To configure this circuit for summation of the input voltages, change the value of the indicated (1 kΩ) resistor to which value?

To configure this circuit for summation of the input voltages, change the value of the indicated (1 kΩ) resistor to which value?

• A. 3 kΩ
• B. 2 kΩ
• C. 4 kΩ
• D. 1.5 kΩ

Answer: (A)

This question hinges on how an inverting summing amplifier combines multiple input voltages. The output is given by Vout = -Rf (V1/R1 + V2/R2 + ...). Each input contributes according to the ratio of the feedback resistor to its own input resistor. To sum the inputs with equal weight, those ratios must be the same for every input; if each input resistor is 3 kΩ, then the feedback resistor should also be 3 kΩ so that the weight is unity for each input (Vout = -(V1 + V2)). With the indicated resistor at 1 kΩ, the weight becomes -Rf/Rin = -1k/3k = -1/3 for each input, so the output would be a third of the sum rather than the full sum. Changing the resistor to 3 kΩ makes the weights equal to -1 for each input, yielding the desired summation behavior. The result is that the circuit now sums the input voltages (with inversion) correctly.

This question hinges on how an inverting summing amplifier combines multiple input voltages. The output is given by Vout = -Rf (V1/R1 + V2/R2 + ...). Each input contributes according to the ratio of the feedback resistor to its own input resistor. To sum the inputs with equal weight, those ratios must be the same for every input; if each input resistor is 3 kΩ, then the feedback resistor should also be 3 kΩ so that the weight is unity for each input (Vout = -(V1 + V2)).

With the indicated resistor at 1 kΩ, the weight becomes -Rf/Rin = -1k/3k = -1/3 for each input, so the output would be a third of the sum rather than the full sum. Changing the resistor to 3 kΩ makes the weights equal to -1 for each input, yielding the desired summation behavior. The result is that the circuit now sums the input voltages (with inversion) correctly.