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Find { v }_{ 0 } in terms of { v }_{ 1 }, { v }_{ 2 }, and { v }_{ 3 }, in the circuit of Fig. 5.77.

Step-by-step

Applying KCL at node a, where node a is the input to the op amp.

\begin{array}{c}\frac{\mathrm{v}_{1}-\mathrm{v}_{\mathrm{a}}}{\mathrm{R}}+\frac{\mathrm{v}_{2}-\mathrm{v}_{\mathrm{a}}}{\mathrm{R}}+\frac{\mathrm{v}_{3}-\mathrm{v}_{\mathrm{a}}}{\mathrm{R}}=0 \text { or } \mathrm{v}_{\mathrm{a}}=\left(\mathrm{v}_{1}+\mathrm{v}_{2}+\mathrm{v}_{3}\right) / 3 \\\mathrm{v}_{\mathrm{o}}=\left(1+\mathrm{R}_{1} / \mathrm{R}_{2}\right) \mathrm{v}_{\mathrm{a}}=\underline{\left(1+\mathbf{R}_{1} / \mathbf{R}_{2}\right)\left(\mathrm{v}_{1}+\mathrm{v}_{2}+\mathrm{v}_{3}\right) / 3}\end{array}

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