Summing amplifier truth check — is the output proportional to the product of the input voltages?

Introduction / Context:
The inverting op-amp summing amplifier is a linear circuit whose output equals the negative weighted sum of its inputs (scaled by resistor ratios). Confusing this with analog multipliers leads to design errors, especially in audio mixing, DAC current-to-voltage conversion, and sensor fusion circuits where linear superposition is required.

Given Data / Assumptions:

• Op-amp in inverting summing configuration with input resistors R_i and feedback resistor R_f.
• Ideal linear operation without saturation.
• No special nonlinear elements are present.

Concept / Approach:
The transfer function is V_out = −R_f * Σ(V_i / R_i). This is a linear superposition (sum) of inputs, each weighted by conductance and flipped in polarity. To realize a product, one would need a different topology, such as log/antilog amplifiers or dedicated analog multipliers, not a simple summing node.

Step-by-Step Solution:

Verification / Alternative check:
Simulate with two inputs: doubling one input doubles its contribution linearly; the output is not the product V1 * V2 unless logarithmic processing is added.

Why Other Options Are Wrong:

Common Pitfalls:
Ignoring resistor tolerances that set weighting accuracy; overdriving the op-amp leading to clipping that distorts summation.

Final Answer:
Incorrect — a summing amplifier outputs a weighted sum, not a product