# Summing Amplifiers Inverting and Non-Inverting

Hey friends, welcome to the Kohiki web  ALL ABOUT ELECTRONICS. So, in this article, we will see how to use this op-amp as a summing amplifier and using this op-amp configuration how we can add the different input voltages.

So, now in the earlier Article of inverting and non-inverting op-amp configuration, we have applied the single input either to the non-inverting or the inverting op-amp terminals. Now, in this article, we will apply the multiple inputs either to the inverting or the non-inverting op-amp terminal and we will see how this configuration can be used as a summing amplifier.

### Inverting Summing Amplifier

Summing Amplifier So, first, we will see the inverting summing amplifier and in this configuration, we will apply the multiple inputs to the inverting input terminal. And we will find the expression of the output voltage in terms of the different input voltages.

So, as you can see here, we have applied the input voltages V1, V2, and V3 to this inverting terminal via resistors R1, R2, and R3. And here let’s assume that current I1, I2, and I3 are flowing through this resistor R1, R2, and R3. And let’s say the current If is flowing through this resistor Rf. And here, amp formula we are assuming the op-amp as the ideal op-amp.

So, no current is going inside this op-amp. And let’s consider this node as node X. Now, in the earlier Article on inverting op-amp configuration, we have seen the concept of virtual ground. And in that concept, we had seen that whenever we are applying the negative feedback to any op-amp, then there is a virtual short exists between the inverting and the non-inverting terminals.

• So, if one terminal is at ground potential, then another terminal will also be at ground potential.
• we can say that it will act as a virtual ground.
• So, this node will have zero potential.
• So, now let’s apply KCL at this node X. So, applying KCL we can write I1 +I2 +I3, which is equal to this current If.
• Now, as this terminal is at ground potential, so the current I1 will be equal to V1 minus zero divides by R1.
• Likewise, this current I2 will be equal toV2 minus zero divides by R2.
• likewise, current I3 will be equal toV3 minus zero divides by R3.
• Now, this current If will be equal to zero minus V out divide by this feedback resistor Rf.
• That is zero minus V out, divide by this feedback resistor Rf.
• So, if we simplify this expression then we can write it as V1 divide by R1, plus V2 divide by R2, plusV3 divide by R3 that is equal to minus V out divide by Rf.

If we Summing Amplifier further simplifies it then we can write it as, V out that is equal to minus, Rf divides by R1 times V1, plus Rf divides by R2 times V2, plus Rf divide by R3 times V3.

Now, we know that if we apply the single input to this non-inverting op-amp configuration, then the output voltage V out can be given as -minus Rf divide by R1 times the input voltage.

Now, here instead of a single input voltage, we have applied multiple input voltages. So, the output voltage will be equal to the algebraic sum of the individual responses.

So, this is the expression of the output voltage in the case of the inverting summing amplifier. Now, in this inverting summing amplifier configuration, let’s assume that the value of R1, R2, and R3 is the same. So, in that case, the output voltage V out will be equal to -Rf divide by R times, V1 plus V2 plus V3.

So, nowhere if the value of Rf is equal toR, then, in that case, our output voltage v out will be equal to -(V1 plus V2 plus V3). So, in this way, we can use this op-amp as an adder and we can add the multiple input voltages.

### Scaling and Addition using Summing Amplifier

So, Summing Amplifier now suppose in this configuration, if R1, R2, and R3 are different then, in that case, the ratio of this feedback resistor over this resistors R1, R2, and R3 will also be different

So, in that case along with the addition, we can also perform the scaling operation. So, in that case, our output voltage Vout will be equal to -(A*V1 +B*V2 +C*V3). Where A, B, and C represent the ratio of this Rf divide by R1, Rf divide by R2, and Rf divide by R3. So, along with addition, we can also perform the scaling operation.

### Averaging operation using Summing Amplifier

So, along with Summing Amplifier this scaling and addition operation, we can also perform the averaging operation using this configuration. So, now let’s see how we can perform the averaging of the different input voltages using this configuration. So, let’s once again assume that the R1, R2, and R3 are having the same value.

