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In a certain electronic device, a three-stage amplifier is desired, whose overall voltage gain is 42 dB. The individual voltage gains of the first two stages are to be equal, while the gain of the third is to be one-fourth of each of the first two. Calculate the voltage gain of each.

Step-by-step

\begin{array}{l}\text { Let } \mathrm{A}_{1}=\mathrm{k},\mathrm{A}_{2}=\mathrm{k}, \text { and } \mathrm{A}_{3}=\mathrm{k} /(4) \\\mathrm{A}=\mathrm{A}_{1} \mathrm{A}_{2} \mathrm{A}_{3}=\mathrm{k}^{3} /(4) \\20 \mathrm{Log}_{10} \mathrm{A}=42 \\\mathrm{Log}_{10} \mathrm{A}=2.1 \longrightarrow \mathrm{A}=10^{2 \cdot 1}=125.89 \\\mathrm{k}^{3}=4 \mathrm{A}=503.57 \\\mathrm{k}=\sqrt[3]{503.57}=7.956 \\\mathrm{A}_{1}=\mathrm{A}_{2}=\underline{7.956}, \mathrm{A}_{3}=\underline{1.989}\end{array}

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