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Design a difference amplifier to have a gain of 2 and a common mode input resistance of 10 kΩ at each input.

Step-by-step

\begin{array}{c}\mathrm{R}_{1}=\mathrm{R}_{3}=10 \mathrm{k} \Omega, \mathrm{R}_{2} /\left(\mathrm{R}_{1}\right)=2 \\\text { i.e. } \quad \mathrm{R}_{2}=2 \mathrm{R}_{1}=20 \mathrm{k} \Omega=\mathrm{R}_{4} \\\text { Verify: } \begin{aligned}\mathrm{v}_{0} &=\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}} \frac{1+\mathrm{R}_{1} / \mathrm{R}_{2}}{1+\mathrm{R}_{3} / \mathrm{R}_{4}} \mathrm{v}_{2}-\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}} \mathrm{v}_{1} \\=& 2 \frac{(1+0.5)}{1+0.5} \mathrm{v}_{2}-2 \mathrm{v}_{1}=2\left(\mathrm{v}_{2}-\mathrm{v}_{1}\right)\end{aligned} \\\text { Thus, } \mathrm{R}_{1}=\mathrm{R}_{3}=\underline{10 \mathrm{k} \Omega}, \mathrm{R}_{2}=\mathrm{R}_{4}=\underline{20 \mathrm{k}} \Omega\end{array}

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