Based on the circuit configuration, Vo equals which expression?

Based on the circuit configuration, Vo equals which expression?

• A. -[0.5 x (V1 + V2)]
• B. -[0.5 x (V1 - V2)]
• C. 0.5 x (V1 + V2)
• D. -[2 x (V1 + V2)]

Answer: (A)

This is an inverting summing amplifier: the two input voltages are added at the inverting input and then inverted by the op-amp. With an ideal op-amp and the noninverting input grounded, the inverting input sits at virtual ground (0 V). The currents from the inputs flow through their equal input resistors, giving i1 = V1/R and i2 = V2/R. The feedback resistor must carry away the sum of these currents, so the current through the feedback path is -Vo/Rf, and KCL at the summing node gives i1 + i2 = -Vo/Rf. Hence Vo = -Rf*(V1/R + V2/R). If the feedback resistor is half the value of the input resistors (Rf = R/2), this becomes Vo = -(R/2)*(V1/R + V2/R) = -0.5*(V1 + V2), which matches the expression.

This is an inverting summing amplifier: the two input voltages are added at the inverting input and then inverted by the op-amp. With an ideal op-amp and the noninverting input grounded, the inverting input sits at virtual ground (0 V). The currents from the inputs flow through their equal input resistors, giving i1 = V1/R and i2 = V2/R. The feedback resistor must carry away the sum of these currents, so the current through the feedback path is -Vo/Rf, and KCL at the summing node gives i1 + i2 = -Vo/Rf. Hence Vo = -Rf*(V1/R + V2/R). If the feedback resistor is half the value of the input resistors (Rf = R/2), this becomes Vo = -(R/2)(V1/R + V2/R) = -0.5(V1 + V2), which matches the expression.