In op-amp applications, which amplifier configuration produces an output that is directly proportional to the algebraic sum (addition) of two or more input voltages?

Introduction:
In analog signal processing with operational amplifiers, engineers often need to combine multiple input signals into a single output that represents their algebraic sum. The configuration that performs this function is known as the summing amplifier (also called an adder). It is widely used in audio mixing, sensor fusion, DAC current-to-voltage conversion, and weighted arithmetic operations.

Given Data / Assumptions:

• We are considering ideal op-amp behavior (very high open-loop gain, infinite input impedance, and zero output impedance) operated with negative feedback in the linear region.
• Multiple input sources are applied through input resistors to the inverting or non-inverting node, depending on the chosen topology.
• The question asks specifically for the configuration whose output is proportional to the addition of the inputs.

Concept / Approach:
The classic inverting summing amplifier ties several input resistors to the inverting input. Because of virtual ground at the summing node, the currents through each input resistor sum at the node and flow through the feedback resistor. The output voltage is thus proportional to the sum of the input voltages (with an overall sign and scaling factor set by resistor ratios). For equal resistors, the magnitude of the output is proportional to the simple sum of the inputs.

Step-by-Step Solution:
Write nodal relation at the inverting input: (V1 − 0)/R1 + (V2 − 0)/R2 + … + (Vn − 0)/Rn = (0 − Vout)/RfSolve for Vout: Vout = −Rf * (V1/R1 + V2/R2 + … + Vn/Rn)Equal-value case: if R1 = R2 = … = Rn = R, then Vout = −(Rf/R) * (V1 + V2 + … + Vn)Therefore, the output is directly proportional to the algebraic sum of inputs (with a sign defined by inversion and weights by resistor ratios).

Verification / Alternative check:
Consider V1 = 1 V and V2 = 2 V with R1 = R2 = R and Rf = R. Then Vout = −(1 + 2) V = −3 V, demonstrating proportional summation. A non-inverting summer can also be built by first forming a passive average and then amplifying, again yielding proportional addition.

Why Other Options Are Wrong:

• Differentiator: Produces output proportional to the time derivative of the input, not the sum of multiple inputs.
• Difference / analog subtractor: Implements subtraction (V1 − V2), not general summation of many inputs.
• Integrator: Produces output proportional to the time integral of the input, not algebraic addition of multiple inputs.

Common Pitfalls:

• Confusing weighted addition with simple buffering; resistor values set the weights.
• Ignoring op-amp saturation; large sums can exceed supply rails.
• Forgetting the inversion sign in the inverting summing configuration; a non-inverting adder avoids inversion but requires a different network.

Final Answer:
summing