Final answer:
A single op-amp circuit can be designed to perform Vo = -3V1 + 3V2 using an inverting amplifier setup with input and feedback resistors that respect the minimum impedance requirement of 10kΩ.
Step-by-step explanation:
Designing an Op-Amp Circuit :To design a circuit that outputs Vo = -3V1 + 3V2, using a single operational amplifier (op-amp), and ensuring that minimum impedance seen by the sources V1 and V2 is 10kΩ, we can use an inverting amplifier configuration. We will set up two branches for V1 and V2, each with their own input resistors (R1 and R2) before combining them at the inverting input of the op-amp. To meet the impedance requirement, R1 and R2 should be at least 10kΩ. Additionally, to achieve the coefficient of -3 for V1, if we consider R3 as the feedback resistor, we can set R1 = R3/3. Similarly, for V2 to have a coefficient of +3, we can introduce a non-inverting configuration via R4 and R5 with R4 = R5/3, where R5 is connected between the op-amp output and the negative input. The non-inverting input of the op-amp is grounded. Finally, to satisfy the equation Vo = -3V1 + 3V2, resistors R4 and R5 must be chosen to scale V2 correctly, ensuring that the non-inverted V2's contribution is equal and opposite to V1's at the output.