From the circuit values, Vo equals which of the following?

From the circuit values, Vo equals which of the following?

• A. 0.5 Vdc
• B. 2.5 Vdc
• C. Vo = -(V1+V2+V3+V4)
• D. The circuit summing is at virtual ground

Answer: (C)

This is an inverting summing amplifier. The four input voltages are applied through equal resistors to the op-amp’s inverting input, while the noninverting input is grounded. Negative feedback forces the inverting input to sit at a virtual ground (approximately 0 V). The currents from each input flow through their resistors into the summing node and must be carried away by the current through the feedback resistor. The total current in the feedback path is i_f = V1/R + V2/R + V3/R + V4/R. The op-amp sets Vo so that this current through the feedback resistor Rf matches i_f, giving Vo = -i_f Rf = -(Rf/R) (V1 + V2 + V3 + V4). If the input and feedback resistors are equal, this simplifies to Vo = -(V1 + V2 + V3 + V4). So the correct relation is Vo equals the negative sum of the four input voltages.

This is an inverting summing amplifier. The four input voltages are applied through equal resistors to the op-amp’s inverting input, while the noninverting input is grounded. Negative feedback forces the inverting input to sit at a virtual ground (approximately 0 V). The currents from each input flow through their resistors into the summing node and must be carried away by the current through the feedback resistor. The total current in the feedback path is i_f = V1/R + V2/R + V3/R + V4/R. The op-amp sets Vo so that this current through the feedback resistor Rf matches i_f, giving Vo = -i_f Rf = -(Rf/R) (V1 + V2 + V3 + V4). If the input and feedback resistors are equal, this simplifies to Vo = -(V1 + V2 + V3 + V4). So the correct relation is Vo equals the negative sum of the four input voltages.