• let’s say the ratio of this Rf divide by R is equal to 1 divide by n.
• Where n represents the number of input voltages that are being applied to this inverting terminal.
• So, in that case, our output voltage Vout will be equal to, minus Rf divide by R times, V1 plus V2 plus V3.
• we put the value of this Rf by R as 1divideby n, that is 1 divided by 3 in this case, then our output voltage will be equal to minus V1 plus V2 plus V3, divide by 3.

So, in this way, Summing Amplifier our output voltage will be the average of the three different input voltages. So, we can also perform the averaging operation using this configuration. So, now let’s see some more applications in which this inverting summing amplifier can be used.

### Application of summing Amplifier

So, as I already told you, this summing amplifier can be used for the operation of addition, averaging as well as scaling. Apart from that, it can also be used to provide the DC offset to the input signals.

• So, suppose if your input voltages are AC signals or let’s say it is coming from some sensor, and if we want to apply some DC offset, then using this configuration we can also apply some DC offset to the incoming signals.
• Likewise, this inverting summing amplifier can also be used for the digital to analog conversion.
• And apart from that, it can also be used for mixing the different audio signals.
• So, these are the different applications in which this summing amplifier can be used.
• Now, theoretically, Summing Amplifier we can add the n number of input voltages to this op-amp configuration, but practically if you see the number of input voltages depends on the power dissipation as well as the total current that can be supplied by the op-amp.
• Because here if you see, the total current is the summation of the individual currents I1, I2, I3 up to In. So, this value should not exceed the maximum value that is supported by the op-amp. Now, one more interesting fact about this inverting op-amp configuration is that all the individual voltage sources are isolated with respect to each other.

Summing Amplifier is because of the concept of virtual ground. Because if you consider the individual voltage sources at a time, then at that time, the remaining voltage sources will act as a short circuit. So, if we consider this voltage source V1, which is acting alone, then at that time, this voltage source V2 and V3 will act as a short circuit.

we can say that they are at ground potential. Now, because of the virtual ground, this node is also at the ground potential. So, we can say that effectively this R2 andR3 do not exist in the circuit. Summing Amplifier So, the effective impedance that is seen by the voltage source V1 is the series resistance R1 of that voltage source.

So, we can say that there is no interference between the different voltage sources. And that is the biggest advantage of this investing summing amplifier. Now, the output of this inverting summing amplifier is the negative voltage. But suppose if we want the positive voltage then what we can do, we can connect one more inverting op-amp which is having unity gain.

So, as you can see here, suppose if we connect one more inverting op-amp, which is having unity gain at this point then the output voltage will be positive.

So, by using one more inverting op-amp, we can get a positive output voltage. So, this is all about the inverting summing amplifier. Now, let’s see what happens when we apply the multiple input voltages at the non-inverting input terminal. So, now in this non-inverting summing amplifier, we have applied the two input voltages at this non-inverting end.

### Non-Inverting Summing Amplifier (with two inputs)

Summing Amplifier we will find the output voltage in terms of the input voltages V1 and V2. Now, we know that in the case of the non-inverting configuration, the output voltage is equal to one plus Rf divide by Ra times the voltage at this node.

Let’s say that is equal to Vplus. So, Summing Amplifier as we have applied the multiple inputs at this end, so first of all, we need to find this voltage Vplus. And we can do so by applying the principle of superposition.

• So, what we will do, we will consider the one voltage source at a time and we will find the voltage at this node. And later on, we will combine the individual responses to get the final response.
• So, first of all, let’s assume that this voltage source V1 is acting alone and we have removed this voltage source V2. That means V2 is equal to zero.
• So, in that case, let’s say the voltage at this point is equal to V1 plus.
• So, V1plus will be equal to R2 divide by (R1plus R2) times this voltage V1.
• Likewise, when we consider this voltage sourceV2 is acting alone, and V1 is equal to zero.
• In that case, the voltage at this point islet’s says V2plus. So, V2plus will be equal to R1 divide by (R1plus R2) times this voltage V2.
• So, in this way, when this voltage sourceV1 and V2 are acting alone, then, in that case, the V1plus will be equal to this value, and V2 plus will be equal to this value. So, the overall voltage Vplu will be equal to the summation of the individual voltages.

