1. Summing Amplifier

2. Introduction
One of the most common applications for an op amp is to algebraically add two (or more) signals or voltages to form the sum of those signals. Such a circuit is known as a summing amplifier, or just as a summer.
The source of these signals might be anything at all. Common input sources are another op amp, some kind of sensor circuit, or an initial constant value. Since we don't have the first two available at this time, we'll use the third source for this experiment.
The point of using an op amp to add multiple input signals is to avoid interaction between them, so that any change in one input voltage will not have any effect on the other input.

4. A summing amplifier is an electrical circuit layout that allows for the addition of more than one signal, creating a sum of all the circuits combined.
The idea behind it is to incorporate multiple sources of input, while keeping each source separate to avoid one of the input sources affecting another. The amplifier allows the user to achieve a voltage sum at output that is calculated at the same rate mathematically as all of the input sources added up.
Essentially, this means the amplifier creates an operational amplifier because when more than one input voltage is entered into a circuit and added together through the course of the circuit, the output voltage is a constant of the sum of all of the input voltages.

5. Cont..,
When a circuit is needed to connect two different microphones to one amplification source and the user wishes to hear both of the microphones through the same source, the circuit used as the microphones are plugged into the amplifier is a simple form of a summing amplifier.
The signal coming into the amplifier from both microphones is able to be heard through the same speaker simultaneously due to the summing amplifier being created.
The use of a summing amplifier is required for any audio mixer machine to function properly because it must be able to receive signals from multiple sources at the same time and let them all be output through one source after being mixed by the user as the signals pass through the circuit.

6. Summing Amplifier Circuit

7. 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:

8. Summing Action
The summing action of this circuit is easy to understand if you keep in mind the main "mission" of the op amp. It's a simple one: keep the potential of the negative terminal very close to the positive terminal.
In this case, keep the negative terminal close to 0V (virtual ground). The op amp essentially nails one leg of R1, R2 and R3 to a 0V potential. This makes it easy to write the currents in these resistors.

9. I1 = V1 / R1;    I2 = V2 / R2;   I3 = V3 / R3
 So what's the current I flowing in RF? According to our friend Kirchoff, we get
I = I1 + I2 + I3
Finally, notice that one leg of RF is also kept at 0V. So the output becomes Vo = -RF x I. Combining these pieces of information, we have a simple description of the amplifier
Vo = - RF ( V1 / R1  +  V2 / R2  +  V3 / R3)
      = - ( V1 · RF / R1  +  V2 · RF / R2  +  V3 · RF / R3 )
As you can see, the gain for each input can be controlled by a single resistor: K1 = -RF/R1,  K2 = -RF/R2 and K3 = -RF/R2.

10. Level Shifter
Summing amplifiers make convenient level shifters. What if you have an audio signal V1= +/-1.0V that needs to be shifted to the input range of an ADC which is 0 to +2V. You also have a -reference voltage available V2=-5V. You can pass the audio signal through R1 with gain K1=-1. You can also add in a +1.0V DC offset using the V2 and R2 .
The gains and resistors are calculated as
Signal Gain     K1 = (+2V - 0V) / (-1V - (+1V)) = -1                           R1 = -RF / K1 = 10k
Offset Gain     K2 = +1 / -5V = -0.2                          R2 = -RF / K2 = 50k

11. Example No1
Find the output voltage of the following Summing Amplifier circuit.
Using the previously found formula for the gain of the circuit

12. 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:

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

14. The End
…..Thank you….