The Summing Amplifier 

The Summing Amplifier is a very flexible circuit based upon the standard Inverting Operational Amplifier configuration that can be used for combining multiple inputs. We saw previously in the inverting amplifier tutorial 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 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 opamp. 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 RF 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, R1, R2, R3 ... 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, 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 as its an inverting amplifier.  
Summing Amplifier Applications 

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 

Another useful application of a Summing Amplifier is as a weighted sum digitaltoanalogue 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 

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 4bits, will ultimately determine the output step voltage as a percentage of the fullscale analogue output voltage. Also, the accuracy of this fullscale 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, commercial available Digitalto Analogue and Analogueto Digital devices are available.  
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 noninverting 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.  
Reproduced with permission from Wayne Storr