Summing Amplifier that is (V1plus) plus (V2 plus)That is equal to R2 divide by (R1 plus R2) time V1, plus R1 divide by (R1 plus R2 ) timesV2.

So, this will be the voltage at this because of the voltage V1 and V2. Summing Amplifier Now, we know that the output voltage is equal to one plus Rf divide by Ra times the voltage at this end. That is equal to Vplus. So, our final output voltage will be equal to one plus Rf divide by Ra times, R2 divide by (R1 plus R2 ) times V1, plus R1 divided by (R1 plus R2 ) times V2. So, this will be the final voltage that we get at the output of this non-inverting summing amplifier.

So, now let’s simplify this equation a bit and let’s assume that this R1 is equal to R2 is equal to R.So, when R1=R2=R, then, in that case, the output voltage v out will be equal to one plusRf divide by Ra times V1 plus V2, divide by 2. Now, if we consider Rf = Ra, in that case, the output voltage Vout will be equal to V1 +V2. That is the addition of the voltage V1 andV2. So, in this way, using this non-inverting summing amplifier also, we can perform the addition.

### Non-Inverting Summing Amplifier (with three inputs)

Now, let’s take the case when we have three different input voltages that are connected to this Summing Amplifier non-inverting terminal. So, as you can see here, we have three different inputs voltages V1, V2, and V3, which are connected to this non-inverting terminal via resistorR1, R2, and R3.

• So, here also, we will consider the one voltage source at a time and we will find the voltage at this non-inverting terminal.
• later on, we will add the individual responses to get the voltage at this non-inverting terminal.
• So, first of all, let’s assume that this voltage source V1 is acting alone and V2 and V3 are equal to zero.
• So, in that case, the circuit will look like this.
• So, the voltage at this point let’s say is equal to V1 plus.
• So, V1 plus will be equal to (R2 in parallelR3) divide by (R1 plus + (R2 in parallel R3 ) ) times this voltage V1.
• So, this is the voltage that you get at this point when this voltage source V1 is acting alone.
• likewise, we can have voltage V2 plus that is equal to, (R1 parallel R3) divide by this R2 plus (R1parallel R3) times this voltage V2.
• this is the expression when the voltage sourceV2 is acting alone. And likewise, we can have V3 plus that is equal to (R2 parallel R1) divide by R3 plus (R2 parallel R1) times this voltage V3.
• So, the total voltage that appears at this point will be the summation of these individual voltages.

So, as you can see here, in this non-inverting Summing Amplifier configuration, as the number of input voltages is increasing, the complexity is also increasing. And to here reduce the complexity, let’s assume that R1, R2, and R3 are equal. So, when all the three values are the same, then the value of V1 plus will be equal to V1/3. Likewise, the value of V2plus will be equal to V2/3. And likewise, V3 plus will be equal to V3.

So, in short, when R1, R2, and R3 are equal in that case, Vplus will be equal to (V1 +V2 +V3 )/3And the output voltage Vout will be equal to(1+ (Rf/Ra)) times V plus. Or we can say that (1+(Rf/Ra)) (V1 +V2+V3)/3So, now suppose if the value of 1+ (Rf/Ra) that is equal to 3, in that case, V out will be equal to V1+V2+V3.

Summing Amplifier So, as you can see here, in this configuration as the number of input voltage increases, the complexity is also increasing. And here, the individual input voltage that appears at this point does not only depend on the value of this V1 and R1, but it also depends upon the different series resistors of the individual voltage sources.

Like, here, in this case, it also depends upon the value of this R2 and R3. So, in this configuration, we can say that the individual voltage sources are not isolated with respect to each other. And they have their own influence on the input voltage that appears at this non-inverting terminal.

So, that is the reason, in most of the practical applications, this inverting summing amplifier is more preferred over this non-inverting summing amplifier. So, that is all about the inverting and the non-inverting summing amplifier.

So, I hope in this Article, you understood this inverting and the non-inverting summing amplifiers.

So, if you have any questions or suggestions, do let me know in the comment section below.

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