What primarily sets the gain of an inverting summing amplifier?

What primarily sets the gain of an inverting summing amplifier?

• A. The ratio of the feedback resistor to the input resistor
• B. The supply voltage
• C. The op-amp input bias current
• D. The output load

Answer: (A)

In an inverting summing amplifier, the closed-loop gain is set by the feedback network, specifically the ratio of the feedback resistor to the input resistor(s). Because negative feedback keeps the inverting input at a virtual ground, the currents from each input flow through the feedback resistor. The output becomes Vout = -Rf × Σ(Vin_i / Rin_i). So the gain contributed by each input is -Rf/Rin_i. If all input resistors are equal, each input has the same gain of -Rf/Rin, and the overall output is -Rf/Rin times the sum of the inputs. The other factors don’t determine the gain in the ideal model: the supply voltage only limits how far you can swing the output, not the linear gain; input bias current mainly causes small offsets rather than changing the gain; and the load affects the ability to deliver the required current without distortion, but the gain itself is governed by the resistor ratio.

In an inverting summing amplifier, the closed-loop gain is set by the feedback network, specifically the ratio of the feedback resistor to the input resistor(s). Because negative feedback keeps the inverting input at a virtual ground, the currents from each input flow through the feedback resistor. The output becomes Vout = -Rf × Σ(Vin_i / Rin_i). So the gain contributed by each input is -Rf/Rin_i. If all input resistors are equal, each input has the same gain of -Rf/Rin, and the overall output is -Rf/Rin times the sum of the inputs.

The other factors don’t determine the gain in the ideal model: the supply voltage only limits how far you can swing the output, not the linear gain; input bias current mainly causes small offsets rather than changing the gain; and the load affects the ability to deliver the required current without distortion, but the gain itself is governed by the resistor ratio.