Final answer:
To create the inverting-summing amplifier with the specified output and an 80kΩ feedback resistor, input resistors should be set as 8kΩ for vᵃ, 20kΩ for vᵂ, and approximately 13.3kΩ for vᵃ. The resulting configuration will meet the output requirements when supplied with ±12 V.
Step-by-step explanation:
To design an inverting-summing amplifier that outputs v₀ = -(10vᵃ + 4vᵂ + 6vᵃ) with an 80kΩ resistor in the feedback path, you'll need to select input resistors for each input channel (vᵃ, vᵂ, vᵃ) which are inversely proportional to their respective gains in the formula. With the feedback resistor Rf being 80kΩ, we calculate the input resistors as follows:
R1 for vᵃ would be Rf/10 = 80kΩ/10 = 8kΩ,
R2 for vᵂ would be Rf/4 = 80kΩ/4 = 20kΩ, and
R3 for vᵃ would be Rf/6 = 80kΩ/6 ≈ 13.3kΩ.
This configuration ensures that the amplifier adheres to the desired output equation, and is powered by a ±12 V power supply. It is important that the actual resistor values may need to be adjusted based on standard resistor values and the tolerance may affect the precision of the gains somewhat.