Inverting Summing Amplifier

Fig.1 Inverting Summing Amplifier

As shown in Fig.1, the op-amp is used as a summing amplifier in the inverting configuration. The inputs to the op-amp (V1, V2, and V3) are applied using the resistors R1, R2, and R3 respectively. The output of the op-amp can be given as

Proof:

Here, assume the op-amp is an ideal op-amp. As shown in Fig.2, let’s say, the current flowing through resistor R1, R2 and R3 are I1, I2, and I3. And current flowing through resistor R_f is I_F.

Fig.2 Currents in the Inverting Summing Amplifier

For an ideal op-amp, no current is flowing into the op-amp terminal. So, applying KCL at node A, it can be written as

If R1 = R2 = R3 = R then

When R_f = R, then Vout = – (V₁ + V₂ + V₃)

And when R1 = R2 = R3 = R and the ratio of Rf and R is selected such that,

where n=number of inputs being applied to the inverting terminal.

Then it can be used as a averaging circuit. For example, in the above circuit when R₁= R₂ = R₃ = R and R = 3 R_f then Vo = – (V₁ + V₂ + V₃)/3

That means output is the average of the three input signals.

Applications of Summing Amplifier

• Summing, Averaging, and Scaling
• For providing DC offset
• Digital to Analog Converters
• Audio Mixer

Non-Inverting Summing Amplifier

Fig.3 Non-Inverting Summing Amplifier

Fig.3 Shows the non-inverting summing amplifier. Where the two inputs V1 and V2 are applied to the non-inverting op-amp terminal through resistor R₁ and R₂.

The output of the op-amp can be given as

Proof:

The output can be found by applying the superposition theorem. To find the output, let’s consider only one input at a time. If V₁ is acting alone and V₂ = 0 (as shown in fig.4), then voltage V₁+ at the non-inverting input is

Fig. 4 Non-Inverting Summing Amplifier (When V₂ = 0)

Similarly, as shown in Fig.5, when voltage V1 = 0 and V2 is acting alone then voltage V₂+ can be given as

Fig.5 Non-Inverting Summing Amplifier (When V₁ = 0)

Considering both inputs simultaneously, the total voltage at the non-inverting input terminal

That means overall output voltage of the op-amp is

When R₁ = R₂ = R then output of the op-amp

And when R_f = R_a then output

For more information about inverting and non-inverting summing amplifier, please check this video:

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