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The output signal is the algebraic sum of individual outputs or in other words it is the sum of all the inputs multiplied by their respective gains. VOUT = VOUT1 + VOUT2 + . . . + VOUTn VOUT = – [(Rf / R1) V1 + (Rf / R2) V2 + . . . + (Rf / Rn) Vn] VOUT = V1 AV1 + V2 AV2 + . . . + Vn AVn VOUT = VIN (1 + (Rf / Ri)) As the output voltage is figured out, we have to now determine the value of VIN. If V1, V2 and V3 are the three main input sources and R1, R2 and R3 are their input resistances, then VIN1, VIN2 and VIN3 are the inputs of respective channels when other corresponding channels are grounded. So, VIN = VIN1 + VIN2 + VIN3 As the concept of virtual ground doesn’t apply here, all channels will have an effect on other channels. Let us calculate the VIN1 portion of the VIN and by simple mathematics, we can easily derive the other two values i.e., VIN2 and VIN3. Coming to VIN1, when V2 and V3 are grounded, their corresponding resistors cannot be ignored as form a voltage divider network. So, VIN1 = V1 [(R2 || R3) / (R1 + (R2 || R3))] Similarly, we can calculate the other two values VIN2 and VIN3 as VIN2 = V2 [(R1 || R3) / (R2 + (R1 || R3))] VIN3 = V3 [(R1 || R2) / (R3 + (R1 || R2))] So, VIN = VIN1 + VIN2 + VIN3 VIN = V1 [(R2 || R3) / (R1 + (R2 || R3))] + V2 [(R1 || R3) / (R2 + (R1 || R3))] + V3 [(R1 || R2) / (R3 + (R1 || R2))] Finally, we can calculate the Output voltage VOUT as VOUT = VIN (1 + (Rf / Ri)) VOUT = (1 + (Rf / Ri)) {V1 [(R2 || R3) / (R1 + (R2 || R3))] + V2 [(R1 || R3) / (R2 + (R1 || R3))] + V3 [(R1 || R2) / (R3 + (R1 || R2))]} If we consider the special equal weighted condition where all the resistors are having the same values, then the output voltage is: VOUT = (1 + (Rf / Ri)) ( (V1 + V2 + V3) / 3) Design of non-inverting summing circuit is approached by first designing the non-inverting amplifier to have the required voltage gain. Then the input resistors are selected as large as possible to suit the type of the op-amp used. Voltage Adder Example