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Exercise Problems · Q15

Q.The output of an Op-amp adder is to be VO=3V1−2V2+5.5V3V_O = 3V_1 - 2V_2 + 5.5V_3. If the value of the feedback resistor is 30 kΩ30\text{ k}\Omega, find the value of R1R_1, R2R_2 and R3R_3.

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[!TLDR]

Using the inverting-adder weights, R1=10 kΩR_1=10\text{ k}\Omega, R2=15 kΩR_2=15\text{ k}\Omega and R3=6011 kΩ≈5.45 kΩR_3=\tfrac{60}{11}\text{ k}\Omega\approx5.45\text{ k}\Omega.

An op-amp adder gives

VO=−Rf ⁣(V1R1+V2R2+V3R3)V_O=-R_f\!\left(\dfrac{V_1}{R_1}+\dfrac{V_2}{R_2}+\dfrac{V_3}{R_3}\right)

To obtain VO=3V1−2V2+5.5V3V_O=3V_1-2V_2+5.5V_3, apply −V1-V_1, V2V_2, −V3-V_3 at the inputs so that the adder's own inversion produces the required signs; the coefficient of each term is then Rf/RnR_f/R_n. Equating coefficients with Rf=30 kΩR_f=30\text{ k}\Omega: …

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