Question *5.88 Figure 5.106 shows an instrumentation amplifier driven by a bridge. Obtain the gain vo/v; of the amplifier. 25 k2 500 k2 20 kQ 30 k2 10 k2 + 40 kΩ 80 kQ 2 kΩ 10 k2 25 k2 500 kQ Figure 5.106 For Prob. 5.88.

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Transcribed Image Text: *5.88 Figure 5.106 shows an instrumentation amplifier driven by a bridge. Obtain the gain vo/v; of the amplifier. 25 k2 500 k2 20 kQ 30 k2 10 k2 + 40 kΩ 80 kQ 2 kΩ 10 k2 25 k2 500 kQ Figure 5.106 For Prob. 5.88.

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Step 15.88simplify the Circmi'apply voltenge divider kule to find\begin{array}{l}V_{A}=v_{i} \times \frac{30}{30+20}=\frac{3}{5} V_{i} \\V_{B}=V_{i} \times \frac{80}{40+80}=\frac{2}{3} V_{i}\end{array}Step 2we are know Instrument AmplifierGain\begin{array}{l}\frac{V_{0}}{\left(V_{B}-V_{A}\right)}=\left(1+\frac{10+10}{2}\right) \times \frac{500}{25} \\V_{0}=(1+10) \times 20\end{array}\Rightarrow \frac{v_{0}}{\frac{2}{3} v_{i}-3 / 5 v_{i}}=(1+10) \times 20\begin{array}{l}\Rightarrow \frac{v_{0}}{V_{i}\left(\frac{2}{3}-3 / 5\right)}=11 \times 20 \\\Rightarrow \frac{v_{0}}{V_{i} \times \frac{10-9}{15}}=11 \times 20\end{array}\Rightarrow \frac{V_{0}}{V_{i} \times \frac{10-9}{15}}=11 \times 20\begin{array}{l}\Rightarrow \frac{v_{0}}{v_{i}}=11 \times 20 \times \frac{1}{153}=\frac{44}{3} \\\Rightarrow \frac{V_{0}}{V_{i}}=\frac{44}{3}=14.666 \\\end{array}So Gain \frac{v_{0}}{v_{1}^{\prime}}=14.666 ...