplifier are connected to potentiometers the individual input signals can be mixed together by varying amounts. For example, measuring temperature, you could add a negative offset voltage to make the display read "0" at the freezing point or produce an audio mixer for adding or mixing together individual waveforms (sounds) from different source channels (vocals, instruments, etc) before sending them combined to an audio amplifier.

Summing Amplifier Audio Mixer