The Summing Amplifier

The Summing Amplifier is another type of operational amplifier circuit configuration that is used to combine the voltages present on two or more 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

summing amplifier

In this simple 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:

summing amplifier formula

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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

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 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 is equal to Rin.

Note that when the summing point is connected to the inverting input of the op-amp the circuit will produce the negative sum of any number of input voltages. Likewise, when the summing point is connected to the non-inverting input of the op-amp, it will produce the positive sum of the input voltages.

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

scaling summing amplifier equation

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

summing amplifier feedback equation

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, R1, R2, R3 … etc.

Sometimes we need a summing circuit to just add together two or more voltage signals without any amplification. By putting all of the resistances of the circuit above to the same value R, the op-amp will have a voltage gain of unity and an output voltage equal to the direct sum of all the input voltages as shown:

unity gain summing amplifier

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, R1, R2, R3 etc, are all equal a “unity gain inverting adder” will be made. However, if the input resistors are of different values a “scaling summing amplifier” is produced which will output a weighted sum of the input signals.

Summing Amplifier Example No1

Find the output voltage of the following Summing Amplifier circuit.

Summing Amplifier

summing op-amp circuit

Using the previously found formula for the gain of the circuit

inverting op-amp gain

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

summing amplifier input gain

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

summing amplifier output voltage

Then the output voltage of the Summing Amplifier circuit above is given as -45 mV and is negative as its an inverting amplifier.

Summing Amplifier Applications

So what can we use summing amplifiers for?. 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 output voltage or 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

summing amplifier audio mixer circuit

Another useful application of a Summing Amplifier is as a weighted sum digital-to-analogue converter. If the input resistors, Rin of the summing amplifier double in value for each input, for example, 1kΩ, 2kΩ, 4kΩ, 8kΩ, 16kΩ, etc, then a digital logical voltage, either a logic level “0” or a logic level “1” on these inputs will produce an output which is the weighted sum of the digital inputs. Consider the circuit below.

Digital to Analogue Converter

digital to analogue converter

Of course this is a simple example. In this DAC summing amplifier circuit, the number of individual bits that make up the input data word, and in this example 4-bits, will ultimately determine the output step voltage as a percentage of the full-scale analogue output voltage.

Also, the accuracy of this full-scale analogue output depends on voltage levels of the input bits being consistently 0V for “0” and consistently 5V for “1” as well as the accuracy of the resistance values used for the input resistors, Rin.

Fortunately to overcome these errors, at least on our part, commercially available Digital-to Analogue and Analogue-to Digital devices are readily available with highly accurate resistor ladder networks already built-in.

In the next tutorial about operational amplifiers, we will examine the effect of the output voltage, Vout when a signal voltage is connected to the inverting input and the non-inverting input at the same time to produce another common type of operational amplifier circuit called a Differential Amplifier which can be used to “subtract” the voltages present on its inputs.


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  • A

    Hi! great tutorial, i dont know much about electronic but i want to create my DIY summing mixer,so i have a few questions about that. Please please, i need your help i cant find in internet the solutions .
    1: i want to sum the signals of a ended audio mix in mi DAW that comes from the line outputs of mi interface, the signals have a line level (4dbu). If i just wan to sum 8 channels signals BUT I DONT NEED CHANGE THEIR VOLUMES, can i just put a 47k resistor and not a variable pot?
    2: what is the function of the capacitors in your diagram and their respective values.
    3:how can i reach a 600 ohm impedance at the output of the operational amp? This is because i want that the summing signal pass through a transformer 1:1.
    thanks, and excuse me for my ignorance.

  • h

    can you do the derivation for summing of non-inverting op amp?

  • s

    waveforms of summer

  • S
    Stevie B

    For the summing amplifier, Rf gain is connected between what would typically be pins 1 and 3, and the wiper (pin 2) isn’t used. Is this correct? What would using the wiper do?

    • Wayne Storr

      This does not make sense, if you use a potentiometer, or trimmer as the feed back resistance, Rf and do not use the wiper, Pin 2, then it is effectively acting as a fixed resistance. The purpose of using a potentiometer configured as a potentiometer or variable resistance is to allow for gain adjustment of the amplifier.

  • p
    pratiksha Dandekar

    Adding means summing

    • Wayne Storr

      Adding is the basic operation that adds two numbers together, the resulting answer is called the sum. So the addition of 2 + 2 gives the sum of 4. Then a summing amplifier gives an output which is the “sum” of adding together its inputs.

  • k

    Do we use it in calc’s. If so suppose i would like to do addition 1000+2000 so for that should i apply 1K,2K volts???

  • J
    Jimson Sanau

    summing amplifier can be add

  • M
    Moses Mutindah

    What if given the following… Rf=1ohm, v1=3 v2=2..R1=250mohm, R2=500mohm, R3=ohm. What is the output voltage

  • H

    Why is it multipled with gain?

    • H

      Rearrange the equation Gain (A) = Vout / Vin and you have : Gain x Vin = Vout . Then you add each gain for each input signal together.

  • D
    Denis Kirchoff

    Now in the case u have R1,R2,R3,,,,,V1,V2 and Rf only…how can i get the voltage output of that summing amp?

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